accidental sameness in aristotle

Accidental Sameness in AristotleAuthor(s): Frank A. LewisSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 42, No. 1 (Jul., 1982), pp. 1-36Published by: SpringerStable URL: http://www.jstor.org/stable/4319537 .

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FRANK A. LEWIS

ACCIDENTAL SAMENESS IN ARISTOTLE

(Received 1 0 July, 198 1)

For the arguments of the sophists deal, so to speak, above all with the accidental; for example, the question whether musical and grammatical are different or the same, and whether musical Coriscus and Coriscus are the same. - Metaphysics E2, 1026bl5-18.

For if it is not the job of the philosopher, who is it who will inquire whether Socrates and Socrates seated are the same?' - Metaphysics G2, 1004bl-3.

In this paper, I offer a formalization of Aristotle's theory of accidental sameness, and attempt to relate that theory to various questions in Aristot- le's ontology. Although in general the formalization can stand on its own, given the principal texts in which Aristotle discusses accidental sameness, some key choices in the formalization are motivated in part by the later discussion of ontology. This is no disadvantage, but merely reflects the expec- ted interdependence between any theory of sameness and matters of ontology.

The ontological matters that intersect with the discussion of accidental sameness concern the question whether Aristotle's ontology includes a special class of entities I call accidental compounds. These are entities of the form, a + p, where a is some substance, ep is an accident of a, and the '+' notation introduces the primitive operation of compounding. In my formalization, accidental sameness is a relation between an accidental compound and a substance. But the primary point about accidental compounds is that they are not identical with substances. Socrates + wise, for example, is not identical with its parent substance, Socrates. The question of whether Aris- totle's ontology makes room for accidental compounds is reflected in the interpretation we give to 'paronymous referring expressions' in Aristotle, 'the pale (one)', 'the musical (one)', 'the (one) seated', and the like. The usual

Philosophical Studies 42 (1982) 1-36. 0031-8116/82/0421-0001$03.60 Copyright ? 1982 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.



2 FRANK A. LEWIS

interpretation construes these as no different from ordinary 'Russellian' definite descriptions: their semantic referent is, perhaps, the unique thing which satisfies the description given. Thus, for example, if Socrates is the (contextually given) one who is seated, then 'the (one) seated' refers to Socra- tes. An unexpected consequence of this interpretation, as we shall see, is that the major classificatory predicates in Aristotle's ontology, '... is a substance' and the like, are referentially opaque. According to the alternative reading to be proposed here, however, 'the (one) seated' refers not to Socrates, if it is Socrates who is seated, but to the accidental compound, Socrates + seated. The idea, then, that '...is a substance' is referentially opaque can be dropped in favour of the view that (for example) Socrates and Socrates + seated are not identical.

Part I contains the formalization of the theory of accidental sameness. In Part II, I review some passages in which Aristotle tries to connect the theory of accidental sameness with inference. In Part III, finally, I pursue the philosophical applications of Aristotle's theory, in particular, its implications for ontology.

I. THE BASIC NOTIONS

1. Paronyms and Accidental Compounds

At the beginning of the Categories, Aristotle spells out a notion which is related in important ways to his notion of an accident:

When things are called after something, in accordance with its name but differing in ending, they are said to be paronyms. Thus, for example, the grammarian gets his name from grammar, the brave gets his from bravery.2 (la12-15)

Although Aristotle does not explicitly separate the two notions, we can distinguish the property of being a paronym from the relation, 'x is a paronym of y'. The two are connected in the natural way: something x is a paronym if and only if there is a suitable y such that x is a paronym of y. The relation, 'x is a paronym of y', is a relation between entities, not between expressions.3 Paronyms too are entities, and not linguistic items. Nonetheless, Aristotle sees a close connection between paronymy and matters of language. Thus, according to Aristotle, a is a paronym of b only if there is a designator a of a and a designator f of b such that a is derived 'with a difference of inflection' from

A. The grammarian, for example, is a paronym of grammar in virtue of the fact



ACCIDENTAL SAMENESS IN ARISTOTLE 3

that he is called '(the) grammarian' and that grammar is called 'grammar'4. Aristotle himself presents syntactical facts of the kind quoted as logically

necessary conditions for paronymy, so that for him, paronymy is essentially tied to matters of syntax. But he also takes paronymy to be a symptom of underlying metaphysical relationships, and it is these we shall want to concen- trate on. Provisionally, therefore, we can treat paronymy as a metaphysical notion, and regard accidental facts of syntax of the kind Aristotle notes as only a mark of paronymy, without being logically necessary conditions for it.5

How, then, are we to understand the metaphysical notion of paronymy? As Aristotle's examples make clear, one important ingredient in paronymy is his notion of an accident. The paronym the generous one, for example, is a paronym of, or is named after, the accident, generosity. Accidents and paronyms are not the same. The difference between them is reflected in Aristotle's chapter on quality (Categories 8) in the contrast between 'qualities' (7rotonMreq) and 'things qualified' (nrot), where the latter are 'spoken of paronymously after' the former (ra KCTrac TaVTr [TtO-T6nr] Tap&wP5jpw Xe'y6eva, Cate- gories 1 Oa29, cf. 8b25). A similar contrast is implied by Aristotle's remark (Categories 6b 11-14) that a paronym from an item in the category of position is not itself a position.6 In this case at least, then, a paronym is not a member of the same category as the accident from which it is constructed. If this result holds generally, then again a paronym is not the same as an accident.7

A more difficult question concerns the relation between paronyms and substances. The simple view is that substances are paronyms. For example, Furth writes

... it's Socrates who is the paronym. So 'bravery' [= the abstract noun] names braveryN, and 'braveA' [ the adjective I names Socrates (if braveryN inheres in Socrates). (Furth, unpublished)

A well-known example of Quine's makes it hard to resist this conclusion. We know that the generous one is so-named after generosity. Now it is false that Socrates is so-named after generosity. But we cannot use this fact in order to conclude that substances are not paronyms, for this would be to overlook the demonstrative in the predicate '... is so-named after ---'. In the claim,

The generous one is so-named after generosity,



4 FRANK A. LEWIS

we need only replace the demonstrative with the predicate it refers back to:

The generous one is named 'generous' after generosity.

and the conclusion that substances are paronyms is ready to hand. For example, if Socrates is the generous one, then he, Socrates, is named 'generous' after generosity, and he is a paronym. For, the opacity of the subject position in the original sentence has now been removed (to be precise, it is now confined to the quotation-mark context, 'generous').

The appeal of this argument, borrowed from Quine's treatment of the Giorgione-Barbarelli case (Quine, 1960, p. 153), is, I think, misleading. The key difference between the paronymy cases and Quine's example lies in the interpretation of referring expressions like 'the generous (one)' in Aristotle. The Quinean treatment just sketched assumes that 'the generous (one)' can be co-referential with 'Socrates' if the circumstances are right, i.e. (in part) if Socrates is generous. This is to give paronymous referring expressions the logic of our definite descriptions. Thus,

the generous one

becomes

the x such that x (alone) is generous.

And then, at least in a wide range of cases, the ordinary apparatus of

reference allows us to interchange expressions of this form for proper names of substances: 'Socrates', and the like.

A preferable view, I think, is that Aristotle's expression 'the generous (one)', for example, does not have the logic of a definite description, 'the x such that x (alone) is generous', but is a name of some entity other than x. What entity might this be? Here, it is useful to compare paronyms, which are the denotation of expressions like 'the generous (one)', with what in the Metaphysics Aristotle calls alternatively 'compounds by way of the other

categories' (KaT&r&r 'aLXXa Kar7fyoptiaq U)OETa, Metaphysics Z4, 1029b22- 27), or 'things spoken of in virtue of an accident' (r&_ V X7eyogv&w Kacra

UVPO6E3KOS, Metaphysics Z6, 1031al9, b22-23, cf. D7). Examples of these latter kinds of entity are the referents of such expressions as 'musical Socra- tes', '(the) pale man', 'Socrates seated', and the like. I shall suppose that paronymous referring expressions are merely elliptical forms of expressions of this




latter sort. Aristotle's remarks at Metaphysics Zl, 1028a25-28, suggest that the elliptical reading of paronymous referring expressions is the correct one:

These (sc. the walking (thing), the seated (thing), the healthy (thing)) are evidently more of the nature of beings, since there is such a thing as a definite subject underlying them (and this is the substance, i.e., the particular), "which is plainly implied in the use of such a designation" [Ross's phrase]; for the good (thing) or the seated (thing) is not said without this.

For example, suppose that Socrates is generous. Then both 'the generous (one)', in a suitable context of utterance, and 'generous Socrates' have the same denotation. Accordingly, I will replace both of these Aristotelian names with the single name, 'Socrates + generous'8. The name 'Socrates + generous' is intended to denote the compound of the substance Socrates and the accident generosity. This view is in the spirit of Aristotle's account in the Catego- ries, where if 'p' is an accidental predicate of a, the accident ep inheres in the underlying substance a. It also recalls exactly Aristotle's reference to compounds (azvO0era) of a substance with an item from a category other than substance at Metaphysics Z4, 1029b22-27 (cited earlier in the paragraph).

We may notice immediately that Socrates is not identical with Socrates + generous. We find a clear reason for taking them to be different in the fact which Aristotle notes (in terms of a different example) at G & C A4, 319b25- 32: they come into existence and go out of existence at different times. For Socrates, the change of becoming unmusical is mere alteration; but for Socra- tes + musical, it is sheer extinction. In the same vein at An. Pr. 47b29-37, Aristotle criticizes the inference from the premisses (i) Musical Mikkalus will perish tomorrow, and (ii) Mikkalus is musical Mikkalus, to the conclusion, (iii) Mikkalus will perish tomorrow. The premisses can be true, Aristotle remarks, but the conclusion false. Musical Mikkalus and Mikkalus exist at different times, then, for Mikkalus may continue to exist after musical Mikkalus has perished. But as before, this fact shows that the two are not identical.

As I mean to use the designator, 'Socrates + generous', therefore, the expression is not a slightly round-about way of naming Socrates (supposing it is Socrates who is generous). It names a different entity: not the substance, but the compound of that substance and the accident, generosity.9

The compound Socrates + generous is a paronym of generosity, even by Aristotle's syntactical criterion, for its name, 'Socrates + generous', is derived



6 FRANK A. LEWIS

at least in part, and with a 'difference in inflection', from the name 'generosity'. Underlying this accident of syntax, however, is the ontological fact that the compound has generosity as a constituent. This ontological fact for Aristotle is what counts in the end, while paronymy fades from his attention. The disadvantage of paronymy is that it is not, in Aristotle's treatment, an exclusively metaphysical notion. At its first appearance in the Categories, for example, it is tied to logically necessary conditions involving language.10 But as Aris- totle himself came to see, the metaphysical facts are unaffected by the accidents of language. For example, at Metaphysics Z4, 1029b27ff, he recognizes that the question whether a pale man is a metaphysical unity or not is not settled by whether the language we use to refer to it is itself complex ('pale man') or simple ('cloak'). Thus paronymy too is in the last resort unuseful because it is too closely tied to matters of language. With Aristotle, then, I shall set aside the notion of a paronym hereafter, and talk instead of an accidental compound (a 'compound by way of an accident', Metaphysics Z4, 1029b22-27), for short, a compound simpliciter.

We can now state our results formally. First, suppose that

(A1) If x + o exists, then x is a substance and ep is an accident."1

The axiom (Al) tells us the category (in both the modern and the Aristotelian sense) of the objects x and y that make up a compound, x + y. Next, we define the notion of a compound:

(Dl) x is an accidental compound (a compound for short) if and only if for some substance y and some accident <p, x = y + op.

A compound in the sense intended here belongs in no single category, but is a cross-categorical hybrid, compounded from a substance and an item from some non-substance category.

One last word about paronyms. As argued earlier, all paronyms are compounds: the required sense of 'compound' is now defined in (Dl). But no substance is a compound in this sense. Hence, no substance is a paronym. It is true, then, that the generous one is a paronym (it is a paronym of generosity). But as before, Socrates is not a paronym, even if he is called 'generous'.




2. Compounds, Accidents, and Accidental Sameness

At least part of the difference between Aristotle's relations 'x is an accident of y' and 'x is accidentally the same as y' lies in the distinction between an accident and a compound. Thus, the relations are subject to these two different type-restrictions: 12

(A2) x is an accident of y only if x is an accident andy is a substance.13 (A3) x is accidentally the same as y only if exactly one of x and y

is a substance and exactly one is a compound."4

The relation 'x is an accident of y' holds between a substance and an accident: for example, Coriscus and the accident, to be approaching. The relation 'x is accidentally the same as y' holds between a substance and a compound: for example, Coriscus and the one approaching. It follows from these two restrictions that 'x is an accident of y' and 'x is accidentally the same as y' are both irreflexive relations, given the assumptions that no substance is an accident, and that no substance is a compound.1"

The relation, 'x is an accident of y', can be defined in terms of the basic notion of a compound:

(D2) p is an accident of a if and only if a + ep exists.

(D2) is meant to recall Aristotle's procedure in the Categories, where he appeals to inherence as a primitive notion in his account of how an item from a non-substance category is predicated of a substance. We can now define the relation, 'x is accidentally the same as y'. By (A3), we know that accidental sameness is a relation between a substance and a compound, (Dl) above specifies that a compound may be unpacked as compound of a substance with an accident. With the aid of (D 1), then, we can define accidental sameness in terms of the relation, 'x is an accident of y':

(D3) a is accidentally the same as b if and only if either there is a ep such that a is of the form b + ep, where p is an accident of b, or there is a 4 such that b is of the form a + 4, where 4 is an accident of a.

For example, let a be the generous one, and let this be accidentally the same as Socrates. Then the generous one is of the form Socrates + generous, where generosity is an accident of Socrates. And Coriscus is accidentally the same as



8 FRANK A. LEWIS

the pale one, since the pale one = Coriscus + pale, and pallor (or pale: the difference in inflection is not always present) is an accident of Coriscus.'6

(D3) shows that the relation 'x is accidentally the same as y' is symmetric, for 'or' in the definiens is commutative. This suggests that the relation is also not transitive. For by symmetry we may have both

(1) The pale one is accidentally the same as Socrates

and

(2) Socrates is accidentally the same as the pale one.

Yet we cannot use (1) and (2) as premisses in order to conclude that

(3) The pale one is accidentally the same as the pale one,

for (3) is ill-formed in view of the type-restriction (A3) above. (There should be no doubt that [3] is unacceptable: the intuition that, on the contrary, [3] is true is explained in Section 3 immediately following.) Accidental sameness, then is symmetric in light of (D3), and not transitive.

A little more argument shows that the relation is intransitive. Suppose that an item a is accidentally the same as b, and that b is accidentally the same as c. By (A3), a is either a substance or a compound. If a is a substance, then by two applications of (A3), b is a compound and c is a substance. By (A3) again, therefore, a cannot be accidentally the same as c. Alternatively, a is a compound. But then b is a substance and c is a compound, by (A3). Again, therefore, a is not accidentally the same as c, by (A3). Hence, the relation is

17 intransitive. The relation 'x is an accident of y' behaves somewhat differently. First,

it is asymmetric, by (A2) and the assumption that no substance is an accident. It is also vacuously both transitive and intransitive. For, suppose that an item a is a accident of something b, and that b is an accident of something c. Then by (A2) above, b is both a substance and an accident, which is impossible. Hence, there are no 'accident chains' with more than two members (ob6e yayp 1rXeto uVgrrXeKerat 6votiu, Metaphysics G4, 1007bl-2), and the relation 'x is an accident of y' is vacuously transitive and intransitive.18 For, the antecedent in the definitions of transitivity and intransitivity, which are conditional in form, is never satisfied:

Transitivity. (x)(y)(z)(Rxy & Ryz -- Rxz). Intransitivity. (x)(y)(z)(Rxy & Ryz -+ - Rxz).




3. Accidental Sameness*

It may seem that there are counter-examples to the type restrictions in (A3) above for accidental sameness, if there can be true sentences of the following sort:

(4) The pale one is accidentally the same as the musical one.

(4) appears to be an assertion of accidental sameness which violates (A3) by relating a compound to a compound. In fact, however, such sentences are assertions of a different kind of accidental sameness, which we will call 'accidental sameness*'. Accidental sameness* is subject to the following type- restriction:

(A4) x is accidentally the same* as y only if x is a compound and y is a compound.

We define the relation in terms of the core notion of simple accidental sameness above:

(D4) x is accidentally the same* as y if and only if there is a unique z such that x is accidentally the same as z and a unique w such that y is accidentally the same as w, and z = w. 19

It follows immediately from (D4) that accidental sameness* is an equivalence relation. The relation is reflexive given the first 'and' in the definiens, for the same reason that conjunction can be accounted reflexive (Quine, 1951, p. 56). It is symmetric, by the commutivity of 'and'. Lastly, the relation is transitive. For, suppose a is accidentally the same* as b, and b is accidentally the same* as c. Then by (D4) there is a unique x such that a is accidentally the same as x, a unique y such that b is accidentally the same as y, and a unique z such that c is accidentally the same as z. But we also know that x = y and y = z. Hence by transitivity, x = z. It follows that a is accidentally the same* as c, by (D4).

4. The relation 'x is an accident* of y'

The distinction between accidental sameness and accidental sameness* is matched by a parallel distinction between the relations 'x is an accident of y' and 'x is an accident* of y'. As we shall see, Aristotle is explicit that these



10 FRANK A. LEWIS

last two are different relations. They differ first in the type-restrictions that apply to each. 'x is an accident of y' is governed by (A2) above. 'x is an accident* of y', by contrast, obeys the following type-restriction:

(A5) x is an accident* of y only if x is an accident and y is an accident.

The difference between (A2) and (A5) mirrors Aristotle's remarks at Metaphysics G4, 1007b 13-17 (cf. 1007b7):

...and at the same time, there is the distinction that, while some things are accidental in this sense, others are accidental in the way in which the musical (is accidental to) So- crates; for in none of the latter cases is the accidental an accident of the accidental, but this is so in the former cases.

But, further, just as the relation 'x is accidentally the same* as y' is explained in terms of ordinary accidental sameness, so 'x is an accident* of y' is defined in terms of the core notion, 'x is an accident of y':

(D5) x is an accident* of y if and only if there is a z such that x is an accident of z and y is an accident of z.

Thus Aristotle remarks at Metaphysics G4, 1 007b2--5:

An accident is not an accident of an accident, unless because both are accidents of the same thing, I mean for example that the pale may be musical and it [= the musical] pale because both are accidents of the man.20

Aristotle insists on distinguishing the relation 'x is an accident* of y' from the core relation because of a commitment to a key doctrine concerning substance. The notions of being a substance and of being a subject are always connected in Aristotle's mind. A leading idea about substance is that substance is the subject of everything, or (as he comes to modify the point in the Metaphysics, for example, Metaphysics 7, 1049a27-36) that it is one of the two kinds of subject.2' In either case, Aristotle cannot allow that an accident should be, in the ordinary sense, an accident of an accident. Apparent counter-examples to this are to be treated by means of (D5), which restores substance to its place as the (one and only) subject of accidents.

Unlike the core relations, 'x is an accident* of y' is an equivalence relation. This result follows immediately from (D5); the arguments are analogous to those that show that accidental sameness* is an equivalence relation in light of (D4). Aristotle asserts that the relation is symmetric at Metaphysics G4, 1007bl2-14.




5. Some Confusions: Accidental Sameness vs. Accidental Sameness*; 'x is an accident of y' vs. 'x is an accident* of y'

There is a strong case for distinguishing Aristotle's two core relations, 'x is an accident of y' and 'x is accidentally the same as y', from the two starred relations. Aristotle himself explicitly separates 'x is an accident of y' and 'x is an accident* of y'; as we have seen, his views about the central role of substance as a subject give him a powerful motivation for doing so. He is not explicit on the second distinction between accidental sameness and accidental sameness*. But the two distinctions are closely parallel, since each pairs a core relation with a second that is defined in terms of the first. So I take the fact that he expressly draws the one distinction as evidence that he would accept the other one too.

There are dangers is not distinguishing clearly between these various relations. Consider accidental sameness and accidental sameness*. There are no formal reasons against adopting a single relation, call it 'ACCIDENTAL SAMENESS', defined as the union of accidental sameness and accidental sameness*. But it is important to keep separate the different sub-relations from which ACCIDENTAL SAMENESS is composed.22 An example of how these may be confused is the argument by Pelletier (1979) for the conclusion that the relation 'x is accidentally the same as y' is symmetric, irreflexive, but not transitive.23 Pelletier argues that the claims

(5) This pale man is accidentally the same as this educated man

and

(6) This educated man is accidentally the same as this pale man

can both be true. Indeed, they are both true if either is, for the relation is symmetric. Yet the further claim

(7) This pale man is accidentally the same as this pale man

is surely false. For Aristotle's relation seems to be irreflexive. Hence, it is also not transitive.

These conclusions suffer from a number of difficulties. Taken as expressions of accidental sameness in the strict sense, the claims (5), (6), and (7) are ill-formed, by the type-restrictions on accidental sameness above. If, on the contrary, we suppose with Pelletier that (5) and (6) can both be true, we



12 FRANK A. LEWIS

must read them as expressions of accidental sameness* (and hence also of ACCIDENTAL SAMENESS):

(8) The pale one is accidentally the same* as the musical one. (9) The musical one is accidentally the same* as the pale one.

But if (7) is to be false, we cannot interpret it in a similar fashion:

(10) The pale one is accidentally the same* as the pale one,

for (10) must be true if either (8) or (9) is true, by elementary logic and the definition of accidental sameness*. Given that (8) or (9) is true, (7) can be false only if we read (7) as an expression of the irreflexive relation, accidental sameness simpliciter. (But (7) will be true if it is read as an assertion of the relation ACCIDENTAL SAMENESS.) So there is no single notion of sameness underlying Pelletier's evaluations of the three claims, and his argument equivocates on two different senses of 'same'.

Pelletier concludes that there is a relation of accidental sameness that is irreflexive, symmetric, and not transitive. This successfully characterizes the core relation of accidental sameness, with one qualification: 'not transitive' in his account can now be firmed up to 'intransitive'. Someone who confuses accidental sameness and accidental sameness* may be tempted to use the weaker description, because he perceives, correctly, that sentences such as (8), (9), and (10) above may all be true together. But it is important to see that this possibility reflects a property of accidental sameness* rather than of accidental sameness simpliciter. Accidental sameness simpliciter is firmly intransitive, while accidental sameness* is equally firmly transitive.

Analogous difficulties surround the distinction between the relations, 'x is an accident of y' and 'x is an accident* of y'. An example is Kirwan's discussion (1977, p. 101) of Aristotle's argument (Metaphysics G4, 1007a32- b 1) that there can be no 'accident chains' of more than two members: that is, any sequence defined by the relation 'x is an accident of y' has at most two members. Kirwan writes, "given that Y coincides in X, it is not possible that any Z should coincide in Y. This is qualified to allow for the transitive case in which Z and Y coincide because both coincide in X" (my italics). Kirwan appears to have the following argument in mind. Suppose y is an accident of x. Then there is no z such that z is an accident of y. This result accords with the argument already sketched in I (2) above. Yet, Kirwan says, it can also happen that




(1 1) y coincides in x

and

(12) z coincides in x,

so that, by symmetric and transitivity, we have

(13) z andy coincide.

But Kirwan is surely wrong in supposing that this latter argument requires any qualification of our previous results. The argument suffers from two flaws. First, it is the relation 'x is an accident* of y' (Kirwan's 'x and y coincide') that is symmetric; the relation 'x is an accident of y' (his 'x coincides in y') is asymmetric. And this difficulty aside, there are still no grounds for appealing to transitivity to help license the move from (11) and (12) to (13). For, while (11) and (12) evidently involve the relation 'x is an accident of y', (13) is concerned rather with the different relation, 'x is an accident* of y'. So there is no one relation here to call transitive in the first place.

6. Counterexamples to the Formalization of Accidental Sameness: Some Troublesome Principles of Inference in the 'Topics'

Elsewhere in the Topics, Aristotle puts forward some principles that are in serious conflict with the apparatus developed above. At Topics 133bl7-21, he says this:

For an attribute that belongs to something qualified by an accident will also belong to the accident taken along with the subject which it qualifies; for example, an attribute that belongs to a man will belong also to a pale man, if he be a pale man, and one that belongs to a pale man will belong also to a man. (Adapted from the Oxford Translation.)

Aristotle's examples here suggest that in his view both of the following exhibit valid patterns of inference:

(14) p is an accident of a & 4 is an accident of a - 4 is an accident of a + (,.

(15) 4 is an accident of a + 4p is an accident of a.

This suggestion raises severe difficulties, however. To generalize the idea of the passage: Aristotle apparently allows us to construct a sequence of accidents and subjects of the following form:



14 FRANK A. LEWIS

<1 is an accident of a

p2 is an accident of a + (pl

p'1 is an accident of (...(a + ))pl + fp-'

Such a sequence is in direct conflict with our account here, for entities of the form (...(a+ <p)...) + e do not exist, by (Al). The Topics passage is also inconsistent with other parts of our reconstruction of Aristotle's scheme. For, if any steps beyond the first in the sequence indicated are possible, we must give up either the claim in (A2) that, wherever x is an accident of y, y is a substance, or the view that nothing is both a substance and a compound.

A passage at Topics 7.1, 1 52a3 1-32, raises similar difficulties. Aristotle says:

Again, look and see if, supposing the one to be the same as something, the other is also the same as it: for if they are not both the same as the same thing, clearly neither are they the same as one another (the Oxford Translation).

These remarks seem to suggest the following principle:

(16) x is accidentally the same as y -* (x is accidentally the same as z e y is accidentally the same as z).

This principle seems to show that Aristotle is willing to regard accidental sameness as not merely symmetric, but in fact an equivalence relation, contrary to the argument in 1(2) above that the relation is both irreflexive and intransitive. That earlier argument was based on the type-restrictions on accidental sameness set out in (A3). But if (16) is correct, those type-restrictions must also go by the board. For, let x be the substance a and y the compound a + p, so that the antecedent of (16) is well-formed by (A3). Then as an instance of the principle, we have (for different values for 'z') either

(17) a is accidentally the same as a + p - (a is accidentally the same as a + 4 - a + <p is accidentally the same as a + 4),

or

(18) a is accidentally the same as a + ep - (a is accidentally the same as b * a + <o is accidentally the same as b).

And in general, every instance of (16) is a counterexample to the type-restrictions in (A3).




The principles of inference exemplified in (14), (15), and (16) directly threaten axioms at the heart of the formalization of accidental sameness offered in earlier sections above. Elsewhere in Aristotle,`however, we find clear evidence that Aristotle has come to reject the troublesome principles of inference. Thus, at Metaphysics G4, 1007blff, Aristotle expressly prohibits sequences of the kind exhibited above, on the grounds that an entity of the form (... (a + fp' )...) + <p' is not a proper subject for accidents: "for, not everything makes up one thing", 1007blO. These strictures accord exactly with our account here, for as we have seen, entities of the form in question do not exist, by (Al). Metaphysics G4, therefore, supports our choice of (A3): the inferential principles illustrated in (14), (15), and (16) are neither valid nor invalid, for portions of each are simply ill-formed. In fact, however, Aristotle is already committed to rejecting these principles by developments in the de Soph. El. Accordingly, the controversial principles at Topics 1 33bl 7- 21 and 152a31-32 can help motivate a wider look at some of Aristotle's more systematic remarks about accidental sameness and its place in inference elsewhere in the Topics and in the de Soph. El.

II. ACCIDENTAL SAMENESS AND INFERENCE

1. Accidental Sameness in the 'Topics'and 'de Soph. El.'

Our subject begins at Topics 1.7. Here, Aristotle introduces a notion of 'numerical sameness', exemplified in those cases where there is "more than one name, but only one thing" (Topics 103a9-10). Numerical sameness comes in three kinds: numerical sameness rendered by definition (the 'most proper and primary' notion of sameness [KvptW.rara ... KctX 7Tp&rwoz, 103a25- 26] ), rendered by proprium, and rendered by accident. Later in the Topics (Topics 7.1), Aristotle refers back to his earlier discussion of numerical sameness,24 and introduces a number of principles of inference based on numerical sameness. Now a modern expectation is that, if two things are the same in some sense, they will, in some suitable way, share their properties. Perhaps the most revealing of Aristotle's principles for us are those that come closest to reflecting this intuition. For example, at Topics 152a33ff, Aristotle says:

Moreover, examine them (sc. things alleged to be numerically the same) in the light of their accidents, or of the things of which they are accidents: for, any accident belonging



16 FRANK A. LEWIS

to the one must also belong to the other, and if the one belongs to anything as an accident, so must the other too. If in any of these respects there is a discrepancy, clearly they are not the same.

Aristotle's remarks here are apparently intended to hold for any kind of numerical sameness, including the weakest kind of numerical sameness, simple accidental sameness. If we restrict ourselves to this weakest notion of accidental sameness, we can extract the following principle from the passage:

(T1) a is accidentally the same as a + ep -- (for all accidents 4) (4 is an accident of a e; 4is an accident of a + ep).

(Ti) is restricted to all those accidents 4 that holds of two things a and a + ep alleged to be accidentally the same. Later in the chater, (TI) is expanded to hold for all predicates whatsoever, without the restriction to accidents (152b25-29). Suppose that two things are numerically the same. Then in general, Aristotle says,

one ought to consider if there is any discrepancy among what is predicated of each in any way whatsoever (rcov birwaoov... KarrJ'yopovM4vcwv), and among what these are predicated of. For everything that is predicated of the one must be predicated of the other, and everything the one is predicated of, the other must be predicated of too. (my italics) 25

From this, we can extract this extension of (Ti):

(T1+) a is accidentally the same as a + -o - (for all 4) (a is subject to 4

*+ a + p is subject to 4).

Other developments in the chapter make it unmistakeable that Aristotle intends this extended principle to hold where '4' is a modal predicate. The principle at 152b34-35, for example, is equivalent to the instance of (Ti+) where '4(x)' ='L(x exists)'26. And at 152b22-24, Aristotle takes discemi- bility in counterfactual situations as sufficient grounds for denying numerical sameness:

...by a supposition, which may be true or may be false (it makes no difference which), one character is annulled and not the other, showing that they are not the same. (my italics)

Thus, if x is numerically the same as y, it is impossible that one should have an attribute which the other lacks. That is,

cL(p(x) 0)

But from this it follows that




L](p(x)) p (y)

by the modal principle,

0L(P -Q) HDP -*LQ.

Finally, the principle at 152blOff too can be interpreted as implying that, where a is numerically the same as b, a is necessarily p if and only if b is necessarily p.23 On this evidence, Aristotle seems committed to holding that (T1) and (T1+) hold in intensional as well as extensional contexts.

In the de Soph. El., however, under pressure from the modal and epistemic paradoxes, Aristotle comes to doubt (TI) and its expansion, (T1+).28 In their place, he proposes the rule:

Flor, only to things that are one and indistinguishable in being is it generally agreed that all the same attributes belong. - (de Soph. El., 179a37-39, cf. Physics G3, 202bl4-16)

More formally:

(T2) If x is numerically the same in being as y, then lp is an attribute of x if and only if ep is an attribute of y. 29

'x is numerically the same in being as y' is a different relation from 'x is accidentally the same as y': both are restrictions (but different restrictions) on the relation of numerical sameness simpliciter introduced in Topics 1.7 (Topics 1.7, 103a25-31).

2. The Troublesome Principles of Inference in the 'Topics' Once More

Aristotle's rejection of (TI) in the de Soph El. allows us to resolve the difficulties raised in 1(6) above conceming the principles (14) and (15). Like those principles, (TI) and its expansion (Tl+) recognize entities of the form a + o as subjects of accidents, in conflict with the claim in (A2) that if x is an accident of y, then y is a substance. More importantly, (TI) is a consequence of (14) and (15), given only the definition (D4). Thus

(14) tp is an accident of a & 4 is an accident of a -; is an accident of a + p

is equivalent by (D3) to



18 FRANK A. LEWIS

(17) a is accidentally the same as a + -p (4 is an accident of a -; is an accident of a + (p).

And given

(15) 4 is an accident of a + <p 4 is an accident of a,

we have

(18) a is accidentally the same as a + -p (4 is an accident of a + tp -* 4 is an accident of a).

(17) and (18) together give (TI).

By rejecting (TI), therefore, Aristotle also rejects the problematic principles (14) and (15).3 This removes the difficulties surrounding the axioms (Al) and (A2) above. The only proviso to add is that, while in the de Soph. El. Aristotle appears to hold that (14), (15), and (Ti) are invalid, he is committed in the Metaphysics to the view that they are neither valid nor invalid, but simply ill-formed.

A similar treatment can be given to the principle (16), derived from Topics 7.1, 152a31-32:

(16) x is accidentally the same as y -* (x is accidentally the same as z e y is accidentally the same as z).

With (16), Aristotle appears to maintain that accidental sameness is an equivalence relation, contrary to the claim in 1(2) that the relation is symmetric, but irreflexive and intransitive. We can now notice, however, that (16) is an instance of the principle (TI), for ';(x)' = 'x is accidentally the same as z'. Since Aristotle rejects (TI) in the de Soph. El., he is no longer committed to (16). Perhaps in the de Soph. El. he would say merely that (16) is invalid; the Metaphysics commits him to the stronger view that it is ill-formed. In either case, (16) no longer offers any threat to (A3).

III. SOME APPLICATIONS OF THE THEORY

1. FirstApplication: A PhilosophicalCharacterization of Accidental Sameness

We are now in a position to consider some philosophical applications of the theory of accidental sameness. I begin with the philosophical characterization




of accidental sameness itself. Does accidental sameness have any immediate counterpart in modern theory? More particularly, what is the relation between Aristotle's notion and modern notions of identity?

First, clearly enough, accidental sameness is not identity in the strict sense. For example, if Coriscus is pale, then Coriscus is accidentally the same as Coriscus + pale, by (D3). But Coriscus is not identical with Coriscus + pale, for the same reason that any compound is non-identical with one of its constituents. And further, as Aristotle recognizes, Coriscus may still exist when Coriscus is no longer pale, that is, when Coriscus + pale has passed out of existence.3"

But are Coriscus and Coriscus + pale perhaps contingently identical? Contingent identity is said to hold between objects that have all their 'obvious' (that is, non-modal, and in general extensional) properties in common. For example, it is said, Hesperus and Phosphorus are one planet in the actual world, since whatever is in fact true of the one is true of the other. But they might not have been the same, the contingent identity theorist will argue, for in other possible worlds they have divergent properties, and are not the same. Hence, they are merely contingently identical.32 At first sight, a notion of contingent identity sits well with (TI), which is a principle of substitution based on accidental sameness and limited to extensional (non- modal, non-epistemic) contexts. And of course the very label, 'accidental sameness', recalls the modern term, 'contingent identity'.

In fact, however, these analogies with contingent identity are misleading. Aristotle's first thoughts in de Soph. El. are that (TI) is invalid: the counter- examples involve intensional predicates, so that it is possible for us to think that (T1) survives as a principle for extensional contexts. In reply to this suggestion: first, as we shall see, there are other counter-examples to (TI) that do not involve intensional predicates. And second, Aristotle's later thoughts in Metaphysics G suggest that no instance of (TI) is true even in extensional contexts. The type-restrictions on accidental sameness in (A3) show that (TI) cannot hold in any context, for all instances of (TI) are ill- formed, by (A3). Both of these arguments show that (TI) cannot function as a 'principle of extensionality'; as a result, a major reason for finding the analogy between accidental sameness and contingent identity attractive disappears.

But in any case, accidental sameness and contingent identity are not the same. If Hesperus and Phosphorus are contingently identical, they must at



20 FRANK A. LEWIS

least be identical in the actual world, as we saw. But of course, Coriscus and Coriscus + pale are not the same entity in any world, actual or otherwise. Coriscus and Coriscus + pale are accidentally the same, but they are not contingently identical. So accidental sameness is not contingent identity.

2. Second Application: Sameness and Ontology

I turn now to connections between the theory of sameness and ontology. A good starting point is the difference between the two substitution theorems (TI) and (T2), and the consequences this difference may have for ontology.

In the Metaphysics, as we have seen, Aristotle is committed to holding that (TI) is simply irl-formed. But his intermediate view, represented in the de Soph. El., seems to be merely that (TI) is invalid. More precisely, (TI) is based on a weak notion of numerical sameness, and so fails in a language containing modal or epistemic predicates, as the paradoxes demonstrate. This leaves open the possibility that (Ti) is valid in a language which lacks modal and epistemic predicates. Suppose that (TI), or the stronger (Tl+), is in fact valid in such a language. Then within that language, we can see no difference between, say, Socrates and Socrates + pale. According to (TI), two objects are accidentally the same only if whatever is an accident of the one is also an accident of the other. (Tl+) generalizes this result for all attributes whatever. Suppose, then, that Socrates and Socrates + pale are accidentally the same. On this assumption, and given a language for which (TI) is the substitution theorem, we have no means for distinguishing Socrates and Socrates + pale by reference to their accidents. And if (Tl+) is our substitution theorem, there are no means whatever for distinguishing the two.

The strengthened theorem (T2), by contrast, is constructed around the stronger notion of sameness in being. This is a stronger kind of sameness in part because it purports to allow substitution in contexts for which (TI) is said to fail. That is, (T2) is a substitution theorem for languages that are not purely extensional. The other side of this coin is that (T2) also introduces a refinement in our view of what should be included in Aristotle's ontology. According to (T2), two objects are the same in being only if they share all the same accidents. So it must treat Socrates and Socrates + pale as different objects, because they are not indiscernible with respect to various modal and epistemic predicates. In reaching this conclusion, we assume that (T2) holds in intensional contexts, and use intensional counterexamples to distinguish Socrates and Socrates + pale.




The difference in ontology which the two principles (TI) and (T2) imply can be illustrated by Aristotle's resolution of a puzzle concerning propria described at Topics 5.4, 133bl5ff. Suppose that the attribute of being one who laughs is a proprium of man, that is, that all and only men are laughers. Suppose also that some object which is a man is also pale. The being a laugher belongs not only to any man, but also to the pale one. Hence, being a laugher is not a proprium of man after all. Aristotle's solution to this puzzle is to point out that the man in question is not without qualification other than the pale one (EVepov darXcZ, b31-32). They are not identical, but at the same time, they are accidentally the same. There are contexts, then, in which they are not discernible one from the other. They are not, for example, distinguished if we ask whether what is a proprium of the one is also a proprium of the other. For example, suppose that Socrates is the pale one in question. Then by (TI) apparently, substitution of 'Socrates + pale' for 'Socrates' in a true sentence of the form

(19) Q is a proprium of Socrates

leads to another true sentence of the form

(20) 4 is a proprium of Socrates + pale.

In fact, the substitution principle (TI) appears to hold good in all contexts of the form, '4 is a proprium of...'. But the apparent success of (TI) in sus- taining substitution here does not show that Socrates and Socrates + pale are identical. In other contexts, substitution in accordance with (TI) fails, as the modal and epistemic paradoxes testify. Aristotle concludes that (T2) is the correct substitution principle to adopt, and this choice commits him to the finer-grained view which (T2) brings of what counts as the same entity.

But can we remain comfortable with the disparity in the view of 'what there is' which (TI) and (T2) suggest? As we have seen, (T1) holds (if at all) only in extensional contexts, while (T2) purports to hold in intensional contexts as well. This view of the matter has led to doubts about the nature of the distinction (T2) permits between Socrates and Socrates + pale. Dancy (1975), for example, concedes that Aristotle distinguishes Socrates and So- crates + pale. At the same time, however, according to Dancy, the difference between them is not the concem of ontology if ontology is a matter of "taking a census of the universe", or is "an inventory by way of response to the bare question 'what is there?' ". In distinguishing Socrates and Socrates + pale,



22 FRANK A. LEWIS

then, "Aristotle is not doing ontology". Dancy's views deserve to be quoted more fully. He writes:

A substance (and) a quality... are just plain different, no holds barred. But a substance (and) a quale... are formally distinct; in particular cases they might be numerically one. For the most part, the last point is not relevant; it becomes relevant only when some sophist produces confusion by ignoring it, and argues, say, that the census-taker must note down two citizens, Callias and Callias educated.... For the most part, talk of substances (and) qualia... has to do with formal distinctions, and all that is meant when one says that a quale is not a substance... is that for something to be a man is not for it to be pale or six feet tall, even where the something is six-foot pallid man.

This suggests that, if doing ontology is a matter of taking a census of the universe, or an inventory by way of response to the bare question 'what is there?' Aristotle is not doing ontology. - (Dancy, p. 368, my italics)

In Dancy's view, then, making the distinction between Socrates and Socrates + pale a part of ontology is akin to the fallacy committed by the sophist who argues that Socrates and Socrates + pale are two separate items for the census-taker to count.33 In fact, he thinks, the distinction between the two is only 'formal' (by this, I take him to mean that the distinction is an intensional one), hence it has no place in ontology.

On this last point, that intensional distinctions do not count in ontology, Dancy is surely at odds with contemporary orthodoxy. On the prevailing view, two things are identical only if they share all their properties, including the intensional ones. All identity is necessary identity, and there is no place for a restricted notion of 'contingent identity', so-called, which will count things identical if they share only all their ordinary, non-modal properties.34

Setting this issue aside, however, is the distinction in any case really an intensional one? I believe that it is not. Dancy argues that the census-taker is indifferent to the distinction between Socrates and Socrates + pale, and so perhaps, in a sense, he is. At least, he will always count exactly one citizen, no more, when he counts Socrates, whether or not Socrates is pale - that is, whether or not Socrates + pale also exists. In this respect, then, a substance and a compound are indistinguishable in the actual world. From the standpoint of ontology, the proper conclusion is, I think, so much the worse for the census-taker. When we do ontology, we can set Socrates down as one, single object, and discover later that there remains a second object to be counted, namely Socrates + pale. This discovery may result from a hypothesis about how things might have been. If Socrates might not have been pale, for example, then Socrates and Socrates + pale are not identical. (This is why we




should not concede that intensional distinctions have no place in ontology.) But the discovery that they are two may also come from changes in how the world actually is. At those times when Socrates exists, but is no longer pale, the census-taker still records one citizen: Socrates. But he does not count Socrates + pale, for Socrates is not pale, so that Socrates + pale does not exist. In this sense, the census-taker is not indifferent to the distinction between Socrates and Socrates + pale. His counting shows that Socrates is not identical with Socrates + pale. The one is not counted exactly when the other is, for they do not exist at the same times.

These same facts also falsify (TI). Socrates is accidentally the same as Socrates + pale, for Socrates is sometimes pale. But there can be ordinary, non-modal properties - being counted at t, for example - that Socrates has but Socrates + pale lacks. The natural emendation to (TI) is to say that (Ti) treats two objects a and a + p as the same, providing they both exist. But this concedes the crucial point, that a and a + o are sometimes distinguished in the actual world, when one exists and the other does not, even though (TI), as emended, fails to separate them.

The upshot of our discussion is this. Aristotle separates Socrates and So- crates + pale by means of intensional counter-examples in combination with (T2), which he claims holds in intensional contexts. (TI), meanwhile, which is purportedly valid for extensional contexts, treats them as indistinguishable. The appearance that the distinction between Socrates and Socrates + pale is an intensional one is nonetheless an illusion. For, (TI) is invalid even in extensional contexts. Socrates and Socrates + pale are distinguished also by their regular, non-modal properties, even though they are accidentally the same. So the distinction between them is not an intensional one.

3. 7hird Application: Sameness, Ontology, and Reference Opacity

A second line of argument also attempts to cloud the distinction between (say) Socrates and Socrates + pale. According to these arguments, the predicates, '... is a substance' and '...is a compound', along with many other classificatory predicates in Aristotle's ontological talk, are referentially opaque. If so, then there is no simple distinction, if there is any clear distinction at all, between the substance, Socrates, and the compound, Socrates + pale.

We may begin by considering once more the moral of the modal and epis-



24 FRANK A. LEWIS

temic paradoxes. The paradoxes teach us that putting 'Socrates + pale' for 'Socrates' in a true sentence of the form

#(ep(Socrates)),

where '#' is any modal or epistemic operator, may lead to a false sentence of the form,

#(Lp(Socrates + pale))

It is a complex matter to assess the failure of substitution in this case. In general, failure of substitution in contexts of the form

# (p(x))

is put down to the opacity of the position occupied by the variable 'x'. It is natural to suppose, then, that the failure of substitution which the modal and epistemic paradoxes dramatize is due to the referential opacity of modal

and epistemic contexts. But is this the moral Aristotle draws from the paradoxes?35 From Aristotle's point of view, it seems, the paradoxes depend on taking to be the same in being entities that are in fact only accidentally the same. Two points are relevant here. First, as we have seen, accidental sameness is not identity. Coriscus and Coriscus + pale are accidentally the same, but they are not identical. Second, our notion of referential opacity, as developed by Quine, is built around our concept of identity, and not around any loose substitute for that notion. A context A is referentially opaque if and only if for some expressions a and f such that a and ,B denote the identical entitV, a context A' is like A except that A contains a where A' contains ,3, but A and A' do not denote the same thing (or, if A and A' are sentences, A and A' do not have the same truth-value). Referential opacity, then, is defined around our notion of identity. Without identity as we con- ceive it, there is no opacity.

The implication of these two points is clear. The epistemic and modal paradoxes do not demonstrate that in general Aristotle regards modal and epistemic contexts as referentially opaque. That question is moot, for his examples in the paradoxes do not test those contexts with entities that are properly identical.

The paradoxes of the deSoph. El. do not show, then, that Aristotle recognizes the opacity of contexts which we ourselves are often disposed to regard




as opaque. It has also been claimed, however, that Aristotle treats as referentially opaque contexts which we would ordinarily suppose were routinely referentially transparent.36 Indeed, in some sense these contexts could be ex- pected to serve as paradigms of the referentially transparent. These further claims, then, are certainly surprising, and it is worth asking if they are also true.

In essence, the claim is that contexts such as

...is a substance

are referentially opaque. The sentence, for example,

(21) Socrates is a substance

is true, but the sentence

(22) The generous one is a substance

is false, even though it is Socrates who is generous.37 Hence, it is argued, the locution, '...is a substance', contains an opaque context, and things are substances only relative to an appropriate general term or appropriate 'substance- predicate'. An obvious extension of the same argument will purport to show that the context

...is a compound

is referentially opaque; and similarly for other contexts like it. These arguments recall a parody offered by David Kaplan (1969) in a

discussion of oblique contexts and indirect denotation in Frege. Consider

(23) Although F.D.R. ran for office many times, F.D.R. ran on television only once.

Kaplan writes:

The natural analysis [of (23)] involves pointing out that the name 'F D.R.' is ambiguous, and that in the second clause it denotes a television show rather than a man. Substitu- tions or any other logical operations based on the assumption that the name has here its usual denotation are pointless and demonstrate nothing. (Kaplan, 1969, p. 117)

Hence, 'only the fanatical mono-denotationalist' would argue that the context

... ran on television only once

is referentially opaque. Kaplan's example turns on the idea that opacity can



26 FRANK A. LEWIS

be traded here for ambiguity (an idea developed at a deeper level by Frege), but his point can apply as easily to the arguments concerning Aristotle above. A tacit assumption in ascriptions of opacity is identity: hence, the charge that '... is a substance' is referentially opaque can be dropped in favour of the view that (for example) Socrates and Socrates + generous are not identical.

This latter view is surely the preferable one to hold, if we take seriously the suggestion that the pale one is a compound of a substance with an accident. Coriscus, for example, has a clear place in the category of substance, while Coriscus + pale is a cross-categorial hybrid, that fits cleanly into no single category. Surely, then, such a compound is not the same entity as a substance?

This argument will not impress those who find the context '... is a substance' and Aristotle's other ontological predicates referentially opaque. Coriscus and Coriscus + pale may be classified differently in Aristotle's categorial scheme, but this is not a sign that they are not identical, for the usual apparatus of reference breaks down when combined with the relevant categorial predicates. In short, these predicates are referentially opaque. How strong is this line of argument?

The argument has little force if we adopt the account of compounds and accidental sameness offered here. Consider this argument:

(24) Coriscus is a substance (25) Coriscus is the pale one

So

(26) The pale one is a substance.

This argument is said to show that the context '... is a substance' is opaque, on the ground that (24) and (25) are both true, while (26) is false. [Without opacity, however, (26) must be true if (24) and (25) are true.] On the account of compounds and accidental sameness given here, however, the argument becomes

(24) Coriscus is a substance (27) Coriscus is accidentally the same as Coriscus + pale.

So

(28) Coriscus + pale is a substance.




This argument is valid, if we trust the extension of (TI), (T1+). But we should not trust (TI) or (T1+), for Aristotle has discarded both in de Soph. El., as we saw. There seem to be no other grounds for supposing that the argument is valid. And if there are not, then our motive for treating the predicate '...is a substance' as referentially opaque is gone. So the conclusion that the predicate is opaque has not demonstrated.

As these last arguments show, a crucial part of the argument for referential opacity in Aristotle's ontological predicates concerns what entities we admit into Aristotle's ontology, and the accompanying account we give of accidental sameness. The different ontological choices are reflected in the differing interpretations we can give to paronymous referring expressions like 'the generous (one)'. Suppose that these do not refer to compounds, as is done explicitly by the term of art introduced here:

Callias + generous,

but have the logic of ordinary (Russellian) definite descriptions:

the x such that x (alone) is generous.

This reading makes it altogether reasonable to use the argument (24)-(26) above to reach the conclusion that, once more, '...is a substance' and many other classificatory predicates in Aristotle^s ontological talk are referentially opaque. But, to look beyond the label, what does this conclusion mean? Why should the ordinary apparatus of reference fail, of all places, in contexts where if anywhere Aristotle means to talk about objects?

Alternatively, paronymous referring expressions have the form 'a + ip' as explained above, and '... is a substance' and the other workhorse predicates in Aristotle's ontological talk are straightforwardly transparent. On this account, his notion of accidental sameness has no immediate counterpart in modern theory. It is not clear that this is a disadvantage. And at least in doing ontology (his way of putting it: talking about roe 'ovrc) Aristotle is doing what we should expect him to do: talking about objects.38'39

University of Arizona



28 FRANK A. LEWIS

NOTES

1 A 'repudiating question': Aristotle means that it is of course the philosopher, none other, who will do the job mentioned. 2 The translation of this passage is discussed in Jones (1972), pp. 117-121. It is worth noticing the use-mention confusion in Aristotle's characterization here: the participle 6 ccnpEpOlvTc and the pronoun da& agree, so that literally, Aristotle says that it is things that differ in ending from the name of the object they are called after. 3 The view that paronymy is a relation between expressions is advanced by W. D. Ross (1936, p. 559). ' This can hardly be a point about which expression, for example, 'grammarian' or grammar', comes first morphologicallv. It is unlikely that the Greek dz'6pelo (English 'brave') is morphologically derivative from &v6pelo ('bravery'), and quite certain that ,ypcI4lcrTtK6c ('grammarian') is not so derivative on 'ypC&pA4TLKfl I sc. TeXvq I ('grammar'). So Aristotle's point must be about the semantics of our use of adjectives: the use of an adjective of a subject can be explained in terms of a relation between that subject and some entity named by a noun which in the ordinary case is syntactically related in some suitable way to the adjective. Although the phenomenon Aristotle is drawing our attention to here is at bottom an ontological one, however, he expresses himself in terms of the accidental syntactical relations between given adjectives and nouns in which that phenomenon is reflected: see the paragraph immediately following in the text, and Note 10 below.

For a more accurate view of the matter, see the end of this section. 6 Aristotle says:

To lie or to stand ITO 66 &VaK6Ea0aL X fUTdv& aL KaOfaOat are not them- selves positions, but they are spoken of paronymously from the positions mentioned (= lying, sitting, standing I) &V&XXtcan, i UT&dULI, ) Kc6O6pcl ).

The infinitives here, 'to lie', 'to stand', and so forth, stand in for uses of the verb to form singular predications, 'a is lying down', 'a is standing', and the like. In this respect, therefore, Aristotle supposes that verbs as well as adjectives are implicated in paronymy: see Jones (1972), p. 121, and Dancy (1975), p. 361. 7 This conclusion goes against the view attributed to Aristotle by Simplicius and Dexip- pus (W. D. Ross, 1952, p. 106) and picked up by Dancy (1975, pp. 368-369) and Note 41, cf. Code (1976b, p. 179), that a paronym is ("from a certain point of view", Dancy, loc. cit.) a member of the same category as the accident from which it is constructed. I take it that this claim is ruled out by Aristotle's remarks at Categories 6b1 1- 14, given only the highly plausible assumption that if an item is not a position, then it is not a member of the category of position. 8 The notation 'x + y' here is meant to express the notion of compounding, which I take to be primitive in Aristotle's theory. The interpretation of this notion is given, informally, by the informal discussion in the following sentences in the text; otherwise, by the later axioms and definitions that employ it. Other associations which this same notation may have in other contexts should be disregarded. 9 The difference between Socrates and Socrates + generous is clearly stated again at Topics 5.4, 133bl5ff. Here, Aristotle distinguishes "that to which something belongs as an accident" (TVi W U, PE00 7KE rt), for example, a man, and "the accident taken together with that to which it belongs as an accident" (7lrp rV/8EPf,K&Tt ... Xao_,VoAvov,y perT&rTOV L Gv,p4e,3ruKev), for example, a pale man: more simply, a thing can be made out to be one thing taken "in itself" (KaO' abT6), another thing taken "with its accident" (Aer& TOV av,00rpKOTOS). The terminology at Metaphysics D29, 1024b29-31, is even more succinct: av&ro, and oavro irenovOoi, for example, Socrates and musical Socrates. See also




the passages at Physics A7, 190a20-21 andB3, 195bl6-21, and the discussions in White (1972), pp. 71-77, Code (1976b), pp. 174-182, and Cohen (1978), p. 391.

Notice that at Topics 5.4, 133blff, Aristotle insists that a man and a pale man are not "simply different" (Trepov d!rXcs), but different because their being is different (&Xo Xe'yeTat rc3 YTEpov ELvaL cTroi, Tr eht'vt). At the same time, then, as we shall see, they can also be accidentally the same. 10 "Logically necessary": see Categories 10a32-b9. As defined by Aristotle, therefore, paronymy appears to be a matter of mere grammatical accident, cf. Owen (1960), p. 175, and Dancy (1975), pp. 362ff. Wherever the syntactic conditions for paronymy are satisfied, however, they are the symptom of some deeper metaphysical point. But the moral can be different in different cases. A compound of form and matter is a paronym of its constituent matter. Physics H3, 245b9, a fact which here provides a criterion for distinguishing the genuine coming-to-be of a substance from mere alteration. The same phenomenon (but without the jargon of paronymy) yields a different moral at Metaphysics Z7, 1033a5-23, and yet a third moral at Metaphysics 07, 1049al8ff, esp. 36-b3, which perhaps represents Aristotle's final thoughts on the subject. Still different varieties of paronymy appear at Eudemian Ethics GI, 1228a36 and Physics G7, 207b9. In the Categories and Topics, paronymy draws attention to a single underlying ontological relation between an accident p and the compound, a + p. But this relation is only accidentally reflected in syntax, and sometimes, syntax fails to reflect the ontological facts altogether (cf. Categories 1 0a32-b9). 1' The theory we are about to present can be called Accidental Compound Theory, after the fact that it is concerned with the relation of compounding solely as it holds between a substance and an accident. There is also in Aristotle an extension of Acciden- tal Compound Theory, in which the relation of compounding holds also between form and matter. Some discussion of this extended theory is given in Lewis (forthcoming), but I ignore it here. For similar reasons, I shall not discuss the controversial claims by Hartman (1977) that the relation of accidental sameness, defined in I(2) below, holds between form and matter, or between mind (or mental events) and body (or bodily events).

There are some respects in which Accidental Compound Theory, as it is presented here, is an idealization of the theory that underlies the scattered references to accidental sameness and accidental compounds in Aristotle's text. In writing (DI) in the text immediately below, for example, I help myself to the modern notion of identity, but it should not be inferred from this that such a notion has a direct counterpart in Aristotle's own theory of the different kinds of sameness. A more serious difficulty is an occasional lack of fit between Accidental Compound Theory and Aristotle's text. (1) In some places (for example, in discussing the so-called "fallacies of accident" at de Soph. El. 166b28-32, 179a27-31 and 35-37, cf. also 178b39-179a3 and Peterson (1969), p. 118, Note 40), Aristotle is willing to speak of entities such as the pale one as accidents. In fact, such entities are clearly of the form, a + ~p, and are accidental compounds in the sense of (Dl). (2) At Plhysics A7, 189b32-190a5, Aristotle draws a distinction between entities that are simple (ori&7rx&, b33), for example, the musical, or the man, and entities that are compound (T& OV-yKeC' eva, b33-34), for example, the musical man. At first sight, this fits nicely the distinction between accidental compounds of the form a + <, and their several ingredients, a and p (cf. A7, l90b20-23: "For, the musical man is a compound of (av'yKetrC1L) (the) man and (the) musical, in a way: for, you can break it down (6taxwuets) into the definitions of these"). But Charlton and others have argued that by '(the) musical' here, Aristotle means 'the thing which is musical' (Charlton, 1970, pp. 70ff, esp. p. 73). On my account, therefore (but not on Charlton's since he adopts the Russellian reading of such expressions ICharlton, p. 731), the musical, like the musical man, is an entity of the form a + ip, although the first is only implicitly com-



30 FRANKA.LEWIS

pound, and the parent substance is expressly identified only in the second case. Perhaps Charlton's reading of Aristotle here is wrong. But if it is not, the distinction drawn in Physics A7 must mark off two cases within the notion of an accidental compound as intended here. (3) At Metaphysics Z6, 1031b22-25, Aristotle notes the ambiguity of the Greek to leukon ("the pale"), which he says, can refer alternatively to the quality pallor, or to the substance that is pale (K(it 'a_p . GV7UJ6J4E7KE XEVK'OV KaL ro6 UV/#eAP?K6V, (b24-25). Perhaps Aristotle means to correct himself two lines later, where "that to which pale is an accident" becomes "the man and the pale man", r; ,Aed 'y&p dwv9pWCrcp K(it TyZ XEVKy, &VOPL.nr (b27, my emphasis). Nevertheless, the passage seems to support the view that expressions like 'the pale (one)' function as Russellian definite descriptions, denoting the substance - let it be Socrates - who is pale, rather than as names for some distinct entity, Socrates + pale. But there is good evidence that at least sometimes, Aristotle intends this latter reading of the expressions in question (some of that evidence comes from earlier parts of Z6 itself: cf. I(I) and Note 9 above). We must conclude either that Aristotle wavers in his reading of such designators, or that he is speaking loosely in the latter part of Z6. Neither alternative is wholly appealing from the interpre- ter's point of view: but such blemishes in Aristotle's account are systematically excluded from the formalization of Accidental Compound Theory offered here. 12 The term 'type-restriction' is perhaps tendentious here. I do not know whether Aris- totle would regard an assertion of, for example, the relation 'x is an accident of y' between an accident and an accident, in violation of (A2) immediately below, as ill-formed, or as simply false. 13 In (A2) and throughout this paper, 'substance' will mean inditvidual substance: wtat in the Categories Aristotle calls 'primary substance', the individual man or the individual horse, later analyzed in the Metaphysics as a compound of matter and form. The require- ment in (A2) regarding the accident-of relation and (individual) substance harks back to a dominant theme in the Categories, that substance is the subject par excellence (Cate- gories 2allff, 34ff, bl5ff, 37ff). It is also central to the attempt in the Posterior Analy- tics to regiment predication. Here, Aristotle lays down that if a sentence expresses a genuine predication, the subject-entity must be a genuine subject, i.e. a substance, and not a combination of a substance with an accident. In all Aristotle's examples in this discussion, a sentence of the form, 'a + p is a p', where ',p' expresses an accident, must be recast as: 'There is an a which happens to he p and is a 'p'. Cf. An. Po. 73b6, 7, 83a2, lOff, An. Pr. 43a35. Lastly, (A2) is a key ingredient in Aristotle's argument in favour of the distinction between substance and accident, and against the view that "everything is said accidentally", at Metaphysics G4, 1007a33ff. 14 Most often, the relation holds between a substance a and an entity b named by expressions of the form, for example, 'musical Socrates': thus, I take b to be of the form a + p (where p is an accident of a). Some examples: man is accidentally the same as pale man (Topics 5.4, 133bl7ff, Metaphysics Z6, 1031al9ff), Coriscus as musical Coriscus (de Soph. kl. 178b39-179al, Metaphysics E2, 1026bl5-18), Socrates as musical Socrates (Metaphysics D9, 1018a2-3, D29, 1024b29-31), and Socrates as Socrates seated (Metaphysics G2, 1004b1-3). In a minority of cases, the relation is between entities a and b where a is a substance but h is named by expressions like 'the approaching (one)', 'the musical (one)' (Topics 1.7, 103a30-31, the seated (one) or the musical (one) is accidentally the same as Socrates; de Soph. El. 179blff, Coriscus is accidentally the same as the approaching (one); Metaphysics Z 1 1, 1037b5 -7, Socrates is accidentally the same as the musical ( thing)). As explained above (p. 4-5), I take expressions of the sort 'the musical (one)' to be elliptical for expressions like 'musical Socrates', in which the parent substance is explicitly mentioned.

F For the irreflexivity of the accident-of relation, see Topics 2. 6, 112b21-26. 16 (D3) is supported by Aristotle's examples at Metaphysics D9, 1017b29-30:




...and man and musical Isc. are said to be the same] because the one is an accident of the other, but the musical (is) a man because (it) is an accident of the man.

Aristotle writes awkwardly here, however, since 'musical' and 'the musical' must occur ambiguously (cf. Miller, 1973, p. 485 and Kirwan, 1971, pp. 149 and 134). On my account, the ambiguity is resolved by distinguishing between (i) a name for the paronym, the musical one, and (ii) a name for the accident, musicality. In the second half of the passage, for example, 'the musical' must refer to the compound, [this] man + musical, while the pronoun, 'it', refers back to the component accident, musicality. Similar remarks hold for the use of 'musical' in the first half of the passage. This reading of the passage is not uncontroversial, however. The ambiguity described is especially harsh, for in each case the word used ambiguously appears only once. Accordingly, the postu- lated second sense must be evoked by a pronoun (O&Tepov, b29), or by the need to supply a subject for the verb ('(it) is an accident of', avM,34iftKe, b30). Writing of a similar case in the two lines immediately preceding (1017b29-28, cited in Note 19 below), Code (1976b, p. 175), argues that the ambiguity suggested is not harsh, but impossible: a similar ambiguity, however, occurs at Z3, 1029a23-24, where -rii o6atcsa must mean: the compound substance: while the pronoun avJrl7, which has ri s abaiaq as its antecedent, must refer to substance in the sense of form. Code's own reading of the passage depends on a different ambiguity, which may in the long run be still harder to accept. One undisputed use of Aristotle's phrase, 'x is-an-accident of (avtip4ifKe) y', is to express a relation between an accident, ip, and a substance, a, which together make up the compound, a + p. Code suggests that in addition to this standard use, the phrase can also express a relation between an entity like the pale one and the substance, for example, Socrates, with which the pale one coincides. In our terms, then, the relation holds between a compound, a + p, and its parent substance, a. On the surface, this proposal makes a tidier job of the opening lines of Metaphysics D9. But the tidiness (as well as the untidiness of the contrary picture) can be exaggerated. My own view is that there is no gain in clarity or economy in the hypothesis that Aristotle uses the single phrase, 'x is-an-accident-of (UV,4PeIP7Ke) y', for both the standard accident-of relation and the relation, 'x coincides with y'. Accordingly, I stand by the reading of the opening lines of Metaphysics D9 sketched above. '7 This conclusion appears to be contradicted at Topics 152a31-32. I shall argue that this passage does not represent Aristotle's final view: see below, Sections 1(6) and 11(2). 18 But the relation is not, for this reason, particularly exotic: compare, for example, the relation, 'x is the husband of y'. 19 (D4) conforms to Aristotle's example at Metaphysics D9, 1017b27-28:

The pale (thing) and the musical (thing) are (accidentally) the same because they are accidents of the same thing.

The continuation of this passage is cited in Note 16 above. On the account adopted here, Aristotle's expressions, 'the pale (thing)' and 'the musical (thing)', are again ambiguous, as explained in Note 16: a contrary view appears in Code (1976b, 175ff), also discussed above. 20 Cf. Metaphysics D7, 1017al5-16:

Whenever we call... the pale (thing) musical or it [= the musical] pale, in this case it is because both are accidents of the same thing;

and An. Po. 83alO-12:

for then [sc. whenever I say that the musical (thing) is pale] I say that the man to whom it is an accident that he is musical, is pale....



32 FRANK A. LEWIS

Notice that the passages quoted from Metaphysics G4 (in the text) and D7 (in this note) are again infected with ambiguities of the kind noted in Notes 11 and 16 above. 21 On this, see Kung (1978) and Lewis (forthcoming). 22 This is done quite correctly in Code (1976b), pp. 177-178. 23 My objection in the text is to the argument Pelletier offers for this conclusion. But the conclusion itself is also flawed. For as we have seen, accidental sameness is irreflexive, symmetric and intransitive, and accidental sameness* is an equivalence relation. AC- CIDENTAL SAMENESS, meanwhile, is non-reflexive, symmetric, and non-transitive. 24 Xe Yero 6fe KVpLLTIrTa TC TWo TO Tvo or pt0,iC Y'z at 15 1 b29-30 refers back to 103a23- 24, &Xtwra 6' bMoXoyovu&wq rTO E'v &pt0Og TrcVTOZv ircpa' mTi gOKL 0KXeiyea0uc (so for example Waitz ad loc., and Pickard-Cambridge in the Oxford Translation), and recalls the notion of numerical sameness in general, as opposed to sameness in species or sameness in genus. Despite the verbal echo, Aristotle does not mean to restrict his discussion in Topics 7.1 to the "literal and primary use" (KVptcLrcTira jt pe' KCict lpdnT ) viz. numerical sameness by definition, referred to at 103a25-26. Cf Peterson (1969), pp. 98-99. 2S Cf. Alexander in Topica 501.19-502.6, cited by Peterson (1969), p. 80, Note 9, for the broad sense of 'is predicated of' (equivalent roughly to 'is true of) here. 2 Aristotle writes,

Moreover, see whether the one can exist without the other: for, if so, they could not be the same. (152b34-35, cf. possibly 151b36-154a4)

More formally,

As a matter of necessity, if x is numerically the same as y, then necessarily, x exists if and only if y exists.

What Aristotle says here indicates that instances of (T1+) hold for where 'p(x)' is the predicate 'El (x exists)'. For, suppose that in fact x and y are numerically the same. Then by the principle at 152b34-35,

O (x exists - y exists).

Bur from this it follows that o (x exists) - El (y exists),

by the modal principle,

0(P -Q) F- OP EOQ.

That is, numerical sameness sustains substitution within the context, 'El (x exists)'. Clearly, this result for the predicate 'exists' can be generalized for all predicates 'p(x)':

O (x is numerically the same as y - (O (sp(x)) -O (p(y)))).

This is the same as saying that (T1+) holds wherever '4' (x)' has the form, 'El (x(x))'. 27 Aristotle writes,

Furthermore, you must note the result of an addition and see whether each added to the same thing fails to produce the same whole; or whether the subtraction of the same thing from each leaves the remainder different. Suppose, for example, someone has stated that a double of a half and a multiple of a half are the same, then, if 'of a half has been subtracted from each, the remainders ought to signify the same thing: but they do not.... (152blO- 15)

"Adding the same thing" to each and "subtracting the same thing" from each here must be understood as a linguistic rather than a metaphysical operation. Suppose a is said to




be numerically the same as a + <p. Then in a test by addition, Aristotle claims, one and the same context

C...

can be added to the terms 'a' and 'a + p' to verify whether a and a + ep are numerically the same. Thus, where a is numerically the same as a + ip, the context

C... a ...

has the same truth-value as

C... a + <p....

where the second context results from the first by replacing the denoting expression 'a' by the denoting expression 'a + p'. Aristotle's remarks here are sufficiently vague that they can easily include reference to modal properties in testing for numerical sameness. To adapt a familiar example, suppose that 9 and the number of the planets are numerically the same. Then if we "add the same thing" to each, the resulting whole should also be the same. That is, the context 'El (... is greater than 8)' can be added to '9' and to 'the number of the planets', and the whole must have the same truth-value in both cases. Thus, if

(a) 9 is numerically the same as the number of the planets

and

(b) 1 (9 > 8),

then by Aristotle's principle

(c) El (the number of the planets > 8).

Aristotle does not explicitly say that the principle at 152b1O applies in modal contexts: but nothing he does say rules out such an application. Again, therefore, Aristotle puts forward a principle of numerical sameness that can permit substitution in modal as well as non-modal contexts. 28 De Soph. El. 168a34-blO and 179a26-b7. On these arguments, see most recently Barnes (1977). Earlier treatments are in Peterson (1969) and White (1972). 29 A different reading of 179a37-39 appears in Kneale (1962, p. 42), and Peterson (1969, pp. 77, 107-108, and 131-4). More recent writers favour the version given in the text: see White (1971, p. 179), Barnes (1977, p. 50), Pelletier (1979, p. 287). 30 Aristotle himself explicitly rejects (15) in the same chapter in which he rejects (TI), de Soph. El. 179a27-31, 35-37: sometimes what holds of the 'thing' holds of 'the accident' too, sometimes not. (Note that in the de Soph. El., Aristotle calls an entity of the form a + p, an accident: cf 179al -2 and Note 11 above.) 31 See G & C 1.4, 319b25-32, and the Mikkalos example at An. Pr. 47b29-37, both quoted in Section 1(1) above. 32 A notable expression of scepticism regarding this account of the Hesperus-Phospherus example occurs in Kripke (1971 and 1972). The best defense of contingent identity known to me is by Gibbard (1975). 33 Compare the fallacy of supposing that i is not a proprium of man if it also belongs to Socrates + pale (Topics 5.4, 133bl5ff, cf. p. 21 above). Aristotle refers to similar 'sophistical' difficulties involving Coriscus in the Lycaeum and Coriscus in the agora at Physics DI 1, 219b20-21. 34 For the controversy over contingent identity, see the references in Note 32 above, and also the remarks in Marcus (1976). 35 The terms, 'referentially opaque', 'referentially transparent', and the like, are of course of modern manufacture. But it is still proper to ask whether in considering the



34 FRANK A. LEWIS

paradoxes Aristotle treats certain contexts as referentially opaque, that is, whether his treatment of the paradoxes fastens on features that for us would count towards referential opacity. An affirmative answer for the epistemic paradox is given in Peterson (1969): my own answer will be negative. 3' This view of Aristotle derives from Peterson (1969), who credits D. C. Bennett with the idea. Peterson's views are endorsed by Pelletier (1979, 290ff), and there are also perhaps reflections of it in Dancy (1975, pp. 365ff) and (1978), pp. 386, 406), and Code (1976a, p. 364), and (1976b), pp. 180-181). 3" The falsity of such sentences as (22) is suggested by some rather equivocal evidence in Metaphysics Zeta. At Z4, 1030a4-6, Aristotle appears to say that substances (for example, Socrates?) satisfy a condition regarding essences that Socrates + pale, for example, does not:

...the pale is not just-what a this (is), since in fact (being) a this belongs to substances only.

A similar point is perhaps made at the end of the chapter (1030b6ff, esp. 12-13). Simi- larly, Aristotle argues in Z6 that in contrast to substances (TO& KcsO' cVnr& XeSoAva), an entity like the pale man (one of T& AXe'YoAva KaTr aVt1#eI77K6Sq) is not the same as its essence. The earlier evidence in the Organon is somewhat less controversial. At de Soph. El. 178b39-179a2, for example, Aristotle declares that musical Coriscus is a such, as opposed to Coriscus himself, who is a this (a condition which is the hallmark of a substance, Categories 3alO). And in the Categories at 3b33ff, Aristotle argues that substance does not admit of degrees, in contrast to Tb XEVKO'V (= the pale (thing)) and ro KO,X'OV (= the beautiful (thing)). Clearly, then, the pale (thing) (an entity of the form a + pale) is not a substance. 38 I have argued against the view that the context '... is a substance' is referentially opaque, that if this view were correct, then in our assertions that make use of such contexts we should no longer be talking about objects. I conclude that we should prefer a non-Russellian reading of expressions such as 'the pale one', so that they refer to accidental compounds, and not to substances. Against this, it may be objected that the arguments used to show that '...is a substance' and similar contexts are referentially opaque rest solely on the alleged failure of substitution within those contexts. This may seem to leave open the possibility that Existential Generalization is still valid in such contexts, so that the conclusion that they are referentially opaque is mistaken. In fact, we may conclude, they are neither referentially opaque nor referentially transparent, but rather, in Loar's terminology, non-extensional but referential: non-extensional, since substitution fails, but referential, since Existential Generalization succeeds (Loar, 1972, 47ff). (Cases in which these two criteria, substitutivity and accessibility to Existential Genera- lization, pull apart are discussed in Loar 119721, and the possibility of applying these ideas to the interpratation of Aristotle is discussed inconclusively in Peterson 119691, Chapter 2.) If the context '...is a substance' is non-extensional but referential, then the truth of our assertion involving such contexts will depend in part on how we refer to the objects we do. But the singular term in subject-position in such a context still occurs referentially, and Existential Generalization is still permitted. Manifestly, then, we are still talking of objects, and the ontological revisions for which I argue in the text are strictly unnecessary. Does this counter-argument succeed? It is easy to think of examples of non-extensional but referential occurrences of singular terms in connection with intentional notions (with a 't'), for example, knowledge contexts:

Jones knows that the Evening Star is a planet with a shorter period of revo- lution than the Earth.

Here, as Loar notes, the singular term, 'the Evening Star', contributes to its containing




sentence in two distinct ways. One contribution is referential, but the other in Loar's account has to do with reporting the details of Jones' representational state, and the description under which he thinks of the object referred to by the singular term. It seems reasonable to require that the claim that a term occurs referentially but non-extensional- ly in a given context must be accompanied by some explanation of this or some other suitable kind. But I have not seen how any such explanation is appropriate to occurrences of singular terms in the context '...is a substance'. What connections, for example, could we draw between this case, and the cases involving propositional attitudes that Loar describes? I shall continue to suppose, therefore, that if the context '...is a substance' is not referentially transparent, then it is, simply, referentially opaque. And as before, I find this last conclusion intolerable, and prefer the simple revision in our view of Aris- totle's ontology proposed in the text. 3 This paper has benefited from hearings at the University of Texas at Austin and the Claremont Colleges, and from the helpful criticisms of Alan Code. Responsibility for the mistakes that remain is mine alone.

BIBLIOGRAPHY

Kenneth Barnes, 'Aristotle on identity and its problems', Phronesis XXII (1977), pp. 48- 62.

W. Charlton, Aristotle's Physics I, II (Oxford, 1970). Alan Code, (a) 'The persistence of Aristotelian matter', Philosophical Studies 29 (1976),

pp. 357-367. Alan Code, (b) 'Aristotle's response to Quine's objections to modal logic', Journal of

Philosophical Logic 5 (1976), pp. 159-186. S. Marc Cohen, 'Essentialism in Aristotle', Review of Metaphysics XXXI (1978), pp.

387-405. R. M. Dancy, 'On some of Aristotle's first thoughts about substance', Philosophical

Review 84 (1975), pp. 338-373. R. M. Dancy, 'On some of Aristotle's second thoughts about substances: Matter', Phi-

losophical Review 87 (1978), pp. 372-413. Montgomery Furth, Unpublished translation, with notes, of Aristotle Metaphysics

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Quine, ed. by D. Davidson and J. Hintikka (D. Reidel, Dodrecht-HolUand, 1969), pp. 178-214; reprinted in Reference and Modality, ed. by Leonard Linsky (Oxford, 1971), pp. 112-144. References here are to the reprinting in Linsky.

Christopher Kirwan, Aristotle's Metaphysics Books G, D, E (Oxford, 1971). Kneale, W. & M., The Development of Logic (Oxford, 1962). Saul Kripke, 'Identity and necessity', in Identity and Individuation, ed. by Milton K.

Munitz (New York, 1971), pp. 135-164. Saul Kripke, 'Naming and necessity', in Semantics of Natural Language, ed. by G. Har-

man and D. Davidson (D. Reidel, Dordrecht-Holland, 1972), pp. 253-355. Frank A. Lewis, 'Form and predication in Aristotle's Metaphysics', in How Things Are:

Studies in Predication, ed. by James Bogen and J. E. McGuire (D. Reidel, Dordrecht- Holland, forthcoming).



36 FRANK A. LEWIS

Brian Loar, 'Reference and propositional attitudes', Philosophical Review 81 (1972) pp. 43-62.

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Francis Jeffry Pelletier, 'Sameness and referential opacity in Aristotle', Nous 13 (1979), pp. 283-311.

Sandra L. Peterson, The Masker Paradox (unpublished Ph.D. dissertation, Princeton, 1969).

W. V. 0. Quine, Mathematical Logic, revised edition (Harvard, 1951). W. V. 0. Quine, Word and Object (Cambridge, Mass., 1960). W. D. Ross (ed.), Aristotle's Physics (Oxford, 1936). W. D. Ross (ed), The Works of Aristotle, Vol. XII, Select Fragments (Oxford, 1952). Nicholas P. White, 'Aristotle on sameness and oneness', Philosophical Review 80 (1971),

pp. 177-197. Nicholas P. White, 'Origins of Aristotle's essentialism', Review of Metaphysics XXVI

(1972), pp. 57-85.



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