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Philosophical Method and The Theory of Predication and Identity HectorNeri Castaneda Noûs, Vol. 12, No. 2. (May, 1978), pp. 189210. Stable URL: http://links.jstor.org/sici?sici=00294624%28197805%2912%3A2%3C189%3APMATTO%3E2.0.CO%3B2C Noûs is currently published by Blackwell Publishing.
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Philosophical Method and The Theory of Predication and Identity INDIANA UNIVERSITY
A main cause of philosophical i l l n e s ~ n e  s i d e ddiet: one nourishes one's thinking with only one kind of example. (Ludwig Wittgenstein, Philosophical Investigations, #593) It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.' (Arthur Conan Doyle, "A Scandal in Bohemia," [7]: 163)
This is at once a study on philosophical method, a sketch of a comprehensive theory of predication, individuation, and identity, and an appraisal of tests for this theory proposed by Romane Clark. Clark's very interesting and challenging "Not Every Object of Thought Has Being: A Paradox in Naive Predication Theory" ([I]) is both ambitious and flattering to me. In it Clark attempts, first, to prove a contradiction in naive predication theory, and it takes my views on predication, individuation, and identity, developed in [2][5], hereafter called the GCCC theory, for reasons that will become plain, as paradigmatic of naive predication theory. In that essay Clark proposes, secondly, a specific argument against the GCCC theory. Clark is absolutely right in claiming that the second is "a less dramatic point which is nonetheless perhaps of greater philosophical interest" than the first one ([I]: 000). Clark's second point is of great importance: it forces serious methodological issues about the connection between data and theory; it places in high relief the need for careful protophilosophical scrutiny of the data. Once the methodological issues are attended to, Clark's special argument against the NOOS 12 (1978) 1978 by Indiana University
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GCCC theory actually supports, rather than attacks, the GCCC theory with its different modes of predication. Clark's first, general point against naive predication theory is embodied in an argument that founders in an unbridgeable gap, at step (VI)8., ([I]: OOO), created by the very crucial premise (I) on which the argument is built. Clark's step (VI)8. violates the distinction between predicate and propositional negation built into (I). Thus, Clark has not established any paradox in naive predication theory, or in the GCCC theory. Nevertheless, he may still be right: the naive theory may be paradoxical, and he may yet be able to establish this with another argument and with another paradigm, a more naive one that neither recognizes different modes of predication nor distinguishes between predicate and propositional negation. With respect to the GCCC theory, the argument can be construed as supporting the GCCC theory by establishing that assumption 8x below (p. OOO), which underlies Clark's step (VI)8.,is false. See appendix for contextual predication. Given the philosophical importance of Clark's second point I will consider it before his first point. Since it has to do with the connection between the GCCC theory and its data, I will first deploy the relevant data and exhibit the way the GCCC theory arises from them. Thus, I will provide a partial sketch of the GCCC theory which complements the excellent (but partial) one given by Clark in [I]: 000. I: THE GCCC THEORY AND SOME OF ITS DATA
1 . A Crucial~Datum.T he historical background of Sophocles' Theban tragedies includes the following truths: (1) Before the pestilence Oedipus believed that the previous King of Thebes was dead;
(2) It is not the case that: before the pestilence Oedipus believed that Antigone's paternal grandfather was dead;
and
(3) Antigone's paternal grandfather was the same as the previous King of Thebes.
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There is also the general principle (ID) Ifx is genuinely or strictly identical withy, then what
ever is true of x is true of y , and vice versa.
It is natural, at least initially, to hold both that: (T) The matrix 'Before the pestilence Oedipus believed
that was dead' expresses something true of a
person referred to by a term of the form 'the such and
such', just in case the sentence obtained from that
matrix by filling in the blank with the term in question,
is true (or expresses a truth),
and that: (S) The sameness of (3) is genuine or strict, though con
tingent, identity. (That is, the antecedent of (ID) is
instanced by (3).)
Now, from (1) and (2) together with (ID), (T), and (S), it follows that: (4) Before the pestilence Oedipus believed that Antigone's paternal grandfather was dead. Clearly, (4) contradicts (2). Hence, the conjunction (1) & (2) & (ID) & (T)& (S) is selfcontradictory. It is an example of the psychological paradox of reference. Hence, at least one of its conjuncts must be false. Which one? 2. Three Complementary Types of Theory of Reference. Conjuncts (1)(3)are considered statements of fact. It is, thus, natural to take them as data. Hence, the natural theoretical choices are the rejections of any of the more abstract statements (ID), (T), and (S). Obviously, the data must be rich, complex, and variegated; the theories must, however, be comprehensive first of all, but as simple as their comprehensiveness allows. Thus, in principle we have three initial types of theory that can be, and must be, developed. We must note right at the outset that all theories of reference must in the end deal with precisely the same set of problems: individuation, identity, and predication. Furthermore, the theoriesmust be developed. It is utterly irresponsible, philosophically speaking, simply to say, for instance, that the principle of identity (ID) does not apply to belief sentences. This assertion cannot be taken seriously ex
cept as a statement of the initial direction in which a theory solving the paradox of reference is to be channeled.
3. The Five Levels of Philosophy. The greatest philosophical illumination appears when different comparable theories are contrasted. By comparable theories I mean theories that cater to the selfsame rich collection of data and are equally developed. Each theory contains a large amount of convention or stipulation. The contrasting of different theories provides at least a partial substitution of divergent underlying conventions. In any case, reality is not fully categorized per se, independently of our conceptual schemes. Thus, experiencing the world through different theories, especially if the theories are utterly diverse, can be the only procedure for discarding the local features of each of the categorizations, and for approaching, in the experience of their contrasts, an experience that is as neutral with respect to our conventions or stipulations as this is feasible: we may perhaps reach by that method an ultimate set ofstructural invariances, which may perhaps be just a network of partial isomorphisms among fully developed comparable theories. Such a network of invariances would constitute our basic objective ontology. It is, therefore, an urgent philosophical imperative that the most diverse ontological views should be developed to the hilt: no alternative view should be left underdeveloped or jettisoned until it is shown to be hopelessly selfinconsistent, or wholly incapable of being extended to accommodate data akin to those for which it was propounded. (That is why I welcome Clark's tests of the GCCC theory.) In short, the philosophical search for the large patterns of the world and of experience is a complex manifold of activities that fall into one or other of the following five levels: (a)protophilosophy : the methodical collection and examination of data so as to distill problems and criteria of theoretical adequacy; (b) symphilosophy, or standard theoretical philosophy; here fall the diverse theorizations in which philosophers have normally engaged in their endeavors to illuminate certain sets of data; (c) diaphilosophy, only very rarely adumbrated, which consists of the search for those structural invariances across fully developed (sym)philosophical theories;
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(d) hypophilosophy, the isolation of those protophenomena Wittgenstein spoke about, which determine the concepts that, given what we and the world are, we have actually evolved for structuring our forms of life; (e)metaphilosophy, the discussions of philosophical method, whatever the level of the problems. At present diaphilosophical investigations are only a visionary dream. We do not yet have fully developed comparable rich philosophical theories to even systematically pose the problems of structural in variance^.^ Obviously, there is no point at all in posing such problems for minor theories, which cater to very small collections of data: they may have to be thrown out under the pressure of additional kin data. At present our working problems lie in the other areas of philosophy. Fortunatley, the largest number of philosophers ever are now working on all but the diaphilosophical fronts. Fortunately also, many logicians of philosophical bent are nowadays developing mathematical structures that may, perhaps, be of value for the formalization of symphilosophical theories. There is also an heightened awareness of the need of careful protophilosophical studies. This is the juncture at which Clark's second argument comes in, as we shall see. (For a discussion of the metaphilosophical hierarchy: protophilosophy, (sym)philosophical theories, formalization of such theories, and settheoretical models, see [6], especially part I and the appendix.) Philosophers tend, naturally, to work on fashionable problems and within fashionable points of view. This is reasonable because the fashions have the virtue of mobilizing a large amount of the needed cooperation for the development in full of philosophical views. T h e fashions stimulate development. Yet in that search for the ontological invariances that constitute our ultimate and collective goal, philosophers developing nonfashionable views are also part of the philosophical team: we all belong to it, both in spite of and also because of our metaphysical differences. This is not merely a correct Carnapian principle of tolerance, it is a necessary Hegelianesque metaphilosophical principle of diaphilosophical system complementation.
4. My Program. As a quick glance at contemporary philosophical production reveals, it is at present fashionable to reject socalled Leibniz's Law (ID) or to reject the close con
nection between thinking and what is thought of, illustrated by (T), a rejection often formulated by saying that the states of mind of a person are not properties of the objects toward which those states are oriented. I have, therefore, chosen to build a complementary theory of individuation, identity, and predication that starts from the rejection of (S). Thus, my inceptive theoretical tenet is this: the sameness between Antigone's paternal grandfather and the previous King of Thebes is not strict id en tit^.^ 5. The GCCC Theory Sketched Out. Clearly, triads like (1)(3) obtain, not only for Oedipus, the previous King of Thebes, and Antigone's paternal grandfather, but for any believer or thinker and most particulars. Each of such triads with true members establishes that some entity, say the F, is the same as, but not strictly identical with, another, say, the G. We shall for convenience speak of an Oedipus'sieve to refer to any such true triad that separates strands of the sameness relation illustrated by (3) above.4 Each of such strands I call an individual guise: guises are the F and the G that are the same object in the way in which Antigone's paternal grandfather and the previous King of Thebes are the same person. This sameness, which implies existence of the guises it relates, I call consubstantiation, and I represent it with 'C*'. Hence, step (3) above is analyzed as (3a) C*(Antigone's paternal grandfather, the previous King of Thebes). The relation C* is an equivalence relation within the realm of existents. It is also governed by a law of consistency and of completeness. (See [2], 15ff (55ff), and [5], 312ff and 322ff.) In the light of additional data (e.g., that the connection between thinking and what is thought of is both indifferent to existence and the selfsame throughout), I distinguish other sameness relations from identity. These are called consociation (represented by 'C**') and conflation (represented by '*C'). I indicate that there may be other similar relation^.^ (See [3] and [2], 17ff (57ff), 26ff (67ff) et al.) The sameness relations are forms of external predication. Thus, (5) The previous King is arrogant
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is ambiguous depending on whether the copula 'is' is understood as expressing one or another form of external predicationor, what is unlikely, as expressing internal predication, to be introduced soon. The three likely interpretations of (5) are: (5a) C*(the previous King, the arrogant previous King); (5b) C**(the previous King, the arrogant previous King); (5c) *C(the previous King, the arrogant previous King). In general, (G.C) "The F is G" is analyzed as %(The F, the GF),"
where 'C' is a variable ranging over the different
forms of external predication.
,Palpably, the network of Oedipus' sieves is like a huge prism: it breaks down each ordinary object into its component individual guises. But what is an individual guise? On the theory of individuation I have developed, as Clark well explains ([1]: 182)each individual guise is an entity composed of a core set of properties and the individuator 'c', which is, thus, the theoretical counterpart of the definite article 'the'.6'~ence, there is a sense in which 'The present King of France is a King' expresses a truth. This sense is simply that in which the property of being a king is included in the guise 'the present King of France'. This is internal predication, and we represent it by putting the predicate in parentheses to the right of the subject, thus: The present King of France (a King).' The above four forms of predication differ in their truth conditions. Here we cannot formulate them in full rigor; we just give the simplest rules. (See [2][5].) For compactness let us represent the set of properties composing a guise a as la/, and the individual guise composed of all the properties of a and the property F as a[F]. We call the guise a[F] the Fprotraction of a . The following are rules of truth of the GCCC theory: (1p.Tl) "a(F)" is true, iff F E la/. (*C.Tl) "*C(a, b)" is true, iff la1 is equivalent to lbl. (C*.Tl) "C*(a, b)" is true, iffa exists and is, in the ordinary sense, contingently identical with (the same as) b.
(C**.Tl) "C**(a,b)" is true, if either (i) the guises a and b are thought of to be the same object, whether a fictional or a real one; or (ii) b is a protraction of the form a[x believes (thinks, supposes, etc.) that is F]; . . .
6. The Twotier Structure of the GCCC Theory. One complexity of my GCCC theory is that it has two levels. The first level is the theory of property composition. For this in [Z] and in [5] I simply adopted the standard functional calculus of the first order. This is, of course, a move of convenience. The formal development of the theory, after all the necessary enrichments, may very well require some revisions of that basic structure. In any case, the second level is a theory of states of affiars or propositions, or truths and falsehoods. This is the level of predication I have discussed above. In order to emphasize the twotier structure of the theory, I suggested in [Z]: 10 (50),that the combinatorial version of the firstorder functional calculus should be used for the first level, as, say, it is formulated in Quine's [9]. This twotier structure allows us to distinguish between the having of aproperty by an individual and the entering of an individual into the composition of a property. This is particularly important in the case of relational states of affairs. For an example consider the role of the individual guises a and b in the equivalent propositions "a is ,,R to b" and "b is,, R'ed by a": a is,, R to b: C*(a, a[Rxb]; b is,, R'ed by a: C*(b,b[Rayl). This distinction between property attribution to and property composition by an individual (whether a guise or not) allows us to distinguish three equivalent propositions, three truths, or states of affairs, which a sentence of the form 'a is R to itself can express, regardless of the sense of the copula. Thus, considering external consubstantiational predication, i.e., taking 'is' as 'is,,', we find the schemata: a is,, Rxa: C*(a, a[Rxa]); a is,, Rax: C*(a, ~[Rax]); a is,, Rxx: C*(a, ~[Rxx]).
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11: CLARK'S SECOND OBJECTION
1.Clark's Description of My ProtoPhilosophicalArgument. On [I], p. 186 Clark describes my use of Oedipus' sieves as follows: Castaiieda considers quadruplets of statements like those below in which 'F' stands for an intentional context and 'a and 'b' stand for referririg expressions by which we and the psychical agents to whom we ascribe beliefs may in our various ways think of things:
2. a is the same as b 4. F(b)
Is this a correct description of what I did above? I am not sure. For one thing, I have been careful to formulate my data in English, since the data are particular matters of fact that we encounter in our experience. It is crucial that they be formulated with as few higher commitments as we can. The contrast between data and theory is at bottom the contrast between degrees of theory. Now, what does Clark mean by the forms 'F(a)' and 'F(b)'? Depending on what interpretation he places on these forms, that is, on what rules govern them, it is true, or false, that my protophilosophical arguments involving Oedipus' sieves have steps of the forms 'F(a)' and 'F(b)'. Clark does not say anything about that. Yet there is a good clear sense in which my Oedipus' sieves do include steps of the forms Clark mentions. This is the sense made explicit by (T)in Section 1.1 above, namely: the sense in which, using double quotes as Quine's corners: (T*) "F( )" is an English sentence matrix, with a blank for a referring term; "F(a)" is the sentence obtained from "F( )" by putting a in the blank. We say that what "F( )" expresses is true of the individual denoted by a. It is of the utmost importance to understand (T*). It is a description of the syntax of certain ordinary language sentences that formulate truths. First, (T*) does not say anything about the scope of the referring term a in the sentence "F(a)". Second, (T*) says nothing about the replaceability of a with another term b in the sense that "F(b)" is true if and only if "F(a)" is true. Third, (T*) says nothing about the theoretical representation of the English sentences of the form "F(a)" in
the GCCC theory. Thus, from the sense in which my Oedipus' sieves have elements of the forms "F(a)" and "F(b)", in Clark's notation, nothing can be inferred about the kind of predication that ties the object denoted by a and what "F( )" expresses. Fourth, given our discussion in Section 1.5 above, especially rule (C**.Tl), that the way in which psychological properties are true of persons or objects is precisely by virtue of consociation, rather than by consubstantiation, the copulation expressed by the parentheses in "F( )" is consociational, not consubstantiational. I made clear on [2]: 37(79) (19) Tom believes that the oldest spy is a spy. . . . Consider the property. . . Tom believes that u is a spy. Undoubtedly this property is possesed by the oldest spy. But this possession is, obviously, not Meinongian predication. But it is not consubstantiation either: it is consociation.
2. Having Properties. The crucial fact that the sense, captured by (T*), in which Oedipus' sieves contain steps of the form "F(a)" is by itself neutral with respect to the type of predication that the GCCC theory assigns to "F(a)". This cannot be overstressed, because a natural way to say that F is true of what a denotes is to say, deleting Quine's corners in displayed formulas, that (6) a has the property F (or Fness). It seems natural to suppose that (6) raises no paradox of reference, i.e., that (6) and (7) a is the same as b imply together
(8) b has the property F (ness). This is one reason why I formulated (ID) and (T)in Section I. 1 above in terms of 'true o f , preferring not to use the expression 'having properties'. Evidently, if (6) & (7) implies (8), the has the property. . .' does not create the paradox context ' of reference. Then, we must own that there are contexts, like those mentioned in (T)in Section I. 1, which express something
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true of individualseven though they do not express properties individuals have. (See Appendix.) On the other hand, one can equate 'being true of with 'having properties'. Then, in the sense in which (T*) describes the condition an expression must meet to express something true of an individual, (T*) also formulates a condition for that individual's having a property. But in this sense of 'having properties', if (6) uses this sense, (6) must create the same paradox of reference that the matrix "F( )" creates. Hence, in this sense of 'having properties' (6) & (7) does not imply (8). I said that I preferred not to use the expression 'has property F' in processing my data. But I do not object to using it. One must, however, be clear about the sense in which it is used. If we use it in the generic sense, the one corresponding to the generic sense of 'true of registered in (T*), then we must understand (6) generically as referentially opaque. This generic sense of 'having properties' or of 'is' is not represented in the GCCC theory; but it is discussed below in the Appendix. Then, in terms of the GCCC theory, we must ask whether the sense of 'has' in (6) is either 'has internally', or 'has,,', or 'has,,,', or 'has,,', or any other that may be required by the extension of the theory to additional data. It is important to fasten firmly to the fact that in the GCCC theory: (9)
"C*(a, b)" does not imply "C**(a, a[F]) + C**(b, b[F])."
3. Clark's External Predication. The two arguments that Clark offers against my GCCC theory are based on a concept of external predication he introduces on the basis of my discussion of consubstantiation on [2],p. 14(546). Clark puts it as follows: A guise is externally F just in case it is consubstantiated with a guise which is internally F. It is an axiom schema that
([I]: 184; I have put small Latin letters for Clark's Greek ones.)
Here the external predication of F to a is represented by "(F(a))", a converse of my internal predication. Now, this external predication is just one case of my external predication, namely, consubstantiational predication. Clark's formula "F(a)" corresponds roughly to my formula "C*(a, a[F])."
I say "roughly" because Clark's definitional axiom schema (I) is not strictly identical with my definition of "C*(a, a[F])." In my definition, in the notation introduced on p. 195, la1 is a subset of la[F]l, whereas the guise b in Clark's (I) need not be such that la1 is a subset of la[F]l. However, if we understand the formula "F(a)" as defined by (I), then with the help of the other laws of consubstantiation (see [2]: 15ff(55ff), [5]: 323f) we can establish the metalinguistic equivalence
Clark is, therefore, correct in claiming that I am committed to axiom schema (I)+rovided, of course, that rue understand that "F(a)" expresses consubstantiationalpredication, i.e., conforms to (10).
4. Warning. It is perfectly clear that the sense of "Fa)" which is required for the truth of schema (I) and of (10) is not the same as (much less identical with) the sense of "F(a)" described in (T*) above. The former pertains to the GCCC theory; the latter pertains to the data. Their properties are quite different. The formula "F(a)" in schema (I) and in (10) contains an expression "F( )" that allows substitutions modulo consubstantiation, whereas, as we noted above, the formula "F(a)" in (T*) and, a fortiori, in Oedipus' sieves, contains an expression "F( )" which does not allow such substitutions. That is why the expression "F( )" in Oedipus' sieves expresses, as we noted above, not consubstantiational, but, rather, consociational, predication. 5.Clark's SecondArgument.Premises (i) and (ii),on [1] p. 000, of Clark's second argument against the GCCC theory take "F(a)" in the external consubstantiational sense of predication characterized by (I) and (10). Since premise (i) is to represent the first elements of an Oedipus' sieve, the argument also involves the expression "F(a)" in the datum sense governed by (T*). As noted above, the datum "F(a)" enters the GCCC theory as a consociational predication. This equivocation prevents the argument from establishing the result Clark thought it establishes. Hence, the GCCC theory has nothing to worry about on this score. Clark's argument is, nevertheless, illuminating, if, instead of construing it as equivocating on datum "F(a)" and theoreti
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cal "F(a)", we construe it as having as an implicit premise the equivalence of the two interpretations of "F(a)". Then the argument establishes that one of the premises is false, and the natural one to choose for this role is precisely that implicit premise. In sum, Clark's second argument is a rigorous proof that datum "F(a)", governed by (T*), is not equivalent to theoretical "F(a)", governed by schema (I) and by (10): datum "F(a)" tells us that the guise a has the property F in a sense different from the consubstantiational sense of theoretical "F(a)". This is precisely an important tenet of the GCCC theory. (See above, and see example (28) in [2], and law (C*S) on p. 323 of [5].) Clark's argument is, thus, a valuable contribution to the exposition of the GCCC theory. 111: CLARK'S "PARADOX
Clark's first point about the objects of thought and the paradox in naive predication theory is also connected with the forms of predication, but it also pertains to the contrast (mentioned in Section 1.6) between property composition and property attribution. It helps stress this distinction. His argument hinges on the property of selfdisplaying. Thisis conceived as the analogue of the sets of naive set theory that have themselves as members. Clark defines selfdisplayingness in terms of the internal predication and consubstantiation characteristic of the GCCC theory. This is his point of taking the GCCC theory as a paradigm of naive predication theory. His definition comes on [I], p. 184, as follows: Consider now those guises, i f any, which exemplify externally that which they contain internally. Such guises might be said t o be "selfdisplaying," and we record this conception i n the following axiom schema: (111)
S D ( b ) t , (F)[b(F)+ (3d)(d(F)& C*(b, d ) ) ] .
The righthand side of (111) is wholly clear. It says that every property internal to guise b is possessed internally by a guise consubstantiated with b. Since every guise has internaliy some property or other, the antecedent b(F) is always satisfied. Hence, the righthand side of (111) is true if and only if the consequent is satisfied. Therefore, the righthand side of (111)
is true only if guise b exists, i.e., is selfconsubstantiated. Hence, every guise satisfies the righthand side of (111) if and only if it exists. Then the property that the righthand side of (111) can be used to define is a property equivalent to existence. If we call that property selfdisplayingness, then every existing guise is selfdisplaying, and vice versa. But what sense of 'is' is this? Obviously the sense in which existence is true of guises, namely, the consubstantiational sense of external predication. There should, therefore, be no paradox in the introduction of the property of being selfdisplaying. Let us turn now to the lefthand side, the definiendum, of Clark's schema (111). It has the form "F(a)" once again. But it must not introduce a new sense for this form. Patently, since Clark's argument lies within the GCCC theory, schema (111) must not have the form "F(a)" with the datum sense described in (T*). Hence, if ambiguity is to be avoided, the definiendum "SD(b)" of schema (111) must use the form "F( )" in the sense of consubstantiational predication governed by schema (I) and by (9) and (10) above. This tallies with the preceding discussion of the righthand side of schema (111). Hence, in analogy with (lo), we have now the metalinguistic schema:
Consider the special guise the selfdisplayer, i.e., c{SD}. Clearly because of the uniqueness condition, this guise does not exist whenever there exists more than one ordinary object, that is, whenever there are guises a and b such that both "C*(a, b)" is false and "C*(a,a) & C*(b,b)" is true. Therefore, as things stand nowadays: (12) "(C*(c{SD}, c{SD))" is true. Now consider Clark's crucial guise d, the nonselfdzsplayer, i.e., c{SD}. Since every existing guise, as noted above, is ,, selfdisplaying. given the consistency of the existing guises, Clark's guise d cannot exist. Therefore, it is the case neither that d is,, nonselfdisplaying nor that d is,, selfdisplaying: (13) "(C*(d, d[ SD])) & (C*(d, d[SD]))" is true. That is, in Clark's notation for external consubstantiational predication:
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(13a) "((SD)(d)) & (SD(d))" is true. Clark derives a contradiction from the second conjunct in (13a). That is the first part of his derivation of his "paradox" in naive predication theory. How come? An examination of Clark's derivation reveals a gap at step 8, on [I], p. 185, namely: 8. On the other hand, instantiating (I), we have  ( S D ( d ) ) o ( 3 b ) ( b (  S D ) & C*(d, b ) ) .
As noted above, (I) holds in the GCCC theory, provided that the form "F(a)" is understood as expressing consubstantiational predication, in accordance with (10). Recall that (I) is:
At step 8 Clark is instantiating the quantifier '(F)' into the constant 'SD' and the quantifier '(a)' into 'd'. But the instantiation of (I) into 'SD' and 'd' yields, not 8, but: 8'. (SD)(a) .(3b)(b(SD)
& C*(a, b)).
Plainly, Clark's step 8 and instantiation 8' are not equivalent. T o be sure, Clark does not need his step 8 for his derivation. He needs only the weaker step 8C. (SD(d))
+
(3b)(b(SD) & C*(d, b)).
This step he can obtain from 8' and
But 8x is not forthcoming. Obviously, the antecedent of 8x is true, for, as we saw above, d does not exist. On the other hand, the consequent of 8x implies that guise d exists. Hence, 8x would allow us to infer that a nonexisting guise exists. In fact, the very axiom schema (I) on which Clark builds his derivation requires that we distinguish between '(F(a))' and '(F)(a)'. The negation sign in "F(a)" is a propositional negation, and the negation in "(F)(a)" is a property negation. They belong to different levels in the twotiered structure of the GCCC theory, as was explained in Section 1.6 above. We can look
upon Clark's argument as reducing to absurdity the implicit premise 8x, which underlies step 8. Clark's argument supports the GCCC theory by bringing forth the need for distinguishing between property negation, within property composition, and propositional negation, within the attribution of properties.s There is, therefore, nothing objectionable in the being of the guises the selfdisplayer and the nonselfdisplayer. Neither one exists. The nonselfdisplayer cannot exist; thus it is in the same ontological position as the round square. Both are equally respectable as objects of thought, as both Clark's and my discussion above have shown. Since the impossibility of existence of the nonselfdisplayer depends on schemata (I) and (111), this guise of Clark's is more interesting than the round square. It should be noted that had Clark's argument been successful it would have shown that the GCCC theory together with his axiom (111) would be paradoxical. From that, of course, it does not follow that the GCCC theory is paradoxical. T o show a paradox in the GCCC theory the argument has to proceed in the primitive notation o the GCCC theory. IV: CONCLUSION
The GCCC theory involves neither of the contradictions discussed by Clark. It has enough complexity to illuminate Oedipus' sieves, accommodate the different ways in which objects have properties, differentiate the ontological status of existing objects from the objects of thoughts, assign their proper place both to patently impossible objects, like the round square, and to less superficially impossible objects, like the nonselfdisplayer of Clark's, etc. Thanks to Clark's valuable probes, the GCCC theory has shown its strength; but it must be tested further. In fact, the much more comprehensive extension of it in [5] should be tested in the forceful way of Clark's tests in [I].
[ l ] Clark, Romane, "Not Every Object of Thought Has Being: A Paradox in Naive Predication Theory," NOUS 12(1978): 181188. [2] Castarieda, HectorNeri, "Thinking and the Structure of the World," Philosophia 4(1974): 340, and Critica VI(1972): 4386. Page references will be of the form 'n(m)', n being the page number in Philosophia and m the corresponding ones in Critica.
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"Identity and Sameness," Philosophia 5(1975): 121150. [3] , [4] "lndividuation and Nonidentity," American Philosophical Quarterly 12(1975): 131140. "Perception, Belief, and the Structure of Physical Objects and Con[5] , sciousness," Synthese 35(1977): 285351. "Ontology and Grammar: T h e General Theory of Properties," Theoria [6] , 42(1976). Thinking and Doing, (Dordrecht, Holland: D. Reidel Publishing Com[6a] , pany, 1975). [7] Doyle, Arthur Conan, The Complete Sherlock Holmes (Garden City, New York: Doubleday & Company, Inc.). [8] Orayen, Raul Armando, "Sobre la Inconsistencia de la Ontologia de Meinong," Cuudernos de Filosofi (Universidad de Buenos Aires), No. 14(1970): 327344. [9] Quine, W. V. 0 . . "Variables Explained Away," Selected Logzc Papers (New York: Random House, 1966). [lo] Parsons, Terence, "Nuclear and Extranuclear Properties, Meinong, and Leibniz," NOOS 12(1978): 137151. [ l 11 Rapaport, William, "Meinongian Theories and a Russellian Paradox,'' NOOS 12(1978): 153180. [12] Renouvier, Charles, Esquise d'une classfication systtmatique des doctrines philosophiques (Paris: Bureau de la Critique Philosophique, Vol. I, 1885, and Vol. 11, 1886). [13] Russell, Bertrand, "Meinong's Theory of Complexes and Assumptions," Mind n.s. 13(1904): 2042 19, 336354, and 59524. [14] Wittgenstein, Ludwig, Philosophical Investigations (New York: T h e Macmillan Company, 1968; translated by G. E. M. Anscombe).
'1 owe this quotation to Christopher Maloney. I am convinced that philosophers infieri may benefit from the several methodological principles that Sherlock Holmes formulates and illustrates in his different adventures, e.g., the need for data, the need for scrutinizing the data, that theories must be based on data, that theories must fit all the data available, that one must have alternative theories, that "there is nothing more deceptive than an obvious fact", etc. (See [7].) lBeing concerned with intersystemic structural invariances, diaphilosophy is a constructive discipline, which has to establish isomorphisms where none may be visible to the untrained eye. Thus, it is quite different from the descriptive and even comparing the incompaimpressionistic comparative studies of recent yearften rable, as when comparing philosophies of the East and of the West in very general terms. Diaphilosophy is also different from the serious and illuminating but merely comparative studies aimed at eclecticism, which have, perhaps, their highest peak in Two types of theory that seem to me to be capable of Renouvier's monumental 1121. consistent development into rich and comprehensive systems and are, yet, mutually incom~atibleare the substrate view of individuation and the bundletheorv. But we d o not have as yet the systems for a diaphilosophic exercise. (On the criteria for a solution of the problem of individuation see [4].) Another great divide, which eventually may prove to be solid material for diaphilosophy, is that separating the theory of propositions as the allencompassing and rich content of mental states and of states of consciousness outlined in [5], and the multiplecontent of propositional attitudes and acts that David Kaplan, John Perry, and Tyler Burge have been working on. In [5] there is, however, a distinction between propositions (or states of affairs) and popositwnal guises. 3For kindred theories within the type I am engaged in developing in full, see Parsons [lo] and Rapaport [ l l ] .
4 0 n other occasions I have referred to Oedipus' sieves as Fregean triads, e.g., at 121: 4(44). 51n [2] and [3] I mentioned transubstantiation as a likely relation to account for individual identity across time. Clark has called my attention to properties that must be predicated externally of guises, which I have not discussed in my earlier papers, for instance, the property some guises possess of being composed of three properties, and the property of being a guise, which all guises have. I am prepared to consider these as cases involving conflation, involving equivalences of sets of the forms {F, G, H} and {F, G, H, being composed of three properties}. But perhaps here we may find it better to introduce another type of external predication. T h e topic certainly needs further study, and Clark's data must be complemented and scrutinized in detail. 61n footnote 2 of his paper ([l]: 188) Clark suggests that the individuator c is "similar to Aquinas' esse." There is indeed a similarity, namely, that there is a certain particularity in the esse of each particular: each one has its own actus essendi, or act of existing. But this particularity is on my view, although perhaps not on Aquinas' view, derived from the fundamental particularity conferred upon each particular (whether existing or not) by its being a d v e r e n t particular from all others. Furthermore, an impossible object, like Clark's own nonselfdisplaying one, is a particular, individuated by the operator Cyet it has, can have, no act of existing. As I read Aquinas, an act of existing corresponds in the GCCC theory to the truth of all the consubstantiation propositions about mutually consubstantiated guises. 71 will ignore here the profound issue about the saturation or unsaturation of the elements in the core sets of guises. The correct view will make the members of such sets saturated and the predicates involved in internal predication unsaturated. (See [6] and Section 1.6 above.) is important to appreciate that Clark's argument is not of the form: . .
'
1. a believes that b is F 2. Then by CastaAeda's (T), 'a believes that is F' expresses a truth, and this truth is the one we can also formulate by 3. b is believed by a to be F. 4. b is the same as d . 5. Hence, d is believed by a to be F. 6. Hence, by the reason in 2: a believes that d is F.
Clark's argument is compatible with the invalidity of step 3 in this argument. This shows that the passive sentence 3 is not equivalent to the active sentence 1. The above argument conf;ses the de dicto constructibn 1 with the de re construction 3. It belongs to the data for the GCCC theory, and neither to the theory nor to the connection between the theory and its data. For another argument, originating in Frege, with which Quine has attacked Fregean senses and could apply to guises, see [3]: 12931. 90bviously,schema (I) demands the distinction between propertycompounding connectives and propositioncompounding ones because this distinction is ultimately demanded by our conception of internal predication. (See principle (Ip.Tl) in Section 1.5 above.) This distinction defuses arguments like Russell's against Meinong's impossible objects. Meinong claimed that the law of noncontradiction does not apply to impossible objects. And Russell could not understand him. The trouble was that Meinong did not distinguish between property attribution and property or individual composition. At the level of property attribution the law of noncontradiction reigns with an iron rule: the attribution of properties to objects, whether impossible or not, cannot violate the law of noncontradiction. Thus, the guise, let us call it m , the thing which is both P a n d  P , allows twoimmediately obvious "analytic" truths: m(P) andm(P); but it also allows two "analytic" falsehoods: (m(P))and (m(P)).Of course, no consubstantiational predication of any property to m is true; in particular, it is an
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"analytic" truth that C*(m, m) & C*(m, m[P]) & C*(m, m[PI). Therefore, antiMeinongian arguments like Russell's in [13] and Orayen's in [a] d o not apply to the GCCC theory.(See [2].)
'TRUE OF' AND CONTEXTUAL PREDICATION
In the preceding essay we have underscored the twotiered character of the Theory of Guises, Consubstantiation, Consociation, and Conflation (the GCCC theory). We noted how the breaking point of Clark's arguments in his derivations of contradictions, as applied to that theory, rather than to a simple guise theory without the twotiered structure, lies in the twotiered distinction the theory makes between negation of properties and negation of propositions (or states of affairs), and between property and proposition composition. We also pointed out how there is a most important difference between a proposition about an individual being true, and the proposition formulatingsomething true of that individual, and the individual in question having a property denoted by a sentence expressing that proposition. (See Sections 56 of Part I and Part I1 above.) This distinction is absent in extensional svstems. like standard auantificational logic. Thus, it is naturally assumed that to say that an individual a , referred to by a term t, has a property Fness, denoted by a monadic open sentence Ax, is tantamout to claiming that the sentence Axllt, obtained from Ax by replacing all free occurrences of nc with free occurrences o f t , is true (or expresses a truth). This is a crucial formal assumption underlying both of Clark's arguments. Thus, these arguments are important variations on the standard simple view of predication characterized by that assumption. In a sense different from Clark's, that view may be called "naive predication theory:' and then we can say that his arguments do show that naive predication theory is paradoxical. We must, therefore, reject the assumption underlying the standard view of predication. An examination of the data connected with (T*) in Part I1 shows that assumption to be false. As we have seen, the GCCC theory rejects that assumption. Now. the GCCC theorv is committed to the view that everv monadic open wellformed sentence denotes a property that can constitute a guise or be a member of a guise core. That is, the following is a thesis of the GCCC theory: A
A
(G.G*) Where r is any wff (wellformed formula) with just one free variable, 3g(g = ~ { r ) ) . This suggests that the property expressed by l? in (G.G*) should be predicable of individual guises. A little reflection on our discussion in Part I1 above, of 'having properties' and 'being true of, reveals,
however, that the GCCC theory does not provide for the general predication to individual guises of properties expressed by sentences with just one free variable. In some cases, there is no problem: the predication involved is consubstantiation, and in others it is consociation, or conflation, as we have explained above. But in general the GCCC theory does not equate having a property with beingpart of a truth. Perhaps that is a limitation of the GCCC theory. Let us, therefore, consider an extended theory, the GCCCC theory, which, by making that equation, provides a way of predicating a property, hereafter called contextual property, that corresponds to an incomplete proposition, whatever this may be. Let us call such predication of contextual properties contextual predicati0n.l This is, of course, a different type of predication from the types already discussed. Let us represent contextual predication both by putting the sentential matrix representing an nadic property of the propositional sort in square brackets, and plaing to the right of such a bracketed expression the list of terms involved in the contextual property in question. The basic axiom of contextual predication is, therefore, this: (Cont. Pred*) (al) . . . (an)([T]al.. . an
Txlllal. . . xnllan),
where I' is any wff containing x,,. . ., x, as its only free variables. Contextual predication is clearly a form of external predication and does have the property Clark needed in his crucial step (VI).8 of his first argument ([I]: OOO), for clearly:

1. [r]a

2. ([T]a) ++ 3. [T]a
(Cont. Pred*)
I'xlla


(Txlla)
(Txlla)
(Cont. Pred. "1)
([T]a)
Negation biconditional; 1

(Cont. Pred.*) [T]a
2, 3; prop. logic
Obviously, (Cont. Pred. * 1) merely reflects the twovalued character of propositions. Patently, (Cont. Pred. "1) does not help to restore Clark's argument (VI): contextual predication does not comply with axiom (I), which, as we have seen, does govern external consubstantiational predication. We must, of course, adopt Clark's attitude and test contextual predication for consistency. If it is not consistent, then we must refuse to extend the GCCC theory to the GCCCC theory. It may be worthwhile to experiment with an example, like Clark's, of the sort of thing that Russell's paradox would suggest. Consider the property of having no internal property, expressed by:
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11. A: 3F(x(F)), where as before 'x(F)' says that x is internally F. This propositional function is not satisfied by any guise, that is to say: 12. 3a3F(a(F)) holds in the GCCC ;heory The GCCC theory is committed by (G.G*) to there being a guise composed of the property formulated in 11, that is: 13. 3f(f = c{3F(x(F))), which we can abbreviate to 3fv = c {A}). Let us call the guise posited by 13, a , i.e.,
Hence,
Clearly,
We also have: 17. [A]a
*  3F(a(F))
18. [A]a
by abbreviation and (Cont. Pred*) 17, 16; modus tollens
Now, 18 is just an abbreviation of
which by (Cont. Pred. "1) above is equivalent to:
Now, 19 is not contradictory. In fact, it is by (Cont. Pred. * l), equivalent to (16). The preceding discussion is interesting. It reveals that, even though every guise must have some property in its core, there is no difficulty for the guise composed of the property of being composed of no properties. As we have noted, in standard extensional quantificational logic, "a has the property Fness" is equated with "(the propositional function) Fx is true of a," which, by virtue of our (T*) in Section 11.1, I have partially equated with "Fxlla is true." The difference between
the first two expressions is absolutely important, as we have seen, when we are dealing with the intensional segments of language and thinking. T h e chief results of our study in this paper can be put as follows:
(T*.A) T h e ordinary and general sense of 'true o f , captured by (T*) as a datum, is analyzable theoretically as including the six forms of predication discussed above: internal predication, consubstantiation, consociation, conflation, strict identity, and contextual predication. Neither of the first five types is reducible to the others. Contextual predication is, by (Cont. Pred."), dispensable. It is, however, an open question whether other types of predication must be distinguished in order to achieve a complete account of the total structure of the world and experien~e.~ In conclusion, the GCCCC theory should be tested for consistency. It seems, importantly, to have the richness Meinong wished for his own theory of objects: any property whatever determines an individual guise, which is a possible object of thought, even if it is itself an impossible object.
'The idea of discussing contextual predication came to me in responding to some comments on the main essay kindly prepared by John Tienson. The need for recognizing contextual predication is one of the important results arising from Clark's essay. 21nconnectionwith the logic of intentions, imperatives, and oughts, I have for 25 years defended the view that a practical copula is required to account for the structure of practical thinking. (See [6a]for a theory of practical thinking built on the largest collection of relevant data.) Thus, what by (T*.A)remains open is whether other forms of predication, besides the six descriptive ones mentioned there and the practical predication involved in practical experience, are required for that complete theory of the structure of the world and of experience.