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Modality

Oxford Handbook of the History of Analytic Philosophy

Sanford Shieh

Department of Philosophy Wesleyan University

Middletown, CT 06459 <Sanford.Shieh@wesleyan.edu>

Modal concepts, especially the Leibnizian notion of possible worlds, are central in contemporary

analytic philosophy. Quite the opposite was the case earlier. Until the 1970s, the default attitude towards

modality among analytic philosophers was some degree of suspicion. My aim in this chapter is to

provide an overview of the grounds and consequences of this distrust, and the ways in which it faded

from the mainstream.

The period of analytic philosophy closest to us contains the heyday of logical positivism and its

decline. Since many contemporary analytic philosophical preoccupations arose in reaction to positivism,

we have an understandable, and not altogether unjustifiable, tendency to think of positivism as an

amalgam of easily identifiable philosophical mistakes, and to project these mistakes onto all of our

predecessors.1 Thus, we take suspicion of modality to have been based on the now discredited anti-

metaphysical empiricist criterion of significance: there are no sensory or observational grounds for modal

sentences, so the only respectable species of necessity consists of a priori analytic truths that are a

product of the meanings conventionally attached to linguistic expressions. With the demise of the

criterion of significance, opposition to modality collapsed.2

The analytic tradition is a complex interweaving of many strands of thought, so this picture is not

entirely false, even of positivism. But there is no doubt that it does not fit the founders of analytic

philosophy, Gottlob Frege, G. E. Moore, and Bertrand Russell, all of whom opposed empiricism and held

no brief against metaphysics. For them lack of empirical grounds is no basis for denial of mind-

independent objectivity. So while they took necessity and possibility to be reducible to more fundamental

logical notions, logic for these thinkers consists of truths about a mind and language independent reality

that extend beyond empirical reality. In addition, their conceptions of the relations among the notions of

necessity, analyticity and apriority differ significantly from the positivists’ views.

Thus there were, in the history of the analytic tradition, at least two main forms of reductionism or

deflationism about modality. Correspondingly, there were two major phases in the passing of anti-

modalist stances. First, it was argued that modal notions are not reducible to logical ones because logic

1 A paradigm of this tendency is Soames (2003), chapters 12 and 13. 2 See Rosen (2001) for a clear account of this view.

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itself requires modal notions. Second, it was argued that modal properties are mind- and language-

independent feature of the world.

I begin with a brief account of Frege, Moore, and Russell. I turn then to two critiques of Russell’s

conception of logic that constitute the first phase: C. I. Lewis’s rejection of Russell’s material implication,

and Ludwig Wittgenstein’s rejection, in Tractatus Logico-Philosophicus (1922 [1921]), of Russell’s view

of the nature of logic. Next I outline Rudolf Carnap’s pragmatically motivated account of modal terms as

expressing pseudo-object properties, which appear to be properties of objects but can in fact be construed

as properties of their designations. Quine’s sharpening and critique of Lewis’s and Carnap’s account of

necessity as analyticity is a pivotal moment in the history recounted here, since the second phase arose in

response to Quine’s critique. Two central planks of Quine’s critique—the difficulties of quantifying into

modal contexts, and the need to resort to essentialism to overcome these difficulties—originate in

Carnap’s notion of pseudo-object property. Opposition to Quine’s modal skepticism appeared as soon as

Quine published his arguments in 1943, but it wasn’t until the 1960s that there was a sustained movement

away from Quine’s views. Among the main works opposing Quine in this period are Ruth Barcan

Marcus (1961), Dagfinn Føllesdal (1961; 1965), Jaakko Hintikka (1963; 1969), A. N. Prior (1963), N. L.

Wilson (1965), Bede Rundle (1965), Richard Cartwright (1968), Leonard Linsky (1969), Alvin Plantinga

(1969;1970), and Saul Kripke (1971; 1972). Naturally it’s not possible to provide adequate analyses of

all these texts here. Rather than setting out a progression of capsule summaries, I focus on two closely

related but distinct responses to Quine’s arguments from the beginning and the end of this period:

Marcus’s revival of a Russellian argument using a conception of proper names as directly referential and

Kripke’s use of our intuitive understanding of modal sentences containing proper names to support a

metaphysical notion of necessity.3

In general I have chosen, at the expense of completeness of coverage, to isolate a few central lines of

development, focusing on philosophically significant views and arguments. I devote more space to the

period up to the 1960s, since it is nowadays comparatively less familiar. Limitations of space force me to

forgo consideration of a number of salient philosophical developments. Apart from the works already

mentioned, I particularly regret not covering the role of modality in motivating Jan Łukasiewicz’s work in

many-valued logic,4 work on modal expressions in the ordinary language philosophy tradition,5 and

Wilfrid Sellars’s (1980) view of laws. Finally, I don’t discuss any of the connected developments in

modal logic.

3 More details on the works I do not treat can be found in Neale (1999). I am very much indebted to the

historical discussion of this paper; in many case it oriented my thinking, even where I disagree with Neale’s emphases and conclusions.

4 The classic statement is Łukasiewicz (1930). 5 For instance, Austin (1979).

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1. Reductionism about Modality: Frege, Moore, and Russell

As noted above, modal notions are neither central nor foundational in the philosophical projects that

inaugurated analytic philosophy: Frege’s use of higher-order quantificational logic in logicism, and

Moore’s and Russell’s collaborative rejection of British Idealism. These philosophers treated modal

notions reductively, explaining them away in terms of logical notions.

One of Frege’s concerns in the early sections of Begriffsschrift (1970 [1879]) is to set out his notions

of judgment, proposition, and conceptual content in contrast to the corresponding notions in traditional

logic. In §4 Frege asserts that his conceptual content does not distinguish between the traditional notions

of apodictic and assertoric judgments. From Frege’s perspective, a judgment in apodictic form merely

“suggests the existence of universal judgments from which [it] can be inferred,” so in characterizing a

proposition as necessary one merely gives “a hint about the grounds for” one’s judgment (ibid., 13).

Similarly, in characterizing a proposition as possible: “either the speaker is suspending judgment by

suggesting that he knows no laws from which the negation of the proposition would follow or he says that

the generalization of this negation is false” (ibid.) Thus for Frege modal predicates do not contribute to

the conceptual contents of judgments in whose expressions they occur, but merely “hint at,” or “suggest”

the existence of deductive relations between those contents and laws or generalizations, and so perhaps

contributes to “coloring and shading.”6 To the extent that such hints are objective features of assertions,

they might be eliminated by explicitly stating these deductive relations.7

In Foundations of Arithmetic (1980 [1884], §3), Frege provides accounts of the analytic/synthetic and

a priori/a posteriori distinctions in terms of kinds of deductive justification. A truth is analytic if its

proof rests ultimately “only on general logical laws and on definitions,” synthetic if its proof also depends

on “truths which are not of a general logical nature, but belong to the sphere of some special science”

(ibid., 3) The notion of analyticity here is recognizable as an ancestor of semantic accounts of analyticity;

but it differs from such accounts since for Frege definitions are supposed to reflect analyses of concepts,

and so are not arbitrarily adopted but have to be justified.8 A truth is a posteriori if its proof requires

appeal to “truths which cannot be proved and are not general, since they contain assertions about

particular objects,” a priori “if … its proof can be derived exclusively from general laws.”9 These

accounts obviously do not rule out truths whose justification depend on general but non-logical laws, and

6 Frege (1984 [1892], 161). 7 If Frege’s notions of universal judgment and of law have irreducibly modal components, then, of course,

these accounts would not succeed in eliminating modal notions. But the consensus is that for Frege universal judgments and laws are simply universal quantificational generalizations understood purely extensionally. Danielle Macbeth argues against this consensus in Frege’s Logic (2005); for critical discussion of her arguments see Shieh (2005).

8 Frege apparently changed his mind on the arbitrariness of definitions. See Shieh (2008). 9 Frege (1980, §3, 3).

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Frege explicitly agrees with Kant in holding that “the truths of geometry [are] synthetic and a priori”

(ibid., §88, 101). Moreover, the distinction between a priori and a posteriori turns simply on the

generality or particularity of grounds, and so does not, without additional premises, imply anything about

whether sensory experience or observation is required. Finally, it’s not obvious that Frege’s views rule

out necessary propositions that are a posteriori. The “suggestion” that a judgment can be inferred from

general laws entails neither that its ultimate grounds in fact contain general laws, nor, even if they do, that

they do not also contain particular truths.

In “Necessity” (1900), Moore claims that “no proposition is necessary in itself,” but only in virtue of

being “connected in a certain way with other propositions” (302). The connection in question Moore

calls “logical priority,” and, in typical Moorean fashion, elucidates by pointing to examples: “when we

say: Here are two chairs, and there are two chairs, and therefore, in all, there are four chairs; it would

commonly be admitted that we presuppose in our conclusion that 2 + 2 = 4” (ibid., 301). This last

presupposed arithmetical truth is logically prior to the particular inference. Strictly for Moore no

proposition is necessary simpliciter, but one proposition is more necessary than another if it is logically

prior to the other but not vice versa.

In The Principles of Mathematics (1903) §430, Russell articulates a radically anti-modal view. He

claims, first, that every proposition is “a mere fact,” and so not necessary (ibid., 454). Second, “there

seems to be no true proposition of which there is any sense in saying that it might have been false. …

What is true, is true; what is false, is false; and concerning fundamentals, there is nothing more to be said”

(ibid.) But although, fundamentally, no proposition is either necessary or possible absolutely, Russell

here follows Moore in adopting an account of relative necessity: “[a] proposition is more or less necessary

according as the class of propositions for which it is a premiss is greater or smaller” (ibid.) As Russell

makes explicit in a later unpublished paper, “Necessity and Possibility” (1994 [1905]), he interprets

Moore’s logical priority in terms of the relation of implication: “p is logically prior to q if q implies p but

p does not imply q” (513).10 Russell’s view of modality in this paper is more nuanced than in Principles.

He observes that if implication is construed materially, Moore’s account has the consequence that all true

propositions have the same degree of necessity. So Russell proposes four other accounts for capturing

ordinary conceptions of necessity, the first two of which analyze necessity respectively as apriority and as

analyticity. The a priori/empirical distinction is, “approximately,” between “propositions not predicating

existence at particular times” and “propositions predicating existence at particular times” (ibid., 510).

Russell notes that the class of propositions thus demarcated has, “obviously, no specially notable logical

10 Russell’s use of letters ‘p’, ‘q’, etc. in formulas, and of quotation marks is, of course, an especially

controversial matter in view of Quine’s accusation that he and Whitehead confused use and mention. I won’t attempt a defensible Russellian usage, but my general policy is to use double quotes to reproduce Russell’s text, and no quotes when using Russell’s formulas in discussing his views, taking these formulas to be intended as expressing generalizations about non-linguistic propositional entities.

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characteristic” (ibid.) Analyticity is explained in terms of a relation that Russell calls “deducibility”: “q is

deducible from p if it can be shown by means of the [axioms of logic] that p implies q,” (ibid., 515), i.e. if

‘p implies q’ is derivable from logical axioms. Analytic propositions are then taken to be just those

deducible from the axioms of logic. Given this account, Russell says, “[i]t is now open to us, if we

choose, to say that a necessary proposition is an analytic proposition, and a possible proposition is one of

which the contradictory is not analytic” (ibid., 515-7). We’ll come back to Russell’s account of

deducibility below; for now note that Russell’s conception of analyticity makes no mention of meaning or

synonymy.

The remaining two analyses of necessity are as follows. First, a proposition is “felt” to be necessary

when it is proved to be true; unfortunately, on Russell’s view of proof this makes every true proposition

necessary. The other in essence explains necessity in terms of quantificational generality: a

“propositional function ‘x has the property φ’ is necessary if it holds of everything” Russell (1994, 518;

second emphasis mine). A proposition is, again, not necessary simpliciter, but necessary with respect to

one of its constituents just in case there is a necessary propositional function obtainable from that

proposition by replacing some or all occurrences of that constituent by variables.

Russell’s overall conclusion from these accounts of necessity in terms of logical notions does not

change substantially from the position of Principles: “there is no one fundamental logical notion of

necessity, [hence] the subject of modality ought to be banished from logic, since propositions are simply

true or false, and there is no such comparative and superlative of truth as is implied by the notions of

contingency and necessity” (ibid., 520).11

2. C. I. Lewis against Russell

Modern modal logic began with C. I. Lewis’s criticisms of the propositional logic of Whitehead’s and

Russell’s Principia Mathematica (1910).12 Lewis’s critique is the first significant reversal of the attitude,

just canvassed, that modal notions are to be explained away rather than used in philosophical

11 Dejnožka (1999) argues that Russell’s analyses of modality lead to definitions of modal notions implying

formal modal logics which, in turn, analyze Russell’s casual talk of possible worlds. Dejnožka fails to take sufficiently seriously Russell’s explicit statements, such as the ones quoted in the text, against the foundational status of modality, and so he misses the fact that Russell’s aim is not to uncover logical principles governing imprecise and intuitive modal concepts but to find various ways to eliminate them.

Nicholas Griffin’s fine account (1980) of Russell’s views of the nature of logic is marred by a similar misreading. Griffin takes Russell to adopt the final analysis of the necessity of propositional functions in “Necessity and Possibility” in order to bolster the view that his logical axioms are necessary. Since this analysis does not apply directly to propositions, there are, unsurprisingly, difficulties for certifying the logic of Principles as necessary. It’s surely easier to take Russell at his word in Principles and “Necessity and Possibility,” and accept that, in this period at least, Russell did not take necessity to be a part of the nature of logic.

12 Lewis is not alone in adopting modal notions in logic as a reaction to Principia; Jan Łukasiewicz is another, see Łukasiewicz (1930). In a series of papers leading up to (1906), Hugh MacColl also formulated logical systems with modal implication connectives. See Russell’s review (1906) of MacColl (1906), MacColl’s criticism of Russell (1903) in (1908), and Russell’s reply (1908).

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explanations. I begin my account of Lewis with a sketch of the key background of his critique, some

aspects of Russell’s conception of propositional logic in the period from Principles to Principia.13

Russell held that logic is “essentially concerned with inference in general, and is distinguished from

various special branches of mathematics mainly by its generality. … What symbolic logic does

investigate is the general rules by which inferences are made ….”(1903, 11). The generality of logic

consists in the applicability of its principles of inference to all subject matters—they are universally

applicable norms of inference.14 Let’s call this feature of logic “maximal generality of application.”

The part of logic that is the propositional calculus “studies the relation of implication between

propositions.” (ibid., 14). To appreciate what this claim amounts to, we have to see that in the period of

Principles, Russell holds a theory of propositions first propounded by G. E. Moore.15 Propositions are

composed of the very entities that they are about.16 Their truth and falsity are not constituted by

correspondence to entities in the world; rather, truth and falsity are unanalyzable properties of

propositions. Propositions are themselves entities, and one of the relations in which these entities can

stand is the relation of implication.17 The relation of implication is just as indefinable as the properties of

truth and falsity (ibid., §16), and is the basis of valid inference: “It is plain that where we validly infer one

proposition from another, we do so in virtue of a relation which holds between the two propositions

whether we perceive it or not …. The relation in virtue of which it is possible for us validly to infer is

what I call material implication” (ibid., 33). A rule of inference is thus a proposition about propositions

standing in the relation of implication. Being a proposition, it is, of course, objectively true or false.

When it is in fact true, inferences we draw in accordance with it are correct. Since logic is maximally

general in application, it comprises those rules of inference that describe of how propositions are related

13 Russell of course is famous for his many changes of mind, and so strictly speaking he did not hold a single

view of logic even in this fairly limited period of philosophical development. I simplify in order to focus on what Lewis might have taken to be Russell’s conception of logic, in order to investigate the motivations for strict implication. Of course this doesn’t mean that according to my story Russell’s views didn’t change at all in this period; two significant changes will come up below.

14 On the reading I’ve been sketching, Russell’s conception of the generality of logic is similar to the normative sense in which Frege takes logic to be maximally general; see MacFarlane (2002, 35-7). Consider, e.g., Frege’s claim that logical laws are “the most general laws” because they “prescribe universally the way in which one ought to think if one is to think at all” Frege (1964, xv). If we gloss the phrase, “if one is to think at all,” as “no matter what one is thinking about,” then we have in essence Russell’s view.

15 See Moore (1899). Russell writes in the Preface of Principles: “On fundamental questions of philosophy, my position, in all its chief features, is derived from Mr. G. E. Moore. I have accepted from him the non-existential nature of propositions … and their independence of any knowing mind” Russell (1903, xviii). The following account of Russell’s view of logic owes much to Hylton (1990), especially. Part II, Chapter 4, and Griffin (1980).

16 A significant qualification on this point is Russell’s theory of denoting concepts, which are constituents of propositions which are not about those concepts but what they denote. See Hylton (1990) and Griffin (1980).

17 Indeed, Russell in Principles holds that only propositions can stand in this relation; see Russell (1903), §16, 15, and §18, axioms (2) and (3).

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by implication, in virtue of being propositions, simpliciter, not in virtue of being about this or that subject

matter.18

Note that implication is not the only relation among propositions figuring in logic. The propositions

related by implication have themselves certain structures given by occurrences of logical constants. For

example, axiom (5) of Principles §18, “p.qp,” states that every proposition is borne the relation of

implication by all those propositions in which it stands in the relation of conjunction to some proposition

(ibid., §18, 6).

A consequence of this view of logic is that, since the principles of logic are themselves propositions,

they can also stand in the relation of implication. Because logic is maximally general in application, i.e.,

because the principles of logic describe how propositions, purely in virtue of being propositions, are

related by implication, they must describe the facts about how the propositions that are logical rules of

inference are related by implication to other propositions. That is to say, the rules of inference that

comprise logic have to be applicable to those very rules, have to govern reasoning about those very rules.

Between Principles and Principia, Russell’s conception of logic changed in (at least) three main

ways. First, Principia incorporates the ramified theory of types. Second, he adopted the multiple-relation

theory of judgment, on which propositions, like classes, are analyzed away. Finally, Russell no longer

took the relation of implication to be indefinable, but “‘p implies q’ is to be defined to mean: ‘Either p is

false or q is true’” (Whitehead and Russell 1910, 94). In spite of these changes, Russell continues to

maintain the generality of logic; he describes Part I, the very beginning of Principia, as “dealing with

such topics as belong traditionally to symbolic logic … in virtue of their generality” (ibid., 87).

Moreover, Russell continues to take valid inference to track implication. “The Theory of Deduction,”

which begins Part I of Principia, is “the theory of how one proposition can be inferred from another,” and

Russell tells us that “in order that one proposition may be inferred from another, it is necessary that the

two should have that relation which makes the one a consequence of the other. When a proposition q is a

consequence of a proposition p, we say that p implies q. Thus deduction depends upon the relation of

implication” (ibid., 90).19

18 I would like to situate my account with respect to a recent controversy over whether Frege or Russell held

“universalist” conceptions of logic which preclude semantic theorizing about logic: Van Heijenoort (1967), Ricketts (1986), Stanley (1996), Tappenden (1997), and Proops (2007). It should be obvious that I’m not claiming that in order to be a principle of logic for Russell, a proposition must quantify over all items whatsoever in his ontology. It is clear that Russell takes some pains in Principles to formulate some principles of deduction as generalizations in which “the variables have an absolutely unrestricted field: any conceivable entity may be substituted for any one of our variables” (1903, §7). However, it is not this feature of those generalizations, but rather the fact that they range over all propositions, that is necessary for them to be principles of logic. The only sense in which Russell’s logic is maximally general on my account is maximal generality of application as norms of inference.

19 Whitehead and Russell (1910, 90). It is not clear that the multiple-relations theory of judgment mentioned in Principia is compatible with this talk of implication as a relation among propositions. But of course it is a vexed question whether the multiple-relations theory is consistent with the ineliminable quantification over propositions and propositional functions required by the logic of Principia. For contrasting views see, e.g., Ricketts (2001, 101-

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Of the changes from Principles only the last is directly relevant to our concerns. Why does Russell

take implication to be definable in Principia? He acknowledges that “there are other legitimate

meanings” of implication, but claims that his definition yields a more “convenient” meaning. The

argument goes as follows. Russell’s definition captures “[t]he essential property that we require of

implication,” namely, true propositions do not imply false ones. This property is essential to implication

because it is “in virtue of this property that implication yields proofs.” What Russell has in mind here

depends on his conception of proof, which consists of establishing truths by inferring them from true

premises20 by modus ponens: if p implies q and p is true, then, provided that true propositions do not

imply false ones, q must be true. It follows that any relation R between propositions such that for any

propositions p and q if

p is true and q is false (1)

then p does not stand in R to q “yields proofs.” It should be clear that there are many (extensionally)

distinct relations that satisfy these requirements, differing on which of the propositions p and q that fail

condition (1) count as standing in that relation. Russell’s definition of implication in essence picks out

from among these relations the one which holds of the most propositions: whenever any propositions p

and q fail to satisfy (1), p materially implies q. This is why Russell takes his definition to give “the most

general meaning compatible with the preservation of” the essential characteristic of implication. The

definition is “convenient” because it does not require distinguishing among ordered pairs of propositions

that fail (1).21

But Russell’s justification of his definition of implication raises a question. How are the logical

axioms of Principia selected? These axioms are supposed to describe which implications hold and so

license deductions. Since in Principia Russell adopts material implication, one might expect that

Russell’s reason for thinking that, e.g. qqp, is an axiom is that, of any two propositions, q and qp,

either the first is false or the second is true. But if so, why does Russell not set forth these reasons when

he presents the logical axioms? Why does Russell, in contrast to Frege, never give elucidatory arguments

for accepting his axioms?22 We will come back to this question below.

I turn now to Lewis. In his early writings on logic, Lewis was in many ways a faithful Russellian.

21) and Klement (2004).

20 Thus, arguments by reductio are strictly speaking not proofs; but Russell thinks that all such arguments can be converted into genuine proofs.

21 Is there an explanation of how Russell came to accept these reasons for the definability of implication? I argue in “The Origins of Strict Implication” that in fact there is less change in Russell’s views than meets the eye.

22 What I mean by “elucidatory argument” is a line of reasoning by going through which one comes simultaneously to grasp a thought and to see that it is true. I follow Burge (2005), in holding that the arguments Frege sets out in discussing his basic laws are precisely such arguments.

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Like Russell, Lewis takes the propositions of logic to be descriptive generalizations which “state”, i.e.

describe, “implication relations between premises … and the desired conclusion” (1913, 428). Moreover,

Lewis holds that “while other branches [of knowledge] find their organon of proof in … logic, this

discipline supplies its own” (ibid., 429). That is, logic is the instrument of proof in all disciplines,

including itself, which is to say that it is maximally general in application. An instrument of proof

provides standards for distinguishing between “ways of reasoning that are correct or valid, as opposed to

… other ways which are incorrect or invalid” (Lewis 1918, 324). This distinction rests on the relation of

implication: “The word [‘implies’] denotes that relation which is present when we ‘validly’ pass from one

assertion, or set of assertions, to another assertion” (ibid.) Hence “[i]t is impossible to escape the

assumption that there is some definite and ‘proper’ meaning of ‘implies’” (ibid.) Since logic is the

universal instrument of proof, “a system of symbolic logic … cannot be a criterion of valid inference

unless the meaning …of ‘implies’ which it involves are ‘proper’” (ibid.; Lewis’s emphases).

In “Implication and the Algebra of Logic” (1912), Lewis presents his most well-known disagreement

with Russell, “the paradoxes of material implication,” “~p(pq)” (*2.21) and “q(pq)” (*2.02)—

which Russell himself in Principles read as “false propositions imply all propositions, and true

propositions are implied by all propositions” (1903, 15). Lewis’s point is that, since we don’t ordinarily

accept that every statement is a logical consequence of any false statement, or that any true statement is

deducible from every statement, these theorems of Principia show that the meaning of implication in

Principia is not “proper.”

It’s unclear how much force this criticism has against Russell. Russell’s logicist project is to prove

the truths of mathematics from the truths of logic, and for Russell, as we saw above, all genuine proof

rests on truths. So, Russell is constrained not to use, in Principia, any of the implications from falsehoods

that he accepts as perfectly valid. For the purposes of Russellian logicism, an implication relation need

only be truth-preserving, and not reflect other aspects of our deductive practice.

But the “paradoxes” are not the only basis for Lewis’s criticism. A less well-known argument against

material implication is that it is not useful in inference. A material conditional can be established on the

basis that its antecedent is false, but then one would not be able to use it in inferring the consequent by

modus ponens. Alternatively, it can be established on the basis that its consequent is true, but then there

would be no point in inferring the consequent by modus ponens.23

Russell himself explicitly addresses this argument:

In fact, inference only arises when ‘not-p or q’ can be known without our knowing already which of the two alternatives it is that makes the disjunction true. Now, the circumstances under which this occurs are those in which certain relations of form exist between p and q. For example, we know that if r implies the negation of s, then s implies the negation of r. Between ‘r implies not-s’ and ‘s implies not-r’ there is a formal relation which enables us to know that the first implies the

23 This argument is discussed in one of the best accounts of Lewis’s strict implication, Curley (1975), at 521-2.

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second, without having first to know that the first is false or to know that the second is true. It is under such circumstances that the relation of implication is practically useful for drawing inferences.

But this formal relation is only required in order that we may be able to know that either the premiss is false or the conclusion is true. It is the truth of ‘not-p or q’ that is required for the validity of the inference; what is required further is only required for the practical feasibility of the inference. (Russell 1919, 153; emphases mine).

The “relations of form” are captured precisely by the axioms of Principia, which Russell here calls

“formal principles of deduction” (ibid., 149); Russell’s reply is that implications are practically useful

when they are deduced from the axioms of logic, in the sense of deducibility we considered in the

previous section. Let’s say that a material implication which can be known to be true but not on the basis

of first knowing the truth-values of the hypothesis or the consequent has “the desired epistemic status.”

Lewis’s counter-argument to this Russellian reply takes us to the heart of his objection to material

implication.24 Lewis asks, how do we know that the axioms of Principia have the desired epistemic

status? Consider one way in which we can explain the truth of Russell’s fifth axiom, (qr) ((pq)

(pr)), by giving the following argument. qr is either true or false. If qr is false, then by definition

the implication (qr)((pq)(pr)) is true. So suppose that it is true. Then either q is false or r is true.

We have now to show that the consequent (pq)(pr) is true. If r is true, then pr has to be true, so

(pq)(pr) is true. So now let’s suppose that q is false. It follows that pq is true if p is true, false if p

is false. If pq is false, then (pq)(pr) is true. So suppose that p is true. Then pr is true, so again

(pq)(pr) is true.

In this argument there are three steps in which we move from a supposition that some proposition is

false to another claim. If these three steps are all inferences, and if our inferences are to be governed by

facts about material implication, then, since a false proposition materially implies any proposition, each of

the conclusions in these transitions can legitimately be the negation of the one actually stated. For

example, an equally legitimate alternative inference to the first step of the argument would be: if qr is

false, then (qr)((pq)(pr)) is also false. But then, the truth of the fifth axiom is not established on

this supposition. Nor can we argue that since it follows by material implication from the falsity of qr

that ‘(qr)((pq)(pr))’ is both true and false, we can, by reductio, conclude that ‘qr’ is true. For, if

we allow this form of argument, then we can establish the truth of every implication from the assumption

of its falsity. So, if we reason in according to material implication, then it’s not clear that we can see that,

or explain how, all of the axioms of Principia are true. That is to say, the inferential resources required to

demonstrate that the propositional axioms of Principia are true on the basis of Russell’s definition of

implication are in conflict with the principles of deduction that can be derived from these axioms. This

24 The following argument is based on a reading of Lewis’s (1917) response to Norbert Wiener’s (1916)

criticism of Lewis’s rejection of the logic of Principia. I give a full account of this argument and its textual bases in “The Origins of Strict Implication.”

11

incoherence internal to the logic of the Principia is the deepest source of Lewis’s criticism of material

implication. This is why Lewis says that one cannot demonstrate the logical connections articulated in

the postulates of Principia “without calling on principles outside the system” (1917, 356). But this then

puts in question whether Russell’s axioms and theorems can count as logic. Since logic is maximally

general in application, it must be its own instrument of proof, and so it must supply any principles which

are needed to establish or explain the correctness of its basic axioms. Thus Russell’s system of material

implication fails to be logic, and moreover, fails according to an aspect of his own conception of logic.

It is in response to this incoherence in Russell’s logic that Lewis introduces modal notions, especially

the notion of strict implication, into logic. Let’s go back to our explanatory argument for the truth of

Russell’s fifth axiom of the propositional calculus. The problem this argument poses for material

implication is that one notorious rule of inference based on that implication allows too much to be

inferred from assumptions of the falsity of some proposition. So, what we need, in order to describe the

inferential standards that are implicit in this argument, are principles of implication that limit what may be

inferred from such assumptions of falsity. Lewis tried out several ways of doing this, settling eventually

on the notion of impossibility.25 That is, he construes, e.g., the first step in the argument as based on this

fact: given the definition of material implication, it is impossible for ‘qr’ to be false and

‘(qr)((pq)(pr))’ not to be true. That is to say, the falsity of ‘qr’ strictly implies the truth of

‘(qr)((pq)(pr))’. This impossibility precludes the correctness of inferring, from the falsity of

‘qr’, anything incompatible with the truth of ‘(qr)((pq)(pr))’.

In developing the systems of strict implication, Lewis did not provide much explanation of these

modal notions. After A Survey of Symbolic Logic (1918), Lewis embraced a version of pragmatism, and

developed a view of the a priori as based on meaning (see in particular (1923; 1929)). He then took

necessity to be based ultimately on the meanings that we associate with our inferential vocabulary. I here

pass over the details of Lewis’s views, noting only that it was assimilated, mainly by Quine, to the

positivists’ account of necessity in terms of analyticity, which will be treated below.

3. Wittgenstein’s Tractatus

Wittgenstein’s Tractatus is one of the most enigmatic philosophical texts of the twentieth century,

and there is controversy over just about every aspect of it. Perhaps the deepest enigma and most

fundamental controversy relates to Wittgenstein’s apparent characterization of the propositions of his text

as nonsense. In addition there are disputes over the targets of Wittgenstein’s criticisms and the structure

of his arguments. I do not intend to take a stance on any of these debates. I begin from the relatively

uncontroversial fact that the Tractatus seems to present, inter alia, a metaphysical account of the world as

25 Lewis starts with “intensional disjunction” in Lewis (1912), goes to “strict implication” in Lewis (1913),

and reaches “impossibility” in Lewis (1914); he stays with “impossibility” in Lewis (1918), and makes the slight change to “possibility” in Lewis and Langford (1932).

12

consisting of facts, a theory of representation centering on the notion of picturing, and, on their basis, an

account of the propositions of logic as tautologies which say nothing, an account sharply at odds with

Russell’s view of logic set out above. Moreover, it is well-documented that preoccupation with Russell’s

views of the nature of logic played a central role in Wittgenstein’s thinking leading up to the Tractatus,

and in that text we find a number of criticisms of these Russellian views.26 I will thus sketch an account

of the tautologousness of the propositions of logic as motivated by dissatisfaction with Russell’s view of

logic, and so in this respect parallel to the impetus for Lewis’s strict implication. The connection with

Lewis goes further. Lewis argued that reasoning involving modal notions is required for us to recognize

the correctness of Russell’s logical axioms. As we will see, the notions of possibility and essence play a

central role in the notion of tautology. It goes without saying that I do not take my account to do anything

like full justice to the subtleties of the Tractatus. In particular, although I will touch on the contrast

between saying and showing which Carnap transforms into a tool for overcoming traditional philosophy, I

will not analyze it.

To begin with, recall that Russell in Principles and Principia took the axioms of logic to be

descriptive generalizations. They describe which propositions stand in the relation of implication to

which propositions. More specifically, the propositions related by implication are themselves described

as having logical properties such as falsity and standing in logical relations such as conjunction and

disjunction. Now, one of the first propositions derived in Principia (*2.08) is the generalization that

every proposition implies itself. Given the definition of implication, an immediate corollary is the

generalization that every proposition disjoined with its negation is true (*2.11). Russell takes the

negation of a proposition p to be a proposition which ascribes falsity to p. So he reads this proposition of

logic as the general truth that every proposition has one of two properties, truth or falsehood.

It is plausible that Tractatus 6.111 expresses a criticism of precisely this Russellian view:

Theories which make a proposition of logic appear substantial are always false. One could e.g. believe that the words ‘true’ and ‘false’ signify two properties among other properties, and then it would appear as a remarkable fact that every proposition possesses one of these properties. This now by no means appears self-evident, no more so than the proposition ‘All roses are either yellow or red’ would sound even if it were true. (Russell 1904, 523-4)

This attribution is supported by the fact Russell writes, shortly after Principles, that “some propositions

are true and some false just as some roses are red and some white …. What is truth and what falsehood,

we must merely apprehend, for both seem incapable of analysis” (1904, 523-4).

Let’s focus on the contrast in this passage between “remarkable” and “self-evident” fact. If truth and

falsity are unanalyzable properties, then the “fact” described by Russell’s logical truth, that every

proposition has exactly one of these properties, would supposedly be “remarkable” rather than “appear

26 This might be as uncontroversial as claims about the Tractatus can be; see Griffin (1980), Ricketts (1996),

Ricketts (2002), and Proops (2002).

13

self-evident.” What does Wittgenstein have in mind here? Suppose someone were to say, “Isn’t it

remarkable that all roses have just one of two colors?” This is an unexceptional thing to say, and one way

of understanding why is that we see no reason why roses couldn’t also be, say, green or black. If this is

right, then Wittgenstein is suggesting that we have reason for thinking that propositions could not be

anything other than either true or false.

Why should we accept this? Why should Russell accept this? Here are two (somewhat speculative)

answers to the second question. First, in Principles §17 Russell rejects the idea of establishing the

independence of a logical axiom by supposing it false and deducing consequences from that supposition,

“[f]or all our axioms are principles of deduction; and if they are true, the consequences which appear to

follow from the employment of an opposite principle will not really follow, so that arguments from the

supposition of the falsity of an axiom are here subject to special fallacies” (1903, 15). Russell clearly

thinks that some difficulty stand in the way of supposing, i.e., conceiving, a logical law to be false, that

doesn’t apply to conceiving of the falsity of even an axiom of Euclidean geometry. If in this sense we

can’t conceive of the falsity of a logical law, then we have a reason for thinking that logical laws couldn’t

fail to hold. Second, as we saw above, one of Russell’s proposals for explicating modality is that a

proposition is necessary if it is deducible from the laws of logic, possible if its negation is not deducible

and so impossible if its negation is deducible, where p is deducible from q just in case the conditional

‘qp’ is derivable from the axioms of logic. By Principia *2.08, every axiom is deducible from itself, so

every law of logic is deducible from the laws of logic. By Principia *2.12, that every proposition implies

its double negations is derivable. Hence the negation of the negation of any axiom is deducible, and so

the negation of any axiom of logic is impossible.

If these two pieces of speculation are right, then we can take Wittgenstein to be pointing to a tension

between Russell’s view of logical propositions as descriptive generalizations and his rather inchoate sense

that they differ in kind from other types of generalizations. Moreover, I take it that in suggesting that it

should be “self-evident” that propositions are either true or false, Wittgenstein means that it should be

inconceivable or impossible for propositions to fail to be true or false. That is to say, what is distinctive

about this proposition of logic is its modal status. Indeed this modal status distinguishes all of logic from

any non-logical truths, however general.

The picture theory of propositions may be taken to explain this inconceivability.27 Propositions are

pictures of facts, and what it is to be a picture is to agree or disagree with the facts. That is, the nature of

picturing, or the essence of a picture, is to agree or disagree with the facts. Since truth is agreement with

the facts and falsity disagreement, it is essential to a proposition that it is either true or false, and so

inconceivable that it could fail to be either.

27 The following sketch owes much to Warren Goldfarb’s (amazingly still) unpublished paper, “Objects,

Names, and Realism in the Tractatus.” Note that on Goldfarb’s view, the account is eventually undermined in the Tractatus.

14

The notion of fact is a central aspect of the metaphysics of the world set out in the initial sections of

the Tractatus. The substance of the world consists of objects, which are eternal, necessarily existing, and

simple in the sense of not having parts. It is essential to objects that it is possible for each to combine or

fail to combine with others in determinate configurations. A determinate configuration of objects is an

atomic fact. The obtaining of any atomic fact is independent of the obtaining of all other atomic facts;

whether or not any one holds has no bearing on whether or not any other holds. (Non-atomic) facts

consist of combinations of the obtaining of atomic facts, and the world is the totality of facts (2, 1.1).

Language pictures reality. Only facts can picture facts. In a picture there is a combination of

pictorial elements, and it is the obtaining of this fact composed of pictorial elements that enables the

picture to represent. The picturing of language has two components. At the bottom level of language

there are names, capable of combining into facts that are elementary propositions. The fact that names

are arranged in a determinate way in an elementary proposition represents that objects are arranged in the

same way in a possible atomic fact. This “same way” is the common logical form shared by the

propositional picture and the possible atomic fact. By combining into a picture of a possible atomic fact,

names in an elementary proposition are representatives of objects that can be combined in that possible

atomic fact. The sense of an elementary proposition is what it represents, a possible atomic fact. If the

possible atomic fact represented obtains, then the representing elementary proposition is true, otherwise

false (4.25); thus an elementary proposition is essentially either true or false.

Since the world is the totality of atomic facts that obtain, the world can be completely described by

specifying which elementary propositions are true and which false (4.26). So, what any non-elementary

proposition pictures cannot go beyond what the totality of elementary propositions represent. Hence

every proposition represents in virtue of the representation of some set of elementary propositions.

Specifically, given a finite set of n elementary propositions, there are 2n possible ways for the n possible

atomic facts represented to hold or fail to hold (4.27), and, correspondingly, 2n ways for the n atomic

propositions to be true or false (4.28). Each way for the n atomic propositions to be true or false is a

truth-possibility of those atomic propositions. A proposition that is analyzed into these elementary

propositions then represents the facts by expressing agreement and disagreement with each of these 2n

truth-possibilities. That proposition is true if any of the truth-possibilities with which it agrees obtains,

false otherwise. The sense of that proposition consists of these agreements and disagreements with

atomic propositions. In this way a proposition is a truth-function of elementary propositions. But one

and the same truth function of elementary propositions can be expressed in different ways, in which

different “logical constant” signs occur. So the logical signs are not representatives of any objects; no

objects play any role in how propositions represent (4.0312).

A proposition corresponds to a class of truth-possibilities, those with which it agrees; these are the

proposition’s truth-conditions (4.41). Since there are 2n truth-possibilities for n elementary propositions,

and each proposition analyzable into these elementary ones either agrees or disagrees with each of these

15

truth-possibilities (4.42), there 22n

possible distinct propositions analyzable into these elementary ones,

and, most importantly, one of these agrees with every truth-possibility and another disagrees with every

truth-possibility. These propositions are, respectively, a tautology and a contradiction (4.46). A

tautology is true no matter which elementary propositions are true; that is, it is true no matter what atomic

facts obtain, no matter how the world is. Its truth is thus independent of how the world is; it is not made

true by correctly picturing the world. The same holds for contradictions with falsity in place of truth. For

such reasons tautologies and contradictions “say nothing,” have “no truth-conditions,” “lack sense”

(4.461), “are not pictures of reality,” and “do not represent any possible situations” (4.462). Nevertheless

it is inconceivable for a tautology to be false (or a contradiction true), for two reasons: to be a proposition

is to agree or disagree with truth-possibilities of elementary propositions, and it has to be possible to

agree (and to disagree) with all truth possibilities. On this account, the essence of propositional

representation and of combination is prior to and determines the necessity of the propositions of logic.

There is a sense in which Wittgenstein’s account of modality is a minimal departure from Russell.

Russell had attempted to reduce all modal concepts to logical ones; Wittgenstein, in contrast, takes what

is distinctive about logic to be its modal status, which in turn rests on the nature of representation. But

Wittgenstein takes the necessity of logic to be the only kind of necessity (6.37).

I turn now to comment briefly on the relationships among necessity, apriority, and analyticity in the

Tractatus. In 6.3211, Wittgenstein writes, “as always, what is certain a priori proves to be something

purely logical,” suggesting an identification of the two. I take it that this identification is a consequence

of taking a priori truth to be explained in terms of logical truth. Thus, if a proposition is knowable a

priori, then its truth depends on no state of affairs in the world. So if knowledge of the truth of a

proposition requires access to facts of any sort, no matter whether this access is through sensory

experience or rational intuition, it would not count as a priori knowledge. From Wittgenstein’s

perspective, Russell’s view of knowledge of the laws of logic as based on non-sensory experience of

abstract non-sensible entities is not a view of a priori knowledge.

It might be thought that since what makes Wittgenstein’s tautologies true is not the world, it must be

their meanings. That is, tautologies are analytic truths. It seems to me that there is a sense in which this

claim might be true, but it’s a bit delicate to make out. To begin with, how are tautologies true in virtue

of meaning? There is, of course, the view that logical truths are true in virtue of the meanings of the

logical constants. But as we saw for Wittgenstein the logical constants are not representatives. He also

claims that they have no sense. So it’s unclear that they have any meaning in virtue of which logical

propositions are true.

Now Wittgenstein does say that “It is the peculiar mark of logical propositions that one can recognize

that they are true from the symbol alone” (6.113). What he has in mind here might be this. While logical

16

constants have neither reference nor sense, they do express operations.28 These operations map patterns

of agreements with truth-possibilities to a pattern of agreement with truth-possibilities. And it is on the

basis of such operations expressed by signs in the symbol for a proposition that that proposition agrees

with all truth-possibilities, i.e., is a tautology. Thus we might think that what underlies our capacity to

recognize a logical proposition as true from its symbol alone is our grasp of the operations expressed by

logical constants. In this sense we can take these operations to constitute the meanings of the logical

constants. On this proposal, the propositions of logic are analytic because we recognize that they are true

in virtue of grasping the meanings (in this sense of meaning) of the logical constants.

But this proposal doesn’t show that tautologies themselves are in some sense true in virtue of the

truth-operations. A tautology is true in virtue of the essence of propositional representation: agreement or

disagreement with truth-possibilities of elementary propositions. So it is unthinkable that there is no

proposition that agrees with all the truth-possibilities of a set of elementary propositions. This is the basis

for the truth of tautologies, and in this account truth-operations play no role. Their role is to enable us to

recognize various symbols as expressing tautologies (6.1262).

There is another conception of analyticity on the basis of which we can take Wittgensteinian

tautologies to be analytic: the Leibnizian-Kantian one of conceptual containment, where the concept of

the predicate is a part of the concept of the subject. Once this containment is made explicit, the analytic

judgment can be seen as akin to stuttering: to judge that all bachelors are unmarried is in fact to judge that

all unmarried males are unmarried, which is perilously close to repeating one self by judging that all

unmarried are unmarried.29 Wittgenstein’s notion of tautology is ultimately modeled on this notion of

conceptual containment. What I have in mind is Wittgenstein’s account of logical consequence: “If p

follows from q, the sense of ‘p’ is contained in the sense of ‘q’” (5.122). If we express this consequence

by the conditional ‘if q then p’, then we have expressed a tautology, in which the consequent is merely

repeating a part of what is expressed by the antecedent. Wittgenstein puts this point thus; “If a god

creates a world in which certain propositions are true, then by that very act he also creates a world in

which all the propositions that follow from them come true” (5.123).

None of the preceding points, however, can be taken at face value, because of Wittgenstein’s

say/show distinction. Two of the key terms that occur in the Tractatus, which I have used in discussing

picturing and logic, are ‘fact’ and ‘object’. Wittgenstein tells us that these terms (among others) “signify

formal concepts” (4.1272). Formal concepts are “pseudo-concepts,” and wherever words for such

pseudo-concepts are used “as … proper concept word[s], there arise nonsensical pseudo-propositions”

(ibid.) Specifically, nonsense results by trying to express that something falls under a formal concept in a

proposition. What such a pseudo-proposition tries to express is rather shown in the symbol for that which

28 See Hylton (1997) 29 See Dreben and Floyd (1991)

17

falls under the formal concept (4.126). Alongside formal concepts there are formal properties, which also

lead to nonsensical propositions. A crucial example consists of “internal properties”—“properties of the

structure of facts” (4.122). According to Wittgenstein, “[a] property is internal if it is unthinkable that its

object does not possess it” (4.123). Now, as we have outlined the Tractatus’s views, the basis of the

necessity of logic is that it is inconceivable that an atomic fact can neither hold nor fail to hold, or that an

elementary proposition can fail to be either true or false. So in our exposition we seem to have ascribed

formal properties to atomic facts and to elementary propositions. But, according to 4.124, “[t]he

existence of an internal property of a possible state of affairs is not expressed by a proposition, but it

expresses itself in the proposition which presents that state of affairs, by an internal property of this

proposition.” However, [i]t would be as nonsensical to ascribe a formal property to a proposition as to

deny it the formal property” (ibid.) Rather, “[t]he expression of a formal property is a feature of certain

symbols” (4.126). So according to the Tractatus, the words occurring in it, on which we relied in our

exposition, are nonsense, just like our exposition itself.

This takes us to a final point about apriority. Perhaps the core of the notion of an a priori truth is the

irrelevance of worldly facts to its justification. Now since it’s the essence of propositional picturing,

rather than any fact pictured, that makes a tautology true, one might conclude that tautologies must be a

priori, since not justified by worldly facts. One might then move on to the further conclusion that what

justify tautologous propositions must be facts about the mechanism of linguistic representation. What we

have just gathered from the show/say distinction, however, is that there are no such facts; the sentences

using which we have attempted to describe this mechanism, according to the Tractatus, are nonsense.

The conclusion seems to be that there are no facts that justify the propositions of logic; perhaps the notion

of justification simply doesn’t apply to them, and so they are neither knowable a priori nor knowable a

posteriori.

4. The Vienna Circle and Carnap’s Logical Syntax of Language

There are, we now know, significant synchronic and diachronic differences among the doctrines held

by members of the Vienna Circle.30 Here my focus will be on the Tractatus’s influence on the Vienna

Circle’s, and in particular on Carnap’s, views of modality.31

Through the influence of A. J. Ayer’s Language, Truth, and Logic (1936), logical positivism is

nowadays frequently taken to be an updating of Humean empiricism with the techniques of modern

mathematical logic. A notorious component of this position is the verifiability criterion of cognitive

significance: a sentence can be meaningful only if it is associated with a method of verification ultimately

30 See, inter alia, Coffa (1991), Friedman (1999), Creath (1999), Richardson (2004), Goldfarb and Ricketts

(1992), Awodey and Carus (2007), and Carus (2007). 31 For a balanced and informative account of how the Vienna Circle received Wittgenstein’s Tractatus, see

Uebel (2006).

18

based on sensory experience. On the basis of this criterion the Circle rejected metaphysical sentences as,

not false, but meaningless nonsense. The verification principle comes from the empiricist view that sense

experience is the only source of genuine knowledge about the world. The main problem that the Circle

saw for empiricism is how to account for knowledge of logic and mathematics, both indispensable to

modern science. Experience might always be different from the way it is, so any truth based on

experience is contingent. In contrast, we have no clear conception of how logical and mathematical truths

might be false. Thus, logico-mathematical knowledge seems a priori, and so to require some faculty of

rational intuition, paving the way to metaphysics. Indeed, logic and mathematics seem no better able to

pass the verifiability test than metaphysics.

The Circle saw, in the Tractarian view of logic as tautology, the key to a consistent empiricism. Since

tautologies owe their truth, not to correct depiction of the world, but to the nature of linguistic

representation, our knowledge of logic does not rest on the sensory sources of genuine knowledge of

worldly facts. Rather, it rests on knowledge of how we represent the world in language, of the rules or

conventions (that we tacitly accept as) governing the use of language. The apparent apriority and

necessity of logic can now be taken to have a linguistic, rather than factual, origin. Of course the

sentences of metaphysics also have no empirical content. So the rejection of metaphysics depends on a

distinction between kinds of contentlessness based on the Tractarian distinction between the senseless and

the nonsensical. The nonsense of metaphysics results from violations of the rules of language, while the

senselessness of tautologies is a byproduct of rules of the language.32

The view just outlined—call it classical positivism—was indeed briefly espoused by the Circle. But

the positivists themselves were aware of an array of difficulties with these classical doctrines, and soon

moved away in a number of diverging directions. For our purposes, the most salient problem of classical

positivism is to show that mathematics, like logic, is tautologous,33 that is, to carry out a type of logicist

reduction of mathematics, to tautologies rather than Frege’s or Russell’s formulations of logic. Carnap

attempted such a reduction, using David Hilbert’s idea of meta-mathematics. Technical difficulties

eventually led Carnap to abandon many details of the Tractarian framework.34 Language becomes

conceived as “a system of rules” (Carnap 1937, 4) not explained in more fundamental terms of picturing

extra-linguistic facts. The study of language thus conceived is “logical syntax.” The notion of tautology,

sentences true in virtue of the mechanism of representation, is replaced by a syntactic notion of

analyticity, sentences formally derivable from the rules of language alone. Logico-mathematical

sentences are analytic, mere auxiliaries for the confirmation of theoretical empirical sentences.

32 See in particular Carnap (1931). 33 This goes against the Tractatus. See Floyd (2005) for arguments against taking the Tractatus to espouse

any form of logicism. 34 For details see especially Awodey and Carus (2007) and Carus (2007).

19

At first these changes still subserve the project of a consistent empiricism. By Syntax, Carnap has

(mostly) abandoned classical positivism.35 For our story, I focus on a form of criticism of traditional

philosophy distinct from the classical charge of nonsensical violations of rules of language. It is directed,

not only at metaphysics, but at controversies, especially over the foundations of mathematics, among

philosophers of an anti-metaphysical orientation, such as members of the Vienna Circle. Carnap found

these debates inconclusive and fruitless, with the parties involved making unclear claims apparently at

cross-purposes. They seem, in fact, just as intractable and confused as disputes over traditional

metaphysical problems. 36 Carnap’s diagnosis of the sterility of such debates seems to be that they stem

from a kind of illusion over the subject matter of philosophical sentences. These sentences “seem to

concern … objects, such as the structure of space and time, the relation between cause and effect, … the

necessity, contingency, possibility or impossibility of conditions, and the like” (Carnap 1935, 59-60). But

this is a “deceptive appearance”; they “really concern linguistic forms” (ibid., 60).37

One source of this diagnosis is the Tractarian notion of a formal property. Recall that, according to

Wittgenstein, the ascription of formal properties in a sentence results in nonsense (4.124), and that “[t]he

expression of a formal property is a feature of certain symbols” (4.126). Now, Carnap rejects

Wittgenstein’s say/show distinction and takes what is shown in language to be features of expressions that

can be described in a meta-language. So formal properties become syntactical properties of expressions

that, somehow, appear to be properties of objects. So formal properties become syntactical properties of

expressions that, somehow, appear to be properties of objects. Slightly more precisely, these are

properties of objects correlated with syntactic properties of expressions in such a way that they hold of an

object just in case the correlated syntactic property holds of a designation of that object. Carnap calls

them “pseudo-object” or “quasi-syntactical” properties. Sentences ascribing pseudo-object properties are

“pseudo-object-sentences” of “the material mode of speech.” They are “like object-sentences as to their

form, but like syntactical sentences as to their contents” (ibid.)

In the case of debates in the foundations of mathematics, for instance, “in the material mode we speak

about numbers instead of numerical expressions,” and this tempts us “to raise questions as to the real

essence of numbers” (ibid., 78-9). Once such questions arise, so does the possibility of such irresoluble

disputes as that between logicists and formalists. The way out of such impasses is to translate pseudo-

object-sentences into their syntactic correlates, sentences in “the formal mode of speech.” The dispute

just mentioned is then dissolved by transformation into two mutually compatible claims about numerical

expressions in distinct formal languages.

35 See Carus (2007) for a detailed examination of tensions in Syntax. 36 See Carnap (1963, 45ff; 1937, xiv-xv). 37 Compare P. M. S. Hacker’s account of the central aspect of the Wittgenstein’s later views, epitomized in the

title of chapter VII of Hacker (1972): “Metaphysics as the Shadow of Grammar.”

20

Modal sentences are also “veiled syntactical sentences” (ibid., 73). We “usually apply modalities …

to conditions, states, events, and such like” (ibid.), using sentences like,

That A is older than B, and B is older than A, is an impossible state.

The formal mode translation of this sentence is:

The sentence ‘A is older than B, and B is older than A’ is contradictory.

More generally, “[i]mpossibility is a quality to which there is a parallel syntactical quality, namely

contradictoriness, because always and only when a state is impossible, is the sentence which describes

this state contradictory”; hence it is a pseudo-object property. The translations of other modal expressions

into syntactical terms are straightforward: “As possibility is the opposite of impossibility, obviously the

parallel syntactical term to ‘logically possible’ is ‘non-contradictory’ …. Analogously, we translate

‘logically necessary’ into ‘analytic’” (ibid., 77).

So far Carnap’s diagnosis of philosophical illusion seems to presuppose that the material mode

“suggests something false … and … the formal mode … tells the unvarnished truth” (Coffa 1991, 325;

emphases mine). In particular, the claim that modal predicates are quasi-syntactical seems to tell us that

necessity, for instance, really is analyticity, and that’s precisely what, according to popular wisdom,

positivism holds. But this view of Carnap’s criticisms is problematic. Carnap uses phrases such as

‘really about’ and ‘object’ to formulate his criticism, but these are the very words that generate

paradigmatic pseudo-object sentences.38 So these criticisms are, by Carnap’s own standards, themselves

in the material mode of speech, i.e., they contain pseudo-object sentences. Carnap takes no pains to hide

this; he explicitly notes in Part V of Syntax that “[e]ven in this book, and especially in this Part, the

material mode of speech has often been employed” (1937, §81, 312). Carnap specifically characterizes

his remarks about what pseudo-object properties really apply to and about philosophical illusion as

“informal,” in contrast to the formal syntactic definition of quasi-syntacticality (1937, §63). Thus when

Carnap says that philosophical sentences are really about language, he recognizes that this is no less

potentially misleading than those very philosophical sentences.

What then is Carnap’s ground for preferring the formal mode? Note to begin with that according to

Carnap the “material mode of speech is not in itself erroneous; it only readily lends itself to wrong use”

(1937, 312). Indeed, “if suitable definitions and rules for the material mode of speech are laid down and

systematically applied, no obscurities or contradictions arise” (ibid.; my emphasis). The reason why

questions generated by material-mode talk lead to apparently irresoluble disputes is that they are posed in

natural languages, which are “too irregular and too complicated to be actually comprehended in a system

of rules” (ibid., 312).

This points to Carnap’s view of “controversies in traditional metaphysics”: “there seemed hardly any

38 On ‘about’ see Carnap (1937, 290), example 12a; ‘object’ is a “universal word” which, used in the material

mode of speech, produces pseudo-object sentence, see Carnap (1937, 293-5).

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chance of mutual understanding, let alone of agreement, because there was not even a common criterion

for deciding the controversy” (1963, 44-5). If indeed there are no common criteria for deciding

metaphysical controversies, then it would be pointless, irrational, to continue these disputes in the form of

trying to find out who is right. A “question of right or wrong must always refer to a system of rules”

(1939: §4, 7), and logical syntax is the construction of languages as systems of rules. Thus the aim of

syntax is to set out criteria that would rationalize pointless philosophical debates. Specifically, Carnap

offers the parties to philosophical disputes the possibilities of adopting a common set of rules for

adjudicating their disagreement, or of reconceiving their opposition, not as a disagreement over the truth

of a doctrine, but as different recommendations about what language, what system of rules, to adopt.

Either way, the dispute would acquire a clear point. This is the reason for preferring the formal mode.

Now it is natural, at this point, to ask: what is the basis of Carnap’s view of the rationality of

disputes? It’s a short step from such a question to intractable philosophical debates over the true nature of

rationality. Thus, Carnap’s conception of rationality is also not a theoretical claim but a practical

proposal. We can take Carnap to ask his audience to compare the state of their philosophical debates with

that of his precise syntactical investigations, and to offer philosophers a way out of the fruitless debates in

which they are stuck. He in effect says to philosophers: you don’t have to take yourself to be advancing a

substantive thesis about reality against other such substantive theses, because I can offer you a way of

looking at what you want, in which it will no longer be unclear what exactly getting it involves, because

you’ll be doing something other than what you took yourself to be doing. In the words of another

philosopher, Carnap’s “aim” is “[t]o shew the fly the way out of the fly-bottle.”39 Thus, Carnap is not

engaged in the same enterprise as traditional philosophy at all; rather, he proposes an activity, syntactical

investigation, to replace traditional philosophizing; he urges philosophers to “change the subject” (Rorty

1982, xiv).40,41

39 Wittgenstein (2001 [1953], §309). 40 This reference to Richard Rorty is not intended to be frivolous. In (1986), Rorty argued that skepticism

arises from assuming that an explanation of the objective truth of language and thoughts requires some “third” thing independent of the “meanings of words and the way the world is” (at 344). So skepticism is defeated when we “realize that the tertia which have made us have skeptical doubts about whether most of our beliefs are true are just not there” (ibid.; emphases mine). That is to say, at this point Rorty took skepticism to be the product of a philosophical illusion, about the existence of tertia, and the refutation of skepticism to follow from the fact that these entities don’t exist. Later however, Rorty corrected himself:

I should not speak, as I sometimes have, of ‘pseudo-problems,’ but rather of problematics and vocabularies which might have proven to be of value but in fact did not. I should not have spoken of ‘unreal’ or ‘confused’ philosophical distinctions, but rather of distinctions whose employment has proved to lead nowhere, proved to be more trouble than they were worth. For pragmatists, the question should always be ‘What use is it?’ rather than ‘Is it real?’ Criticism of other philosophers’ distinctions and problematics should charge relative inutility rather than ‘meaninglessness’ or ‘illusion’ or ‘incoherence’ Rorty (1998, 45, emphases mine ).

41 Note how Carnap’s pragmatic attitude towards traditional philosophy is of a piece with his Principle of Tolerance (1937, §17, 52).

22

The upshot of this radical pragmatism for Carnap’s theory of modality is that any claim to the effect

that, e.g., for Carnap the property of necessity is really analyticity is in the material mode and misleading.

The significance of Carnap’s theory consists in the philosophical perplexities displaced by the syntactic

explication of necessity as analyticity. Let’s look at two philosophical tangles that Carnap proposes to

treat with his theory of modality in Syntax.

First, Carnap sees the dispute between Russell and Lewis on the nature of implication as similar to

debates over the foundations of mathematics. He characterizes Russell’s “opinion” that implication “is a

relation between propositions” as a material mode claim that is correct if ‘proposition’ is understood as

“that which is designated by a sentence” (Carnap 1937, 253). Once we think of implication in such a

way, we are tempted to ask, what exactly is this relation? Since, “‘to imply’ in the English language

mean the same as ‘to contain’ or ‘to involve’,” we are tempted to take it to be “the consequence-relation”

(ibid., 255). Succumbing to this temptation, “Lewis and Russell—they are agreed on this point—look

upon the consequence-relation … as … on the same footing as sentential connectives” (ibid., 254). This

leads to wrangles about which propositions containing the implication symbol correctly describe the

logical consequence relation, i.e., which logical system is correct.

The dissolution of this dispute rests on Carnap’s explications of ordinary imprecise conceptions of

logical consequence in precise syntactical metalinguistic terms. From the perspective of such

explications, Carnap takes Lewis to be right in the following sense. If the consequence relation is to be

expressed by a “sentential connective,” say ‘<’, so that “‘A < B’ is demonstrable if ‘B’ is a consequence

of ‘A’,” then neither “Russell’s implication” nor any “of the so-called truth-functions … can express the

consequence-relation at all” (ibid.) Thus, Lewis “believed himself compelled to introduce intensional

sentential connectives, namely, those of strict implication and of the modality-terms” (ibid.) But, given

Carnap’s explications of consequence, one sees that Lewis’s move is not compulsory. One can, instead,

distinguish “the consequence-relation [as] a relation between sentences” from “implication [which] is not

a relation between sentences”; in the formal mode, “‘consequence’ [is] a predicate of the syntax-

language,” while “‘’ is a symbol of the object-language” (ibid., 253-4; emphases in the text). Thus,

pace Lewis, we are not forced to “think that the symbol of implication ought really to express the

consequence-relation, and count it as a failure on the part of this symbol that it does not do so” (ibid.,

255). The language of Principia is perfectly “adequate for the construction both of logic and of

mathematics,” and “in it necessarily valid sentences can be proved and a sentence which follows from

another can be derived from the former” (ibid., 253). While there is nothing objectionable in the

“requirement that a language be capable of expressing necessity, possibility, the consequence-relation,

etc.,” we do not, in the case of Principia, have to insist that to satisfy this requirement we need “anything

supplementary to [it],” because we can simply “formulat[e its] syntax” (ibid., 253-4).42

42 Carnap’s view here bears comparison with Robert Brandom’s (1994; 2000) view that logical vocabulary

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Given this context for Carnap’s theory of modality in Syntax, we can see that Carnap is not claiming

that necessity is a syntactic property, but rather proposing the use of the meta-linguistic predicate

‘analytic’ in the place of the object language predicate ‘necessary’, in order to explicate our imprecise

ideas of logical consequence. The point of the proposal is to allow Russellian extensional logicians and

Lewisian modal logicians to see that there is no need to argue over whose logic is the right one.43

Second, Carnap addresses a problem deriving from what he takes to be Wittgenstein’s notions of

essential or internal properties. These are defined in the material modes as follows: a “property of an

object c is called an essential property of c, if it is inconceivable that c should not possess it (or: if c

necessarily possesses it)” (Carnap 1937, 304). This problem is particularly significant in the subsequent

history of modality:

Let us take as the object c … the father of Charles. [B]eing related to Charles is an essential property of c, since it is inconceivable that the father of Charles should not be related to Charles. But being a landowner is not an essential property of the father of Charles. For, even if he is a landowner, it is conceivable that he might not be one. On the other hand, being a landowner is an essential property of the owner of this piece of land. For it is inconceivable that the owner of this piece of land should not be a landowner. Now, however, it happens to be the father of Charles who is the owner of this piece of land. [Thus] it is both an essential and not an essential property of this man to be a landowner. (Ibid.)

Carnap proposes to dissolve this apparent contradiction by translation of the second-order pseudo-object

property of being an essential property to the syntactical property of relative analyticity: a predicate is

analytic relative to a sequence of “object designations” just in case the sentence resulting from filling the

place-holders of the predicate with these terms is analytic. Applying this translation scheme to the

problematic essential properties of the example, the contradiction disappears because “‘landowner’ is an

analytic predicate in relation to the object-designation ‘the owner of this piece of land’, but it is not an

analytic predicate in relation to the object-designation ‘the father of Charles’” (ibid.) We now see that the

“fault of” the material mode definition of essential property “lies in the fact that it is referred to the one

object instead of to the object-designations, which may be different even when the object is the same”

(ibid.)

5. Quine, I: the Carnapian Background

The roots of Quine’s critiques of modality go back to the phase of his philosophical development

when he was “very much [Carnap’s] disciple” (1976a, 41). Specifically, in lectures in 1934 expounding

play primarily an expressive role in making inferential proprieties explicit. The syntactic correlate of Lewis’s strict implication connective is the consequence predicate of the syntax language, and we have already seen what syntax language predicates are the correlates of Lewis’s other modal connectives: the impossibility connective is correlated with ‘contradictory’, the possibility connective with ‘non-contradictory’, and the necessity connective with ‘analytic’ Carnap (1935, 73-4, 77; 1937, §69, 250-1).

43 I am very much indebted to Gary Ebbs for the formulation of this point.

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Carnap’s Syntax views,44 Quine characterizes modal expressions as a “quasi-syntactic,” “material idiom”

whose use leads us to lose

sight of what we are talking about; … we appear to be talking about certain nonlinguistic objects, when all we need be talking about is the sign or signs themselves which are used for denoting those objects. [T]he expressions of modality … are for all the world properties not of names, or sentences, but of things or situations. These modality-properties or pseudo-properties then involve us in difficulties from which we turn to metaphysics for extrication. (1990 [1934], 98)

In particular, use of modal expressions lead us to “talk of a realm of possibility as distinct from the realm

of actuality,” and this raises “problems as to how fragments of the possible are actualized, and what it

means for a possibility to be actualized, and why certain possibilities are actualized rather than others”

(ibid., 94-5). The remedy, naturally, is syntax; when “the syntactic formulation is used, so that whatever

in effect concerns language is made explicitly to concern language, these difficulties vanish” (ibid., 98,

emphases mine). As we will see, Quine’s rejection of modality is decisively shaped by this Carnapian

view that modal properties are pseudo-object properties, and by Carnap’s replacement of necessity by

(syntactic) analyticity.

The idea of “losing sight of what we are talking about” suggests that the problem is forming a false

view of what we’re talking about. This suggestion seems confirmed by Quine’s going on to say, “in the

quasi-syntactic idiom we appear to be talking about certain nonlinguistic objects.” At this point one

expects Quine to go on to tell us what we are really talking about. But that’s not what Quine tells us.

Instead, he says that we don’t have to be talking about what we might think we’re talking about. That is

to say, there is an alternative to our conception of the subject matter of our modal discourse. Moreover,

Quine urges that this alternative conception is better, because it does not lead to metaphysical difficulties.

In other words, this alternative is better, not because it is correct, identifies the true subject of our talk, but

because it keeps us out of trouble. This is confirmed by what Quine says at the end of the passage, that in

syntactic formulation “whatever in effect concerns language is made explicitly to concern language.”

Quine does not say that the quasi-syntactical idiom “in fact” concerns language, but only “in effect.”

That is, Quine suggests that we don’t actually know what quasi-syntactical sentences are about, but also

that, given a syntactic translation, we can take them “in effect” to be about language. Thus, Quine’s

standard for favoring the syntactic over the quasi-syntactic alternative is a pragmatic one, just as Carnap’s

is.

But Quine’s pragmatism is not quite the same as Carnap’s. Carnapian pragmatism, as we saw,

operates at the level of a choice between pursuing traditional philosophical problems and constructing

linguistic frameworks. The choice is: do we change the subject or not? The relation of the successor

subject to the predecessor can be one of explication, but needn’t be. Quinean pragmatism, in contrast,

44 The significance of these lectures was brought to my attention by Hylton (2001). Those familiar with

Hylton’s essay will see that my reading of this text differs in a number of respects from his.

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applies to the choice between competing scientific hypotheses. One hypothesis is that our talk of

possibility and impossibility commits us to positing a realm of possibilia and impossibilia alongside

actual things. The other hypothesis is that this talk only commits us to actual concrete and abstract

entities, including the objects of syntactic claims. The first hypothesis not only multiplies entities, and so

runs afoul of Occam’s Razor, but involves us in intractable issues about, inter alia, the properties and

individuation of these entities. The second has neither the additional ontological commitments nor the

burden of answering these additional questions. Thus, our best scientific methodology dictates that we

adopt the second hypothesis over the first.45

One of the metaphysical problems of modality Quine mentions is: what does it mean for a possibility

to be actualized? Much of Quine’s critique of modality stems from this problem. Quine’s objection, at

bottom, is that he doesn’t see any clear meaning in claims about what is possible or necessary. Quine

divides such claims into two types, and his criticisms fall correspondingly into two groups. The first type

consists of claims ascribing necessity or possibility to statements, in traditional terminology, ascriptions

of necessity de dicto, for example,

It is necessary that 9 > 7

It is possible that the number of planets is less than 7

The second type consists of claims ascribing modal properties to individuals, traditionally termed claims

of necessity de re, such as

9 is necessarily greater than 7

and generalizations involving modal properties, such as

Something is possibly less than 7

As I mentioned, the target of Quine’s critique rests on an account of necessity in terms of analyticity,

an account original with Lewis, “sharpened in formulation by Carnap” (1960, 195). The principal thesis

of the account is that “the result of applying ‘necessarily’ to a statement is true if, and only if, the original

statement is analytic” (Quine 1943, 121). Analyticity here is not Carnap’s syntactic conception but

Quine’s well-known account: “a statement is analytic if by putting synonyms for synonyms … it can be

turned into a logical truth,” where a “logical truth is … deducible by the logic of truth functions and

quantification from true statements containing only logical signs” (1947, 44, 43).46 In addition, note that

45 In one sense, this is also a charge of illusion. But if it is a case of illusion here, it is of the same kind as the

illusion we were under when we thought that the existence of aether explains some electromagnetic phenomena, or the existence of four humors explains some physiological phenomena. The upshot of this is that from Quine’s perspective the danger of the material mode is that it may lead us to commitments that are to be rejected as false on our best theory of the world. This is the perspective from which to grasp Quine’s rejection of modality. What are rejected are the apparent commitments of modal talk in the material mode, and so with it that material mode talk itself.

46 Note that for Quine here deducibility “can be expanded into purely syntactical terms by an enumeration of the familiar rules, which are known to be complete; and the reference to ‘logical signs’ can likewise be expanded by enumeration of the familiar primitives” (1947, 43). Note in addition that Quine later gave what he takes to be a

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although Quine rarely explicitly mentions it, there is a link between this notion of analyticity and a

conception of apriority.47 This goes through a view of the relation between synonymy and understanding:

“[t]o determine the synonymity of two names or other expressions it should be sufficient to understand

the expressions; but to determine that two names designate the same object, it is commonly necessary to

investigate the world” (Quine 1943, 119). Let’s call this view the synonymy thesis. Given this thesis and

the account of analyticity, it follows that an analytic statement can be determined as true without

investigating the world.

Given this background, Quine argues, against de dicto modal claims, that there is no clear distinction

between necessary truth and plain truth, because there is no clear distinction between analytic truth and

plain truth. I will not discuss these Quinean criticisms, since they rest entirely on Quine’s rejection of a

clear analytic/synthetic distinction, a topic with no specific connection with modality. The problem with

de re modal claims is that if one tried to make sense of them in terms of the analyticity conception of

necessity, then they either do not describe concrete material objects, or do not have determinate truth

conditions. Moreover, to make sense of such claims one must abandon the analyticity conception of

necessity, and adopt questionable non-trivial forms of essentialism, what Quine calls “Aristotelian”

essentialism.

6. Quine II: The Substitution and Quantification Arguments

As first presented in “Notes on Existence and Necessity,” (1943)48 Quine’s critique seems to be a

two-part argument. The first part is based on two things. One is the logical law of the “indiscernibility of

identicals” (ibid., 113; emphases in text). The other is the notion of purely designative occurrences of a

singular term, or “name” in Quine’s terminology in this paper. He writes, “The relation of name to the

object whose name it is, is called designation …. An occurrence of the name in which the name refers

simply to the object designated, I shall call purely designative” (ibid., 114). If a name occurs purely

designatively in a statement, then that statement says something, truly or falsely, of the object designated

by that name. Moreover, if an object is designated by two names, then “whatever can be said about” it by

a statement in which one of its names occur purely designatively is exactly the same as what is said about

it by any statement that results from replacing that name by the other name. So if one of these statements

says something truly of the object, what the other statement says “should be equally true of” the object

(ibid.)49 Quine assumes that if a statement of identity is true, then the names occurring in it designate the

more general characterization of logical truth in terms of substitution and grammar (1986, Chapter 4).

47 So far as I can tell, the term ‘a priori’ appears only once in Quine’s writings on modality, in (1976b, 159). 48 This is Quine’s first presentation of his critique in English; it was first put forward in Portuguese, but

published later than the English translation, in Quine (1944). In addition, a very compressed version of part of the argument appears in footnote 22 of Quine (1941, at 16).

49 On this construal the indiscernibility of identicals is used twice: first to show that the same thing is said by

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same object. The conclusion of this line of reasoning is the principle of substitutivity: “given a true

statement of identity, one of its two terms may be substituted for the other in any true statement [in which

they occur purely designatively] and the result will be true” (ibid., 113; emphases in text).

On the basis of the substitutivity principle, Quine argues that whenever substitution of names which

occur in a true identity for one another in a statement fails to preserve truth-value—whenever, as I shall

put it, there is a substitution failure—“the occurrence to be supplanted is not purely designative, and …

the statement depends not only upon the object but on the form of the name. For it is clear that whatever

can be affirmed about the object remains true when we refer to the object by any other name” (ibid., 114).

So far Quine’s argument yields a general thesis about singular terms: they do not occur purely

designatively in statements involved in a substitution failure. In order to apply this conclusion to

modality, Quine argues for a, by-now famous, case of modal substitution failure.

The identity:

The number of planets = 9 (2)

is a truth (so far as we know at the moment) of astronomy.50 The names the number of planets’ and ‘9’ are not synonymous; they do not have the same meaning. This fact is emphasized by the possibility, ever present, that (2) be refuted by the discovery of another planet. (Ibid., 119)

… The statement:

9 is necessarily greater than 7 (3)

is equivalent to

‘9 > 7’ is analytic

and is therefore true (if we recognize the reducibility of arithmetic to logic).

On the other hand the statement …:

The number of planets is necessarily greater than 7, (4)

[is] false, since …

The number of planets is greater than 7

[is] true only because of circumstances outside logic. (Ibid., 121)

The conclusion, as expected, is that “the occurrence of the name ‘9’ in (3) is not purely designative”

(ibid., 123). Let’s call this first part of Quine’s critique “the substitution argument.”

The second part of Quine’s argument also begins at a general level. He starts by arguing that

existential generalization is justified only from purely designative occurrences of names: “[t]he idea

behind such inference is that whatever is true of the object designated by a given substantive is true of

something; and clearly the inference loses its justification when the substantive in question does not

the two statements, and again to show that the single item that is said is true. Note also that here it is the (onto)logical law governing properties of identity that underlies the principle governing substitution inferences.

50 This identity of course came to express a falsehood on August 24, 2006, when the XXVIth General Assembly of the International Astronomical Union passed the final resolution on the definition of a planet.

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happen to designate” (ibid., 116) It follows that whenever there is substitution failure, existential

generalization is not warranted. At this point it seems that Quine can simply apply this general claim to

the substitution failures in modal statements that he had already established, to conclude that that

existential generalization from singular terms in modal contexts is unwarranted. But this is not how

Quine proceeds. Instead, he propounds a problem with specifying the object that makes an existential

generalization into a modal context true:

[T]he expression:

~ (x) ~ x is necessarily greater than 7,

that is, ‘There is something which is necessarily greater than 7’, is meaningless. For, would 9, that is, the number of planets, be one of the numbers necessarily greater than 7? But such an affirmation would be at once true in the form (3) and false in the form (4). (Ibid., 123)

It’s not immediately clear what role this problem plays in Quine’s criticism, and so not clear how exactly

the second part of the criticism works. Let’s call the second part, however it works, “the quantification

argument.” Eventually Quine will make more explicit that these apparently extra considerations are not

superfluous, and that his objection to quantifying into modal contexts is not a straightforward application

of the conclusion of the substitution argument. But before getting to that, let’s turn to the first objections

raised against Quine’s critique, which can be broadly divided into Fregean and Russellian responses.

7. Fregean Replies to Quine

Alonzo Church, in a review (1943) of “Notes,” in effect agrees with Quine that if a=b is a true

identity statement, and if when a and b are substituted for one another the occurrences of these two terms

in the statements that result are all purely designative, then there can be no substitution failure. From this

conditional one can infer that if there is substitution failure, then either a=b is not a true identity, or

these occurrences of a and b do not designate a single object. Church sees Quine as assuming that if the

terms figure in a true identity, they must designate the same object in all their occurrences if they

designate anything at all, and thereby concluding that in cases of substitution failure they do not designate

at all when they occur in the statements involved in that failure. But the assumption is not mandatory.

Church draws on Frege’s distinction between “the ordinary (gewöhnlich) and the oblique (ungerade) use

of a name” to provide an alternative (1943, 45). When names occur in oblique contexts such as those

induced by modal operators, one can take them to designate, not their ordinary denotations, but their

ordinary senses. In the present case if a and b have different senses, then in a modal context they do

designate, but distinct entities; moreover, these entities are both distinct from the single object both terms

designate when occurring in the true identity. Since the designations of singular terms in true identities

differ from their designations in oblique contexts, the indiscernibility of identicals no longer justifies the

principle of substitutivity. Moreover, quantification into oblique contexts is legitimated by taking the

variable of quantification to range over intensional entities such as senses and attributes.

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Carnap advances what seems to be a similar reply in Meaning and Necessity (1947) in terms of his

“method of extension and intension.” One way of understanding this method is as a semantic theory that

associates two entities with each expression of a language-system, its extension and its intension. The

semantical rules then licenses intersubstitution of singular terms in an oblique context only when they

have the same intension. Moreover, variables of quantification range over both extensions and intensions.

A quantification into an oblique context is determined as true or false by intensions in the range of the

variable of quantification, while quantification into extensional contexts is determined by the extensions

in the range of the variable.51

8. Russellian Replies to Quine, I: the Theory of Descriptions

Church (1942) advances another objection based on Russell’s theory of descriptions. Church points

out that Quine’s case of substitution failure in the footnote 22 of “Whitehead and the Rise of Modern

Logic” (Quine 1941) involves statements in which a definite description occurs. Hence, if one applies

Russell’s theory to eliminate these descriptions, the inference Quine presents would no longer have the

logical form of substituting one singular term for another.

This objection is developed most fully by Smullyan in (1948), who points out that, according to

Russell’s theory of descriptions, in the conclusion of Quine’s example of substitution failure,

The number of planets is necessarily greater than 7 (4)

there are two possible scopes for the description ‘the number of planets’. So the description can be

eliminated in two ways. If we use ‘Nξ’ for ‘ξ numbers the planets’, and take the description to have wide

scope with respect to the modal expression, the result of eliminating the description according to Russell’s

theory is

(x)(y)((Ny y=x) & □(x>7)) (5)

That is,

The number x that uniquely numbers the planets is such that necessarily x is greater than 7.

If we take the description to have narrow scope, the result of eliminating it is

□[(x)(y)((Ny y=x) & (x>7))] (6)

That is,

It is necessary what whatever number uniquely numbers the planets is greater than 7.

51 One might indulge in a slight anachronism and take Church and Carnap both to hold that singular terms

have two semantic values in the sense of Dummett (1978, 120-22), one which contributes to determining the truth values of statements in which the terms occur in extensional contexts, and another for occurrences in intensional contexts.

Carnap goes to some trouble to argue that the method of extension and intension can be stated in a “neutral metalanguage” in which there do not occur two classes of singular terms, one for extensions and the other for intensions (1947, §§ 34-8). In such a neutral meta-language the semantics of singular terms is not stated in terms of two types of semantic values.

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The first premise of the supposed substitution failure is

The number of planets = 9 (2)

Eliminating the description, we obtain

(x)(y)((Ny y=x) & x=9) (7)

That is,

The number that uniquely numbers the planets is identical to 9.

The second premise is

9 is necessarily greater than 7 (3)

i.e.

□(9>7) (8)

From these premises it clearly follows that

The number that uniquely numbers the planets is necessarily greater than 7.

But this is just the wide scope interpretation of the conclusion. Indeed, in the logic of Principica one can

derive (5) from (7) and (8). Interpreted in this way, Quine’s example not only does not consist in a

substitution inference, but is also not an invalid argument. Invalidity results only if in the conclusion the

description is taken to have narrow scope; i.e., (6) does not follow from (7) and (8).

9. Quine II: Quine’s Replies, the Purification Argument, and an Apparent Standoff

Quine’s response, in “Reference and Modality,” to the introduction of intensional entities is to argue

that this maneuver results in an ontology which “purifie[s the] universe” of material objects and leaves

only intensional objects in their place.52 I will present a version of Quine’s argument that extrapolates

from what he writes in this essay; call it the purification argument. The problem arises from statements in

which quantifiers bind variables both inside and outside modal contexts. Quantified modal logic, as it

was first formulated by Marcus,53 is committed to such statements. For Marcus derives, in her version of

quantified S4 with identity, a theorem that has come to be known as the thesis of the necessity of

identity:54

(x)(y)(x=y □(x=y)) (9)

52 This essay appears in three different versions, Quine (1953;1961a;1980); the quoted phrase appears at 150

in all versions. 53 In Barcan (1946a;1946b;1947). Marcus provides extensions of two of the Lewis systems with

quantificational axioms and an axiom governing quantifiers and modal operators now known as the Barcan formula. Three months after the first two of Marcus’s papers Carnap (1946) sets out a quite different account of quantification and modality, based on a semantic construction whose relation to the Lewis axioms systems is not obvious.

54 Theorem 2.33 and an immediate corollary of it, in Barcan (1947), assert that material identity is strictly equivalent to both strict identity and the necessity of strict identity.

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Quine asks, can the values of the variables in this quantification include concrete material objects? If so,

then consider one such object, “the planet Venus as a material object” (1953, 151). Two names for this

planet are ‘Morning Star’ and ‘Evening Star’. So by universal instantiation from (9) we obtain

Morning Star = Evening Star □(Morning Star = Evening Star) (10)

The antecedent of (10) is a statement of identity in which these names occur in an extensional context.

Since these expressions both name Venus, that planet is their ordinary denotation or extension. Since

they thus have the same ordinary denotation or extension, it follows that the identity statement that is the

antecedent of (10) is true. These names occur in an intensional context in the consequent of (10), and so

to evaluate its truth-value, one has to consider the oblique denotations or intension of the names. Now

Quine assumes that ‘Morning Star’ and ‘Evening Star’ are “heteronymous names” (ibid.); i.e., they differ

in meaning. Hence it’s plausible that they differ in oblique denotation or intension. It follows that the

consequent of (10) is false. The upshot is that in order for (9) to be true, the entities in the range of its

quantifiers have to satisfy the condition that any two names referring to any such entity are synonymous.

This condition is not, however, satisfied by “concrete material objects.” Such objects, in general, may

have distinct designations such that it takes empirical investigation for us to know that they refer to a

single object. Hence, by the synonymy thesis, these terms are not synonymous.

If we look at Marcus’s formal proof, we can see that the line of reasoning underlying it is the

following. First, suppose that being necessarily identical to a particular object is a property. Then, the

indiscernibility of identity implies that, for any objects x and y, if x is identical to y, then x has the

property of being necessarily identical to x just in case y also has this property. But it is surely impossible

for anything to be different from itself. So, x is necessarily identical to x. Hence y also is necessarily

identical to x. Thus, from Quine’s perspective the purification argument can also be taken to show that if

there are any objects with distinct non-synonymous names then necessary identity to an object is not a

property of objects.

Quine’s initial replies to Smullyan are undermined by mistakes about the theory of descriptions in

Principia. Specifically, Quine claimed that Smullyan’s solution requires an “alteration” in the treatment

of descriptions in Principia, because in Principia all wide and narrow scope eliminations of descriptions

are provably equivalent (1953, 155; 1961b, 154). But in fact in Principia the equivalence is established

only for extensional contexts; Quine’s claim is removed from the third (1980) version of the paper.55

Eventually Quine settled on the following response:

[I]f we are to bring out Russell’s distinction of scopes we must make two contrasting applications of Russell’s contextual definition of description. But when the description is in a non-substitutive position, one of the two contrasting applications of the contextual definition is going to require quantifying into a non-substitutive position. So the appeal to scopes of descriptions does not justify such quantification, it just begs the question. (1969, 338)

55 For more details see Marcus (1990) and Neale (1999).

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Quine’s point is that, in order to claim that Quine’s purported case of substitution failure can be taken

instead to be a valid argument, Smullyan analyzes the conclusion as

(x)(y)((Ny y=x) & □(x>7)) (5)

But (5) existentially quantifies into a modal context. So, Smullyan must presuppose that such

quantifications are meaningful. But this assumption begs the question against Quine’s overall conclusion

that such quantifications are meaningless.

But Quine’s presentation of his case, which we have followed so far, suggests that this overall

conclusion is supported by the thesis that singular terms occurring in modal contexts are not purely

designative. Moreover, the ground of that thesis is substitution failures in modal contexts. So, from

Smullyan’s perspective, it is Quine who has begged the question. For Smullyan can take his argument to

show that if modal quantifications are meaningful, then Quine’s examples are not genuine cases of

substitution failure. So, in order to take his examples as genuine substitution failures, Quine must already

reject the meaningfulness of modal quantifications.

Neither side, it seems, has provided an argument that is compelling for the other. But this standoff

itself presupposes that Quine’s only ground against quantifying in is substitution failure, and that

Smullyan’s only ground against substitution failure requires Russell’s theory of descriptions. As we will

now see, neither of these presuppositions is true.

10. Quine III: The Quantification Argument Revisited

Let’s come back to the question we left hanging at the end of section 6: how exactly does substitution

failure bear on the meaninglessness of quantification? A moment of reflection suggests a problem.

Suppose we accept that if both ‘9’ and ‘the number of planets’ occur designatively in

9 is necessarily greater than 7 (3)

and

The number of planets is necessarily greater than 7 (4)

then these sentences do not differ in truth-value. Now, given that they do differ in truth-value, we can

conclude that not both ‘9’ and ‘the number of planets’ occur designatively, i.e., that at least one does not.

However, it is compatible with this conclusion that one of these two terms does occur designatively. If

that’s the case, then the truth-value of one of the two affirmations of the predicate ‘necessarily greater

than 7’, i.e., one of (3) and (4), is determined only by the object designated. Thus it doesn’t follow that

whether this predicate is truly affirmed of an entity is invariably determined by the terms used to single

out those entities, and so it doesn’t follow that there is no account of the truth conditions of existential

generalizations from (3) or (4).56

56 The problem just sketched is a simplified version of an objection due to David Kaplan in (1986), section III.

33

Moreover, why should we infer, from the fact that one occurrence of a singular term in a context is

not purely designative, to the conclusion that variables occurring in this context would also not be purely

designative? On a widespread view of Tarski’s account of quantification, the role of variables of

quantification in specifying the truth conditions of quantified sentences is exhausted by assignments of

objects to variables.57 Thus, so long as there is a coherent account of what it is for an open sentence to be

true under an assignment of an object to a variable, there is also a coherent account of quantification.

Whether or not singular terms in the positions occupied by variables are purely designative seems quite

irrelevant.58

Recall now that in “Notes” Quine does not explicitly base the quantification argument on the

substitution argument, and that he raises, with respect to statements existentially quantifying into modal

contexts, a problem of specifying the objects that satisfy the matrices of the quantifications. In this

section I show that, beginning with some exchanges with Carnap, Quine thought of these questions as

forming a quantification argument separate from the substitution argument. Moreover, I will suggest a

way of making sense of this argument in terms of Carnap’s notion of pseudo-object property.

In a letter to Carnap Quine says, “I’m going to try to make the essential theoretical point of my article

[“Notes”] without use either of the term ‘designation’ … or of the formal theory of identity” (Carnap and

Quine 1990, 325). He does this with the following argument:

Let us agree, for purpose of the example, to regard the following statement as true:

It is impossible that the capital city of Venezuela be outside Venezuela (11)

From this it would seem natural, by existential generalization, to infer the following:

x it is impossible that x be outside Venezuela (12)

Now just what is the object x that is considered, in inferring (12) from (11), to be incapable of being outside Venezuela? …. It is a certain mass of adobe et al., viz, the capital city itself. And it is this mass of adobe that is (apparently) affirmed, in (11), to be incapable of being outside Venezuela. Hence the apparent justice, intuitively, of the inference of (12) from (11). However, that same mass of adobe et al. is affirmed in the following true statement (apparently) to be capable of being outside Venezuela:

It is possible that the native city of Bolivar be outside Venezuela (13)

Justification of (12) by (11) is thwarted by (13), for (13) has just as much right to consideration as (11) so far as the mass of adobe in question is concerned. (Carnap and Quine 1990, 325; emphases mine).

Let’s begin with Quine’s claim that in sentence (11), it is a city, a mass of adobe, etc., that is

apparently affirmed to have a certain modal property. That is to say, Quine’s claim is that (11) seems to

be an ascription of a property to a city. Moreover, if (11) is indeed such an ascription, then it does

warrant the conclusion that something has that property, since that property appears to be a property

57 As Kaplan puts it, variables are prototypical devices of direct reference. 58 See Kazmi (1987, 97, 99).

34

which cities have. But is (11) in fact the ascription of a property of cities to a city? If it is, then the

correctness of this ascription should not be sensitive to “the form of the name” of that object. However, if

(11) ascribes a property to a city, is there any reason to think that (13) does not? If not, then (13) has “as

much” a claim as (11) to being an ascription of the very same property that is ascribed in (11) to the very

same city mentioned by (13). But (13) has a different truth-value from (11). Since a single city is

designated in these two sentences, this difference in truth-values cannot be accounted for if the truth

conditions of the sentences consists in a single predicate’s being true of that city. Some other features of

the two singular terms must play a role; equivalently, the applicability of the predicate must be sensitive

to those other features. The obvious feature in which these terms differ is their syntactic form. Hence I

take Quine to reason that, in the absence of a different account, we have to think that whether the

predicate is true of an object is fixed by the syntactic form of designations of those objects. So the

property ascribed in (11) is not a genuine property of cities after all.59

Now, all this talk of what property seems to be ascribed, and what property is in fact ascribed should

remind you of the notion of pseudo-object property, which seems to be a property of objects, but is in fact

a property of linguistic expressions. Let’s recall, furthermore, that according to Carnap what makes a

property φ pseudo-object is that whether φ holds of an object is determined by whether a syntactical

property correlated with φ holds of that object’s designations, that is, it is determined by the syntactical

forms of those designations. Thus, the difference in truth-value between (11) and (13), in spite of the

identity of the object mentioned in these sentences, shows that they are ascriptions of a pseudo-object

property. Quine’s argument, up to this point, shows that the modal property of being necessarily greater

than 7 is a pseudo-object property.

So what then is the problem with quantifying into modal contexts? The problem is an instance of a

general problem of generalizing over pseudo-object properties. Affirmations of pseudo-object properties

of specific objects are unproblematic; they can be eliminated in favor of their translations into formal

mode sentences.60 But with (objectual) quantification the situation is different. The truth-value of a

quantification something is φ is determined by whether the predicate φ is truly affirmed of each

member of the universe of discourse, independently of what terms, if any, designate that member. But,

whether an object has a pseudo-object property can vary depending on how that object is designated, and

there is no account of how to determine whether a designation-less object has that property. So

quantificational generalizations about pseudo-object properties have no determinate truth conditions.

59 Plantinga (1974, Appendix) presents a closely related account of why, according to Quine, modalized

predicates do not express genuine properties. 60 Note that around the time that Quine formulated these arguments Carnap came to adopt semantics, and so to

give up the notions of pseudo-object and quasi-syntactical property. Nevertheless Carnap continued to work with a successor notion, that of a quasi-logical property. A reformulation of Quine’s arguments in terms of quasi-logical properties introduces a number of complications that I can’t go into here.

35

The present quantification argument clearly is not independent of substitution failures. But it is not

based on the conclusion of the substitution argument, namely, that the singular terms involved in a

substitution failure are not purely referential. One might put the point in this way. According to the

present argument, substitution failure shows, not that there is something non-standard about the

functioning of the singular terms in question, but that there is something non-standard about the

functioning of the predicate in question. That is, the problem lies in the very idea of an open sentence

formed from a pseudo-object context being satisfied by an object. So the argument is not affected by the

view that variables are directly referential. Suppose we grant that variables are devices of direct

reference, so all they contribute to the truth conditions of open sentences in which they occur are the

objects assigned to them. On this construal of variables, they are, as it were, formless singular terms. But

then variables lack precisely those features demanded by pseudo-object contexts for determining whether

those contexts are true of the objects assigned to the variables. So direct referentiality does not make

objectual quantifying into a pseudo-object context coherent.61

However, since the argument is still based on substitution failures, it is open to Church’s and

Smullyan’s Russellian objections. In particular, since in Quine’s example sentences (11) and (13) the

singular terms are descriptions, one might hold that neither of these sentences is an ascription of a

property to a city. Hence the difference in their truth-values has no implications for the nature of the

property expressed by the predicate occurring in these sentences.

I take it that it is to answer such objections that Quine writes, in “Reference and Modality,”

Whatever is greater than 7 is a number, and any given number x greater than 7 can be uniquely determined by any of various conditions, some of which have ‘x > 7’ as a necessary consequence and some of which do not. One and the same number x is uniquely determined by the condition:

x x x x x (14)

and by the condition:

There are exactly x planets, (15)

but (14) has ‘x > 7’ as a necessary consequence while (15) does not. Necessary greaterness than 7 makes no sense as applied to a number x; necessity attaches only to the connection between ‘x > 7’ and the particular method (14), as opposed to (15), of specifying x. (1953, 149)

This is yet another version of the quantification argument. The conclusion, again, is that since whether an

61 In (1987), Mark Richard argues that an objectual account of quantification is consistent with failures of

substitution. The principal idea underlying this argument is that in a Tarskian account of quantification the notion of satisfaction by sequences requires variables to be indexed by a set of the same ordinal type as those sequences of maximal ordinal type, and nothing in the idea of objectual quantification rules out variant accounts of satisfaction that depend on conditions involving the index set. From our perspective, this idea simply makes variables into names with form, and so Quine would not accept such variant accounts of quantification as purely objectual. (Quine would point to the failure of the relettering law on Richard’s account as confirmation of this.) Richard argues that in the case of open sentences in which variables occur within the scope of propositional attitude verbs, such variant accounts of satisfaction have theoretical advantages over Quine’s theory of de re ascriptions of belief, which tacitly employs the orthodox account. Quine, in my view, can respond by arguing that the advantages can also be captured by his de dicto account of belief ascription; but that is a topic for another day.

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object has the property of being necessarily greater than 7 depends on which open sentence it satisfies,

this property is pseudo-object.

Let’s look at the quantification argument in a slightly different way. As we saw, Quine began by

accepting Carnap’s explication of necessity, considered as a pseudo-object property of states of affairs, in

terms of metalinguistic predicates of sentences describing these states of affairs. Modulo doubts about

analyticity, Quine never rejects this explication. His critique of modality relates to Carnap’s explication

of necessary properties of objects in terms of relative analyticity. As we saw above, Carnap explicates the

claim that something has a necessary property by the (metalinguistic) claim that a sentence formed by

putting a designation of the object in the placeholder of a predicate expressing the corresponding non-

modal property is analytic. Since different designations or specifications lead to different verdicts about

the analyticity of the resulting sentences, and so different verdicts about whether the necessary property

holds of the object, it follows from this Carnapian account that modal properties are pseudo-object as

well. This is hardly a surprising conclusion to reach from the view that necessity is a pseudo-object

property of states of affairs. Quine, however, goes on from this conclusion to argue that (objectual)

quantificational generalizations over pseudo-object properties have no determinate truth conditions. But

then there is no meaningful explication of modal properties of objects.62

11. Quine IV: Anti-Essentialism

In face of the revised quantification arguments, how could one confer determinate truth conditions on

a generalization involving a modal predicate, when different verdicts on whether this predicate is true or

false of an object result from different specifications of that object? One way to accomplish this is, for

each object, to retain all the positive verdicts and throw out all the negative ones, or vice versa. This is

what Quine means by “adopting an invidious attitude toward certain ways of uniquely specifying [the

object], and favoring other ways” (1961a, 155). But, Quine asks, what basis is available for rejecting

some specifications and retaining others? All these conditions are, after all, ex hypothesi satisfied by the

object. It is at this point that Quine brings in “Aristotelian essentialism”: the favored specifications are

those “somehow better revealing the ‘essence’ of the object” (ibid.)

What Quine has in mind is a feature of a traditional conception of essential properties: if an object

loses an essential property then it ceases to exist.63 Let’s illustrate Quine’s line of thinking with an

62 Burgess (1997) and Neale (1999) also argue that Quine’s argument against quantifying in is independent of

substitution failures. They do not discuss its connection to Carnap’s notion of relative analyticity in Syntax. 63 Many are skeptical of the Aristotelian pedigree of Quine’s essentialism. But Aristotle would surely accept

that, in order to be an essential property of something, that thing couldn’t exist without having the property. Of course, on Aristotle’s conception, this modal feature is not sufficient for the property to be essential, because he requires essential properties to have explanatory priority with respect to other properties having this feature. (See Shields (2007, 99-105) or a fuller account of Aristotle on essence.) It follows that all Aristotelian essential properties are Quinean ones, but perhaps not vice versa.

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example. Suppose the specification of 8 as the successor of 7 expresses an essential property of 8, and

suppose that being even follows analytically from being the successor of 7. Consider now the claim that

8 is not even. Since being even follows analytically from being the successor of 7, it follows from this

claim that 8 is not the successor of 7. But since being the successor of 7 is essential to 8, anything distinct

from the successor of 7 is not 8. So we reach the logical contradiction that 8 is not 8. Thus the claim that

8 is not even is contradictory; hence being even is a necessary property of 8. Consider now, in contrast,

the non-essential property of 8 of numbering the planets. Being a non-essential property of 8, failure to

number the planets is not sufficient for diversity from 8, and so the claim that 8 does not number the

planets fails to lead to any contradiction. Strictly this line of reasoning does not show that the notion of

essential property is required to confer determinate truth conditions on quantificational generalizations

over modal properties; essence merely suffices for determinate truth conditions. Quine’s conclusion

should then be a challenge to explain objectual quantification over modal properties without invoking the

notion of essential property.

Of course the force of this challenge depends on whether there is anything wrong with essentialism.

Quine’s most well-known objection to essentialism is based on a version of the example motivating

Carnap’s explication of the notion of essential property:

Mathematicians may conceivably be said to be necessarily rational and not necessarily two-legged; and cyclists necessarily two-legged and not necessarily rational. But what of an individual who counts among his eccentricities both mathematics and cycling? Is this concrete individual necessarily rational and contingently two-legged or vice versa? Just insofar as we are talking referentially of the object, with no special bias toward a background grouping of mathematicians as against cyclists or vice versa, there is no semblance of sense in rating some of his attributes as necessary and others as contingent. Some of his attributes count as important, and others as unimportant, yes; some as enduring and others as fleeting; but none as necessary or contingent. (Quine 1960, 199)

The Carnapian background is key to understanding Quine’s argument. Recall that Carnap took the case

of the landowning father, c, to lead to an apparent contradiction via the Tractarian account of essential

property: c is both essentially a landowner and not essentially a landowner. Carnap resolves this

contradiction by appeal to relative analyticity, so that c is essentially a landowner relative to one

description but not relative to another. But essentialism abjures appeal to descriptions or conditions

satisfied by objects for determining whether they possess essential properties. So the Carnapian method

of resolving such apparent contradictions is no longer available. In terms of Quine’s example, if, in

accordance with essentialism, we are barred from appealing to the conditions of being a mathematician

and being a cyclist, i.e., to “a background grouping of mathematicians as against cyclists or vice versa,”

nothing stands in the way of inferring that mathematical cyclists are both necessarily rational and not

necessarily rational, which is why “there is no semblance of sense” in the characterization of objects’

“attributes as necessary and others as contingent” according to essentialism.

This line of argument is hardly conclusive. An obvious essentialist response is that the supposed

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contradiction arises only because Quine’s basis for claiming that a mathematical cyclist is necessarily

rational is a condition—being a mathematician—that she satisfies only contingently.64 So in fact

essentialism has the resources for resisting the supposed contradiction, by claiming that mathematical

cyclists are not necessarily rational, because not essentially mathematicians. But from Quine’s

perspective this response takes us to another question: what justifies, without any appeal to conditions

that someone satisfies, the claim that she is not essentially a mathematician? This question has particular

weight for Carnap. It is not that Carnap rejects essentialist metaphysics out of hand; he would have no

objection to the notion of essence so long as it is explicated in precise terms. But Carnap’s explication of

essence is precisely that which essentialism rejects. So, for Carnap, unless there is some way other than

essentialism for providing quantifications into modal contexts with determinate truth conditions, it’s

unclear why the use of modal expressions should not simply be rejected altogether.

Quine’s argument plausibly has force not only against Carnap. If one rejects Carnap’s relative

analyticity as the basis for predicating essential and contingent properties, what should be put in its place?

Thus, at bottom, Quine is not claiming that essentialism is objectionable because it leads to

contradictions. Quine is, rather, posing a challenge to essentialism: what coherent and non-arbitrary

standards are there for determining the correctness of ascriptions of essential properties, and for doing so

without appeal to conditions satisfied by the objects of the ascriptions?

12. Russellian Responses, II: Smullyan and Marcus

As mentioned in section 8 above, Smullyan has another objection to Quine’s substitution arguments.

This is based on the claim that “if ‘Evening Star’ and ‘Morning Star’ proper-name the same individual

they are synonymous” (Smullyan 1947, 140). This conception of proper names is arguably held by Mill,

so nowadays it would be called a Millian view. On this view we can substitute either of ‘Evening Star’

and ‘Morning Star’ for the other in the statement ‘Evening Star = Morning Star’ to obtain synonymous

statements ‘Evening Star = Evening Star’ and ‘Morning Star = Morning Star’. By Quine’s lights both of

these latter statements are logical truths. Hence by Quine’s account of analyticity ‘Evening Star =

Morning Star’ is analytic and so by the analyticity account of necessity ‘□(Evening Star = Morning Star)’

is true. Smullyan’s Millian view of proper name is a flat rejection of Quine’s assumption that these two

names of the concrete material object (the planet) Venus are heteronymous. Given this rejection, it is

possible to take the necessity of identity to hold at least of the material object that is Venus, provided that

we refer to it by the synonymous names ‘Evening Star’ and ‘Morning Star’.

Both Quine and a Fregean like Church would reject such Millianism about proper names, for the

same reason. As Church puts it in a review of F. B. Fitch’s (1949),

Fitch … holds (with Smullyan) that two proper names of the same individual must be

64 See in particular Marcus (1961, 317-319).

39

synonymous. It would seem to the reviewer that, as ordinarily used, ‘the Morning Star’ and ‘the Evening Star’ cannot be taken to be proper names in this sense; for it is possible to understand the meaning of both phrases without knowing that the Morning Star and the Evening Star are the same planet. Indeed, for like reasons, it is hard to find any clear example of a proper name in this sense. (Church 1950, 63)65

What underlies this objection is clearly the synonymy thesis. An obvious move for Smullyan and Fitch to

make in response would be to question this connection, and defend the view that understanding need not

be sufficient for knowledge of synonymy. But neither, so far as I know, pursues this line of response to

Church-Quine objection, or, for that matter, explains fully their Millian conception of proper names. As a

result, this early objection to Quine had little immediate influence.66

By invoking synonymy, Smullyan and Fitch suggest that they think true identities are necessary

because reducible via non-empirical facts about meaning to non-empirical logical truths. Their

unappreciated contribution is to point to an unquestioned assumption—that understanding two

expressions is always sufficient for knowing whether they are synonymous—underlying an apparently

decisive stumbling block for proceeding along this route. But their opposition to Quine does not put into

question the conception of necessity as analyticity that is the target of Quine’s critique.

Marcus’s paper, “Modalities and Intensional Languages” (1961), marks the beginnings of a sea-

change in our philosophical conception of modality. The principal aim of the part of the paper on which I

focus is to defend her theorem of the necessity of identity against Quine’s purification argument.

Marcus’s defense begins with a version of an argument advanced by Russell in “The Philosophy of

Logical Atomism” (1918, 212). Marcus writes,

Consider … the claim that

aIb (16)

is a true identity. Now if (16) is such a true identity, then a and b are the same thing. [(16)] doesn’t say that a and b are two things which happen, through some accident, to be one. … If, then, (16) is true, it must say the same thing as

aIa. (17)

But (17) is surely a tautology, and so (16) must surely be a tautology as well. This is precisely the import of my theorem [of the necessity of identity]. (1961, 308)

We can divide this argument into five steps. First, if a statement of identity, with distinct expressions a

and b flanking the identity symbol ‘I’, is true, then a and b denote a single thing. Second, since a and b

denote a single thing, this identity statement says the same thing as the true identity aIa . Third, if two

statements say the same thing, then if either is a tautology so is the other. Fourth, since aIa is a

tautology, it follows by the last two steps that the true identity aIb is also a tautology. Finally, since

65 In fact Fitch in the article Church reviews here says nothing about synonymy; he merely cites Smullyan as

showing that on the assumption that the terms occurring in Quine’s examples are proper names ‘~□(Morning Star = Evening Star’ “would clearly be false” Fitch (1949, 138).

66 Marcus’s review of Smullyan (1947, 140) is a notable exception.

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aIb is a tautology, it is necessarily true.

This way of parsing the argument highlights three questions. First, what is an identity statement?

That is, what kinds of expression do a and b have to be in order for aIb to be an identity statement?

Second, what is it for two sentences or statements to say the same thing? Perhaps more generally, what

does a statement say? Third, what is a tautology for Marcus?

Let’s take up the second question first. The second step of the argument suggests that what is said by

an identity statement is (at least partly) individuated by the entities denoted by the expressions flanking

the symbol of identity. It is because, by the first step of the argument, all occurrences of expressions

flanking the identity symbol in the statements (16) and (17) denote a single entity that these statements

say the same thing. This suggests that these identity statements say the same thing because they are about

the same entity, and asserts the same thing of that entity, namely, that it is self-identical. If so, then this

suggest that, in general, what a statement says, to put it using Tractarian terms, is something like the state

of affairs that it depicts.

Let’s turn now to Marcus’s notion of tautology. The final step of the argument obviously suggests

the Tractarian-positivist account of necessity in terms of tautology. This raises the question whether her

conception of tautology the same as the Tractarian one. A closely related question is raised by her

description of the conclusion of her argument as “to say of an identity (in the strongest sense of the word)

that it is true, it must be tautologically true or analytically true” (ibid., 309-10). Here Marcus seems to

equate tautology with analyticity, and so, in light of the last step of her argument, we might ask, is her

conception of necessity the same as the positivist analyticity view of necessity? Given our contemporary

tendency to identify all conceptions of modality in the analytic tradition with the positivist conception, we

are likely to be satisfied with a superficial reading of Marcus’s text and conclude that the answer to both

question is yes. But some attention to what she actually writes puts this answer in question.

To begin with, Tractarian tautologies, as we have seen, say nothing. By contrast, as we have just

argued, for Marcus true identity statements that are tautologies depict states of affairs. Now it might be

objected that this consideration is not decisive because, if tautologies say nothing, then in a vacuous sense

they all say the same thing,67 and isn’t this thesis precisely that which underlies the third step of Marcus’s

argument? But the argument just presented starts from the claim that tautologies say nothing, to reach the

conclusion that they all (vacuously) say the same thing. The role of the third step in Marcus’s argument,

however, is to allow a transition from the identification of a single thing said by two statements in the

67 We can make this idea more precise in the following way. Suppose we represent the logical form of claims

to the effect that a statement says something as the existence of something to which the statement stand in the relation of saying. Then, using ‘Sξζ’ to express the relation of saying, the claim that t1 says nothing is

~(x)(St1x) . So if t2 also says nothing, then it follows that (x)(St1x St2x). We can take this last claim to represent the vacuous sense in which t1 and t2 say the same thing. Obviously there is another way of construing the logical form of claiming that two statements p and q say the same thing— (x)(Spx & Sqx) —which is incompatible with the claim that t1 and t2 both say nothing.

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second step to the conclusion that both of these statements are tautologies. This inferential move

presupposes that there is something said by these statements which wind up being classified as

tautologies. So Marcus’s reasoning is incompatible with the view that tautologous statements say

nothing.

Let’s now consider whether the analyticity conception of necessity plays any role in Marcus’s

argument. In doing this we will answer the first question raised above about that argument. Let’s

observe, to start with, that the Russellian argument that we have been discussing is not, by itself,

Marcus’s full defense of the necessity of identity. The reason is that the Russellian argument operates

under the assumption that aIb is a true identity statement, and part of Marcus’s objection to Quine is

that in his purification argument he assumes, uncritically, that the sentence ‘Morning Star is identical to

Evening Star’ is a genuine identity statement. Marcus claims, against Quine, that in order for a statement

of the form aIb to be a genuine identity statement, the singular terms occurring in it have to function in

a particular way. It is in order to make this functioning explicit that Marcus introduces the notion of

“tags.” In her view, singular terms in natural languages function in many complex ways that are not

easily distinguished. Tags, in contrast, are artificial expressions stipulated to function in just one way,

and so provide an idealized model of one aspect of the working of ordinary singular terms. Marcus’s

claim is that statements with tags flanking the identity symbol are the genuine identity statements to

which her Russellian argument applies.

Tagging is the result of putting some (finite) set of randomly generated natural numbers in a one-to

one correspondence with “all the entities countenanced as things by some particular culture through its

own language” (Marcus 1961, 310).68 Each of these numbers is then an “identifying tag [that] is a proper

name of the thing” to which it is correlated. The crucial feature of tags is that they have “no meaning”

(ibid., 309). Since tags have no meanings, the concept of synonymy applies at best only vacuously to

them.69

Now none of the foregoing considerations tells us yet what are Marcus’s conceptions of tautology and

of necessity. I suggest that Marcus uses ‘tautology’ in something like the way that Russell does when

Russell tells us that being a tautology is a “peculiar quality [that] belongs to logical propositions and not

68 If we take Marcus at her word here, we have to take tagging to be, strictly in the first place a syntactic

correlation of the singular or descriptive referring expressions of the language of a culture with a set of numbers. 69 If one is determined to insist that Marcus subscribes to the positivists’ analyticity conception of necessity,

one might seize on the fact that meaningless tags can be vacuously synonymous to claim that her argument for the necessity of true identities between tags must after all depend on considerations of synonymy, as Smullyan’s and Fitch’s objections to Quine do. But this line of interpretation fails because, if synonymy among tags rests on their lack of meaning, then all tags are synonymous. It follows that all identity statements between tags can be transformed into an instance of the law of identity by substitution of synonyms and so are, not just true, but necessarily so. This of course yields the unacceptable conclusion that necessarily there are no distinct tagged entities. The reasonable conclusion to draw at this point is that synonymy plays no role in Marcus’s argument for the necessity of true identities, and that she is not operating with the positivists’ analyticity conception of necessity.

42

to others,” which he doesn’t “know how to define” (1918, 205). That is to say, for Marcus to be a

tautology is to be logically true.70 We also know that if two statements depict the same state of affairs,

then one of them is a tautology just in case the other is. This suggests that a statement is a tautology just

in case what it depicts holds as a matter of logic. In particular, the state of affairs depicted by a true

identity statement is the self-identity of some object; since it is a logical law that every object is self-

identical, this state of affairs holds as a matter of logic.

All this indicates how far Marcus’s view is from the Tractarian and positivist conceptions of logical

truths as saying nothing about the world. For Marcus statements concerning ordinary material objects can

be logically true, in virtue of describing facts involving such objects that hold as a matter of logic.

Since for Marcus the necessity of genuine identities does not rest on analyticity, she does not face the

question why knowledge of certain identities requires empirical investigation, rather than mere

knowledge of meaning or linguistic reflection. But if for her true identities between tags are necessary

because logically true, she faces a variant of this question. Quine puts it, in (1961b), as follows:

We may tag the planet Venus, some fine evening, with the proper name ‘Hesperus’. We may tag the same planet again, some day before sunrise, with the proper name ‘Phosphorus’. When at last we discover that we have tagged the same planet twice, our discovery is empirical. And not because the proper names were descriptions. (327)

If this identity between two tags can be established only by empirical investigation, how could it be

logically true? If it is logically true, wouldn’t we be able to establish its truth by deductive reasoning

alone, without appeal to empirical evidence?71

Marcus has, in the text of “Modalities,” the materials for a reply to this argument. However, as we

will see below, at the time this paper was presented to the Boston Colloquium in the Philosophy of

Science and subsequently published, Marcus arguably did not have a fully worked out reply based on this

material. So I present an elaboration of a line of response suggested by, but not present in, the text. Let’s

start with the following passage:

You may describe Venus as the evening star and I may describe Venus as the morning star, and we may both be surprised that as an empirical fact, the same thing is being described. But it is not an empirical fact that

Venus I Venus (18)

70 Contrast this picture with that which underlies the Quine-Church objection to Smullyan. On that view, if ‘a’

and ‘b’ abbreviate distinct co-referential singular terms, then the true identity statement ‘a=b’ can be, at best, analytically true, but not logically true.

71 Perhaps a version of this argument also moved Russell to hold that “[i]f one asserts ‘Scott is Sir Walter,’ the way one would mean it would be that one was using the names as descriptions” Russell (1918, 212). If ‘a’ and ‘b’ are genuine names then ‘a=a’ and ‘a=b’ make the same assertion, and one would not bother to assert this “tautology.” And the reason, to put it the terms of Russell (1905), is that one may wonder whether Scott is Sir Walter without wondering whether Scott is Scott. So Russell concludes that, as these expressions figure in ordinary assertions, ‘Scott’ and ‘Sir Walter’ are not logically proper names. Given different epistemic attitudes to these two statements, they do not make the same assertion.

43

and if ‘a’ is another proper name for Venus [that]72

Venus I a. (Marcus 1961, 310) (19)

The crucial contrast here is between empirical fact and non-empirical fact. What Marcus characterizes as

empirical is the fact that the same thing is described by two expressions. What the two statements, (18)

and (19) describe, however, is a single, non-empirical fact. In line with what I have argued above, what

(18) and (19) describe is the fact that Venus is self-identical. This fact holds as a matter of logic, and so is

not known on the basis of empirical investigation. What empirical investigation establishes is that

distinct expressions describe the same thing. There is no reason not to extend this last point to tags. That

is, empirical investigation may be required to establish that distinct tags tag the same thing. Now, we can

grant, for instance, that it is a truth of astronomy that Hesperus is the same thing as Phosphorus, while it is

not a truth of astronomy that Hesperus is the same thing as Hesperus. But, why should it follow from this

that the two statements

Hesperus = Phosphorus (20)

Hesperus = Hesperus (21)

describe distinct facts? Moreover, why should it follow that what astronomical investigation is required

to establish is that the fact depicted by (20) holds? We can hold, instead, that in the case of the true

identity statement (20), empirical investigation does not establish that the fact it describes—the self-

identity of an object—holds. Rather, empirical investigation establishes that statement (20) depicts this

fact of self-identity, by establishing that the two tags occurring in (20) tag that object. On this view,

empirical investigation is not the basis for knowing that what (20) says holds, for what (20) says holds as

a matter of logic, and so necessarily. Note that on this view what is said by (both) (20) and (21) is

necessary, but not known a posteriori; what is known a posteriori is that what (20) says is the same as

what (21) says.

This view suggests a picture of naming. The idea is that, merely by naming something, we don’t

invariably thereby acquire all the information that can be acquired about the name, because we may lack

information about its bearer. In Quine’s example, for instance, merely tagging the planet Venus

obviously does not give us complete information about its physical properties, such as its mass or orbit, or

the relations in which it stands to other physical objects, such as its distance from the Sun. But, in

addition, this tagging does not give us full information about the relations in which Venus stands to other

names in our language. This suggests a rough distinction between facts about properties and relation of

the bearers of names exclusive of their connection to our language, and facts about their relations to our

words. Both sets of facts are empirical. But the latter are also linguistic.

This distinction, I take it, might be what Marcus tries to express in the following passage in the

published “Discussion” of her paper:

72 Inserted in the reprinting of Marcus (1961) in Marcus (1993).

44

If ‘Evening Star’ and ‘Morning Star’ are considered to be two proper names for Venus, then finding out that they name the same thing as ‘Venus’ names is different from finding out what is Venus’ mass, or its orbit. It is perhaps admirably flexible, but also very confusing to obliterate the distinction between such linguistic and properly empirical procedures. (Marcus et al. 1962, 142)

But from “Discussion” it is also not clear that Marcus had the foregoing distinction in mind. For,

immediately preceding the passage just quoted, Marcus writes, “if a single object had more than one tag,

there would be a way of finding out such as having recourse to a dictionary or some analogous inquiry,

which would resolve the question as to whether the two tags denote the same thing” (ibid.) This remark

suggests that facts about the identity of the bearer of names are purely linguistic, and so not also partly

empirical. This remark led Kripke to ascribe to Marcus the view that facts about the reference of tags are

purely linguistic facts (1971, 75, n. 7, 1980,100). But it should be clear that it stands in some tension with

the view suggested by the text of “Modalities,” which is that such facts are not purely empirical but also

partly linguistic.

13. The Passing of Quinean Anti-Essentialism: Kripke

Marcus’s arguments in “Modalities” provide a conception of necessity not tied to analyticity, and a

view of how objects as such, independent of conditions they satisfy, can possess necessary properties

such as self-identity. But, as Quine makes clear in a letter to Carnap in 1943, these are not the properties

existential statements about which are problematic: “I had argued that … the ‘N’ of necessity … could

not govern matrices whose variables were quantified in a wider context. Naturally I did not hold that

trouble would always arise, regardless of what matrix followed ‘N’; for, trivial and harmless cases could

readily be got by letting the matrix contain its variable merely in such a manner as ‘x = x’” (Carnap and

Quine 1990, 371). The modal properties to which Quine objects are those whose ascriptions are fixed,

not by logic, but by Carnapian relative analyticity. For these, as we just saw, Quine propounds a

dilemma: either existential statements purportedly about them have no determinate truth conditions, or

there is no principled essentialist account of their ascription to objects. So Quine should have been aware

that it is an overstatement to take his argument to rule out all quantification into modal contexts.

Moreover, until Quine’s contribution to the discussion on Marcus’s “Modalities,” he did not make

clear what he meant by claiming quantified modal logic is committed to essentialism. In that discussion

Quine explicitly disavowed claiming that essentialist claims are theorems of syntactic or semantic

characterizations of quantificational reasoning involving modal operators.73 What Quine means, as we

saw above, is that some quantifications into modal contexts can be furnished with determinate truth

conditions by assuming essential properties.74

Finally, as we saw in the last section, Quine’s objection to essentialism is not that essential properties

73 See Marcus et al. (1962, 140). 74 On this point compare Ballarin (2004).

45

lead to contradictions and so are incoherent, but that without something like relative analyticity it’s a

question what principled grounds underlie attributions of essential properties.

Quine’s overstatements and unclarities led to the impression that he holds that all quantification into

modal contexts require essentialism, that essentialist claims are theorems of quantified modal logics, and

that essential properties, to use Kantian language, generate antinomies. This impression led to

illuminating work by Marcus and Terence Parsons making precise and distinguishing clearly notions of

essential property, and showing that essentialist claims are not theorems of systems of quantified modal

logic as characterized by Kripke semantics.75 This work, together with the contributions in the 1960s

mentioned in my introductory remarks, made it increasingly plausible that essentialism is no minefield of

antinomies. Of course the intelligibility of essentialism in this sense doesn’t answer Quine’s underlying

demand for principled grounds for the ascription of essential properties that do not rely on conditions

satisfied by the objects of these ascriptions. But it contributed to a growing sense that it’s unclear why

such Quinean questions have to be answered. As Marcus puts it, a “sorting of attributes (or properties) as

essential or inessential to an object or objects is not wholly a fabrication of metaphysicians,” since the

“distinction is frequently used by philosophers and nonphilosophers alike without untoward perplexity”

(1971, 187).

The most influential expression of the growing consensus against Quinean doubts about essentialism

are in Kripke’s “Identity and Necessity” (1971) and “Naming and Necessity” (1972). The explication,

criticism, and defense of Kripke’s views in these works is very much a part of contemporary philosophy,

and obviously it is no part of my brief to give an account of these debates. I will focus on a line of

argument in defense of essentialism critical for the contemporary post-Quinean view of modality.

Kripke’s starting point is the intuitive basis of essentialism:

[I]t is very far from being true that this idea [that a property can meaningfully be held to be essential or accidental to an object independently of its description] is a notion which has no intuitive content, which means nothing to the ordinary man. Suppose that someone said, pointing to Nixon, ‘That’s the guy who might have lost’. Someone else says ‘Oh no, if you describe him as “Nixon”, then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost’. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. The first man would say, and with great conviction, ‘Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaign been different, might have been the loser, and someone else the winner; or there might have been no election at all. …. On the other hand, the term “Nixon” is just a name of this man’. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. (1972, 265)

Here Kripke displays ordinary uses of language which seem to show that there exists a pervasive pre-

philosophical and intuitive agreement on ascriptions of essential and accidental properties to objects,

independent of how they’re described. In the presence of systematic non-collusive agreement on

75 Marcus (1961;1967;1971); Parsons (1967;1969).

46

essentialist claims, there is no need to specify the principles underlying these claims in order to justify

their use.76 We saw above that the intuitive, pre-philosophical basis of essentialism has been noted.

Much of the power of Kripke’s argument derives from the success of his presentation of samples of what

we would ordinarily say in eliciting our intuition of the naturalness of uses of modal vocabulary in

apparently essentialist ways.

The next stage of Kripke’s defense consists of two arguments drawing consequences from

essentialism, consequences that seemed problematic in the Quinean philosophical climate of the time.

The first argument, as presented in “Identity and Necessity,” begins explicitly from a now well-known

example of “what advocates of essentialism have held,” namely, “being made of wood, and not of ice,

might be an essential property of this lectern” (Kripke 1971, 89). If being made of wood and not ice is

essential to being a table, then “the statement that this table, if it exists at all, was not made of ice, is

necessary” (ibid.) But, Kripke observes, this statement “certainly is not something that we know a priori.

What we know is that first, lecterns usually are not made of ice, they are usually made of wood. This

looks like wood. It does not feel cold and it probably would if it were made of ice. Therefore, I conclude,

probably this is not made of ice. Here my entire judgment is a posteriori” (ibid.) The upshot is that we

msut distinguish “between the notions of a posteriori and a priori truth on the one hand, and contingent

and necessary truth on the other hand” (ibid., 87-8).

The second argument is in essentials, the same as Marcus’s Russellian defense of the necessity of

identity discussed in section 11 above. Here Kripke begins by arguing, again from our supposed intuitive

agreement over modal and essentialist claims, for the now received view that proper names are rigid

designators. On the basis of the notion of rigid designation Kripke then reasons as follows:

If names are rigid designators, then there can be no question about identities being necessary, because ‘a’ and ‘b’ will be rigid designators of a certain man or thing x. Then even in every possible world, a and b will both refer to this same object x, and to no other, and so there will be no situation in which a might not have been b. That would have to be a situation in which the object which we are also now calling ‘x’ would not have been identical with itself. (Ibid., 89)

Clearly, for Kripke, the identity a=b is necessarily true because the situation that it describes is the

self-identity of the referent—x—of both a and b, and this self-identity holds in all possible worlds. The

ground for this last claim is surely that self-identity holds as a matter of logic. So, the basis of Kripke’s

reasoning here is the same as that which underlies Marcus’s defense of the necessity of identity discussed

above. The main difference is that Kripke uses the claim that proper names in natural languages are rigid

designators, while Marcus introduces tags, artificial expressions stipulated to function in a way that

captures some aspects of ordinary names. Rigid designation is explained in modal terms, as sameness of

reference in all counterfactual circumstances. Tagging, in contrast, is explained in semantic terms, as the

76 Kripke’s argument is thus of the same form as Grice’s and Strawson’s (1956) reply to Quine’s attack on the

analytic/synthetic distinction.

47

absence of descriptive mediation between expression and referent. In both cases some type of non-

descriptional singular term have to flank the identity sign in order for the resulting statements to be

genuine identity statements, and all genuine identities are necessary if true. The upshot here is that some

of these necessary true identities can be established as true only on the basis of empiricial, a posteriori

evidence.

The connection between the two arguments can made clear by a reformulation of the second. As we

have seen, perhaps even Quine, not to mention “advocates of essentialism,” would accept that self-

identity is an essential property of any object. Now if both a and b in a=b are rigid designators, then

this statement, if true, is the ascription of self-identity to the denotation of a and b, and so is necessary.

But for many names a and b the statement a=b is “certainly not something we know a priori.”

We have already seen why Quine takes the upshot of Marcus’s defense of the necessity of identity to

be problematic: all genuine (non-descriptional) identities are necessary because logically true, how could

some of them be knowable only on the basis of empirical evidence? The final stage of Kripke’s argument

begins with a diagnosis of a generalization of Quine’s worry: how could a necessary truth be justifiable

only on the basis of empirical evidence? Kripke suggests that we find this idea hard to accept because we

have the intuition that empirical evidence could always have been different from what it in fact was, and

so it could always have turned out that a statement, which in fact is established by evidence, would not be

so established. Thus, intuitively, we think we can imagine how astronomical investigation might have

established that Hesperus is not Phosphorus, or how we could find, after taking the lectern apart, that it’s

made of ice after all.

Kripke’s response is to reconstrue these intuitions. For example, he argues that our intuition that we

“can actually imagine circumstances that [we] would call circumstances in which Hesperus would not

have been Phosphorus” (ibid.) should be reconstrued as an intuition of counterfactual circumstances in

which the descriptive conditions actually used to fix the referents of the names ‘Phosphorus’ and

‘Hesperus’ are satisfied by distinct entities, so at least one of these entities is distinct from the planet

Venus. But these are not circumstances in which the one object actually picked out by these reference-

fixing conditions is not self-identical. If in these counterfactual circumstances the names ‘Hesperus’ and

‘Phosphoru’ had still been introduced by the actual reference-fixing conditions, these names would not

have referred to the same thing. But that is not to say that Hesperus, the actual planet Venus, would not

have been identical to itself, i.e., to Phosphorus. Rather, as Kripke puts it, in these counterfactual

circumstances “we would not have called Hesperus ‘Hesperus’” (ibid.)77 The reconstrual strategy thus

removes the principal intuitive obstacles to our acquiescing in our intuitive acceptance of essentialism.

With the absorption of this Kripkean argument for meeting Quine’s challenge to modality, the

77 See della Rocca (1996) for a detailed account of Kripke’s reconstrual strategy, and della Rocca (2002) for

doubts about its success.

48

rehabilitation of modal concepts in analytic philosophy is complete. Modal concepts, if not essentialism,

are now an unquestioned part of analytic philosophical discourse, as is the distinction between

metaphysical necessity on the one hand, and analyticity and apriority on the other. Whether the

arguments of Marcus and Kripke (and those others I could not discuss here) that underlie this attitude to

modality are indeed sufficient as a reply to Quine is matter for another occasion.

49

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