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Theory and History of Ontology by Raul Corazzon | e-mail: [email protected]

Complete and Annotated Bibliography of Nino Cocchiarella (1986 - 2018)

The Conceptual Realism of Nino Cocchiarella

Annotated Bibliography of His Writings 1966-1985

ESSAYS

Cocchiarella, Nino. 1986. "Frege, Russell and Logicism: A LogicalReconstruction." In Frege Synthesized: Essays on the Philosophical andFoundational Work of Gottlob Frege, edited by Haaparanta, Leila and Hintikka,Jaakko, 197-252. Dordrecht: Reidel.Reprinted as Chapter 2 in Logical Studies in Early Analytic Philosophy, pp.64-118."Logicism by the end of the nineteenth century was a philosophical doctrinewhose time had come, and it is Gottlob Frege to whom we owe its arrival.“Often,” Frege once wrote, “it is only after immense intellectual effort, whichmay have continued over centuries, that humanity at last succeeds in achievingknowledge of a concept in its pure form, in stripping off the irrelevantaccretions which veil it from the eyes of the mind” (Frege, The Foundations ofArithmetic, [Fd], xix). Prior to Frege logicism was just such a concept whosepure form was obscured by irrelevant accretions; and in his life’s work it wasFrege who first presented this concept to humanity in its pure form anddeveloped it as a doctrine of the first rank.That form, unfortunately, has become obscured once again. For today, as weapproach the end of the twentieth century, logicism, as a philosophical doctrine,is said to be dead, and even worse, to be impossible. Frege’s logicism, or thespecific presentation he gave of it in Die Grundgesetze der Arithmetik, ([Gg]),fell to Russell’s paradox, and, we are told, it cannot be resurrected. Russell’sown subsequent form of logicism presented in [PM], moreover, in effect givesup the doctrine; for in overcoming his paradox, Russell was unable to reduceclassical mathematics to logic without making at least two assumptions that arenot logically true; namely, his assumption of the axiom of reducibility and hisassumption of an axiom of infinity regarding the existence of infinitely manyconcrete or nonabstract individuals.Contrary to popular opinion, however, logicism is not dead beyond redemption;that is, if logicism is dead, then it can be easily resurrected. This is not to saythat as philosophical doctrines go logicism is true, but only that it can belogically reconstructed and defended or advocated in essentially the samephilosophical context in which it was originally formulated. This is trueespecially of Frege’s form of logicism, as we shall see, and in fact, by turning tohis correspondence with Russell and his discussion of Russell’s paradox, we areable to formulate not only one but two alternative reconstructions of his form of

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Complete and Annotated Bibliography of Nino Cocchiarella https://www.ontology.co/biblio/cocchiarella-biblio-two.htm

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logicism, both of which are consistent (relative to weak Zermelo set theory).In regard to Russell’s form of logicism, on the other hand, our resurrection willnot apply directly to the form he adopted in [PM] but rather to the form he wasimplicitly advocating in his correspondence with Frege shortly after thecompletion of [POM]. In this regard, though we shall have occasion to refer tocertain features of his later form of logicism, especially in our concludingsection where a counterpart to the axiom of reducibility comes into the picture,it is Russell’s early form of logicism that we shall reconstruct and be concernedwith here.Though Frege’s and Russell’s early form of logicism are not the same,incidentally, they are closely related; and one of our goals will be to reconstructor resurrect these forms with their similarity in mind. In particular, it is ourcontention that both are to be reconstructed as second order predicate logics inwhich nominalized predicates are allowed to occur as abstract singular terms.Their important differences, as we shall see, will then consist in the sort ofobject each takes nominalized predicates to denote and in whether the theory ofpredication upon which the laws of logic are to be based is to be extensional orintensional." (pp. 64-65 of the reprint)ReferencesFrege, Gottlob, [Fd] The Foundations of Arithmetic, trans, by J. L. Austin,Harper & Bros., N.Y. 1960.Frege, Gottlob, [Gg] Die Grundgesetze der Arithmetik, vols. 1 and 2,Hildesheim, 1962.Russell, Bertrand, [PM] Principia Mathematica, coauthor, A. N. Whitehead,Cambridge University Press, 1913.Russell, Bertrand, [POM] The Principles of Mathematics, 2nd ed., W. W.Norton & Co., N.Y., 1937.

———. 1986. "Conceptualism, Ramified Logic, and Nominalized Predicates."Topoi.An International Review of Philosophy no. 5:75-87."The problem of universals as the problem of what predicates stand for inmeaningful assertions is discussed in contemporary philosophy mainly in termsof the opposing theories of nominalism and logical realism. Conceptualism,when it is mentioned, is usually identified with intuitionism, which is not atheory of predication but a theory of the activity of constructing proofs inmathematics. Both intuitionism and conceptualism are concerned with thenotion of a mental construction, to be sure, and both maintain that there canonly be a potentially infinite number of such constructions. But whereas thefocus of concern in intuitionism is with the construction of proofs, inconceptualism our concern is with the construction of concepts. This differencesets the two frameworks apart and in pursuit of different goals, and in fact it isnot at all clear how the notion of a mental construction in the one framework isrelated to that in the other. This is especially true insofar as mathematicalobjects, according to intuitionism, are nothing but mental constructions,whereas in conceptualism concepts are anything but objects. In any case,whatever the relation between the two, our concern in this paper is withconceptualism as a philosophical theory of predication and not withintuitionism as a philosophy of mathematics.

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Now conceptualism differs from nominalism insofar as it posits universals,namely, concepts, as the semantic grounds for the correct or incorrectapplication of predicate expressions. Conceptualism differs from logicalrealism, on the other hand, insofar as the universals it posits are not assumed toexist independently of the human capacity for thought and representation.Concepts, in other words, are neither predicate expressions nor independentlyreal properties and relations. But then, at least for the kind of conceptualism wehave in mind here, neither are they mental images or ideas in the sense ofparticular mental occurrences. That is, concepts are not objects (saturatedindividuals) but are rather cognitive capacities, or cognitive structures otherwisebased upon such capacities, to identify and classify or characterize and relateobjects in various ways. Concepts, in other words, are intersubjectivelyrealizable cognitive abilities which may be exercized by different persons at thesame time as well as by the same person at different times. And it is for thisreason that we speak of concepts as objective universals, even though they arenot independently real properties and relations.As cognitive structures, however, concepts in the sense intended here are notFregean concepts (which for Frege are independently real unsaturated functionsfrom objects to truth values). But they may be modeled by the latter (assumingthat there are Fregean concepts to begin with) -especially since as cognitivecapacities which need not be exercized at any given time (or even ever for thatmatter), concepts in the sense intended here also have an unsaturated naturecorresponding to, albeit different from, the unsaturated nature of Fregeanconcepts. Thus, in particular, the saturation (or exercise) of a concept in thesense intended here results not in a truth value but a mental act, and, if overtlyexpressed, a speech act as well. The un-saturatedness of a concept consists inthis regard in its non-occurrent or purely dispositional status as a cognitivecapacity, and it is the exercise (or saturation) of this capacity as a cognitivestructure which informs particular mental acts with a predicable nature (or witha referential nature in the case of concepts corresponding to quantifierexpressions)." (pp. 75-76)

———. 1987. "Rigid Designation." In Encyclopedic Dictionary of Semiotics.Vol. 2, edited by Sebeok, Thomas A., 834. Berlin: Mouton de Gruyter.

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———. 1987. "Russell, Bertrand." In Encyclopedic Dictionary of Semiotics.Vol. 2, edited by Sebeok, Thomas A., 840-841. Berlin: Mouton de Gruyter.

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———. 1988. "Predication Versus Membership in the Distinction betweenLogic as Language and Logic as Calculus." Synthese no. 75:37-72.Contents: 0. Introduction; 1. The problem with a set-theoretic semantics ofnatural language; 2. Intensional logic as a new theoretical framework forphilosophy; 3.The incompleteness of intensional logic when based onmembership; 4. Predication versus membership in type theory; 5. Second orderpredicate logic with nominalized predicates; 6. A set theoretic semantics withpredication as fundamental; 7. Concluding remarks."There are two major doctrines regarding the nature of logic today. The first isthe view of logic as the laws of valid inference, or logic as calculus. This viewbegan with Aristotle's theory of the syllogism, or syllogistic logic, and in time

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evolved first into Boole's algebra of logic and then into quantificational logic.On this view, logic is an abstract calculus capable of various interpretationsover domains of varying cardinality. Because these interpretations are given interms of a set-theoretic semantics where one can vary the universe at will andconsider the effect this, has on the validity of formulas, this view is sometimesdescribed as the set-theoretic approach to logic (see van Heijenoort ["Logic asLanguage and Logic as Calculus", Synthese 17,] 1967, p. 327).The second view of logic does not eschew set-theoretic semantics, it should benoted, and it may in fact utilize such a semantics as a guide in the determinationof validity. But to use such a semantics as a guide, on this view, is not the sameas to take that semantics as an essential characterization of validity. Indeed,unlike the view of logic as calculus, this view of logic rejects the claim that aset-theoretic definition of validity has anything other than an extrinsicsignificance that may be exploited for certain purposes (such as proving acompleteness theorem). Instead, on this view, logic has content in its own rightand validity is determined by what are called the laws of logic, which may bestated either as principles or as rules. Because one of the goals of this view is aspecification of the basic laws of logic from which the others may be derived,this view is sometimes called the axiomatic approach to logic." (p. 37)(...)"Concluding Remarks. The account we have given here of the view of logic aslanguage should not be taken as a rejection of the set-theoretical approach or asdefense of the metaphysics of possibilist logical realism. Rather, our view isthat there are really two types of conceptual framework corresponding to ourtwo doctrines of the nature of logic. The first type of framework is based onmembership in the sense of the iterative concept of set; although extensionalityis its most natural context (since sets have their being in their members), it maynevertheless be extended to include intensional contexts by way of a theory ofsenses (as in Montague's sense-denotation intensional logic). The second typeof framework is based on predication, and in particular developments it isassociated with one or another theory of universals. Extensionality is not themost natural context in this theory, but where it does hold and extensions areposited, the extensions are classes in the logical and not in the mathematicalsense.Russell's paradox, as we have explained, has no real bearing on set-formation ina theory of membership based on the iterative concept of set, but it does beardirectly on concept-formation or the positing or universals in a theory based onpredication. As a result, our second type of framework has usually been thoughtto be incoherent or philosophically bankrupt, leaving us with the set-theoreticalapproach as, the only viable alternative. This is why so much of analyticphilosophy in the 20th Century has been dominated by the set-theoreticalapproach. Set theory, after all, does seem to serve the purposes of a mathesisuniversalis.What is adequate as a mathesis universalis, however, need not also therefore beadequate as a l ingua philosophica or characteristica universalis. In particular,the set-theoretic approach does not seem to provide a philosophically satisfyingsemantics for natural language; this is because it is predication and notmembership that is fundamental to natural language. An adequate semantics for


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natural language, in other words, seems to demand a conceptual frameworkbased on predication and not on membership.(...)We do not maintain, accordingly, that we should give up the set-theoreticapproach, especially when dealing with the philosophy and foundations ofmathematics, or that only a theory of predication associated with possibilistlogical realism will provide an adequate semantics for natural language. In bothcases we may find a principle of tolerance, if not outright pluralism, the moreappropriate attitude to take." (pp. 69-70)

———. 1989. "Philosophical Perspectives on Formal Theories of Predication."In Handbook of Philosophical Logic. Vol. 4. Topics in the Philosophy ofLanguage, edited by Gabbay, Dov and Guenthner, Franz, 253-326. Dordrecht:Reidel.Contents: 1. Predication and the problem of universal 254; 2. Nominalism 256;3. A nominalistic semantics for predicative second order logic 261; 4.Nominalism and modal logic 266; 5 . Conceptualism vs . nominalism 270; 6.Constructive conceptualism 273; 7. Ramification of constructive conceptualism280; 8. Holistic conceptualism 286; 9. Logical realism vs holistic conceptualism289; 10. Possibilism and actualism in modal logical realism 292; 11. Logicalrealism and cssentialism 301; 12. Possibilism and actualism withinconceptualism 306; 13. Natural realism and conceptualism 313; 14. Aristotelianessentialism and the logic of natural kinds 318; References 325-326."Predication has been a central, if not the central, issue in philosophy since atleast the lime of Plato and Aristotle. Different theories of predication have infact been the basis of a number of philosophical controversies in bothmetaphysics and epistemology, not the least of which is the problem ofuniversals. In what follows we shall be concerned with what traditionally havebeen the three most important types of theories of universals. namely,nominalism, conceptualism, and realism, and with the theories of predicationwhich these theories might be said to determine or characterize.Though each of these three types of theories of universals may be said to havemany variants, we shall ignore their differences here to the extent that they donot characterize different theories of predication. This will apply especially tonominalism where but one formal theory of predication is involved. In bothconceptualism and realism, however, the different variants of each type do notall agree and form two distinct subtypes each with its own theory of predication.For this reason we shall distinguish between a constructive and a holistic formof conceptualism on the one hand, and a logical and a natural realism on theother. Constructive conceptualism, as we shall see, has affinities withnominalism with which it is sometimes confused, and holistic conceptualismhas affinities with logical realism with which it is also sometimes confused.Both forms of conceptualism may assume some form of natural realism as theircausal ground; and natural realism in turn must presuppose some form ofconceptualism as its background theory of predication. Both forms of realismmay be further divided into their essentialist and non-essentialist variants (andin logical realism even a form of anti-essentialism), and though an essentialistlogical realism is sometimes confused with Aristotelian essentialism, the latter

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is really a form of natural realism with natural kinds as the only essentialproperties objects can have." (pp. 253-254)

———. 1989. "Russell's Theory of Logical Types and the Atomistic Hierarchyof Sentences." In Rereading Russell: Essays on Bertrand Russell's Metaphysicsand Epistemology, edited by Savage, C.Wade and Anderson, C.Anthony, 41-62.Minneapolis: University of Minnesota Press.Reprinted as Chapter 5 in Logical Studies in Early Analytic Philosophy, pp.193-221."Russell’s philosophical views underwent a number of changes throughout hislife, and it is not always well-appreciated that views he held at one time camelater to be rejected; nor, similarly, that views he rejected at one time came laterto be accepted. It is not well-known, for example, that the theory of logicaltypes Russell described in his later or post-[PM] philosophy is not the same asthe theory originally described in [PM] in 1910-13; nor that some of the moreimportant applications that Russell made of the theory at the earlier time cannotbe validated or even significantly made in the framework of his later theory.What is somewhat surprising, however, is that Russell himself seems not tohave realized that he was describing a new theory of logical types in his laterphilosophy, and that as a result of the change some of his earlier logicalconstructions, including especially his construction of the different kinds ofnumbers, were no longer available to him.In the original framework, for example, propositional functions areindependently real properties and relations that can themselves have propertiesand relations of a higher order/type, and all talk of classes, and therebyultimately of numbers, can be reduced to extensional talk of properties andrelations as “single entities,” or what Russell in [POM] had called “logicalsubjects.” The Platonic reality of classes and numbers was replaced in this wayby a more fundamental Platonic reality of propositional functions as propertiesand relations. In Russell's later philosophy, however, “a propositional functionis nothing but an expression. It does not, by itself, represent anything. But it canform part of a sentence which does say something, true or false” (Russell, MyPhilosophical Development, ([MPD]), 69). Surprisingly. Russell even insiststhat this was what he meant by a propositional function in [PM]. “Whiteheadand I thought of a propositional function as an expression containing anundetermined variable and becoming an ordinary sentence as soon as a value isassigned to the variable: ‘x is human’, for example, becomes an ordinarysentence as soon as we substitute a proper name for V. In this view . . . thepropositional function is a method of making a bundle of such sentences”([MPD], 124). Russell does realize that some sort of change has come about,however, for he admits, “I no longer think that the laws of logic are laws ofthings; on the contrary, I now regard them as purely linguistic” (ibid., 102).(...)Now it is not whether [PM] can sustain a nominalistic interpretation that is ourconcern in this essay, as we have said, but rather how it is that Russell came tobe committed in his later philosophy to the atomistic hierarchy and thenominalistic interpretation of propositional functions as expressions generatedin a ramified second order hierarchy of languages based on the atomistic

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hierarchy. We shall pursue this question by beginning with a discussion of thedifference between Russell’s 1908 theory of types and that presented in [PM] in1910. This will be followed by a brief summary of the ontology that Russelltook to be implicit in [PM], and that he described in various publicationsbetween 1910 and 1913. The central notion in this initial discussion is whatRussell in his early philosophy called the notion of a logical subject, orequivalently that of a “term” or “single entity”. (In [PM], this notion wasredescribed as the systematically ambiguous notion of an “object.”) Asexplained in chapter 1 this notion provides the key to the various problems thatled Russell in his early philosophy to the development of his different theoriesof types, including that presented in [PM]. This remains true, moreover, evenwhen we turn to Russell’s later philosophy, i.e., to his post-[PM] views, onlythen it is described as the notion of what can and cannot be named in a logicallyperfect language. The ontology of these later views is what Russell calledlogical atomism, and it is this ontology that determines what Russell describedas the atomistic hierarchy of sentences. In other words, it is the notion of whatcan and cannot be named in the atomistic hierarchy that explains how Russell,however unwittingly, came to replace his earlier theory of logical types by thetheory underlying the atomistic hierarchy of sentences as the basis of a logicallyperfect language." (pp. 193-195 of the reprint)ReferencesPOM] Russell, Bertrand, The Principles of Mathematics, 2d ed. (NY., Norton &Co., 1938).[PM] Russell, Bertrand and Alfred Whitehead, Principia Mathematica, vol. 1(1910), vol. 2 (1912), and vol. 3 (1913) (London: Cambridge Univ. Press,).

———. 1989. "Conceptualism, Realism and Intensional Logic." Topoi.AnInternational Review of Philosophy no. 7:15-34.Contents: 0. Introduction 15; 1. A conceptual analysis of predication 16; 2.Concept-correlates and Frege's double correlations thesis 17; 3. Russell'sparadox in conceptual realism 18: 4. What are the natural numbers and wheredo they come from? 22; 5. Referential concepts and quantifier phrases 24; 5.Singular reference 24; 7. The intensions of refrential concepts as components ofapplied predicable concepts 26; 8. Intensional versus extensional predicableconcepts 28; 9. The intentional identity of intensional objects 29; Notes 31;Reference 33-35."0. IntroductionLinguists and philosophers are sometimes at odds in the semantical analysis oflanguage. This is because linguists tend to assume that language must besemantically analyzed in terms of mental constructs, whereas philosophers tendto assume that only a platonic realm of intensional entities will suffice. Theproblem for the linguist in this conflict is how to explain the apparent realistposits we seem to be committed to in our use of language, and in particular inour use of infinitives, gerunds and other forms of nominalized predicates. Theproblem for the philosopher is the old and familiar one of how we can haveknowledge of independently real abstract entities if all knowledge mustultimately be grounded in psychological states and processes. In the case ofnumbers, for example, this is the problem of how mathematical knowledge is

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possible. In the case of the intensional entities assumed in the semanticalanalysis of language, it is the problem of how knowledge of even our ownnative language is possible, and in particular of how we can think and talk toone another in all the ways that language makes possible.I believe that the most natural framework in which this conflict is to be resolvedand which is to serve as the semantical basis of natural language is anintensional logic that is based upon a conceptual analysis of predication inwhich what a predicate stands for in its role as a predicate is distinguished fromwhat its nominalization denotes in its role as a singular term. Predicates in sucha framework stand for concepts as cognitive capacities to characterize and relateobjects in various ways, i.e. for dispositional cognitive structures that do notthemselves have an individual nature, and which therefore cannot be the objectsdenoted by predicate nominalizations as abstract singular terms. The objectspurportedly denoted by nominalized predicates, on the other hand, areintensional entities, e.g. properties and relations (and propositions in the case ofzero-place predicates), which have their own abstract form of individuality,which, though real, is posited only through the concepts that predicates standfor in their role as predicates. That is, intensional objects are represented in thislogic as concept-correlates, where the correlation is based on a logicalprojection of the content of the concepts whose correlates they are.(...)Before proceeding, however, there is an important distinction regarding thenotion of a logical form that needs to be made when joining conceptualism andrealism in this way. This is that logical forms can be perspicuous in either oftwo senses, one stronger than the other. The first is the usual sense that appliesto all theories of logical form, conceptualist or otherwise; namely, that logicalforms are perspicuous in the way they specify the truth conditions of assertionsin terms of the recursive operations of logical syntax. In this sense, fully appliedlogical forms are said to be semantic structures in their own right. In the secondand stronger sense, logical forms may be perspicuous not only in the way theyspecify the truth conditions of an assertion, but in the way they specify thecognitive structure of that assertion as well. To be perspicuous in this sense, alogical form must provide an appropriate representation of both the referentialand the predicable concepts that underlie an assertion.Our basic hypothesis in this regard will be that every basic assertion is the resultof applying just one referential concept and one predicable concept, and thatsuch an applied predicable concept is always fully intensionalized (in a sense tobe explained). This will place certain constraints on the conditions for when acomplex predicate expression is perspicuous in the stronger sense — such asthat a referential expression can occur in such a predicate expression only in itsnominalized form. (A similar constraint will also apply to a defining orrestricting relative clause of a referential expression.) In the cases where arelational predicable concept is applied, the assumption that there is still but onereferential concept involved leads to the notion of a conjunctive referentialconcept, a notion that requires the introduction in intensional logic of specialquantifiers that bind more than one individual variable. Except for brieflynoting the need for their development, we shall not deal with conjunctivequantifiers in this essay." (pp. 15-16)


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———. 1991. "Conceptualism." In Handbook of Metaphysics and Ontology,edited by Smith, Barry and Burkhardt, Hans, 168-174. Munich: PhilosophiaVerlag.Conceptualism is one of the three types of theories regarding the nature ofuniversals described by Porphyry in his introduction to Aristotle's Categories.The other two are nominalism and realism. Because a universal, according toAristotle, is that which can be predicated of things (De Int. 17a39), thedifference between these three types of theories lies in what it is that each takesto be predicable of things. In this regard we should distinguish predication inlanguage from predication in thought, and both from predication in reality,where there is no presumption that one kind of predication precludes the others.All three types of theories agree that there is predication in language, inparticular that predicates can be predicated of things in the sense of being trueor false of them. Nominalism goes further in maintaining that only predicatescan be predicated of things, that is, that there are no universals other than thepredicate expressions of some language or other. Conceptualism opposesnominalism in this regard and maintains that predicates can be true or false ofthings only because they stand for concepts, where concepts are the universalsthat are the basis of predication in thought. Realism also opposes nominalism inmaintaining that there are real universals, viz. properties and relations, that arethe basis of predication in reality." (p. 168)(...)"Conceptualism is by no means a monolithic theory, but has many forms, somemore restrictive than others, depending on the mechanisms assumed as the basisfor concept-formation. None of these forms, in themselves, precludes beingcombined with a realist theory, whether Aristotelian (as in conceptual naturalrealism) or Platonist (as in conceptual intensional realism), or both. Someconceptualists, such as Sellars, have made it a point to disassociateconceptualism from any form of realism regarding abstract entities, but thatdisassociation has nothing to do with conceptualism as a theory about the natureof predication in thought. Conceptualism’s shift in emphasis from metaphysicsto psychology, in other words, while important in determining what kind oftheory is needed to explain predication in thought, should not be taken asjustifying a restrictive form of conceptualism that precludes both a natural andan intensional realism." (p. 174)

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———. 1991. "Logic V: Higher Order Logics." In Handbook of Metaphysicsand Ontology, edited by Smith, Barry and Burkhardt, Hans, 466-470. Munich:Philosophia Verlag."Higher-order logic goes beyond first-order logic in allowing quantifiers toreach into the predicate as as well as the subject positions of the logical forms itgenerates. A second feature, usually excluded in standard formulations ofsecond-order logic, allows nominal-ized forms of predicate expressions (simpleor complex) to occur in its logical forms as abstract singular terms. (E.g.,‘Socrates is wise’, in symbols W(s), contains ‘is wise’ as a predicate, whereas‘Wisdom is a virtue’, in symbols V(W), contains ‘wisdom’ as a nominalizedform of that predicate. ‘Being a property is a property’, in symbols P(P), or withλ-abstracts, PλxP(x)), where λχΡ(χ) is read ‘to be an x such that x is a property’,

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contains both the predicate ‘is a property’ and a nominalized form of thatpredicate, viz. ‘being a property’. Frege’s well-known example, ‘The conceptHorse is not a concept’, contains ‘the concept Horse’ as a nominalized form ofthe predicate phrase ‘is a horse’.)" (p. 466)

———. 1991. "Ontology, Fomal." In Handbook of Metaphysics and Ontology,edited by Smith, Barry and Burkhardt, Hans, 640-647. Munich: PhilosophiaVerlag."Formal ontology is the result of combining the intuitive, informal method ofclassical ontology with the formal, mathematical method of modern symboliclogic, and ultimately identifying them as different aspects of one and the samescience. That is, where the method of ontology is the intuitive study of thefundamental properties. modes, and aspects of being, or of entities in general,and the method of modern symbolic logic is the rigorous construction of formal,axiomatic systems, formal ontology, the result of combining these two methods,is the systematic, formal, axiomatic development of the logic of all forms andmodes of being. As such, formal ontology is a science prior to all others inwhich particular forms, modes, or kinds of being are studied." (p. 641)

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———. 1991. "Russell, Bertrand." In Handbook of Metaphysics and Ontology,edited by Smith, Barry and Burkhardt, Hans, 796-798. Munich: PhilosophiaVerlag."Russell held a number of different metaphysical positions throughout hiscareer, with the idea of logic as a logically perfect language being a commontheme that ran through each.(...)"A fundamental notion of Russell’s logical realism, sometimes also calledontological logicism, was that of a propositional function, the extension ofwhich Russell took to be a class as many. Initially, as part of his response to theproblem of the One and the Many, Russell had assumed that each propositionalfunction was a single and separate entity over and above the many propositionsthat were its values, and, similarly, that to each class as many therecorresponded a class as one. Upon discovering his paradox, Russell maintainedthat we must distinguish a class as many from a class as one, and that a class asone might not exist corresponding to a class as many. He also concluded that apropositional function cannot survive analysis after all, but ‘lives’ only in thepropositions that are its values, i.e. that propositional functions are nonentities."(...)"As a result of arguments given by Ludwig Wittgenstein in 1913, Russell, from1914 on, gave up the Platonistic view that properties and relations could belogical subjects. Predicates were still taken as standing for properties andrelations, but only in their role as predicates; i.e., nominalized predicates wereno longer allowed as abstract singular terms in Russell’s new version of hislogically perfect language. Only particulars could be named in Russell's newmetaphysical theory, which he called logical atomism, but which, unlike hisearlier 1910-13 theory, is a form of natural realism, and not of logical realism,since now the only real properties and relations of his ontology are the simplematerial properties and relations that are the components of the atomic facts thatmake up the world. Complex properties and relations in this framework are

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simply propositional functions, which, along with propositions, are now merelylinguistic expressions. (Russell remained unaware that as a result of the changein his metaphysical views from logical to natural realism his original theory oftypes was restricted to the much weaker sub-theory of ramified second-orderlogic, and that he could no longer carry through his logicist programme. Thisreinforced the confusion of nominalists into thinking that Russell’s earliertheory of types could be given a nominalistic interpretation, since such aninterpretation is possible for ramified second-order logic.)" (pp. 797-798)

———. 1991. "Quantification, Time and Necessity." In PhilosophicalApplications of Free Logic, edited by Lambert, Karel, 242-256. New York:Oxford University Press.Contents: 0. Introduction; 1. A Logic a Actual and Possible Objects; 2. ACompleteness Theorem for Tense Logic; 3. Modality Within Tense Logic; 4.Some Observations on Quantifiers in Modal and Tense Logic; 5. ConcludingRemarks.Abstract: "A logic of actual and possible objects is formulated in which"existence" and "being", as second-level concepts represented by first-order(objectual) quantifiers, are distinguished. A free logic of actual objects is thendistinguished as a subsystem of the logic of actual and possible object. Severalcomplete first-order tense logics are then formulated in which temporal versionsof possibilism and actualism are characterized in terms of the free logic ofactual objects and the wide logic of actual and possible objects. It is then shownhow a number of different modal logics can be interpreted within quantifiedtense logic, with the latter providing a paradigmatic framework in which todistinguish the interplay between quantifiers, tenses and modal operators andwithin which we can formulate different temporal versions of actualism andpossibilism.""The fundamental assumption of a logic of actual and possible objects is thatthe concept of existence is not the same as the concept of being. Thus, eventhough necessarily whatever exists has being, it is not necessary in such a logicthat whatever has being exists; that is, it can be the case that there be somethingthat does not exist. No occult doctrine is needed to explain the distinctionbetween existence and being, for an obvious explanation is already at hand in aframework of tense logic in which being encompasses past, present, and futureobjects (or even just past and present objects) while existence encompasses onlythose objects that presently exist. We can interpret modality in such aframework, in other words, whereby it can be true to say that some things donot exist. Indeed, as indicated in Section 3, infinitely many different modallogics can be interpreted in the framework of tense logic. In this regard, wemaintain, tense logic provides a paradigmatic framework in which possibilism(i.e., the view that existence is not the same as being, and that therefore therecan be some things that do not exist) can be given a logically perspicuousrepresentation.Tense logic also provides a paradigmatic framework for actualism as the viewthat is opposed to possibilism; that is, the view that denies that the concept ofexistence is different from the concept of being. Indeed, as we understand ithere, actualism does not deny that there can be names that have had denotations

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in the past but that are now denotationless, and hence that the statement thatsome things do not exist can be true in a semantic metalinguistic sense (as astatement about the denotations, or lack of denotations, of singular terms). Whatis needed, according to actualism, is not that we should distinguish the conceptof existence from the concept of being, but only that we should modify the waythat the concept of existence (being) is represented in standard first-orderpredicate logic (with identity). A first-order logic of existence should allow forthe possibility that some of our singular terms might fail to denote an existentobject, which, according to actualism, is only to say that those singular termsare denotationless rather than what they denote are objects (beings) that do notexist. Such a logic for actualism amounts to what nowadays is called freelogic." (pp. 242-243)

———. 1992. "Conceptual Realism Versus Quine on Classes and Higher-OrderLogic." Synthese no. 90:379-436.Contents: 0. Introduction; 1. Predication versus Membership; 2. Old versusNew Foundations; 3. Concepts versus ultimate Classes; 4. Frege versus Quineon Higher-Order Logic; 5. Conceptualism versus Nominalism as FormalTheories of predication; 6. Conceptualism Ramified versus NominalismRamified; 7. Constructive Conceptual Realism versus Quine's view ofConceptualism as a Ramified Theory of Classes; 8. Holistic ConceptualRealism versus Quine's Class Platonism.Abstract: "The problematic features of Quine's 'set' theories NF and ML are aresult of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-orderlogic of predication with nominalized predicates as abstract singular terms. Weadopt a modified Fregean position called conceptual realism in which theconcepts (unsaturated cognitive structures) that predicates stand for aredistinguished from the extensions (or intensions) that their nominalizationsdenote as singular terms. We argue against Quine's view that predicatequantifiers can be given a referential interpretation only if the entities predicatesstand for on such an interpretation are the same as the classes (assumingextensionality) that nominalized predicates denote as singular terms. Quine'salternative of giving predicate quantifiers only a substitutional interpretation iscompared with a constructive version of conceptual realism, which with a logicof nominalized predicates is compared with Quine's description ofconceptualism as a ramified theory of classes. We argue against Quine's implicitassumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's classPlatonism.""According to Quine, in one of his later works, the pioneers in modern logic,such as Frege and Russell, overestimated the kinship between membership andpredication and in that way came to view set theory as logic (Quine 1970, p.65). Such a claim, we maintain, is both false and misleading. Frege and Russelldid assume a logical kinship between predication and membership, but whatthey meant by membership was membership in a class as the extension of aconcept (where a concept is a predicable entity, i.e., a universal in the traditionalsense) and not membership in a set. Sets, unlike classes, as we have said, have

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their being in their members, and in that regard there need be no kinship at allbetween predication and membership in a set. Classes in the logical sense, onthe other hand, have their being in the concepts whose extensions they are,which means that any theory of membership in a class presupposes asuperseding theory of predication. (3) Frege and Russell did not view set theoryas logic, but they each did develop a theoryof classes and they each did so based on a superseding higher-order theory ofpredication." (p. 382)

———. 1992. "Cantor's Power-Set Theorem Versus Frege's Double-CorrelationThesis." History and Philosophy of Logic no. 13:179-201.Abstract: "Frege’s thesis that second-level concepts can be correlated with first-level concepts and that the latter can be correlated with their value-ranges is indirect conflict with Cantor’s power-set theorem, which is a necessary part of theiterative, but not of the logical, concept of class. Two consistent second-orderlogics with nominalised predicates as abstract singular terms are described inwhich Frege’s thesis and the logical notion of a class are defended and Cantor’stheorem is rejected. Cantor’s theorem is not incompatible with the logicalnotion of class, however. Two alternative similar kinds of logics are alsodescribed in which Cantor’s theorem and the logical notion of a class areretained and Frege’s thesis is rejected.""There is another problem with Russell’s solution, however, in addition to thatof the relativisation of classes to each logical type. This problem has to do withthe fact that the particular theory of types that Russell adopted is a theory oframified types, which, unlike the theory of simple types, is based on aconstructive (i.e. ‘predicative’) comprehension principle. Such a constructiveapproach is not without merit, but it does affect the logical notion of a class in afundamental way. In particular, because of the kind of constructive constraintsimposed by the theory on the comprehension principle, Cantor’s theorem,which involves objects of different types, cannot be proved in such a framework(cf. Quine 1963, 265). That is not objectionable in itself, but it does not get atthe root of the matter of the real conflict between Cantor’s power-set theoremand the logical notion of class as represented by an impredicativecomprehension principle.An impredicative comprehension principle is provable in the theory of simpletypes. But in this framework, as in the theory of ramified types as well,Russell’s paradox cannot even be stated (because of the gramatical constraintson the conditions of well-formedness), which means that the description of theclass upon which Russell’s paradox is based is meaningless. Thus, not onlymust the universal class be relativised and duplicated, potentially, infinitelymany times in order to avoid Russell’s paradox on this approach, but theparadox must itself be ruled as meaningless. The theory of types, whethersimple or ramified, is not really a solution of the problem so much as a way ofavoiding it altogether.There is another way in which we can preserve our logical intuitions and notgive up the logical notion of a class in favor of the mathematical (i.e. in favor ofset theory), and yet in which not only is Cantor’s theorem formulable but so isRussell’s paradox—though, of course, the latter will no longer be provable.

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Indeed, there is not just one such way, but at least two (both of whichthemselves have two alternatives). On the first, it is not the logical notion of aclass that must be rejected as the way of resolving Russell’s paradox, butCantor’s theorem instead. This rejection is not ad hoc or arbitrary on thisapproach, but is based on a more general principle, which we refer to as Frege’sdouble-correlation thesis. It is this approach that we shall turn to first. On thesecond and alternative approach, which we shall turn to later, the trouble lies inneither Cantor’s theorem nor in the assumption that there is a universal class(both of which can be retained without contradiction on this approach), butrather in how the logic of identity is to be applied in certain contexts. On thisapproach, the claim that a contradiction results by combining Cantor’s theoremwith the assumption that the universal class exists is not a ‘truism’ after all butis outright false."ReferencesQuine, W. V. 1963 Set theory and its logic, Cambridge, Mass. (HarvardUniversity Press).

———. 1993. "On Classes and Higher-Order Logic: A Critique of W.V.O.Quine." Philosophy and the History of Science.A Taiwanese Journal no.2:23-50.Abstract: "The problematic features of Quine's set theories NF and ML resultfrom compressing the higher-order predicate logic of type theory into a first-order logic of membership, and can be resolved by turning to a second-orderpredicate logic with nominalized predicates as abstract singular terms. Amodified Fregean position, called conceptual realism, is described in which theconcepts (unsaturated cognitive structures) that predicates stand for aredistinguished from the extensions (or intensions) that their nominalizationsdenote as abstract singular terms. Quine's view that conceptualism cannotaccount for impredicative concept-formation is rejected, and a holisticconceptual realism is compared with Quine's class Platonism."

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———. 1995. "Knowledge Representation in Conceptual Realism."International Journal of Human-Computer Studies no. 43:697-721."Knowledge representation in Artificial Intelligence (AI) involves more thanthe representation of a large number of facts or beliefs regarding a givendomain, i.e. more than a mere listing of those facts or beliefs as data structures.It may involve, for example, an account of the way the properties and relationsthat are known or believed to hold of the objects in that domain are organizedinto a theoretical whole - such as the way different branches of mathematics, orof physics and chemistry, or of biology and psychology, etc., are organized, andeven the way different parts of our commonsense knowledge or beliefs aboutthe world can be organized. But different theoretical accounts will apply todifferent domains, and one of the questions that arises here is whether or notthere are categorial principles of representation and organization that applyacross all domains regardless of the specific nature of the objects in thosedomains. If there are such principles, then they can serve as a basis for a generalframework of knowledge representation independently of its application toparticular domains. In what follows I will give a brief outline of some of thecategorial structures of conceptual realism as a formal ontology. It is this system

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that I propose we adopt as the basis of a categorial framework for knowledgerepresentation." (p. 697)(...)" Concluding remarks. We have given here only an overview or sketch ofconceptual realism as a formal ontology, i.e. as a theory of logical form havingboth conceptual and ontological categories - but in which the latter arerepresented in terms of the former. The categories of natural kinds and ofnatural properties and relations, for example, are represented in terms of thecategories of sortals and predicable concepts, respectively, and the category ofabstract objects is represented in terms of the process of conceptualnominalization (reification) as a subcategory of objects. Not all of thesecategories or parts of this formal ontology will be relevant in every domain ofknowledge representation, but each is relevant at least to some domains and isneeded in a comprehensive framework for knowledge representation. In thosedomains where certain categorial distinctions are not needed - such as thatbetween predicative and impredicative concepts, or that between predicableconcepts and natural properties and relations, or between sortal concepts andnatural kinds, etc. - we can simply ignore or delete the logical forms inquestion. What must remain as the core of the system is the intensional logicaround which all of the other categories are built - namely, the second-orderpredicate logic with nominalized predicates as abstract singular terms that wecall HST*-lambda. It is this core, I believe, that can serve as a universalstandard by which to evaluate other representational systems." (p. 721)

———. 1996. "Conceptual Realism as a Formal Ontology." In FormalOntology, edited by Poli, Roberto and Simons, Peter, 27-60. Dordrecht: Kluwer.Contents: 1. Introduction; 2. Substitutional versus Ontological Interpretations ofQuantifiers; 3. The Importance of the Notion of Unsaturedness in FormalOntology; 4. Referential and Predicable Concepts Versus Immanent Objects ofReference; 5. Conceptual Natural Realism and the Analogy of Being BetweenNatural and Intelligible Universals; 6. Conceptual Natural Realism andAristotelian Essentialism; 7. Conceptual Intensional Realism versus ConceptualPlatonism and the Logic of Nominalized Predicates8. Concluding Remarks.Abstract: "Conceptualism simpliciter, wheter constructive or holistic, providesan account of predication only in thought and language, and represents in thatregard only a truncated formal ontology. But conceptualism can be extended toan Aristotelian conceptual natural realism in which natural properties andrelations (and natural kinds as well) can be analogically posited correspondingto some of Our concepts, thereby providing an account of predication in thespace-time causal Order as well. In addition, through a pattern of reflexiveabstraction corresponding to the process of nominalization in language (and inwhich abstract objects are hypostatized corresponding to our concepts asunsaturated cognitive structures), conceptualism can also be extended to aconceptual Platonism or intensional realism that can provide an account of boththe intensional objects of fiction and the extensional objects of mathematics.Conceptual realism is thus shown to be a paradigm formal ontology in whichthe distinctions between abstract reality, natural reality, and thought and

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language are properly represented, and in which the traditional oppositionbetween Platonism and Aristotelianism is finally overcome by properly locatingtheir different functions, and the way each should be rep resented, in formalontology.""Concluding Remarks. As this informal sketch indicates, conceptual realism, bywhich we mean conceptual natural realism and conceptual intensional realismtogether, provides the basis of a general conceptual-ontological framework,within which, beginning with thought and language, a comprehensive formalontology can be developed. Not only does conceptual realism explain how, innaturalistic terms, predication in thought and language is possible, but, inaddition, it provides a theory of the nature of predication in reality through ananalogical theory of properties and relations. In this way, conceptual realismcan be developed into a reconstructed version of Aristotelian realism, includinga version of Aristotelian essentialism. In addition, through the process ofnominalization, which corresponds to a reflexive abstraction in which weattempt to represent our concepts as if they were objects, conceptualism can bedeveloped into a conceptual intensional realism that can provide an account notonly of the abstract reality of numbers and other mathematical objects, but ofthe intensional objects of fiction and stories of all kinds, both true and false, andincluding those stories that we systematically develop into theories about theworld. In this way, conceptual realism provides a framework not only for theconceptual and natural order, but for the mathematical and intensional order aswell. Also, in this way, conceptual realism is able to reconcile and provide aunified account both of Platonism and Aristotelian realism, includingAristotelian essentialism - and it does so by showing how the ontologicalcategories, or modes of being, of each of these ontologies can be explained interms a conceptualist theory of predication and its analogical extensions." (p.60)

———. 1997. "Formally Oriented Work in the Philosophy of Language." InRoutledge History of Philosophy. Vol. X - The Philosophy of Meaning,Knowledge and Value in the 20th Century, edited by Canfield, John, 39-75.New York: Routledge.Contents: 1. The notion of a Characteristica Universalis as a philosophicallanguage; 2. The notion a a logically perfect language as a regulating ideal; 3.The theory of logical types; 4. Radical empiricism and the logical constructionof the world; 5. The logical empiricist theory of meaning; 6. Semiotic and thetrinity of syntax, semantics and pragmatics; 7. Pragmatics from a logical pointof view; 8. Intensional logic; 9. Universal Montague grammar; 10. Speech-acttheory and the return to pragmatics.Abstract: "One of the perennial issues in philosophy is the nature of the variousrelationships between language and reality, language and thought, and languageand knowledge. Part of this issue is the question of the kind of methodologythat is to be brought to bear on the study of these relationships. Themethodology that we shall discuss here is based on a formally orientedapproach to the philosophy of language, and specifically on the notion of alogically ideal language as the basis of a theory of meaning and a theory ofknowledge."

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———. 1997. "Conceptual Realism as a Theory of Logical Form." RevueInternationale de Philosophie:175-199."The central notion in the philosophy of logic is the notion of a logical form,and the central issue is which theory of logical form best represents ourscientific (including our mathematical) and commonsense understanding of theworld. Here, by a theory of logicalform, we mean not only a logical grammar in the sense of a system of formationrules characterizing the well-formed expressions of the theory, but also a logicalcalculus characterizing what is valid (i.e., provable or derivable) in the theory.The representational role of the logical forms of such a theory consists in thefact that they are perspicuous in the way they specify the truth conditions, andthereby the validity, of formulas in terms of the recursive operations of logicalsyntax. In conceptualism we also require that logical forms be perspicuous inthe way they represent the cognitive structure of our speech and mental acts,including in particular the referential and predicable concepts underlying thoseacts.The purpose of a theory of logical form, accordingly, is that it is to serve as ageneral semantical framework by which we can represent in a logicallyperspicuous way our commonsense and scientific understanding of the world,including our understanding of ourselvesand the cognitive structure of our speech and mental acts. So understood, thelogical forms of such a theory are taken to be semantic structures in their ownright, relative to which the words, phrases, and (declarative) sentences of a(fragment of) natural language, or of a scientific or mathematical theory, are tobe represented and interpreted. The process by which the expressions of anatural language or scientific theory are represented and interpreted in such atheory — relative to the aims, purposes and pragmatic considerations regardinga given context or domain of discourse — amounts to a logical analysis of thoseexpressions. (A different group of aims, purposes, etc., might give a finer- or acoarser-grained analysis of the domain.)Ideally, where the syntax of a target language or theory has been recursivelycharacterized, such an analysis can be given in terms of a preciselycharacterized theory of translation (1). Usually, however, the analysis is giveninformally.In what follows I will briefly describe and attempt to motivate some (but notall) aspects of a theory of logical form that I associate with the philosophicalsystem I call conceptual realism. The realism involved here is really of twotypes, one a natural realism (amounting to a modem form of Aristotelianessentialism) and the other an intensional realism (amounting to a modem, butalso mitigated, form of Platonism). The core of the theory is a second-orderlogic in which predicate expressions (both simple and complex) can benominalized and treated as abstract singular terms (in the sense of beingsubstituends of individual variables). In this respect the core is really a form ofconceptual intensional realism, which is the only part of the system we willdiscuss here (2)." (pp. 175-176)(1) See Montague (1969) for a description of such a theory of translation (forMontague’s type-theoretical intensional logic).(2) See Cocchiarella (1996), §§ 5-6, for a description of conceptual natural

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realism as a modem form of Aristotelian Essentialism.ReferencesCocchiarella, N.B. (1996), “ Conceptual Realism as a Formal Ontology”, inFormal Ontology, R. Poli and P. Simons, eds., Kluwer Academic press,Dordrecht, pp. 27-60.Montague, R.M. (1969), “ Universal Grammar”, in Formal Philosophy, Selectedpapers of Richard Montague, edited by R.H. Thomason, Yale University Press,New Haven, 1974.

———. 1998. "Property Theory." In Routledge Encyclopedia of Philosophy -Vol. 7, edited by Craig, Edward, 761-767. New York: Routledge.Abstract: "Traditionally, a property theory is a theory of abstract entities thatcan be predicated of things. A theory of properties in this sense is a theory ofpredication -just as a theory of classes or sets is a theory of membership. In aformal theory of predication, properties are taken to correspond to some (or all)one-place predicate expressions. In addition to properties, it is usually assumedthat there are n-ary relations that correspond to some (or all) n-place predicateexpressions (for n > 2). A theory of properties is then also a theory of relations.In this entry we shall use the traditional labels 'realism' and 'conceptualism' as aconvenient way to classify theories. In natural realism, where properties andrelations are the physical, or natural, causal structures involved in the laws ofnature, properties and relations correspond to only some predicate expressions,whereas in logical realism properties and relations are generally assumed tocorrespond to all predicate expressions.Not all theories of predication take properties and relations to be the universalsthat predicates stand for in their role as predicates. The universals of conceptualism, for example. are unsaturated concepts in the sense of cognitive capacitiesthat are exercised (saturated) in thought and speech. Properties and relations inthe sense of intensional Platonic objects may still correspond to predicateexpressions, as they do in conceptual intensional realism, but only indirectly asthe intensional contents of the concepts that predicates stand for in their role aspredicates. In that case, instead of properties and relations being what predicatesstand for directly, they are what nominalized predicates denote as abstractsingular terms. It is in this way that concepts - such as those that the predicatephrases 'is wise', 'is triangular' and 'is identical with' stand for - are distinguishedfrom the properties and relations that are their intensional contents - such asthose that are denoted by the abstract singular terms 'wisdom', 'triangularity' and'identity, respectively. Once properties are represented by abstract singularterms, concepts can be predicated of them, and, in particular, a concept can bepredicated of the property that is its intensional content. For example, theconcept represented by 'is a property' can be predicated of the property denotedby the abstract noun phrase 'being a property', so that 'being a property is aproperty' (or, 'The property of being a property is a property') becomes well-formed. In this way, however, we are confronted with Russell's paradox of (theproperty of) being a non-self-predicable property, which is the intensionalcontent of the concept represented by ' is a non-self-predicable property'. Thatis, the property of being a non-self- predicable property both falls and does notfall under the concept of being a non-self-predicable property (and therefore

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both falls and does not fall under the concept of being self-predicable)." (p. 761)

———. 1998. "The Theory of Types (Simple and Ramified)." In RoutledgeEncyclopedia of Philosophy - Vol. 9, edited by Craig, Edward, 359-362. NewYork: Routledge.Abstract: "The theory of types was first described by Bertrand Russell in 1908.He was seeking a logical theory that could serve as a framework formathematics and, in particular, a theory that would avoid the so-called 'vicious-circle' antinomies, such as his own paradox of the property of those propertiesthat are not properties of themselves - or, similarly, of the class of those classesthat are not members of themselves. Such paradoxes can be thought of asresulting when logical distinctions are not made between different types ofentities and, in particular, between different types of properties and relationsthat might be predicated of entities, such as the distinction between concreteobjects and their properties, and the properties of those properties, and so on. In'ramified' type theory, the hierarchy of properties and relations is, as it were,two-dimensional, where properties and relations are distinguished first by theirorder, and the by their level within each order. In 'simple' type theory propertiesand relations are distinguished only by their orders." (p. 359)

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———. 1998. "Reference in Conceptual Realism." Synthese no. 114:169-202.Contents: 1. The core of Conceptual Intensional Realism; 2. Referentialconcepts, simple and complex; 3. Geach's negation and complex predicatearguments; 4. Active versus deactivated referential concepts; 5. Deactivationand Geach's arguments; 6. Relative pronouns and referential concepts; 7.Relative pronouns as referential expressions; 8. Concluding remarks.Abstract: "A conceptual theory of the referential and predicable concepts usedin basic speech and mental acts is described in which singular and general,complex and simple, and pronominal and non-pronominal, referential conceptsare given a uniform account. The theory includes an intensional realism inwhich the intensional contents of predicable and referential concepts arerepresented through nominalized forms of the predicate and quantifier phrasesthat stand for those concepts. A central part of the theory distinguishes betweenactive and deactivated referential concepts, where the latter are represented bynominalized quantifier phrases that occur as parts of complex predicates. PeterGeach's arguments against theories of general reference in "Reference andGenerality" are used as a foil to test the adequacy of the theory. Geach'sarguments are shown to either beg the question of general as opposed tosingular reference or to be inapplicable because of the distinction betweenactive and deactivated referential concepts.""Concluding Remarks. We do not claim that the theory of relative pronouns asreferential expressions proposed in Section 7 is unproblematic, it should benoted. If it should turn out that it cannot be sustained, then we still have thetheory proposed in Section 6, where relative pronouns are taken as anaphoricproxies for non-pronominal referential expressions. In other words, whether theproposal of Section 7 is sustained or not, we maintain that Geach's argumentsagainst complex names and general reference do not work against the kind ofconceptualist theory we have presented here.We also do not claim to have proved that our conceptualist theory of reference

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resolves all problems about reference, but only that it has passed an initial testof adequacy as far as Geach's arguments in (Geach Reference and Generalitythird edition, 1980) are concerned. It is our view that a conceptualist theory iswhat is needed to account for reference and predication in our speech andmental acts, and that only a theory of the referential and predicable conceptsthat underlie the basic forms of such acts will suffice. Such a theory, wemaintain, must provide a uniform account of general as well as singularreference, and, in terms of the referential and predicable concepts involved in aspeech or mental act, it must distinguish the logical forms that represent thecognitive structure of that act from the logical forms that only represent its truthconditions. That, in any case, is the kind of conceptualist theory we haveattempted to describe and defend here." (p. 198)

———. 2000. "Russell's Paradox of the Totality of Propositions." NordicJournal of Philosophical Logic no. 5:25-37.Abstract: "Russell’s ‘‘new contradiction’’ about ‘‘the totality of propositions’’has been connected with a number of modal paradoxes. M. Oksanen hasrecently shown how these modal paradoxes are resolved in the set theory NFU.Russell’s paradox of the totality of propositions was left unexplained, however.We reconstruct Russell’s argument and explain how it is resolved in twointensional logics that are equiconsistent with NFU. We also show howdifferent notions of possible worlds are represented in these intensional logics.""In Appendix B of his 1903 Principles of Mathematics (PoM), Russelldescribed a ‘‘new contradiction’’ about ‘‘the totality of propositions’’ that his‘‘doctrine of types’’ (as described in Appendix B) was unable to avoid. (1)In recent years this ‘‘new contradiction’’ has been connected with a number ofmodal paradoxes, some purporting to show that there cannot be a totality of truepropositions, (2) or that even the idea of quantifying over the totality ofpropositions leads to contradiction. (3) A number of these claims have beendiscussed recently by Mika Oksanen and shown to be spurious relative to theset theory known as NFU. (4) In other words, if NFU is used instead of ZF asthe semantical metalanguage for modal logic, the various ‘‘paradoxes’’ aboutthe totality of propositions (usually construed as the totality of sets of possibleworlds) can be seen to fail (generally because of the existence of a universal setand the failure of the general form of Cantor’s power-set theorem in NFU). It isnot clear, however, how Russell’s own paradox about the totality ofpropositions is resolved on this analysis, and although Oksanen quotedRussell’s description of the paradox in detail, he did not show how it isexplained in NFU after his resolution of the other related modal paradoxes; infact, it is not at all clear how this might be done in NFU.One reason why Russell’s argument is difficult to reconstruct in NFU is that it isbased on the logic of propositions, and implicitly in that regard on a theory ofpredication rather than a theory of membership. A more appropriate medium forthe resolution of these paradoxes, in other words, would be a formal theory ofpredication that is a counterpart to NFU.Fortunately, there are two such theories, λHST* and HST*λ, that areequiconsistent with NFU and that share with it many of the features that make ita useful framework within which to resolve a number of paradoxes, modal or

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otherwise. (5)" (pp. 25-26)(1) PoM, p. 527.(2) See, e.g., Grim 1991, pp. 92f.(3) See, e.g., Grim 1991, p. 119 and Jubien 1988, p. 307.(4) See Oksanen 1999. NFU is a modified version of Quine’s system NF. It wasfirst described in Jensen 1968 and recently has been extensively developed inHolmes 1999.(5) See Cocchiarella 1986, chapters IV and VI for proofs of the connection ofNFU with these systems. Also, see Cocchiarella 1985 for how these systems arerelated to Quine’s systems NF and ML. For a discussion of the refutation ofCantor’s power-set theorem inthese systems, see Cocchiarella 1992.ReferencesCocchiarella, N. B. 1985. Frege’s double-correlation thesis and Quine’s settheories NF and ML. Journal of Philosophical Logic, vol. 4, pp. 1–39.Cocchiarella, N. B. 1986. Logical Investigations of Predication Theory and theProblem of Universals. Bibliopolis Press, Naples, 1985.Cocchiarella, N. B. 1992. Cantor’s Power-Set Theorem Versus Frege’s Double-Correlation Thesis, History and Philosophy of Logic, vol. 13, 179–201.Holmes, R. 1999. Elementary Set Theory with a Universal Set. Cahiers duCentre de Logique, Bruylant-Academia, Louvain-la-Neuve, Belgium.Grim, P. 1991. The Incomplete Universe. MIT Press, Cambridge, MA.Jensen, R. 1968. On the consistency of a slight (?) modification of Quine’s NewFoundations. Synthese, vol. 19, pp. 250–263.Oksanen, M. 1979. The Russell-Kaplan paradox and other modal paradoxes; anew solution. Nordic Journal of Philosophical Logic, vol. 4, no. 1, pp. 73–93.Russell, B. 1937. The Principles of Mathematics, 2nd edition. W. W. Norton &Co., N.Y.

———. 2001. "A Logical Reconstruction of Medieval Terminist Logic inConceptual Realism." Logical Analysis and History of Philosophy no. 4:35-72.Abstract: "The framework of conceptual realism provides a logically ideallanguage within which to reconstruct the medieval terminist logic of the 14thcentury. The terminist notion of a concept, which shifted from Ockham's earlyview of a concept as an intentional object (the fitcum theory) to his later view ofa concept as a mental act (the intellectio theory), is reconstructed in thisframework in terms of the idea of concepts as unsaturated cognitive structures.Intentional objects ( ficta) are not rejected but are reconstructed as the objetifiedintensional contents of concepts. Their reconstruction as intensional objects isan essential part of the theory of predication of conceptual realism. It is bymeans of this theory that we are able to explain how the identity theory of thecopula, which was basic to terminist logic, applies to categorical propositions.Reference in conceptual realism is not the same as supposition in terministlogic. Nevertheless, the various "modes" of personal supposition of terministlogic can be explained and justified in terms of this conceptualist theory ofreference.""Conclusion. The framework of conceptual realism provides a logically ideallanguage within which to reconstruct the medieval terminist logic of the 14th

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century. The terminist notion of a concept, which shifted from Ockham’s earlyview of a concept as an intentional object (the f ictum theory) to his later viewof a concept as a mental act (the intellectio theory), is reconstructed in thisframework in terms of the notion of a concept as an unsaturated cognitivestructure. Referential and predicable concepts in particular are unsaturatedcognitive structures that mutually saturate each other in mental acts, analogousto the way that quantifier phrases and predicate expressions mutually saturateeach other in language. Intentional objects ( ficta) are not rejected but arereconstructed as the objectified intensional contents of concepts, i.e., asintentional objects obtained through the process of nominalization — and inthat sense as products of the evolution of language and thought. Theirreconstruction as intensional objects is an essential part of the theory ofpredication of conceptual realism. In particular, the truth conditions determinedby predicable concepts based on relations — including the relation the copulastands for — are characterized in part in terms of these objectified intensionalcontents. It is by means of this conceptualist theory of predication that we areable to explain how the identity theory of the copula, which was basic toterminist logic, applies to categorical propositions.Reference in conceptual realism, based on the exercise and mutual saturation ofreferential and predicable concepts, is not the same as supposition in terministlogic. Nevertheless, the various “modes” or types of personal supposition areaccounted for in a natural and intuitive way in terms of the theory of referenceof conceptual realism. Ockham’s application of merely confused supposition tocommon names occurring within the scope of an intensional verb is rejected, asit should be, but its rejection is grounded on the notion of a deactivatedreferential concept—a deactification that, because of the intensionality of thecontext in question, cannot be “activated,” the way it can be in extensionalcontexts." (p. 71)

———. 2001. "Logic and Ontology." Axiomathes.An International Journal inOntology and Cognitive Systems no. 12:127-150.Contents: 1. Logic as Language versus Logic as Calculus; 2. Predication versusMembership; 3. The vagaries of Nominalism; 4. The Vindication (Almost) ofLogical Realism; 5. Conceptualism Without a Transcendental Subject; 6.Conceptual Natural realism and the Analogy of being Between Natural andConceptual Universals; 7. Conceptual Intensional Realism; 8. ConcludingRemarks.Abstract: "A brief review of the historical relation between logic and ontologyand of the opposition between the views of logic as language and logic ascalculus is given. We argue that predication is more fundamental thanmembership and that different theories ofpredication are based on different theories of universals, the three mostimportant being nominalism, conceptualism, and realism. These theories can beformulated as formal ontologies, each with its own logic, and compared withone another in terms of their respective explanatory powers. After a brief surveyof such a comparison, we argue that an extended form of conceptual realismprovides the most coherent formal ontology and, as such, can be used to defendthe view of logic as language."

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"Concluding Remarks: Despite our extended discussion and defense ofconceptual realism, the fact remains that this is a formal ontology that can bedescribed and compared with other formal ontologies in the set-theoreticframework of comparative formal ontology. Set theory, as we have said,provides a convenient mathematical medium in which both the syntax and anextrinsic semantics of different formal ontologies can be formulated, which thencan be compared and contrasted with one another in their logical anddescriptive powers. This is the real insight behind the view of logic as calculus.But membership is at best a pale shadow of predication, which underliesthought, language and the different categories of reality. Set theory is not itselfan adequate framework for general ontology, in other words, unless based on atheory of predication (as in Quine's nominalist-platonism). Only a formal theoryof predication based on a theory of universals can be the basis of a generalontology. This is the real insight behind the view of logic as language. But thereare alternative theories of universals, and therefore alternative formal theoriesof predication, each with its own logic and theory of logical form. A rationalchoice can be made only by formulating and comparing these alternatives incomparative formal ontology, a program that can best be carried out in settheory. Among the various alternatives that have been formulated andinvestigated over the years, the choice we have made here, for the reasonsgiven, is what we have briefly described above as conceptual realism, whichincludes both a conceptual natural realism and a conceptual intensional realism.Others may make a different choice. As Rudolf Carnap once said: "Everyone isat liberty to build up his own logic, i.e. his own form of language, as hewishes." But then, at least in the construction of a formal ontology, we all havean obligation to defend our choice and to give reasons why we think one systemis better than another. In this regard, we do not accept Carnap's additionalinjunction that in logic, there are no morals." (pp. 145-146)Translated in Italian by Flavia Marcacci with revision by Gianfranco Basti, as:Logica e Ontologia in Aquinas. Rivista Internazionale di Filosofia, 52, 2009.

———. 2001. "A Conceptualist Interpretation of Leśniewski's Ontology."History and Philosophy of Logic no. 22:29-43.Contents: 1. Introduction 29; 2. Leśniewski’s Ontology as a First-Order Theory29; 3. The Logic of Names in Conceptual Realism 31; 4. A ConceptualistInterpretation of Leśniewski’s System 35; 5. Reduction of Leśniewski’s Theoryof Definitions 39; 6. Consistency and Decidability 40; References 43.Abstract: "A first-order formulation of Leśniewski’s ontology is formulated andshown to be interpretable within a free first-order logic of identity extended toinclude nominal quantification over proper and common-name concepts. Thelatter theory is then shown to be interpretable in monadic second-orderpredicate logic, which shows that the first-order part of Leśniewski’s ontologyis decidable.""Introduction. One of the important applications of Leśniewski’s system ofontology, sometimes also called the logic of (proper and common) names, (1)has been as a logistic framework that can be used in the reconstruction ofmedieval terminist logic. (2) This is especially so because the basic relation ofLeśniewski’s system, singular inclusion, amounts to a version of the two-name

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theory of the copula. (3) An alternative reconstruction of medieval terministlogic can also be given within the logistic framework of conceptual

———. 1986. "Frege, Russell and Logicism: A Logical Reconstruction." InFrege Synthesized: Essays on the Philosophical and Foundational Work ofGottlob Frege, edited by Haaparanta, Leila and Hintikka, Jaakko, 197-252.Dordrecht: ReidelReprinted as Chapter 2 in Logical Studies in Early Analytic Philosophy, pp.64-118."Logicism by the end of the nineteenth century was a philosophical doctrinewhose time had come, and it is Gottlob Frege to whom we owe its arrival.“Often,” Frege once wrote, “it is only after immense intellectual effort, whichmay have continued over centuries, that humanity at last succeeds in achievingknowledge of a concept in its pure form, in stripping off the irrelevantaccretions which veil it from the eyes of the mind” (Frege, The Foundations ofArithmetic, [Fd], xix). Prior to Frege logicism was just such a concept whosepure form was obscured by irrelevant accretions; and in his life’s work it wasFrege who first presented this concept to humanity in its pure form anddeveloped it as a doctrine of the first rank.That form, unfortunately, has become obscured once again. For today, as weapproach the end of the twentieth century, logicism, as a philosophical doctrine,is said to be dead, and even worse, to be impossible. Frege’s logicism, or thespecific presentation he gave of it in Die Grundgesetze der Arithmetik, ([Gg]),fell to Russell’s paradox, and, we are told, it cannot be resurrected. Russell’sown subsequent form of logicism presented in [PM], moreover, in effect givesup the doctrine; for in overcoming his paradox, Russell was unable to reduceclassical mathematics to logic without making at least two assumptions that arenot logically true; namely, his assumption of the axiom of reducibility and hisassumption of an axiom of infinity regarding the existence of infinitely manyconcrete or nonabstract individuals.Contrary to popular opinion, however, logicism is not dead beyond redemption;that is, if logicism is dead, then it can be easily resurrected. This is not to saythat as philosophical doctrines go logicism is true, but only that it can belogically reconstructed and defended or advocated in essentially the samephilosophical context in which it was originally formulated. This is trueespecially of Frege’s form of logicism, as we shall see, and in fact, by turning tohis correspondence with Russell and his discussion of Russell’s paradox, we areable to formulate not only one but two alternative reconstructions of his form oflogicism, both of which are consistent (relative to weak Zermelo set theory).In regard to Russell’s form of logicism, on the other hand, our resurrection willnot apply directly to the form he adopted in [PM] but rather to the form he wasimplicitly advocating in his correspondence with Frege shortly after thecompletion of [POM]. In this regard, though we shall have occasion to refer tocertain features of his later form of logicism, especially in our concludingsection where a counterpart to the axiom of reducibility comes into the picture,it is Russell’s early form of logicism that we shall reconstruct and be concernedwith here.Though Frege’s and Russell’s early form of logicism are not the same,

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incidentally, they are closely related; and one of our goals will be to reconstructor resurrect these forms with their similarity in mind. In particular, it is ourcontention that both are to be reconstructed as second order predicate logics inwhich nominalized predicates are allowed to occur as abstract singular terms.Their important differences, as we shall see, will then consist in the sort ofobject each takes nominalized predicates to denote and in whether the theory ofpredication upon which the laws of logic are to be based is to be extensional orintensional." (pp. 64-65 of the reprint)ReferencesFrege, Gottlob, [Fd] The Foundations of Arithmetic, trans, by J. L. Austin,Harper & Bros., N.Y. 1960.Frege, Gottlob, [Gg] Die Grundgesetze der Arithmetik, vols. 1 and 2,Hildesheim, 1962.Russell, Bertrand, [PM] Principia Mathematica, coauthor, A. N. Whitehead,Cambridge University Press, 1913.Russell, Bertrand, [POM] The Principles of Mathematics, 2nd ed., W. W.Norton & Co., N.Y., 1937.

———. 1986. "Conceptualism, Ramified Logic, and Nominalized Predicates."Topoi.An International Review of Philosophy no. 5:75-87.The problem of universals as the problem of what predicates stand for inmeaningful assertions is discussed in contemporary philosophy mainly in termsof the opposing theories of nominalism and logical realism. Conceptualism,when it is mentioned, is usually identified with intuitionism, which is not atheory of predication but a theory of the activity of constructing proofs inmathematics. Both intuitionism and conceptualism are concerned with thenotion of a mental construction, to be sure, and both maintain that there canonly be a potentially infinite number of such constructions. But whereas thefocus of concern in intuitionism is with the construction of proofs, inconceptualism our concern is with the construction of concepts. This differencesets the two frameworks apart and in pursuit of different goals, and in fact it isnot at all clear how the notion of a mental construction in the one framework isrelated to that in the other. This is especially true insofar as mathematicalobjects, according to intuitionism, are nothing but mental constructions,whereas in conceptualism concepts are anything but objects. In any case,whatever the relation between the two, our concern in this paper is withconceptualism as a philosophical theory of predication and not withintuitionism as a philosophy of mathematics.Now conceptualism differs from nominalism insofar as it posits universals,namely, concepts, as the semantic grounds for the correct or incorrectapplication of predicate expressions. Conceptualism differs from logicalrealism, on the other hand, insofar as the universals it posits are not assumed toexist independently of the human capacity for thought and representation.Concepts, in other words, are neither predicate expressions nor independentlyreal properties and relations. But then, at least for the kind of conceptualism wehave in mind here, neither are they mental images or ideas in the sense ofparticular mental occurrences. That is, concepts are not objects (saturatedindividuals) but are rather cognitive capacities, or cognitive structures otherwise

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based upon such capacities, to identify and classify or characterize and relateobjects in various ways. Concepts, in other words, are intersubjectivelyrealizable cognitive abilities which may be exercized by different persons at thesame time as well as by the same person at different times. And it is for thisreason that we speak of concepts as objective universals, even though they arenot independently real properties and relations.As cognitive structures, however, concepts in the sense intended here are notFregean concepts (which for Frege are independently real unsaturated functionsfrom objects to truth values). But they may be modeled by the latter (assumingthat there are Fregean concepts to begin with) -especially since as cognitivecapacities which need not be exercized at any given time (or even ever for thatmatter), concepts in the sense intended here also have an unsaturated naturecorresponding to, albeit different from, the unsaturated nature of Fregeanconcepts. Thus, in particular, the saturation (or exercise) of a concept in thesense intended here results not in a truth value but a mental act, and, if overtlyexpressed, a speech act as well. The un-saturatedness of a concept consists inthis regard in its non-occurrent or purely dispositional status as a cognitivecapacity, and it is the exercise (or saturation) of this capacity as a cognitivestructure which informs particular mental acts with a predicable nature (or witha referential nature in the case of concepts corresponding to quantifierexpressions)." (pp. 75-76)

———. 1987. "Rigid Designation." In Encyclopedic Dictionary of Semiotics.Vol. 2, edited by Sebeok, Thomas A., 834. Berlin: Mouton de Gruyter.

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———. 1987. "Russell, Bertrand." In Encyclopedic Dictionary of Semiotics.Vol. 2, edited by Sebeok, Thomas A., 840-841. Berlin: Mouton de Gruyter.

31.

———. 1988. "Predication Versus Membership in the Distinction betweenLogic as Language and Logic as Calculus." Synthese no. 75:37-72Contents: 0. Introduction; 1. The problem with a set-theoretic semantics ofnatural language; 2. Intensional logic as a new theoretical framework forphilosophy; 3.The incompleteness of intensional logic when based onmembership; 4. Predication versus membership in type theory; 5. Second orderpredicate logic with nominalized predicates; 6. A set theoretic semantics withpredication as fundamental; 7. Concluding remarks."There are two major doctrines regarding the nature of logic today. The first isthe view of logic as the laws of valid inference, or logic as calculus. This viewbegan with Aristotle's theory of the syllogism, or syllogistic logic, and in timeevolved first into Boole's algebra of logic and then into quantificational logic.On this view, logic is an abstract calculus capable of various interpretationsover domains of varying cardinality. Because these interpretations are given interms of a set-theoretic semantics where one can vary the universe at will andconsider the effect this, has on the validity of formulas, this view is sometimesdescribed as the set-theoretic approach to logic (see van Heijenoort ["Logic asLanguage and Logic as Calculus", Synthese 17,] 1967, p. 327).The second view of logic does not eschew set-theoretic semantics, it should benoted, and it may in fact utilize such a semantics as a guide in the determinationof validity. But to use such a semantics as a guide, on this view, is not the same

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as to take that semantics as an essential characterization of validity. Indeed,unlike the view of logic as calculus, this view of logic rejects the claim that aset-theoretic definition of validity has anything other than an extrinsicsignificance that may be exploited for certain purposes (such as proving acompleteness theorem). Instead, on this view, logic has content in its own rightand validity is determined by what are called the laws of logic, which may bestated either as principles or as rules. Because one of the goals of this view is aspecification of the basic laws of logic from which the others may be derived,this view is sometimes called the axiomatic approach to logic." (p. 37)(...)"Concluding Remarks. The account we have given here of the view of logic aslanguage should not be taken as a rejection of the set-theoretical approach or asdefense of the metaphysics of possibilist logical realism. Rather, our view isthat there are really two types of conceptual framework corresponding to ourtwo doctrines of the nature of logic. The first type of framework is based onmembership in the sense of the iterative concept of set; although extensionalityis its most natural context (since sets have their being in their members), it maynevertheless be extended to include intensional contexts by way of a theory ofsenses (as in Montague's sense-denotation intensional logic). The second typeof framework is based on predication, and in particular developments it isassociated with one or another theory of universals. Extensionality is not themost natural context in this theory, but where it does hold and extensions areposited, the extensions are classes in the logical and not in the mathematicalsense.Russell's paradox, as we have explained, has no real bearing on set-formation ina theory of membership based on the iterative concept of set, but it does beardirectly on concept-formation or the positing or universals in a theory based onpredication. As a result, our second type of framework has usually been thoughtto be incoherent or philosophically bankrupt, leaving us with the set-theoreticalapproach as, the only viable alternative. This is why so much of analyticphilosophy in the 20th Century has been dominated by the set-theoreticalapproach. Set theory, after all, does seem to serve the purposes of a mathesisuniversalis.What is adequate as a mathesis universalis, however, need not also therefore beadequate as a lingua philosophica or characteristica universalis. In particular,the set-theoretic approach does not seem to provide a philosophically satisfyingsemantics for natural language; this is because it is predication and notmembership that is fundamental to natural language. An adequate semantics fornatural language, in other words, seems to demand a conceptual frameworkbased on predication and not on membership.(...)We do not maintain, accordingly, that we should give up the set-theoreticapproach, especially when dealing with the philosophy and foundations ofmathematics, or that only a theory of predication associated with possibilistlogical realism will provide an adequate semantics for natural language. In bothcases we may find a principle of tolerance, if not outright pluralism, the moreappropriate attitude to take." (pp. 69-70)


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———. 1989. "Philosophical Perspectives on Formal Theories of Predication."In Handbook of Philosophical Logic. Vol. 4. Topics in the Philosophy ofLanguage, edited by Gabbay, Dov and Guenthner, Franz, 253-326. Dordrecht:ReidelContents: 1. Predication and the problem of universal 254; 2. Nominalism 256;3. A nominalistic semantics for predicative second order logic 261; 4.Nominalism and modal logic 266; 5 . Conceptualism vs . nominalism 270; 6.Constructive conceptualism 273; 7. Ramification of constructive conceptualism280; 8. Holistic conceptualism 286; 9. Logical realism vs holistic conceptualism289; 10. Possibilism and actualism in modal logical realism 292; 11. Logicalrealism and cssentialism 301; 12. Possibilism and actualism withinconceptualism 306; 13. Natural realism and conceptualism 313; 14. Aristotelianessentialism and the logic of natural kinds 318; References 325-326."Predication has been a central, if not the central, issue in philosophy since atleast the lime of Plato and Aristotle. Different theories of predication have infact been the basis of a number of philosophical controversies in bothmetaphysics and epistemology, not the least of which is the problem ofuniversals. In what follows we shall be concerned with what traditionally havebeen the three most important types of theories of universals. namely,nominalism, conceptualism, and realism, and with the theories of predicationwhich these theories might be said to determine or characterize.Though each of these three types of theories of universals may be said to havemany variants, we shall ignore their differences here to the extent that they donot characterize different theories of predication. This will apply especially tonominalism where but one formal theory of predication is involved. In bothconceptualism and realism, however, the different variants of each type do notall agree and form two distinct subtypes each with its own theory of predication.For this reason we shall distinguish between a constructive and a holistic formof conceptualism on the one hand, and a logical and a natural realism on theother. Constructive conceptualism, as we shall see, has affinities withnominalism with which it is sometimes confused, and holistic conceptualismhas affinities with logical realism with which it is also sometimes confused.Both forms of conceptualism may assume some form of natural realism as theircausal ground; and natural realism in turn must presuppose some form ofconceptualism as its background theory of predication. Both forms of realismmay be further divided into their essentialist and non-essentialist variants (andin logical realism even a form of anti-essentialism), and though an essentialistlogical realism is sometimes confused with Aristotelian essentialism, the latteris really a form of natural realism with natural kinds as the only essentialproperties objects can have." (pp. 253-254)

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———. 1989. "Russell's Theory of Logical Types and the Atomistic Hierarchyof Sentences." In Rereading Russell: Essays on Bertrand Russell's Metaphysicsand Epistemology, edited by Savage, C.Wade and Anderson, C.Anthony, 41-62.Minneapolis: University of Minnesota PressReprinted as Chapter 5 in Logical Studies in Early Analytic Philosophy, pp.193-221."Russell’s philosophical views underwent a number of changes throughout his

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life, and it is not always well-appreciated that views he held at one time camelater to be rejected; nor, similarly, that views he rejected at one time came laterto be accepted. It is not well-known, for example, that the theory of logicaltypes Russell described in his later or post-[PM] philosophy is not the same asthe theory originally described in [PM] in 1910-13; nor that some of the moreimportant applications that Russell made of the theory at the earlier time cannotbe validated or even significantly made in the framework of his later theory.What is somewhat surprising, however, is that Russell himself seems not tohave realized that he was describing a new theory of logical types in his laterphilosophy, and that as a result of the change some of his earlier logicalconstructions, including especially his construction of the different kinds ofnumbers, were no longer available to him.In the original framework, for example, propositional functions areindependently real properties and relations that can themselves have propertiesand relations of a higher order/type, and all talk of classes, and therebyultimately of numbers, can be reduced to extensional talk of properties andrelations as “single entities,” or what Russell in [POM] had called “logicalsubjects.” The Platonic reality of classes and numbers was replaced in this wayby a more fundamental Platonic reality of propositional functions as propertiesand relations. In Russell's later philosophy, however, “a propositional functionis nothing but an expression. It does not, by itself, represent anything. But it canform part of a sentence which does say something, true or false” (Russell, MyPhilosophical Development, ([MPD]), 69). Surprisingly. Russell even insiststhat this was what he meant by a propositional function in [PM]. “Whiteheadand I thought of a propositional function as an expression containing anundetermined variable and becoming an ordinary sentence as soon as a value isassigned to the variable: ‘x is human’, for example, becomes an ordinarysentence as soon as we substitute a proper name for V. In this view . . . thepropositional function is a method of making a bundle of such sentences”([MPD], 124). Russell does realize that some sort of change has come about,however, for he admits, “I no longer think that the laws of logic are laws ofthings; on the contrary, I now regard them as purely linguistic” (ibid., 102).(...)Now it is not whether [PM] can sustain a nominalistic interpretation that is ourconcern in this essay, as we have said, but rather how it is that Russell came tobe committed in his later philosophy to the atomistic hierarchy and thenominalistic interpretation of propositional functions as expressions generatedin a ramified second order hierarchy of languages based on the atomistichierarchy. We shall pursue this question by beginning with a discussion of thedifference between Russell’s 1908 theory of types and that presented in [PM] in1910. This will be followed by a brief summary of the ontology that Russelltook to be implicit in [PM], and that he described in various publicationsbetween 1910 and 1913. The central notion in this initial discussion is whatRussell in his early philosophy called the notion of a logical subject, orequivalently that of a “term” or “single entity”. (In [PM], this notion wasredescribed as the systematically ambiguous notion of an “object.”) Asexplained in chapter 1 this notion provides the key to the various problems thatled Russell in his early philosophy to the development of his different theories


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of types, including that presented in [PM]. This remains true, moreover, evenwhen we turn to Russell’s later philosophy, i.e., to his post-[PM] views, onlythen it is described as the notion of what can and cannot be named in a logicallyperfect language. The ontology of these later views is what Russell calledlogical atomism, and it is this ontology that determines what Russell describedas the atomistic hierarchy of sentences. In other words, it is the notion of whatcan and cannot be named in the atomistic hierarchy that explains how Russell,however unwittingly, came to replace his earlier theory of logical types by thetheory underlying the atomistic hierarchy of sentences as the basis of a logicallyperfect language." (pp. 193-195 of the reprint)ReferencesPOM] Russell, Bertrand, The Principles of Mathematics, 2d ed. (NY., Norton &Co., 1938).[PM] Russell, Bertrand and Alfred Whitehead, Principia Mathematica, vol. 1(1910), vol. 2 (1912), and vol. 3 (1913) (London: Cambridge Univ. Press,).

———. 1989. "Conceptualism, Realism and Intensional Logic." Topoi.AnInternational Review of Philosophy no. 7:15-34Contents: 0. Introduction 15; 1. A conceptual analysis of predication 16; 2.Concept-correlates and Frege's double correlations thesis 17; 3. Russell'sparadox in conceptual realism 18: 4. What are the natural numbers and wheredo they come from? 22; 5. Referential concepts and quantifier phrases 24; 5.Singular reference 24; 7. The intensions of refrential concepts as components ofapplied predicable concepts 26; 8. Intensional versus extensional predicableconcepts 28; 9. The intentional identity of intensional objects 29; Notes 31;Reference 33-35."0. IntroductionLinguists and philosophers are sometimes at odds in the semantical analysis oflanguage. This is because linguists tend to assume that language must besemantically analyzed in terms of mental constructs, whereas philosophers tendto assume that only a platonic realm of intensional entities will suffice. Theproblem for the linguist in this conflict is how to explain the apparent realistposits we seem to be committed to in our use of language, and in particular inour use of infinitives, gerunds and other forms of nominalized predicates. Theproblem for the philosopher is the old and familiar one of how we can haveknowledge of independently real abstract entities if all knowledge mustultimately be grounded in psychological states and processes. In the case ofnumbers, for example, this is the problem of how mathematical knowledge ispossible. In the case of the intensional entities assumed in the semanticalanalysis of language, it is the problem of how knowledge of even our ownnative language is possible, and in particular of how we can think and talk toone another in all the ways that language makes possible.I believe that the most natural framework in which this conflict is to be resolvedand which is to serve as the semantical basis of natural language is anintensional logic that is based upon a conceptual analysis of predication inwhich what a predicate stands for in its role as a predicate is distinguished fromwhat its nominalization denotes in its role as a singular term. Predicates in sucha framework stand for concepts as cognitive capacities to characterize and relate

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objects in various ways, i.e. for dispositional cognitive structures that do notthemselves have an individual nature, and which therefore cannot be the objectsdenoted by predicate nominalizations as abstract singular terms. The objectspurportedly denoted by nominalized predicates, on the other hand, areintensional entities, e.g. properties and relations (and propositions in the case ofzero-place predicates), which have their own abstract form of individuality,which, though real, is posited only through the concepts that predicates standfor in their role as predicates. That is, intensional objects are represented in thislogic as concept-correlates, where the correlation is based on a logicalprojection of the content of the concepts whose correlates they are.(...)Before proceeding, however, there is an important distinction regarding thenotion of a logical form that needs to be made when joining conceptualism andrealism in this way. This is that logical forms can be perspicuous in either oftwo senses, one stronger than the other. The first is the usual sense that appliesto all theories of logical form, conceptualist or otherwise; namely, that logicalforms are perspicuous in the way they specify the truth conditions of assertionsin terms of the recursive operations of logical syntax. In this sense, fully appliedlogical forms are said to be semantic structures in their own right. In the secondand stronger sense, logical forms may be perspicuous not only in the way theyspecify the truth conditions of an assertion, but in the way they specify thecognitive structure of that assertion as well. To be perspicuous in this sense, alogical form must provide an appropriate representation of both the referentialand the predicable concepts that underlie an assertion.Our basic hypothesis in this regard will be that every basic assertion is the resultof applying just one referential concept and one predicable concept, and thatsuch an applied predicable concept is always fully intensionalized (in a sense tobe explained). This will place certain constraints on the conditions for when acomplex predicate expression is perspicuous in the stronger sense — such asthat a referential expression can occur in such a predicate expression only in itsnominalized form. (A similar constraint will also apply to a defining orrestricting relative clause of a referential expression.) In the cases where arelational predicable concept is applied, the assumption that there is still but onereferential concept involved leads to the notion of a conjunctive referentialconcept, a notion that requires the introduction in intensional logic of specialquantifiers that bind more than one individual variable. Except for brieflynoting the need for their development, we shall not deal with conjunctivequantifiers in this essay." (pp. 15-16)

———. 1991. "Conceptualism." In Handbook of Metaphysics and Ontology,edited by Smith, Barry and Burkhardt, Hans, 168-174. Munich: PhilosophiaVerlagConceptualism is one of the three types of theories regarding the nature ofuniversals described by Porphyry in his introduction to Aristotle's Categories.The other two are nominalism and realism. Because a universal, according toAristotle, is that which can be predicated of things (De Int. 17a39), thedifference between these three types of theories lies in what it is that each takesto be predicable of things. In this regard we should distinguish predication in

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language from predication in thought, and both from predication in reality,where there is no presumption that one kind of predication precludes the others.All three types of theories agree that there is predication in language, inparticular that predicates can be predicated of things in the sense of being trueor false of them. Nominalism goes further in maintaining that only predicatescan be predicated of things, that is, that there are no universals other than thepredicate expressions of some language or other. Conceptualism opposesnominalism in this regard and maintains that predicates can be true or false ofthings only because they stand for concepts, where concepts are the universalsthat are the basis of predication in thought. Realism also opposes nominalism inmaintaining that there are real universals, viz. properties and relations, that arethe basis of predication in reality." (p. 168)(...)"Conceptualism is by no means a monolithic theory, but has many forms, somemore restrictive than others, depending on the mechanisms assumed as the basisfor concept-formation. None of these forms, in themselves, precludes beingcombined with a realist theory, whether Aristotelian (as in conceptual naturalrealism) or Platonist (as in conceptual intensional realism), or both. Someconceptualists, such as Sellars, have made it a point to disassociateconceptualism from any form of realism regarding abstract entities, but thatdisassociation has nothing to do with conceptualism as a theory about the natureof predication in thought. Conceptualism’s shift in emphasis from metaphysicsto psychology, in other words, while important in determining what kind oftheory is needed to explain predication in thought, should not be taken asjustifying a restrictive form of conceptualism that precludes both a natural andan intensional realism." (p. 174)

———. 1991. "Logic V: Higher Order Logics." In Handbook of Metaphysicsand Ontology, edited by Smith, Barry and Burkhardt, Hans, 466-470. Munich:Philosophia Verlag.Higher-order logic goes beyond first-order logic in allowing quantifiers to reachinto the predicate as as well as the subject positions of the logical forms itgenerates. A second feature, usually excluded in standard formulations ofsecond-order logic, allows nominal-ized forms of predicate expressions (simpleor complex) to occur in its logical forms as abstract singular terms. (E.g.,‘Socrates is wise’, in symbols W(s), contains ‘is wise’ as a predicate, whereas‘Wisdom is a virtue’, in symbols V(W), contains ‘wisdom’ as a nominalizedform of that predicate. ‘Being a property is a property’, in symbols P(P), or withλ-abstracts, PλxP(x)), where λχΡ(χ) is read ‘to be an x such that x is a property’,contains both the predicate ‘is a property’ and a nominalized form of thatpredicate, viz. ‘being a property’. Frege’s well-known example, ‘The conceptHorse is not a concept’, contains ‘the concept Horse’ as a nominalized form ofthe predicate phrase ‘is a horse’.)" (p. 466)

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———. 1991. "Ontology, Fomal." In Handbook of Metaphysics and Ontology,edited by Smith, Barry and Burkhardt, Hans, 640-647. Munich: PhilosophiaVerlag.Formal ontology is the result of combining the intuitive, informal method ofclassical ontology with the formal, mathematical method of modern symbolic

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logic, and ultimately identifying them as different aspects of one and the samescience. That is, where the method of ontology is the intuitive study of thefundamental properties. modes, and aspects of being, or of entities in general,and the method of modern symbolic logic is the rigorous construction of formal,axiomatic systems, formal ontology, the result of combining these two methods,is the systematic, formal, axiomatic development of the logic of all forms andmodes of being. As such, formal ontology is a science prior to all others inwhich particular forms, modes, or kinds of being are studied." (p. 641)

———. 1991. "Russell, Bertrand." In Handbook of Metaphysics and Ontology,edited by Smith, Barry and Burkhardt, Hans, 796-798. Munich: PhilosophiaVerlag.Russell held a number of different metaphysical positions throughout his career,with the idea of logic as a logically perfect language being a common themethat ran through each.(...)"A fundamental notion of Russell’s logical realism, sometimes also calledontological logicism, was that of a propositional function, the extension ofwhich Russell took to be a class as many. Initially, as part of his response to theproblem of the One and the Many, Russell had assumed that each propositionalfunction was a single and separate entity over and above the many propositionsthat were its values, and, similarly, that to each class as many therecorresponded a class as one. Upon discovering his paradox, Russell maintainedthat we must distinguish a class as many from a class as one, and that a class asone might not exist corresponding to a class as many. He also concluded that apropositional function cannot survive analysis after all, but ‘lives’ only in thepropositions that are its values, i.e. that propositional functions are nonentities."(...)"As a result of arguments given by Ludwig Wittgenstein in 1913, Russell, from1914 on, gave up the Platonistic view that properties and relations could belogical subjects. Predicates were still taken as standing for properties andrelations, but only in their role as predicates; i.e., nominalized predicates wereno longer allowed as abstract singular terms in Russell’s new version of hislogically perfect language. Only particulars could be named in Russell's newmetaphysical theory, which he called logical atomism, but which, unlike hisearlier 1910-13 theory, is a form of natural realism, and not of logical realism,since now the only real properties and relations of his ontology are the simplematerial properties and relations that are the components of the atomic facts thatmake up the world. Complex properties and relations in this framework aresimply propositional functions, which, along with propositions, are now merelylinguistic expressions. (Russell remained unaware that as a result of the changein his metaphysical views from logical to natural realism his original theory oftypes was restricted to the much weaker sub-theory of ramified second-orderlogic, and that he could no longer carry through his logicist programme. Thisreinforced the confusion of nominalists into thinking that Russell’s earliertheory of types could be given a nominalistic interpretation, since such aninterpretation is possible for ramified second-order logic.)" (pp. 797-798)

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———. 1991. "Quantification, Time and Necessity." In Philosophical40.


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Applications of Free Logic, edited by Lambert, Karel, 242-256. New York:Oxford University PressContents: 0. Introduction; 1. A Logic a Actual and Possible Objects; 2. ACompleteness Theorem for Tense Logic; 3. Modality Within Tense Logic; 4.Some Observations on Quantifiers in Modal and Tense Logic; 5. ConcludingRemarks.Abstract: "A logic of actual and possible objects is formulated in which"existence" and "being", as second-level concepts represented by first-order(objectual) quantifiers, are distinguished. A free logic of actual objects is thendistinguished as a subsystem of the logic of actual and possible object. Severalcomplete first-order tense logics are then formulated in which temporal versionsof possibilism and actualism are characterized in terms of the free logic ofactual objects and the wide logic of actual and possible objects. It is then shownhow a number of different modal logics can be interpreted within quantifiedtense logic, with the latter providing a paradigmatic framework in which todistinguish the interplay between quantifiers, tenses and modal operators andwithin which we can formulate different temporal versions of actualism andpossibilism.""The fundamental assumption of a logic of actual and possible objects is thatthe concept of existence is not the same as the concept of being. Thus, eventhough necessarily whatever exists has being, it is not necessary in such a logicthat whatever has being exists; that is, it can be the case that there be somethingthat does not exist. No occult doctrine is needed to explain the distinctionbetween existence and being, for an obvious explanation is already at hand in aframework of tense logic in which being encompasses past, present, and futureobjects (or even just past and present objects) while existence encompasses onlythose objects that presently exist. We can interpret modality in such aframework, in other words, whereby it can be true to say that some things donot exist. Indeed, as indicated in Section 3, infinitely many different modallogics can be interpreted in the framework of tense logic. In this regard, wemaintain, tense logic provides a paradigmatic framework in which possibilism(i.e., the view that existence is not the same as being, and that therefore therecan be some things that do not exist) can be given a logically perspicuousrepresentation.Tense logic also provides a paradigmatic framework for actualism as the viewthat is opposed to possibilism; that is, the view that denies that the concept ofexistence is different from the concept of being. Indeed, as we understand ithere, actualism does not deny that there can be names that have had denotationsin the past but that are now denotationless, and hence that the statement thatsome things do not exist can be true in a semantic metalinguistic sense (as astatement about the denotations, or lack of denotations, of singular terms). Whatis needed, according to actualism, is not that we should distinguish the conceptof existence from the concept of being, but only that we should modify the waythat the concept of existence (being) is represented in standard first-orderpredicate logic (with identity). A first-order logic of existence should allow forthe possibility that some of our singular terms might fail to denote an existentobject, which, according to actualism, is only to say that those singular termsare denotationless rather than what they denote are objects (beings) that do not


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exist. Such a logic for actualism amounts to what nowadays is called freelogic." (pp. 242-243)

———. 1992. "Conceptual Realism Versus Quine on Classes and Higher-OrderLogic." Synthese no. 90:379-436Contents: 0. Introduction; 1. Predication versus Membership; 2. Old versusNew Foundations; 3. Concepts versus ultimate Classes; 4. Frege versus Quineon Higher-Order Logic; 5. Conceptualism versus Nominalism as FormalTheories of predication; 6. Conceptualism Ramified versus NominalismRamified; 7. Constructive Conceptual Realism versus Quine's view ofConceptualism as a Ramified Theory of Classes; 8. Holistic ConceptualRealism versus Quine's Class Platonism.Abstract: "The problematic features of Quine's 'set' theories NF and ML are aresult of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-orderlogic of predication with nominalized predicates as abstract singular terms. Weadopt a modified Fregean position called conceptual realism in which theconcepts (unsaturated cognitive structures) that predicates stand for aredistinguished from the extensions (or intensions) that their nominalizationsdenote as singular terms. We argue against Quine's view that predicatequantifiers can be given a referential interpretation only if the entities predicatesstand for on such an interpretation are the same as the classes (assumingextensionality) that nominalized predicates denote as singular terms. Quine'salternative of giving predicate quantifiers only a substitutional interpretation iscompared with a constructive version of conceptual realism, which with a logicof nominalized predicates is compared with Quine's description ofconceptualism as a ramified theory of classes. We argue against Quine's implicitassumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's classPlatonism.""According to Quine, in one of his later works, the pioneers in modern logic,such as Frege and Russell, overestimated the kinship between membership andpredication and in that way came to view set theory as logic (Quine 1970, p.65). Such a claim, we maintain, is both false and misleading. Frege and Russelldid assume a logical kinship between predication and membership, but whatthey meant by membership was membership in a class as the extension of aconcept (where a concept is a predicable entity, i.e., a universal in the traditionalsense) and not membership in a set. Sets, unlike classes, as we have said, havetheir being in their members, and in that regard there need be no kinship at allbetween predication and membership in a set. Classes in the logical sense, onthe other hand, have their being in the concepts whose extensions they are,which means that any theory of membership in a class presupposes asuperseding theory of predication. (3) Frege and Russell did not view set theoryas logic, but they each did develop a theoryof classes and they each did so based on a superseding higher-order theory ofpredication." (p. 382)

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———. 1992. "Cantor's Power-Set Theorem Versus Frege's Double-CorrelationThesis." History and Philosophy of Logic no. 13:179-201

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Abstract: "Frege’s thesis that second-level concepts can be correlated with first-level concepts and that the latter can be correlated with their value-ranges is indirect conflict with Cantor’s power-set theorem, which is a necessary part of theiterative, but not of the logical, concept of class. Two consistent second-orderlogics with nominalised predicates as abstract singular terms are described inwhich Frege’s thesis and the logical notion of a class are defended and Cantor’stheorem is rejected. Cantor’s theorem is not incompatible with the logicalnotion of class, however. Two alternative similar kinds of logics are alsodescribed in which Cantor’s theorem and the logical notion of a class areretained and Frege’s thesis is rejected.""There is another problem with Russell’s solution, however, in addition to thatof the relativisation of classes to each logical type. This problem has to do withthe fact that the particular theory of types that Russell adopted is a theory oframified types, which, unlike the theory of simple types, is based on aconstructive (i.e. ‘predicative’) comprehension principle. Such a constructiveapproach is not without merit, but it does affect the logical notion of a class in afundamental way. In particular, because of the kind of constructive constraintsimposed by the theory on the comprehension principle, Cantor’s theorem,which involves objects of different types, cannot be proved in such a framework(cf. Quine 1963, 265). That is not objectionable in itself, but it does not get atthe root of the matter of the real conflict between Cantor’s power-set theoremand the logical notion of class as represented by an impredicativecomprehension principle.An impredicative comprehension principle is provable in the theory of simpletypes. But in this framework, as in the theory of ramified types as well,Russell’s paradox cannot even be stated (because of the gramatical constraintson the conditions of well-formedness), which means that the description of theclass upon which Russell’s paradox is based is meaningless. Thus, not onlymust the universal class be relativised and duplicated, potentially, infinitelymany times in order to avoid Russell’s paradox on this approach, but theparadox must itself be ruled as meaningless. The theory of types, whethersimple or ramified, is not really a solution of the problem so much as a way ofavoiding it altogether.There is another way in which we can preserve our logical intuitions and notgive up the logical notion of a class in favor of the mathematical (i.e. in favor ofset theory), and yet in which not only is Cantor’s theorem formulable but so isRussell’s paradox—though, of course, the latter will no longer be provable.Indeed, there is not just one such way, but at least two (both of whichthemselves have two alternatives). On the first, it is not the logical notion of aclass that must be rejected as the way of resolving Russell’s paradox, butCantor’s theorem instead. This rejection is not ad hoc or arbitrary on thisapproach, but is based on a more general principle, which we refer to as Frege’sdouble-correlation thesis. It is this approach that we shall turn to first. On thesecond and alternative approach, which we shall turn to later, the trouble lies inneither Cantor’s theorem nor in the assumption that there is a universal class(both of which can be retained without contradiction on this approach), butrather in how the logic of identity is to be applied in certain contexts. On thisapproach, the claim that a contradiction results by combining Cantor’s theorem


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with the assumption that the universal class exists is not a ‘truism’ after all butis outright false."ReferencesQuine, W. V. 1963 Set theory and its logic, Cambridge, Mass. (HarvardUniversity Press).

———. 1993. "On Classes and Higher-Order Logic: A Critique of W.V.O.Quine." Philosophy and the History of Science.A Taiwanese Journal no.2:23-50Abstract: "The problematic features of Quine's set theories NF and ML resultfrom compressing the higher-order predicate logic of type theory into a first-order logic of membership, and can be resolved by turning to a second-orderpredicate logic with nominalized predicates as abstract singular terms. Amodified Fregean position, called conceptual realism, is described in which theconcepts (unsaturated cognitive structures) that predicates stand for aredistinguished from the extensions (or intensions) that their nominalizationsdenote as abstract singular terms. Quine's view that conceptualism cannotaccount for impredicative concept-formation is rejected, and a holisticconceptual realism is compared with Quine's class Platonism."

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———. 1995. "Knowledge Representation in Conceptual Realism."International Journal of Human-Computer Studies no. 43:697-721.Knowledge representation in Artificial Intelligence (AI) involves more than therepresentation of a large number of facts or beliefs regarding a given domain,i.e. more than a mere listing of those facts or beliefs as data structures. It mayinvolve, for example, an account of the way the properties and relations that areknown or believed to hold of the objects in that domain are organized into atheoretical whole - such as the way different branches of mathematics, or ofphysics and chemistry, or of biology and psychology, etc., are organized, andeven the way different parts of our commonsense knowledge or beliefs aboutthe world can be organized. But different theoretical accounts will apply todifferent domains, and one of the questions that arises here is whether or notthere are categorial principles of representation and organization that applyacross all domains regardless of the specific nature of the objects in thosedomains. If there are such principles, then they can serve as a basis for a generalframework of knowledge representation independently of its application toparticular domains. In what follows I will give a brief outline of some of thecategorial structures of conceptual realism as a formal ontology. It is this systemthat I propose we adopt as the basis of a categorial framework for knowledgerepresentation." (p. 697)(...)" Concluding remarks. We have given here only an overview or sketch ofconceptual realism as a formal ontology, i.e. as a theory of logical form havingboth conceptual and ontological categories - but in which the latter arerepresented in terms of the former. The categories of natural kinds and ofnatural properties and relations, for example, are represented in terms of thecategories of sortals and predicable concepts, respectively, and the category ofabstract objects is represented in terms of the process of conceptualnominalization (reification) as a subcategory of objects. Not all of these

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categories or parts of this formal ontology will be relevant in every domain ofknowledge representation, but each is relevant at least to some domains and isneeded in a comprehensive framework for knowledge representation. In thosedomains where certain categorial distinctions are not needed - such as thatbetween predicative and impredicative concepts, or that between predicableconcepts and natural properties and relations, or between sortal concepts andnatural kinds, etc. - we can simply ignore or delete the logical forms inquestion. What must remain as the core of the system is the intensional logicaround which all of the other categories are built - namely, the second-orderpredicate logic with nominalized predicates as abstract singular terms that wecall HST*-lambda. It is this core, I believe, that can serve as a universalstandard by which to evaluate other representational systems." (p. 721)

———. 1996. "Conceptual Realism as a Formal Ontology." In FormalOntology, edited by Poli, Roberto and Simons, Peter, 27-60. Dordrecht: KluwerContents: 1. Introduction; 2. Substitutional versus Ontological Interpretations ofQuantifiers; 3. The Importance of the Notion of Unsaturedness in FormalOntology; 4. Referential and Predicable Concepts Versus Immanent Objects ofReference; 5. Conceptual Natural Realism and the Analogy of Being BetweenNatural and Intelligible Universals; 6. Conceptual Natural Realism andAristotelian Essentialism; 7. Conceptual Intensional Realism versus ConceptualPlatonism and the Logic of Nominalized Predicates8. Concluding Remarks.Abstract: "Conceptualism simpliciter, wheter constructive or holistic, providesan account of predication only in thought and language, and represents in thatregard only a truncated formal ontology. But conceptualism can be extended toan Aristotelian conceptual natural realism in which natural properties andrelations (and natural kinds as well) can be analogically posited correspondingto some of Our concepts, thereby providing an account of predication in thespace-time causal Order as well. In addition, through a pattern of reflexiveabstraction corresponding to the process of nominalization in language (and inwhich abstract objects are hypostatized corresponding to our concepts asunsaturated cognitive structures), conceptualism can also be extended to aconceptual Platonism or intensional realism that can provide an account of boththe intensional objects of fiction and the extensional objects of mathematics.Conceptual realism is thus shown to be a paradigm formal ontology in whichthe distinctions between abstract reality, natural reality, and thought andlanguage are properly represented, and in which the traditional oppositionbetween Platonism and Aristotelianism is finally overcome by properly locatingtheir different functions, and the way each should be rep resented, in formalontology.""Concluding Remarks. As this informal sketch indicates, conceptual realism, bywhich we mean conceptual natural realism and conceptual intensional realismtogether, provides the basis of a general conceptual-ontological framework,within which, beginning with thought and language, a comprehensive formalontology can be developed. Not only does conceptual realism explain how, innaturalistic terms, predication in thought and language is possible, but, inaddition, it provides a theory of the nature of predication in reality through an

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analogical theory of properties and relations. In this way, conceptual realismcan be developed into a reconstructed version of Aristotelian realism, includinga version of Aristotelian essentialism. In addition, through the process ofnominalization, which corresponds to a reflexive abstraction in which weattempt to represent our concepts as if they were objects, conceptualism can bedeveloped into a conceptual intensional realism that can provide an account notonly of the abstract reality of numbers and other mathematical objects, but ofthe intensional objects of fiction and stories of all kinds, both true and false, andincluding those stories that we systematically develop into theories about theworld. In this way, conceptual realism provides a framework not only for theconceptual and natural order, but for the mathematical and intensional order aswell. Also, in this way, conceptual realism is able to reconcile and provide aunified account both of Platonism and Aristotelian realism, includingAristotelian essentialism - and it does so by showing how the ontologicalcategories, or modes of being, of each of these ontologies can be explained interms a conceptualist theory of predication and its analogical extensions." (p.60)

———. 1997. "Formally Oriented Work in the Philosophy of Language." InRoutledge History of Philosophy. Vol. X - the Philosophy of Meaning,Knowledge and Value in the 20th Century, edited by Canfield, John, 39-75.New York: RoutledgeContents: 1. The notion of a Characteristica Universalis as a philosophicallanguage; 2. The notion a a logically perfect language as a regulating ideal; 3.The theory of logical types; 4. Radical empiricism and the logical constructionof the world; 5. The logical empiricist theory of meaning; 6. Semiotic and thetrinity of syntax, semantics and pragmatics; 7. Pragmatics from a logical pointof view; 8. Intensional logic; 9. Universal Montague grammar; 10. Speech-acttheory and the return to pragmatics.Abstract: "One of the perennial issues in philosophy is the nature of the variousrelationships between language and reality, language and thought, and languageand knowledge. Part of this issue is the question of the kind of methodologythat is to be brought to bear on the study of these relationships. Themethodology that we shall discuss here is based on a formally orientedapproach to the philosophy of language, and specifically on the notion of alogically ideal language as the basis of a theory of meaning and a theory ofknowledge."

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———. 1997. "Conceptual Realism as a Theory of Logical Form." RevueInternationale de Philosophie:175-199.The central notion in the philosophy of logic is the notion of a logical form, andthe central issue is which theory of logical form best represents our scientific(including our mathematical) and commonsense understanding of the world.Here, by a theory of logicalform, we mean not only a logical grammar in the sense of a system of formationrules characterizing the well-formed expressions of the theory, but also a logicalcalculus characterizing what is valid (i.e., provable or derivable) in the theory.The representational role of the logical forms of such a theory consists in thefact that they are perspicuous in the way they specify the truth conditions, and

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thereby the validity, of formulas in terms of the recursive operations of logicalsyntax. In conceptualism we also require that logical forms be perspicuous inthe way they represent the cognitive structure of our speech and mental acts,including in particular the referential and predicable concepts underlying thoseacts.The purpose of a theory of logical form, accordingly, is that it is to serve as ageneral semantical framework by which we can represent in a logicallyperspicuous way our commonsense and scientific understanding of the world,including our understanding of ourselvesand the cognitive structure of our speech and mental acts. So understood, thelogical forms of such a theory are taken to be semantic structures in their ownright, relative to which the words, phrases, and (declarative) sentences of a(fragment of) natural language, or of a scientific or mathematical theory, are tobe represented and interpreted. The process by which the expressions of anatural language or scientific theory are represented and interpreted in such atheory — relative to the aims, purposes and pragmatic considerations regardinga given context or domain of discourse — amounts to a logical analysis of thoseexpressions. (A different group of aims, purposes, etc., might give a finer- or acoarser-grained analysis of the domain.)Ideally, where the syntax of a target language or theory has been recursivelycharacterized, such an analysis can be given in terms of a preciselycharacterized theory of translation (1). Usually, however, the analysis is giveninformally.In what follows I will briefly describe and attempt to motivate some (but notall) aspects of a theory of logical form that I associate with the philosophicalsystem I call conceptual realism. The realism involved here is really of twotypes, one a natural realism (amounting to a modem form of Aristotelianessentialism) and the other an intensional realism (amounting to a modem, butalso mitigated, form of Platonism). The core of the theory is a second-orderlogic in which predicate expressions (both simple and complex) can benominalized and treated as abstract singular terms (in the sense of beingsubstituends of individual variables). In this respect the core is really a form ofconceptual intensional realism, which is the only part of the system we willdiscuss here (2)." (pp. 175-176)(1) See Montague (1969) for a description of such a theory of translation (forMontague’s type-theoretical intensional logic).(2) See Cocchiarella (1996), §§ 5-6, for a description of conceptual naturalrealism as a modem form of Aristotelian Essentialism.ReferencesCocchiarella, N.B. (1996), “ Conceptual Realism as a Formal Ontology” , inFormal Ontology, R. Poli and P. Simons, eds., Kluwer Academic press,Dordrecht, pp. 27-60.Montague, R.M. (1969), “ Universal Grammar” , in Formal Philosophy,Selected papers of Richard Montague, edited by R.H. Thomason, YaleUniversity Press, New Haven, 1974.

———. 1998. "Property Theory." In Routledge Encyclopedia of Philosophy -Vol. 7, edited by Craig, Edward, 761-767. New York: Routledge

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Abstract: "Traditionally, a property theory is a theory of abstract entities thatcan be predicated of things. A theory of properties in this sense is a theory ofpredication -just as a theory of classes or sets is a theory of membership. In aformal theory of predication, properties are taken to correspond to some (or all)one-place predicate expressions. In addition to properties, it is usually assumedthat there are n-ary relations that correspond to some (or all) n-place predicateexpressions (for n > 2). A theory of properties is then also a theory of relations.In this entry we shall use the traditional labels 'realism' and 'conceptualism' as aconvenient way to classify theories. In natural realism, where properties andrelations are the physical, or natural, causal structures involved in the laws ofnature, properties and relations correspond to only some predicate expressions,whereas in logical realism properties and relations are generally assumed tocorrespond to all predicate expressions.Not all theories of predication take properties and relations to be the universalsthat predicates stand for in their role as predicates. The universals of conceptualism, for example. are unsaturated concepts in the sense of cognitive capacitiesthat are exercised (saturated) in thought and speech. Properties and relations inthe sense of intensional Platonic objects may still correspond to predicateexpressions, as they do in conceptual intensional realism, but only indirectly asthe intensional contents of the concepts that predicates stand for in their role aspredicates. In that case, instead of properties and relations being what predicatesstand for directly, they are what nominalized predicates denote as abstractsingular terms. It is in this way that concepts - such as those that the predicatephrases 'is wise', 'is triangular' and 'is identical with' stand for - are distinguishedfrom the properties and relations that are their intensional contents - such asthose that are denoted by the abstract singular terms 'wisdom', 'triangularity' and'identity, respectively. Once properties are represented by abstract singularterms, concepts can be predicated of them, and, in particular, a concept can bepredicated of the property that is its intensional content. For example, theconcept represented by 'is a property' can be predicated of the property denotedby the abstract noun phrase 'being a property', so that 'being a property is aproperty' (or, 'The property of being a property is a property') becomes well-formed. In this way, however, we are confronted with Russell's paradox of (theproperty of) being a non-self-predicable property, which is the intensionalcontent of the concept represented by ' is a non-self-predicable property'. Thatis, the property of being a non-self- predicable property both falls and does notfall under the concept of being a non-self-predicable property (and thereforeboth falls and does not fall under the concept of being self-predicable)." (p. 761)

———. 1998. "The Theory of Types (Simple and Ramified)." In RoutledgeEncyclopedia of Philosophy - Vol. 9, edited by Craig, Edward, 359-362. NewYork: RoutledgeAbstract: "The theory of types was first described by Bertrand Russell in 1908.He was seeking a logical theory that could serve as a framework formathematics and, in particular, a theory that would avoid the so-called 'vicious-circle' antinomies, such as his own paradox of the property of those propertiesthat are not properties of themselves - or, similarly, of the class of those classesthat are not members of themselves. Such paradoxes can be thought of as

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resulting when logical distinctions are not made between different types ofentities and, in particular, between different types of properties and relationsthat might be predicated of entities, such as the distinction between concreteobjects and their properties, and the properties of those properties, and so on. In'ramified' type theory, the hierarchy of properties and relations is, as it were,two-dimensional, where properties and relations are distinguished first by theirorder, and the by their level within each order. In 'simple' type theory propertiesand relations are distinguished only by their orders." (p. 359)

———. 1998. "Reference in Conceptual Realism." Synthese no. 114:169-202Contents: 1. The core of Conceptual Intensional Realism; 2. Referentialconcepts, simple and complex; 3. Geach's negation and complex predicatearguments; 4. Active versus deactivated referential concepts; 5. Deactivationand Geach's arguments; 6. Relative pronouns and referential concepts; 7.Relative pronouns as referential expressions; 8. Concluding remarks.Abstract: "A conceptual theory of the referential and predicable concepts usedin basic speech and mental acts is described in which singular and general,complex and simple, and pronominal and non-pronominal, referential conceptsare given a uniform account. The theory includes an intensional realism inwhich the intensional contents of predicable and referential concepts arerepresented through nominalized forms of the predicate and quantifier phrasesthat stand for those concepts. A central part of the theory distinguishes betweenactive and deactivated referential concepts, where the latter are represented bynominalized quantifier phrases that occur as parts of complex predicates. PeterGeach's arguments against theories of general reference in "Reference andGenerality" are used as a foil to test the adequacy of the theory. Geach'sarguments are shown to either beg the question of general as opposed tosingular reference or to be inapplicable because of the distinction betweenactive and deactivated referential concepts.""Concluding Remarks. We do not claim that the theory of relative pronouns asreferential expressions proposed in Section 7 is unproblematic, it should benoted. If it should turn out that it cannot be sustained, then we still have thetheory proposed in Section 6, where relative pronouns are taken as anaphoricproxies for non-pronominal referential expressions. In other words, whether theproposal of Section 7 is sustained or not, we maintain that Geach's argumentsagainst complex names and general reference do not work against the kind ofconceptualist theory we have presented here.We also do not claim to have proved that our conceptualist theory of referenceresolves all problems about reference, but only that it has passed an initial testof adequacy as far as Geach's arguments in (Geach Reference and Generalitythird edition, 1980) are concerned. It is our view that a conceptualist theory iswhat is needed to account for reference and predication in our speech andmental acts, and that only a theory of the referential and predicable conceptsthat underlie the basic forms of such acts will suffice. Such a theory, wemaintain, must provide a uniform account of general as well as singularreference, and, in terms of the referential and predicable concepts involved in aspeech or mental act, it must distinguish the logical forms that represent thecognitive structure of that act from the logical forms that only represent its truth

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conditions. That, in any case, is the kind of conceptualist theory we haveattempted to describe and defend here." (p. 198)

———. 2000. Lógica Como Lenguaje Y Lógica Como Cálculo: Su Papel En LaTeoría De La Atribución. Heredia, Costa Rica: Departamento de Filosofia,Universidad NacionalColeccion Prometeo n. 20.

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———. 2000. "Russell's Paradox of the Totality of Propositions." NordicJournal of Philosophical Logic no. 5:25-37Abstract: "Russell’s ‘‘new contradiction’’ about ‘‘the totality of propositions’’has been connected with a number of modal paradoxes. M. Oksanen hasrecently shown how these modal paradoxes are resolved in the set theory NFU.Russell’s paradox of the totality of propositions was left unexplained, however.We reconstruct Russell’s argument and explain how it is resolved in twointensional logics that are equiconsistent with NFU. We also show howdifferent notions of possible worlds are represented in these intensional logics.""In Appendix B of his 1903 Principles of Mathematics (PoM), Russelldescribed a ‘‘new contradiction’’ about ‘‘the totality of propositions’’ that his‘‘doctrine of types’’ (as described in Appendix B) was unable to avoid. (1)In recent years this ‘‘new contradiction’’ has been connected with a number ofmodal paradoxes, some purporting to show that there cannot be a totality of truepropositions, (2) or that even the idea of quantifying over the totality ofpropositions leads to contradiction. (3) A number of these claims have beendiscussed recently by Mika Oksanen and shown to be spurious relative to theset theory known as NFU. (4) In other words, if NFU is used instead of ZF asthe semantical metalanguage for modal logic, the various ‘‘paradoxes’’ aboutthe totality of propositions (usually construed as the totality of sets of possibleworlds) can be seen to fail (generally because of the existence of a universal setand the failure of the general form of Cantor’s power-set theorem in NFU). It isnot clear, however, how Russell’s own paradox about the totality ofpropositions is resolved on this analysis, and although Oksanen quotedRussell’s description of the paradox in detail, he did not show how it isexplained in NFU after his resolution of the other related modal paradoxes; infact, it is not at all clear how this might be done in NFU.One reason why Russell’s argument is difficult to reconstruct in NFU is that it isbased on the logic of propositions, and implicitly in that regard on a theory ofpredication rather than a theory of membership. A more appropriate medium forthe resolution of these paradoxes, in other words, would be a formal theory ofpredication that is a counterpart to NFU.Fortunately, there are two such theories, λHST* and HST*λ, that areequiconsistent with NFU and that share with it many of the features that make ita useful framework within which to resolve a number of paradoxes, modal orotherwise. (5)" (pp. 25-26)(1) PoM, p. 527.(2) See, e.g., Grim 1991, pp. 92f.(3) See, e.g., Grim 1991, p. 119 and Jubien 1988, p. 307.(4) See Oksanen 1999. NFU is a modified version of Quine’s system NF. It wasfirst described in Jensen 1968 and recently has been extensively developed in

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Holmes 1999.(5) See Cocchiarella 1986, chapters IV and VI for proofs of the connection ofNFU with these systems. Also, see Cocchiarella 1985 for how these systems arerelated to Quine’s systems NF and ML. For a discussion of the refutation ofCantor’s power-set theorem inthese systems, see Cocchiarella 1992.ReferencesCocchiarella, N. B. 1985. Frege’s double-correlation thesis and Quine’s settheories NF and ML. Journal of Philosophical Logic, vol. 4, pp. 1–39.Cocchiarella, N. B. 1986. Logical Investigations of Predication Theory and theProblem of Universals. Bibliopolis Press, Naples, 1985.Cocchiarella, N. B. 1992. Cantor’s Power-Set Theorem Versus Frege’s Double-Correlation Thesis, History and Philosophy of Logic, vol. 13, 179–201.Holmes, R. 1999. Elementary Set Theory with a Universal Set. Cahiers duCentre de Logique, Bruylant-Academia, Louvain-la-Neuve, Belgium.Grim, P. 1991. The Incomplete Universe. MIT Press, Cambridge, MA.Jensen, R. 1968. On the consistency of a slight (?) modification of Quine’s NewFoundations. Synthese, vol. 19, pp. 250–263.Oksanen, M. 1979. The Russell-Kaplan paradox and other modal paradoxes; anew solution. Nordic Journal of Philosophical Logic, vol. 4, no. 1, pp. 73–93.Russell, B. 1937. The Principles of Mathematics, 2nd edition. W. W. Norton &Co., N.Y.

———. 2001. "A Logical Reconstruction of Medieval Terminist Logic inConceptual Realism." Logical Analysis and History of Philosophy no. 4:35-72Abstract: "The framework of conceptual realism provides a logically ideallanguage within which to reconstruct the medieval terminist logic of the 14thcentury. The terminist notion of a concept, which shifted from Ockham's earlyview of a concept as an intentional object (the fitcum theory) to his later view ofa concept as a mental act (the intellectio theory), is reconstructed in thisframework in terms of the idea of concepts as unsaturated cognitive structures.Intentional objects (ficta) are not rejected but are reconstructed as the objetifiedintensional contents of concepts. Their reconstruction as intensional objects isan essential part of the theory of predication of conceptual realism. It is bymeans of this theory that we are able to explain how the identity theory of thecopula, which was basic to terminist logic, applies to categorical propositions.Reference in conceptual realism is not the same as supposition in terministlogic. Nevertheless, the various "modes" of personal supposition of terministlogic can be explained and justified in terms of this conceptualist theory ofreference.""Conclusion. The framework of conceptual realism provides a logically ideallanguage within which to reconstruct the medieval terminist logic of the 14thcentury. The terminist notion of a concept, which shifted from Ockham’s earlyview of a concept as an intentional object (the fictum theory) to his later view ofa concept as a mental act (the intellectio theory), is reconstructed in thisframework in terms of the notion of a concept as an unsaturated cognitivestructure. Referential and predicable concepts in particular are unsaturatedcognitive structures that mutually saturate each other in mental acts, analogous

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to the way that quantifier phrases and predicate expressions mutually saturateeach other in language. Intentional objects (ficta) are not rejected but arereconstructed as the objectified intensional contents of concepts, i.e., asintentional objects obtained through the process of nominalization — and inthat sense as products of the evolution of language and thought. Theirreconstruction as intensional objects is an essential part of the theory ofpredication of conceptual realism. In particular, the truth conditions determinedby predicable concepts based on relations — including the relation the copulastands for — are characterized in part in terms of these objectified intensionalcontents. It is by means of this conceptualist theory of predication that we areable to explain how the identity theory of the copula, which was basic toterminist logic, applies to categorical propositions.Reference in conceptual realism, based on the exercise and mutual saturation ofreferential and predicable concepts, is not the same as supposition in terministlogic. Nevertheless, the various “modes” or types of personal supposition areaccounted for in a natural and intuitive way in terms of the theory of referenceof conceptual realism. Ockham’s application of merely confused supposition tocommon names occurring within the scope of an intensional verb is rejected, asit should be, but its rejection is grounded on the notion of a deactivatedreferential concept—a deactification that, because of the intensionality of thecontext in question, cannot be “activated,” the way it can be in extensionalcontexts." (p. 71)

———. 2001. "Logic and Ontology." Axiomathes.An International Journal inOntology and Cognitive Systems no. 12:127-150Contents: 1. Logic as Language versus Logic as Calculus; 2. Predication versusMembership; 3. The vagaries of Nominalism; 4. The Vindication (Almost) ofLogical Realism; 5. Conceptualism Without a Transcendental Subject; 6.Conceptual Natural realism and the Analogy of being Between Natural andConceptual Universals; 7. Conceptual Intensional Realism; 8. ConcludingRemarks.Abstract: "A brief review of the historical relation between logic and ontologyand of the opposition between the views of logic as language and logic ascalculus is given. We argue that predication is more fundamental thanmembership and that different theories ofpredication are based on different theories of universals, the three mostimportant being nominalism, conceptualism, and realism. These theories can beformulated as formal ontologies, each with its own logic, and compared withone another in terms of their respective explanatory powers. After a brief surveyof such a comparison, we argue that an extended form of conceptual realismprovides the most coherent formal ontology and, as such, can be used to defendthe view of logic as language.""Concluding Remarks: Despite our extended discussion and defense ofconceptual realism, the fact remains that this is a formal ontology that can bedescribed and compared with other formal ontologies in the set-theoreticframework of comparative formal ontology. Set theory, as we have said,provides a convenient mathematical medium in which both the syntax and anextrinsic semantics of different formal ontologies can be formulated, which then

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can be compared and contrasted with one another in their logical anddescriptive powers. This is the real insight behind the view of logic as calculus.But membership is at best a pale shadow of predication, which underliesthought, language and the different categories of reality. Set theory is not itselfan adequate framework for general ontology, in other words, unless based on atheory of predication (as in Quine's nominalist-platonism). Only a formal theoryof predication based on a theory of universals can be the basis of a generalontology. This is the real insight behind the view of logic as language. But thereare alternative theories of universals, and therefore alternative formal theoriesof predication, each with its own logic and theory of logical form. A rationalchoice can be made only by formulating and comparing these alternatives incomparative formal ontology, a program that can best be carried out in settheory. Among the various alternatives that have been formulated andinvestigated over the years, the choice we have made here, for the reasonsgiven, is what we have briefly described above as conceptual realism, whichincludes both a conceptual natural realism and a conceptual intensional realism.Others may make a different choice. As Rudolf Carnap once said: "Everyone isat liberty to build up his own logic, i.e. his own form of language, as hewishes." But then, at least in the construction of a formal ontology, we all havean obligation to defend our choice and to give reasons why we think one systemis better than another. In this regard, we do not accept Carnap's additionalinjunction that in logic, there are no morals." (pp. 145-146)Translated in Italian by Flavia Marcacci with revision by Gianfranco Basti, as:Logica e Ontologia in Aquinas. Rivista Internazionale di Filosofia, 52, 2009.

———. 2001. "A Conceptualist Interpretation of Leśniewski's Ontology."History and Philosophy of Logic no. 22:29-43Contents: 1. Introduction 29; 2. Leśniewski’s Ontology as a First-Order Theory29; 3. The Logic of Names in Conceptual Realism 31; 4. A ConceptualistInterpretation of Leśniewski’s System 35; 5. Reduction of Leśniewski’s Theoryof Definitions 39; 6. Consistency and Decidability 40; References 43.Abstract: "A first-order formulation of Leśniewski’s ontology is formulated andshown to be interpretable within a free first-order logic of identity extended toinclude nominal quantification over proper and common-name concepts. Thelatter theory is then shown to be interpretable in monadic second-orderpredicate logic, which shows that the first-order part of Leśniewski’s ontologyis decidable.""Introduction. One of the important applications of Leśniewski’s system ofontology, sometimes also called the logic of (proper and common) names, (1)has been as a logistic framework that can be used in the reconstruction ofmedieval terminist logic. (2) This is especially so because the basic relation ofLeśniewski’s system, singular inclusion, amounts to a version of the two-nametheory of the copula. (3) An alternative reconstruction of medieval terministlogic can also be given within the logistic framework of conceptualrealism, however.(4) This system is preferable in part because, unlikeLeśniewski’s ontology, it is not committed to an extensional framework, whichis important in the logical analysis of the tensed and modal modification(ampliation) of the terms (names) of medieval logic. (5) It is also possible, as

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we show below, to reduce or reconstruct Leśniewski’s ontology within thelogistic framework of conceptual realism."(1) See, e.g. Lejewski 1958, p. 152, Slupecki 1955 and Iwanuś 1973.(2) See, e.g. Henry 1972.(3) Singular inclusion, as represented by e in the formula 'a e b’, read as 'a is b’,was the only undefined constant of Leśniewski’s original system of ontology.The system could also be based either on partial, weak of strong inclusion as theonly primitive as well. See Lejewski 1958, pp. 154-156.(4) See Cocchiarella 2001. For an account of conceptual realism as a formalontology see Cocchiarella 1996.(5) One might, of course, add tense and modal operators to Leśniewski’sontology, even though he himself was against such a move.ReferencesCocchiarella, N. B. 1996. 'Conceptual Realism as a Formal Ontology' , in R.Poli and P. Simons, eds. Formal Ontology Dordrecht: Kluwer Academic pp.27-60.Cocchiarella, N. B. 2001. 'A logical reconstruction of medieval terminist logicin conceptual realism', Logical Analysis and History of Philosophy 4, 35-72.Henry, D. P. 1972. Medieval Logic and Metaphysics, London: HutchisonUniversity Library.Iwanuś, B. 1973. 'On Leśniewski’s Elementary Ontology', Studia Logica XXXI,73-119. [reprinted in LS, pp. 165-215]Lewjewski, C. 1958. 'On Leśniewski's Ontology’ , Ratio 1, 150-176. [reprintedin LS, pp. 123-148]Slupecki, J. 1955. 'S. Leśniewski's Calculus of Names' , Studia Logica III, 7-72.[reprinted in LS, pp. 59-122][LS = Leśniewski's Systems. Ontology and Mereology, edited by Jan T. J.Srzednicki and V. F. Rickey; Assistant Editor: J. Czelakowski, The Hague:Martinus Nijhoff 1984.]

———. 2002. "On the Logic of Classes as Many." Studia Logica no.70:303-338Abstract: "The notion of a “class as many” was central to Bertrand Russell’searly form of logicism in his 1903 Foundations of Mathematics. There is noempty class in this sense, and the singleton of an urelement (or atom in ourreconstruction) is identical with that urelement. Also, classes with more thanone member are merely pluralities— or what are sometimes called “pluralobjects”— and cannot as such be themselves members of classes. Russell didnot formally develop this notion of a class but used it only informally. In whatfollows, we give a formal, logical reconstruction of the logic of classes as manyas pluralities (or plural objects) within a fragment of the framework ofconceptual realism. We also take groups to be classes as many with two or moremembers and show how groups provide a semantics for plural quantifierphrases.""There is a notion of a class that has been ignored by most, but not all,philosophers. (4) This is the notion of a “ class as many,” as described, e.g., byBertrand Russell in his 1903 Principles of Mathematics. (5) A class in this senseis the extension of a common count noun, i.e., the extension of what

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traditionally has been called a common name. (6) The three important featuresof this notion are, first, that a vacuous common name, i.e., a common name thatnames nothing, has no extension, which is not the same as having anempty class as its extension. Thus, according to Russell, “there is no such thingas the null class, though there are null class-concepts,” i.e., commonnameconcepts that have no extension. (7) Secondly, the extension of a common namethat names just one thing (in the sense of an urelement) is just that one thing. Inother words, unlike the singleton sets of set theory, which are not identical withtheir single member, the class that is the extension of a common name thatnames just one thing (urelement) is none other than that one thing."(...)"We believe that this notion of a class, or of a group, can be usefully developedas part of the broader framework of conceptual realism that we have describedelsewhere. (11)" (pp. 304-305)(4) See, e.g., Simons 1982 for one proposed formulation of this notion.Simons’s formulation is different from the one we give here. Simons doubts thatthere can be “an exact logic for the quantificatory uses” of common names,which is what the present system isbased on. Also, whereas the present system relies on only one type of“objectual” variable (having both “atoms” and classes as many as values),Simons has three: one for “individuals,” another for “pluralities,” and a third for“neutrals.” There are a number of otherdifferences as well, but we will not go into them here.(5) See Russell 1903, chapter VI. Russell’s view in this book precedes his laterno-classes doctrine.(6) Strictly speaking, Russell distinguishes between a common name, e.g.,‘man’, and its plural form, ‘men’, and then takes the latter to denote the class asmany of men (§67). We do not distinguish common names from their pluralforms here, and we describe the class as many simply as the extension of thecommon name (and the concept it stands for).(7) Russell 1903, §69(11) See, e.g., Cocchiarella 1996 for a description of conceptual realism as aformal ontology.ReferencesCocchiarella, Nino B., 1996, “ Conceptual Realism as a Formal Ontology,” inFormal Ontology, Poli, R. and P.M. Simons, eds., Kluwer Academic Press,Dordrecht: 27-60.Russell, Bertrand, 1903, The Principles of Mathematics, second edition, Norton& Co., N.Y., 1938.Simons, Peter M., 1982, “ Plural Reference and Set Theory,” in Parts andMoments, Studies in Logic and Formal Ontology, Barry Smith, ed., PhilosophiaVerlag, Munich and Vienna: 199-260.

———. 2002. "Logical Necessity Based on Carnap's Criterion of Adequacy."Korean Journal of Logic no. 5:1-21Abstract: "A semantics for logical necessity, based on Carnap’s criterion ofadequacy, is given with respect to the ontology of logical atomism. A calculusfor sentential (propositional) modal logic is described and shown to be complete

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with respect to this semantics. The semantics is then modified in terms of arestricted notion of ‘all possible worlds’in the interpretation of necessity andshown to yield a completeness theorem for the modal logic S5. Such a restrictednotion introduces material content into the meaning of necessity so that, inaddition to atomic facts, there are "modal facts" that distinguish one world fromanother.""...in what follows we will construct a semantics for logical necessity based onRudolf Carnap’s criterion of adequacy and the metaphysical framework oflogical atomism, a semantics, we maintain, that provides a clear and preciseaccount of the connection between logical truth and logical necessity— at leastwith respect to this kind of metaphysical framework. (4)" (p. 2)(4) There are reasons to think that no other sort of metaphysical framework cansucceed in adequately explaining the connection between logical truth andlogical necessity. This is not to say, however, that other frameworks cannotaccount for notions of necessity other than logical necessity.

———. 2003. "Conceptual Realism and the Nexus of Predication."Metalogicon no. 16:45-70Abstract: "The nexus of predication is accounted for in different ways indifferent theories of universals. We briefly review the account given innominalism, logical realism (modern Platonism), and natural realism. Our maingoal is to describe the account given in a modern form of conceptualismextended to include a theory of intensional objects as the contents of ourpredicable and referential concepts.""Introduction. A universal, according to Aristotle, is what can be predicated ofthings. (1) But what exactly do we mean in saying that a universal can bepredicated of things? How, or in what way, do universals function in the nexusof predication?In the history of philosophy, there are three major types of theories that dealwith the problem of universals and that purport to answer these questions: (2)(1) Nominalism: According to this theory there are no universals, and there ispredication only in language; that is, only predicates can be predicated ofthings, and the only nexus of predication is the linguistic nexus between subjectand predicate expressions.(2) Realism: There are real universals, i.e., universals in reality, that arepredicated of things, and the function of predication in language is to representpredication in reality. Different versions of realism explain the nexus ofpredication in reality in different ways.(3) Conceptualism: There are conceptual universals, e.g., predicable concepts,that underlie predication in thought, and the nexus of predication in thoughtunderlies the nexus of predication in language.All three theories agree that there is predication in language though each has adifferent account of how that kind of predication is possible and what itrepresents. The theory we will describe here in some detail is a modern form ofconceptualism.Unlike traditional conceptualism (e.g., British empiricism), the conceptualismwe describe here is not based on a theory of “ideas” (Vorstellungen), and itincludes an intensional realism based on an evolutionary account of concept-

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formation. In this paper, our mainpurpose is to describe the conceptualist account of the nexus of predication.Before turning to conceptualism, we will make some brief observations aboutnominalism and realism and our methodology." (pp. 45-46)(1) De Interpretatione, 17 a 39.2 These three theories were first described by Porphyry in his [Isagoge or]Introduction to Aristotle’s Categories.

———. 2005. "Denoting Concepts, Reference, and the Logic of Names,Classes as Many, Groups and Plurals." Linguistics and Philosophy no.28:135-179Abstract: "Bertrand Russell introduced several novel ideas in his 1903Principles of Mathematics that he later gave up and never went back to in hissubsequent work. Two of these are the related notions of denoting concepts andclasses as many. In this paper we reconstruct each of these notions in theframework of conceptual realism and connect them through a logic of namesthat encompasses both proper and common names, and among the lattercomplex as well as simple common names. Names, proper or common, andsimple or complex, occur as parts of quantifier phrases, which in conceptualrealism stand for referential concepts, i.e., cognitive capacities that inform ourspeech and mental acts with a referential nature and account for theintentionality, or directedness, of those acts. In Russell's theory, quantifierphrases express denoting concepts (which do not include proper names). Inconceptual realism, names, as well as predicates, can be nominalized andallowed to occur as "singular terms", i.e., as arguments of predicates. Occurringas a singular term, a name denotes, if it denotes at all, a class as many, where, asin Russell's theory, a class as many of one object is identical with that oneobject, and a class as many of more than one object is a plurality, i.e., a pluralobject that we call a group. Also, as in Russell's theory, there is no empty classas many. When nominalized, proper names function as "singular terms" just theway they do in so-called free logic. Leśniewski's ontology, which is also calleda logic of names can be completely interpreted within this conceptualistframework, and the well-known oddities of Leśniewski's system are shown notto be odd at all when his system is so interpreted. Finally, we show how thepluralities, or groups, of the logic of classes as many can be used as thesemantic basis of plural reference and predication. We explain in this wayRussell's "fundamental doctrine upon which all rests," i.e., "the doctrine that thesubject of a proposition may be plural, and that such plural subjects are what ismeant by classes [as many] which have more than one term" ([Principles ofMathematics], p. 517).""Bertrand Russell introduced several novel ideas in his 1903 Principles ofMathematics [PoM] that he later gave up and never went back to in hissubsequent work. Two of these are the related notions of denoting concepts andclasses as many. Russell explicitly rejected denoting concepts in his 1905 paper,"On Denoting". Although his reasons for doing so are still a matter of somedebate, they depend in part on his assumption that all concepts, includingdenoting concepts, are objects and can be denoted as such. (1) Classes of anykind were later eliminated as part of Russell’s "no-classes" doctrine, according

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to which all mention of classes was to be contextually analyzed in terms ofreference to either propositions, as in Russell’s 1905 substitution theory, orpropositional functions as in Principia Mathematica [PM]. The problem withclasses, as Russell and Whitehead described it in [PM], is that "if there is suchan object as a class, it must be in some sense one object. Yet it is only of classesthat many can be predicated. Hence, if we admit classes as objects, we mustsuppose that the same object can be both one and many, which seemsimpossible" (p. 72).Both notions are worthy of reconsideration, however, even if only in asomewhat different, alternative form in a conceptualist framework that Russelldid not himself adopt. In such a framework, which we will briefly describe here,Russell’s assumption that all concepts are objects will be rejected in favor of aconceptualist counterpart to Frege’s notion of unsaturatedness, and we willreconsider the idea of a class as many somehow being both one and many." (pp.135-136)

———. 2008. "Infinity in Ontology and Mind." Axiomathes.An InternationalJournal in Ontology and Cognitive Systems no. 18:1-24Abstract: "Two fundamental categories of any ontology are the category ofobjects and the category of universals. We discuss the question whether eitherof these categories can be infinite or not. In the category of objects, thesubcategory of physical objects is examined within the context of differentcosmological theories regarding the different kinds of fundamental objects inthe universe.objects are discussed in terms of sets and the intensional objects of conceptualrealism. The category of universals is discussed in terms of the three majortheories of universals: nominalism, realism, and conceptualism. The finitude ofmind pertains only to conceptualism. We consider the question of whether ornot this finitude precludes impredicative concept formation. An explication ofpotential infinity, especially as applied to concepts and expressions, is given.We also briefly discuss a logic of plural objects, or groups of single objects(individuals), which is based on Bertrand Russell's (1903, The Principles ofMathematics, 2nd edn. (1938). Norton & Co, NY) notion of a class as many.The universal class as many does not exist in this logic if there are two or moresingle objects; but the issue is undecided if there is just one individual. We notethat adding plural objects (groups) to an ontology with a countable infinity ofindividuals (single objects) does not generate an uncountable infinity of classesas many.""Introduction.Ontology, as originally described by Aristotle, is the study of being qua being,where being is not univocal but is divided into different categories. The twomost fundamental categories are those of universals and objects respectively.Here, by a universal, and again we follow Aristotle, we mean that which can bepredicated of things.1 Predication, of course, is what connects universals withobjects. One important aspect of the role, or significance, of infinity inontology, accordingly, is whether or not either of these categories, i.e., thecategory of objects or the category of universals, is, or can be, infinite. Howinfinity applies to mind in this regard is the question of whether or not there are,

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or can be, infinitely many concepts as intelligible universals, and whether or notthe finitude of the human mind places limitations on the concepts that can beconstructed.The methodology of ontology, which, as we have said, is divided into differentcategories, is the analysis of those categories and the laws connecting them withone another, including in particular the nature of predication. The clearest andmost precise way to analyze these categories is through the development ofwhat is known as formal ontology, where the logico-grammatical forms andprinciples of a logistic system are formulated for the purpose of representing thedifferent categories and the laws connecting them.2 A formal ontology in whichontological and logical categories are combined in a unified framework willthen amount to a comprehensive deductive framework that is prior to all othersin both logical and ontological structure. By proving the consistency of such alogistic system we can thereby show that the intuitive ontological frameworkassociated with it is consistent as well.One important role of infinity in ontology, accordingly, can be understood as thedetermination of whether or not any of the categories of being, and in particularthe categories of objects and universals, are, or can be, infinite as part of such aformal framework. In what follows we will consider some possible answers tothis question." (p. 2)References(1) Aristotle, De Interpretatione 17a39.(2) For a more detailed account of formal ontology, see Cocchiarella (2007,Chap. 1).

———. 2009. "Mass Nouns in a Logic of Classes as Many." Journal ofPhilosophical Logic no. 38:343-361Abstract: "A semantic analysis of mass nouns is given in terms of a logic ofclasses as many. In previous work it was shown that plural reference andpredication for count nouns can be interpreted within this logic of classes asmany in terms of the subclasses of the classes that are the extensions of thosecount nouns. A brief review of that account of plurals is given here and it isthen shown how the same kind of interpretation can also be given for massnouns.""Why is the semantics of mass nouns so problematic? One reason, apparently, isthat unlike count nouns, which have determinate extensions, mass nouns haveextensions that in some cases are said to be indeterminate. The objects in theextension of a count noun are unproblematic because those objects are generallydiscrete and well-delineated, and hence can be individuated. The objects in theextension of a mass noun, especially mass nouns for different kinds of stuff, aresaid to be “diffuse” and indeterminate, on the other hand, because there areoften an indefinite number of ways to refer them separately as well as togetheras wholes. (1)A number of proposals have been made and criticized about the extensions ofmass nouns. (2) We will not review those proposals and criticisms here butinstead will present a proposal of our own based on what has been called “thesimplest plan” of all. (3) We will defend this “plan” in terms of a logicalframework designed to represent a form of conceptualism in which the logical

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forms that represent the cognitive structure of our speech and mental acts aredistinguished from the logical forms that represent the truth conditions anddeductive relations of those acts." (pp. 343-344)(1) Cp. Bunt [1], p. 53.(2) See Pelletier [8] for a review and discussion of some of these proposals.(3) Pelletier 74, p. 94 f.References[1] Bunt, H. (1981). On the why, the how, and the whether of a count/massdistinction among adjectives. In J. A. G. Groenendijk, T. M. V. Janssen, & M. J.B. Stokof (Eds.), Formal methods in the study of language, Part 1. Amsterdam:Mathematish Centrum.[8] Pelletier, F. J. (1974). On some proposal for the semantics of mass nouns.Journal of Philosophical Logic, 3, 87–108.9. Pelletier, F. J. (1975). Non-singular reference: Some preliminaries.Philosophia, 5(4), 451–465 (reprinted in: Pelletier, F. J. (1979) Mass terms:Some philosophical problems, Reidel, Dordrecht, pp. 1–14).

———. 2009. "Reply to Gregory Landini's Review of Formal Ontology andConceptual Realism." Axiomathes.An International Journal in Ontology andCognitive Systems:143-153.1. Some Initial Ontological Distinctions.In our discussion of Greg Landini's review, we should distinguish how thelogical systems lHST* and HST*l that I have developed are to be understood inmy reconstructions of Gottlob Frege's and Bertrand Russell's Principles ofmathematics (1903) ontologies as opposed to how HST*l is understood as a(proper) part of my ontology of conceptual realism. Both of these systems aretype-free second-order predicate logics that allow predicate expressions(complex or simple) and formulas (propositional forms) to be nominalized andoccur in formulas as abstract singular terms.(1)The main logical difference between these systems, as Landini notes, is thatwhereas lHST* contains standard first-order logic (with identity) as a properpart, the system HST*l is free of existential presuppositions regarding singularterms, including nominalized predicates as abstract singular terms, which isessential to any argument for Russell's paradox of predication. In particular,nominalization of the Russell predicate that is not predicable of itself turns outto be denotationless in HST*l as an abstract singular term.The main ontological difference between Russell's and Frege's ontologies is thatone is intensional and the other is extensional. Russell's (1903) ontology isbased on predication as the ontological nexus of propositions, whereas Frege'sis based on predication as a function from properties and relations to truthvalues. (2) In conceptual realism, predication is based on the mutual saturationof referential and predicable concepts as unsaturated complementary cognitivestructures, the result being a speech or mental act. (3)In Russell's ontology, a nominalized predicate denotes, as an abstract singularterm, the very same property or relation (in-intension) that the predicate standsfor in its role as a predicate. In Frege's ontology, a nominalized predicatedenotes the extension (value range, Wertverläufe) of the concept or relation(qua function from objects to truth values) that the predicate stands for in

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predicate position; and in conceptual realism, a nominalized predicate denotesthe intension of the concept (qua cognitive structure) that the predicate standsfor in its role as a predicate. Because what a predicate stands for and what itsnominalization denotes are not the same type of entity in either Frege's ontologyor my conceptual realism, the fact that a nominalized predicate, on pain ofcontradiction, might fail to denote as an abstract singular term does not affectthe objective reality of what that predicate stands for in its role as a predicate.That is why the system HST*l can be used in a reconstruction of Frege'sontology as well as in my conceptual realism. The system lHST* will alsosuffice for a reconstruction of Frege's ontology, but a free first-order predicatelogic is essential to my analysis of plurals and mass nouns in terms of the logicof classes as many developed in my book, which means that only HST*l isappropriate for conceptual realism.On the other hand, for a reconstruction of Russell's ontology, wherenominalized predicates denote the same property or relation they stand for intheir role as predicates, only the system lHST* is appropriate. That is, because itis the same entity involved in both roles in Russell's ontology, we cannot in thatframework both affirm the being of what a predicate stands for in its role as apredicate, and also deny that being in the nominalization of the predicate as anabstract singular term." (p. 143)(1) There is of course a type distinction between object terms and predicates inthese systems; but unlike the situation in type theory there is no hierarchy ofpredicates of different types.(2) Frege's Begriffe are really Eigenshaften, and in our in present context wherewe want to distinguish concepts as cognitive capacities from Frege's Begriffe, itis better to speak of his Begriffe as properties instead.(3) We assume in this discussion a distinction between predication in language,predication in our speech and mental acts, and predication as the nexus ofpropositions or of states of affairs, or, in Frege's case, as functional application.

———. 2009. "Reply to Andriy Vasylchenko's Review of Formal Ontologyand Conceptual Realism." Axiomathes.An International Journal in Ontologyand Cognitive Systems:167-178.Adriy Vasylchenko makes the interesting observation that our references arefrequently emotionally charged. A comprehensive theory of reference,Vasylchenko suggests, should include an account of this phenomenon. Weagree.Indeed, as we will see, the theory of reference in conceptual realism can be usedto explain an important feature of our emotional states when we read a novel, orwatch a play, a movie, or even when viewing a painting. This feature, which inaesthetics is called psychical distance, is connected in part with the differencebetween active and deactivated reference in conceptual realism. We will take upthat issue at the end this reply.There is, however, an important misunderstanding in Vasylchenko's review ofhow the notion of existential presupposition applies -- or, as he claims, fails toapply -- to fictional objects and more generally to the abstract intensionalobjects of conceptual realism. We will discuss this latter issue first, and thenturn to the issue of our emotional states and psychical distance when reading

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fiction or watching a play or a film, and perhaps even when having an aestheticexperience in general." (p. 167)

———. 2009. "Logica E Ontologia." Aquinas.Rivista Internazionale diFilosofia no. 52:7-50Italian translation by Flavia Marcacci, revised by Gianfranco Basti of Logic andOntology (2001).

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———. 2010. "Actualism Versus Possibilism in Formal Ontology." In Theoryand Applications of Ontology. Vol. 1: Philosophical Perspectives, edited byPoli, Roberto and Seibt, Johanna, 105-118. Dordrecht: Springer.Comparative formal ontology is the study of how different informal ontologiescan be formalized and compared with one another in their overall adequacy asexplanatory frameworks. One important criterion of adequacy of course isconsistency, a condition that can be satisfied only by formalization.Formalization also makes explicit the commitments of an ontology.There are other important criteria of adequacy as well, however, in addition toconsistency and transparency of ontological commitment. One major suchcriterion is that a formal ontology must explain and provide an ontologicalground for the distinction between being and existence, or, if the distinction isrejected, an adequate account of why it is rejected. Put simply, the problem is:Can there be things that do not exist? Or is being the same as existence?Different formal ontologies will answer these questions in different ways.The simplest account of the distinction between being and existence is thatbetween actualism and possibilism, where by existence we mean physicalexistence, i.e., existence as some type of physical object; and by being we meanpossible physical existence, i.e., physical existence in some possible world.According to possibilism, there are objects that do not now exist but could existin the physical universe, and hence being is not the same as existence. Inactualism being is the same as existence.Possibilism: There are objects (i.e., objects that have being or) that possiblyexist but that do not in fact exist.Therefore: Existence ≠ Being.Actualism: Everything that is (has being) exists.Therefore: Existence = Being.Now the implicit understanding in formal ontology of both possibilism andactualism is that the objects that the quantifier phrases in these statements rangeover are values of the variables bound by the first-order quantifiers ∀and ∃(forthe universal and existential quantifiers, respectively), and hence that what hasbeing (on the level of objects) is a value of the (object) variables bound by thesequantifiers. In other words, to be (an object, or thing) in both actualism andpossibilism is to be a value of the bound object variables of first-order logic.This means that in possibilism, where being is not the same as existence,existence must be represented either by different quantifiers or by a predicate,e.g., E!, which is the predicate usually chosen for this purpose.Another criterion of adequacy for a formal ontology is that it must explain theontological grounds, or nature, of modality, i.e., of such modal notions asnecessity and possibility, and in particular the meaning of possible physicalexistence. If the modalities in question are strictly formal, on the other hand, as

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is the case with logical necessity and possibility, then it must explain the basisof that formality.This criterion cannot be satisfied by a set-theoretic semantics alone, especiallyone that allows for arbitrary sets of possible worlds (models) and so-calledaccessibility relations between those worlds. Such a semantics may be usefulfor showing the consistency of a modal logic, or perhaps even as a guide to ourintuitions in showing its completeness; but it does not of itself provide anontological ground for modality, or, in the case of logical modalities, explainwhy those modalities are strictly formal.We restrict our considerations here to how physical existence, both actual andpossible, is represented in a formal ontology. This does not mean that the formalontologies considered here cannot be extended so as to include an account ofhow abstract objects might be represented as well, if allowed at all." (pp.105-106)

———. 2010. "Predication in Conceptual Realism." Axiomathes no. 20:1-21Abstract: "Conceptual realism begins with a conceptualist theory of the nexusof predication in our speech and mental acts, a theory that explains the unity ofthose acts in terms of their referential and predicable aspects. This theory alsocontains as an integral part an intensional realism based on predicatenominalization and a reflexive abstraction in which the intensional contents ofour concepts are "object"-ified, and by which an analysis of predication withintensional verbs can be given. Through a second nominalization of thecommon names that are part of conceptual realism's theory of reference (viaquantifier phrases), the theory also accounts for both plural reference andpredication and mass noun reference and predication. Finally, a separate nexusof predication based on natural kinds and the natural properties and relationsnomologically related to those natural kinds, is also an integral part of theframework of conceptual realism."

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———. 2013. "Representing Intentional Objects in Conceptual Realism."Humana.Mente no. 25:1-24Special number edited by Laura Mari (Scuola Normale Superiore of Pisa) andMichele Paolini Paoletti (University of Macerata): Meinong Strikes Again.Return to Impossible Objects 100 Years Later.Abstract: "In this paper we explain how the intentional objects of our mentalstates can be represented by the intensional objects of conceptual realism. Wefirst briefly examine and show how Brentano’s actualist theory of judgment andhis notion of an immanent object have a clear and natural representation in ourconceptualist logic of names. We then briefly critically examine Meinong’stheory of objects before turning finally to our own representation of intentionalobjects in terms of the intensional objects of conceptual realism. We concludeby explaining why existence-entailing concepts are so basic to ourcommonsense framework and how these concepts and their intensions can beused to model Meinong’s ontology."

67.

———. 2015. "Two Views of the Logic of Plurals and a Reduction of One tothe Other." Studia Logica no. 103:757-780Abstract: "There are different views of the logic of plurals that are now in

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circulation, two of which we will compare in this paper. One of these is basedon a two-place relation of being among, as in 'Peter is among the juvenilesarrested'. This approach seems to be the one that is discussed the most inphilosophical journals today. The other is based on Bertrand Russell's earlynotion of a class as many, by which is meant not a class as one, i.e., as a singleentity, but merely a plurality of things. It was this notion that Russell used toexplain plurals in his 1903 Principles of Mathematics; and it was this notionthat I was able to develop as a consistent system that contains not only a logicof plurals but also a logic of mass nouns as well.We compare these two logics here and then show that the logic of the Amongrelation is reducible to the logic of classes as many.""There are di¤erent views of the logic of plurals that are now in circulation. (1)One of these is based on a two-place relation of being among, as in ‘Peter isamong the juveniles arrested’. This approach seems to be the one that isdiscussed the most in philosophical journals today. The other is based onBertrand Russell’s early notion of a class as many, by which is meant not a classas one, i.e., as a single entity, but a mere plurality of things. It was this notionthat I developed in 2002 as a provably consistent system that contains not only alogic of plurals but also a logic of mass nouns as well. (2) It also contains, as weshow in this paper, the plural logic based on the Among relation. We will firstcompare these two logics here and then show that the logic of the Amongrelation in Linnebo [2004] is reducible to the logic of classes as many.We will first briefly discuss the plural logic based on the Among relation asdescribed by Linnebo. Then we will brie‡y explain the basics of the logic ofclasses as many, and finally we will show how the logic of the Among relationis reducible to the logic of classes as many." (p. 757)(1) See, e.g., Boolos [1984], Schein [1993], Cocchiarella [2002], McKay[2006], and Linnebo [2004].(2) See Cocchiarella [2002], [2007] chapter 11, and [2009].References[1] Boolos, George, 1984, “To Be Is To Be a Value of a Variable (or to Be SomeValues of Some Variables),” Journal of Philosophy, 81: 430–50.[3] Cocchiarella, Nino B., 2002, “On the Logic of Classes as Many,” StudiaLogica, 70: 303–38.[5] Cocchiarella, Nino B., 2007, Formal Ontology and Conceptual Realism,Springer, Synthese Library vol. 339, Dordrecht.[6] Cocchiarella, Nino B., 2009, “Mass Nouns in a Logic of Classes as Many,”Journal of Philosophical Logic, vol. 38, no. 3: 343–361.[12] Linnebo, Øystein “Plural Quantification,” 2004, Stanford Encyclopedia ofPhilosophy, revised 2010.[13] McKay, Thomas, 2006, Plural Predication, Oxford: Oxford UniversityPress.[15] Schein, Barry, 1993, Plurals and Events, Cambridge, MA: MIT Press.[16] Tarski, A., 1965, “A Simplified Formulation of Predicate Logic withIdentity,”Arch. f. Math. Logik und Grundl. vol. 7: 61–79.

———. 2016. "On Predication, a Conceptualist View." In Philosophy andLogic of Predication, edited by Stalmaszczyk, Piotr, 53-92. Bern: Peter Lang

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Abstract:"Predication, as the nexus between a subject and a predicateexpression, is the basis of the unity of a speech act, including speech acts in theplural and speech acts that involve mass nouns. A speech act, of course, is anovert expression of a mental act, e.g., a judgment; and therefore the unity of aspeech act such as an assertion is really the unity of the judgment that underliesthat act. Such a mental act, and therefore the speech act as well, has a unitybased on how the referential and predicable roles of the subject and predicateexpressions combine and function together respectively. What we propose hereis to explain this unity of predication in terms of a conceptualist theory oflogical forms that we claim underlies at least some important aspects of thoughtand natural language. Our conceptualist logic also contains an account of themedieval identity (two-name) theory of the copula, as well as an account ofplural and mass noun reference and predication, the truth conditions of whichare based on a logic of plurals and mass nouns."

———. 2017. Epistemological Ontology and Logical Form in Russell's LogicalAtomismNot yet published.Unpublished paper; preprint available on academia.edu.Abstract: "Logical analysis, according to Bertrand Russell, leads to and endswith logical atomism, an ontology of atomic facts that is epistemologicallyfounded on sense-data, which Russell claimed are mind-independent physicalobjects. We first explain how Russell’s 1914–1918 epistemological version oflogical atomism is to be understood, and then, because constructing logicalforms is a fundamental part of the process of logical analysis, we briefly look atwhat has happened to Russell’s type theory in this ontology. We then turn to theproblem of explaining how the logical forms of Russell’s new logic can explainboth the forms of atomic facts and yet also the sentences of natural language.The main problem is to explain the logical forms for belief and desire sentencesand how those forms correspond to the logical forms of the facts of logicalatomism."

70.

———. 2017. Russell's Logical Atomism 1914-1918: EpistemologicalOntology and Logical Form.Unpublished paper, available on this site.Abstract:"Logical analysis, according to Bertrand Russell, leads to and endswith logical atomism, an ontology of atomic facts that is epistemologicallyfounded on sense-data, which Russell claimed are mind-independent physicalobjects. We first explain how Russell's 1914-1918 epistemological version oflogical atomism is to be understood, and then, because constructing logicalforms is a fundamental part of the process of logical analysis, we briefly look atwhat has happened to Russell's type theory in this ontology. We then turn to theproblem of explaining whether or not the logical forms of Russell's new logiccan explain both the forms of atomic facts and yet also the sentences of naturallanguage, especially those about beliefs. The main problem is to explain thelogical forms for belief and desire sentences and how those forms do notcorrespond to the logical forms of the facts of logical atomism.""

71.

———. 2018. A Modal-Ontological Argument and Leibniz's View of Possible72.


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Worlds.Unpublished paper, available on this site.Abstract: "We critically discuss an ontological argument that purports to provenot only that God, or a God-like being, exists, but in addition that God'sexistence is necessary. This requires turning to a modal logic, S5 in particular,in which the argument is presented. We explain why the argument fails. We thenattempt a second version in which one of its premises is strengthened. Thatattempt also fails because of its use of the Carnap-Barcan formula in a contextin which that formula is not valid. A third is presented as well using the propername 'God' as a singular term, but it too fails for the same reason, though in alater section we show how this last argument can be validated under a re-interpretation of the quantifiers of the background logic. In our later sections,we explain what is wrongwith the original first premise as a representation of what Leibniz meant by theconsistency of God's existence, specifically as God's existence in a possibleworld. Possible worlds exist only as ideas in God's mind, and the consistency ofGod's existence cannot be God's existence in a possible world. Realismregarding possible worlds must be rejected. Only our world is real, the result ofan ontological act of creation. We also explain in a related matter whyaccording to Leibniz, Boethius, Aquinas and other medieval philosophers,God's omniscience does not imply fatalism."

ESSAYS TRANSLATED IN SPANISH AND ITALIAN

Cocchiarella, Nino. 2000. Lógica Como Lenguaje y Lógica Como Cálculo: suPapel en la Teoría de la Atribución. Heredia, Costa Rica: Departamento deFilosofia, Universidad Nacional.Coleccion Prometeo n. 20.

1.

———. 1974. "La Semantica della Logica del Tempo." In La Logica delTempo, edited by Pizzi, Claudio, 318-347. Torino: Boringhieri.Italian translation of the third chapter of the unpublished Ph. D. Thesis: TenseLogic: A Study of Temporal Reference, (1966).

2.

———. 2009. "Logica e Ontologia." Aquinas.Rivista Internazionale diFilosofia no. 52:7-50.Italian translation by Flavia Marcacci, revised by Gianfranco Basti of Logic andOntology (2001).

3.

STUDIES ABOUT THE WORK OF NINO COCCHIARELLA

Bonevac, Daniel. 1991. "Critical Review of: Nino B. Cocchiarella, LogicalInvestigations of Predication Theory and the Problem fo Universals." Noûs no.25:221-230.

1.


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Chierchia, Gennaro. 1984. Topics in the Syntax and Semantics of Infinitives andGerunds, University of Massachusetts.Unpublished Ph. D. Thesis available at UMI Dissertation Express, referencenumber 8410273.

2.

———. 1985. "Formal Semantics and the Grammar of Predication." LinguisticInquiry no. 16:417-443.

3.

Freund, Max A. 1989. Formal Investigations of Holistic Realist RamifiedConceptualism, Indiana University.Unpublished Ph. D. Thesis available at UMI Dissertation Express, referencenumber 9020685.

4.

———. 1991. "Consideraciones logico-epistemicas relativa a una forma deconceptualismo ramificado." Critica no. XXIII (69):47-72."An intuitive interpretation of constructive knowability is first developed. Then,an epistemic second order logical system (which formalizes logical aspects ofthe interpretation) is constructed. A proof of the relative consistency of such asystem is offered. Next, a formal system of intensional arithmetic (whoselogical basis is the aforementioned second order system) is stated. It is provedthat such a formal system of intensional arithmetic entails a theorem, whosecontent would show possible limitations to constructive knowability."

5.

———. 1992. "Un sistema logico de segundo orden conceptualista conoperadores lambda ramificados." Critica no. XXIV (72):3-25."We develop a second order logical system with ramified lambda operators,having ramified conceptualism as its philosophical background. Such a systemis shown to relatively consistent. Finally, we construct a non-standard secondorder semantics and prove a completeness theorem with respect to a notion ofvalidity, provided by the semantics, and certain extensions of the second ordersystem."

6.

———. 1994. "The Relative Consistency of System RRC* and Some of ItsExtensions." Studia Logica no. 53:351-360.

7.

———. 1996. "A Minimal Logical System for the Computable Concepts andEffective Knowability." Logique et Analyse no. 37:339-366.

8.

———. 1996. "Semantics for Two Second-Order Logical Systems: =RRC* andCocchiarella's RRC*." Notre Dame Journal of Formal Logic no. 37:483-505.

9.

———. 1996. "A Minimal Logical System for the Computable Concepts andEffective Knowability - Some Corrections." Logique et Analyse no. 37:411-412.

10.

———. 2000. "A Complete and Consistent Formal System for Sortals." StudiaLogica no. 65:1-15.

11.

———. 2001. "A Temporal Logic for Sortals." Studia Logica no. 69:351-380.12.

Landini, Gregory. 1986. Meinong Reconstructed Versus Early RussellReconstructed: A Study in the Formal Ontology of Fiction, Indiana University.Unpublished Ph. D. Thesis available at UMI Dissertation Express, referencenumber 8617784.

13.

———. 1990. "How to Russell another Meinongian: a Russellian theory of14.


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fictional objects versus Zalta's theory of abstract objects." GrazerPhilosophische Studien no. 37:93-122.

———. 1998. Russell's Hidden Substitutional Theory. New York: OxfordUniversity Press.

15.

———. 2009. "Cocchiarella's Formal Ontology and the paradoxes ofhyperintensionality." Axiomathes.An International Journal in Ontology andCognitive Systems no. 19:115-142.

16.

Meyer, Robert K. 1972. "Identity in Cocchiarella's T*." Noûs no. 6:189-197.17.

Orilia, Francesco. 1996. "A Contingent Russell's Paradox." Notre Dame Journalof Formal Logic no. 37:105-111.

18.

Park, Woosuk. 1990. "Scotus, Frege, and Bergmann." The Modern Schoolmanno. 67:259-273.

19.

———. 2001. "On Cocchiarella's retroactive theory of reference." The LogicaYearbook 2000:79-90.

20.

———. 2016. "Where have all the Californian tense-logicians gone?" Synthese.To appear in Synthese."Arthur N. Prior, in the Preface of Past, Present and Future, made clear hisindebtedness to “the very lively tense-logicians of California for manydiscussions”. Strangely,with a notable exception of Copeland (Logic andreality: essays on the legacy of Arthur Prior, 1996), there is no extensivediscussion of these scholars (as a group, if not a school) in the literature on thehistory of tense logic. In this paper, I propose to study how Nino B.Cocchiarella, as one of the Californian tense-logicians, interacted with Prior inthe late 1960s. By gathering clues from their correspondence available atVirtual Lab for Prior Studies, I will highlight some of the differences betweentheir views on tense-logic, which might still have far-reaching philosophicalimplications. I will conclude with a sketchof how to study in what ways Priorand Cocchiarella influenced some other Californian tense-logicians."

21.

Prior, Arthur Norman. 1967. Past, Present and Future. New York: OxfordUniversity Press.Various references to the unpublished Ph.D. thesis by Nino Cocchiarerlla.

22.

Simms, John Carson. 1980. "A realist semantics for Cocchiarella's T*." NotreDame Journal of Formal Logic no. 21:1-32.

23.

Turner, Raymond. 1985. "Three theories of nominalized predicates." StudiaLogica no. 44:165-186.

24.

Vasylchenko, Andriy. 2009. "The problem of reference to nonexistents inCocchiarella's Conceptual Realism." Axiomathes.An International Journal inOntology and Cognitive Systems no. 29:155-166."This article is a critical review of Cocchiarella's theory of reference. Inconceptual realism, there are two central distinctions regarding reference: first,between active and deactivated use of referential expressions, and, second,between using referential expressions with and without existentialpresupposition. Cocchiarella's normative restrictions on the existential

25.


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presuppositions of reference lead to postulating two fundamentally differentkinds of objects in conceptual realism: realia or concrete objects, on the onehand, and abstract intensional objects or nonexistents, on the other. Accordingto Cocchiarella, nonexistents can be referred to only without existentialpresuppositions. However, referring to nonexistents with existentialpresuppositions is an ordinary human practice. To account for this fact,Cocchiarella's normative theory of reference should be supplemented by adescriptive account of referring."

Yu, Yung-Ping. 1995. Generality and Reference. An Examination of Denoting inRussell's Principles of Mathematics, University of Iowa.Unpublished Ph. D. Thesis available at UMI Dissertation Express, referencenumber 9603108.

26.

Zacker, David J. 1996. A Study in the Temporal Ontology of Tense Logic,Michigan State University.Unpublished Ph. D. Thesis available at UMI Dissertation Express, referencenumber 9631366.

27.


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RELATED PAGES

On the website "Theory and History of Ontology" (www.ontology.co)

Frege's Ontology: Being, Existence, and Truth

Bertrand Russell's Ontological Development

The Ontology of Wittgenstein's Tractatus

Edmund Husserl: Formal Ontology and Transcendental Logic

Stanislaw Lesniewski's Logical Systems: Protothetic, Ontology, Mereology

Living Ontologists


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PAGES IN PDF FORMAT

I am grateful to Professor Nino Cocchiarella, Dr. Woosuk Park (editor of the Korean Journalof Logic) and to Professor Inkyo Chung, President of Korean Association of Logic for thepermission to publish the essay Logical necessity based on Carnap's criterion of adequacy.

The following papers are posted with the kind permission of Professor Nino Cocchiarella:

"Conceptual Realism as Formal Ontology" Roberto Poli, Peter Simons (eds.),Formal Ontology, Dordrecht/Boston/London, Kluwer 1996, pp. 27-60, NijhoffInternational Philosophy Series, vol. 53. (256 KB). This essay is reproduced with thekind authorization of Kluwer Academic Publishers.

"Logic and Ontology", in: Axiomathes vol. 12, (2001) pp. 117-150 (Italiantranslation by Flavia Marcacci, revised by Gianfranco Basti: "Logica e ontologia",Aquinas.Rivista Internazionale di Filosofia 52: 7-50 (2009).

"Logical Necessity Based on Carnap's Criterion of Adequacy", Korean Journal ofLogic, vol. 5 n. 2 (2002), pp. 1-21.

"Conceptual Realism and the Nexus of Predication", Metalogicon vol. 16, 2 (2003),pp. 45-70.

"Denoting Concepts, Reference, and the Logic of Names, Classes as Many, Groupsand Plurals", Linguistics and Philosophy vol. 28 n. 2 (2005), pp. 135-179.

"Russell's Logical Atomism 1914-1918: Epistemological Ontology and LogicalForm", unpublished essay (will be removed after publication).

Deontic Logic, unpublished notes based on a course given on modal logic in the late1960s at the State University of California at San Francisco.

Gustav Bergmann on Ideal Languages, unpublished lecture presented at IndianaUniversity at the Gustav Bergmann Memorial Conference (October 30-21, 1992).

A Modal-Ontological Argument and Leibniz's View of Possible Worlds, unpublishedpaper (2018)

Some Remarks on Stoic Logic

Diodorus's Master Argument

The last two papers were written at request of Professor Giuseppe Addona, of the Liceoginnasio of Benevento (Italy) for his Italian students and can also be found (with an Italiantranslation) on his Website.

The essays published in the Notre Dame Journal Formal Logic are available at ProjectEuclid; some of other essays are available at Jstor or at Academia.edu.


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complete and annotated bibliography of nino cocchiarella · complete and annotated bibliography of...

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