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1 Symposium: On Determinables and Resemblance Author(s): S. Körner and J. Searle Source: Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 33 (1959), pp Published by: Blackwell Publishing on behalf of The Aristotelian Society Stable URL: Accessed: 29/04/ :38 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. The Aristotelian Society and Blackwell Publishing are collaborating with JSTOR to digitize, preserve and extend access to Proceedings of the Aristotelian Society, Supplementary Volumes.

2 ON DETERMINABLES AND RESEMBLANCE PROF. S. KtiRNER AND MR. J. SEARLE I-By S. KiSRNER INEXACT concepts, i.e., concepts having border-line cases, are involved in various propositions and theories the analysis of which is either plainly unsatisfactory or at the least, highly controversial. It seems both plausible and heuristically sound to anticipate that by giving proper attention to the logic of inexact concepts some light may be thrown on the structure of those propositions and on the theories in which they play a part. I have argued elsewhere that the logic of inexact concepts provides us with useful equipment for clarifying the logical status both of empirical laws of nature (which relate inexact empirical characteristics) and of the theories of applied mathematics (which relate inexact empirical to exact mathematical characteristics).1 In this paper I use the logic of inexact concepts in an effort to clarify the notion of resemblance which is applied, e.g., when we assert of a green and blue thing that they resemble each other in respect of-the determinable-colour, or that two objects resemble each other in any more general way. As regards the definition (given in Section 1 below) of the logical relations which may hold between inexact concepts, I am faced with the awkward choice of either repeating former statements with hardly any change or assuming that I need not do so-the reader of this paper being already well acquainted with what I have had to say in the matter. The former alternative appears to me to be much the more reasonable and I proceed upon it. 1. On the logical relations between concepts. I call a rule, say r, for the assignment or refusal of a sign, say U, an inexact 1 See ' On the Nature of Pure and Applied Mathematics' in Ratio No. 3 and Chapter XI of Conceptual Thinking Cambridge 1955, Dover (New York), 1959.

3 126 S. KiRNER rule, and U an inexact concept, if the following two conditions are fulfilled. The first concerns the possible results of applying U to objects. These are: (a) that the assignment of U to some object would conform to r whereas the refusal would violate it; in which case the object, we may say, is a positive candidate for U and, for the person making the assignment, a positive instance of U; (b) that the refusal of U to some object would conform to r whereas the assignment would violate it; in which case the object is a negative candidate for U and, for the person making the refusal, a negative instance of U; (c) that both the assignment and the refusal of U to some object would conform to r; in which case the object is a neutral candidate for U. For the person who assigns U to the object it will be a positive instance of U; for the person who refuses U to the object, a negative instance of U. The second condition concerns the nature of the neutral candidates for an inexact concept U. If we define a concept, say V, by requiring that the neutral candidates for U be the positive candidates of V, then V will again have positive, negative and neutral candidates. (Example: Let U be the inexact concept 'green' and V the concept 'having the neutral candidates for 'green' as its positive candidates'. V is inexact.) The inexactness of a concept, i.e., the possibility of its having neutral candidates, depends on the rules which govern its use, and not on the actual inventory of the world. 'Green' would e.g., remain inexact if there were no colours. An exact concept on the other hand cannot have neutral candidates. For such a concept, the distinction between candidates and instances has no point; clause (c) of the first condition above, likewise the entire second condition, have no application. The concepts (attributes, predicates, statement-functions etc.) of standard logic and mathematics are all exact or at least are required and assumed to be so-for example by Frege.2 The following definitions of the logical relations between concepts apply to both exact concepts and inexact. Let U and 2 Frege, Grundgesetze der Arithmetik Jena 1903, esp. Vol. II? 56.

4 ON DETERMINABLES AND RESEMBLANCE 127 V be two concepts governed respectively by r (U) and r (V); and let S, be a finite set of objects. Apply r (U) and r (V) to the members of S, collecting the positive instances of U into the " associated set " [U], and similarly the positive instances of V into [V]1. Between the two associated sets the following relations may obtain: (1) [U], < [V], (proper inclusion)-also, of course [U]1> [V], and [U], I [V], (bilateral inclusion); (2) [U]I/[V], (exclusion); and (3) [U] O0 [ V], (proper overlap, where each of the two finite sets has at least one member not common to both). Next, amplify S, by one or more objects into S2 and apply r (U) and r (V) to all members of S2thus getting the "amplified associated sets " [U]2 and [V]2. The relations between these again may be: [U]2 < [V]2, [U],/[V]2, [U]2 0 [V]2. If the relation, between the original and the amplified sets be the same, I shall say that the relation is preserved in the amplification or briefly that it is preserved. The possible logical relations between concepts, including inexact ones, may now be defined in terms of the preservability of the relations between their associated sets-preservability, like exactness or inexactness of a concept, being independent of the inventory of the world: (1) U < V by " Inclusion is the only preservable relation between any two associated sets of U and V." The relation is the familiar inclusion. (2) U/V by " Exclusion is the only preservable relation between any two associated sets of U and V." The relation is the familiar exclusion. (3) U O V by " Overlap is the only preservable relation between any two associated sets of Uand V." The relation is the familiar overlap. (4) V by " Inclusion and overlap are both preservable between any two associated sets of U and V." The relation will be called " inclusion-overlap ".

5 128 s. KOiRNER (5) U O Vby "Exclusion and overlap are both preservable relations between any two associated sets of U and V." The relation will be called " exclusion-overlap." Between exact concepts only the first three relations can hold and it is on this fact that e.g., the Euler diagrams are based. An example of (5) would be any two concepts U and V (say U = ' green' and V = ' blue ') such that although every positive candidate for U is a negative candidate for V and every positive candidate for V a negative candidate for U, U and Vhave common neutral candidates. If no such object is elected as a positive instance of U and of V, [U]/[V] will be preserved; otherwise [U] O [V]. Similar examples can be provided for (4). Clearly U ( V must be distinguished from ((U < V) or (U O V)) since the former statement asserts the preservability of inclusion and overlap between the associated sets, whereas the latter asserts the preservability of one or the other. Similarly (4) is not an alternation of (2) and (3).-From a purely combinatorial standpoint the following further possibilities can arise: (6) No relation preservable, (7) inclusion and exclusion preservable, (8) inclusion, exclusion and overlap preservable. But a sign used in accordance with rules allowing any of these is-on any view of conceptual thinking-not used as a concept. Our definitions of the five logical relations are based on the assumption that we are free to " elect" a neutral candidate, say of a xo, concept, say U, as a positive or negative instance of U independently of previous elections of x0 or any other object as a positive or negative candidate of U or any other concept. This freedom, which may be restricted by further conventions, implies that the relation of an inexact concept U to itself is U and not U < U. It will-after the definition of the absolute complement U of U-equally become clear that the relation between U and U is U 0 U and not U/U. 2. Sums, products and complements. Just as the number of possible logical relations between concepts is increased by admitting inexact concepts in addition to exact ones, so is the number increased of ways of forming new concepts from already

6 ON DETERMINABLES AND RESEMBLANCE 129 available ones by means of logical connectives. In defining them we have considerable freedom. A guiding principle for redefining " complement ", " sum" and " product" of two or more concepts has been the requirementhat for exact concepts they should reduce to the usual ones. This is the principle observed also, for example, when operations which have been defined for one class of numbers are redefined for a wider class. The sum of two-exact or inexact-concepts, say U and V, is determined by the following stipulation: An object is a positive candidate of (U + V)-in words, U or V-if, and only if, it is a positive candidate either of U or of V or of both; it is a negative candidate of (U + V) if and only if it is a negative candidate of both; it is a neutral candidate of (U + V) in all other cases. The definition, though needed here only for pairs of concepts, can easily be extended to any finite sum. Since the sum is defined in terms of candidates for its members-and not in terms of candidates and instances-the stipulation can be represented diagrammatically after the fashion of the truth-tables. If U and V have no neutral candidates (U + V) is the sum of two exact concepts. We now turn to the notion of the product (U. V) of two concepts. An object is a positive candidate of (U. V) if, and only if, it is a positive candidate of both; it is a negative candidate of (U. V) if, and only if, it is a negative candidate of one or both of them; it is a neutral candidate of (U. V) in all other cases. For exact concepts this reduces to the usual definition. The general definition of the complement is this: Two concepts U and U are absolute complements of each other if, and only if, a positive candidate of U is a negative candidate of U; a negative candidate of U is a positive candidate of U; and a neutral candidate of U is a neutral candidate of U. For exact concepts this again gives the usual definition. (I am using the term " absolute complement " because later in this essay I shall be introducing, under the name of " determinate complement" a notion which has no parallel in the logic of exact concepts.) The generalized definitions of sum, product and complement I

7 130 S. K6RNER are consistent. Their application yields theorems which are for the most part obvious generalizations of theorems of exact logic. For example, we have U + V = U. V in the sense that by our definitions an object is a positive, negative or neutral candidate of U + V if, and only if, it is respectively a positive, negative or neutral candidate of U. V. On the whole the definitions of 'sum', 'product' and 'absolute complement' correspond to common uses of 'or', ' and ' and ' not'. If we call the concept for which every object is a positive candidate the universal concept and the concept for which every object is a negative candidate the null-concepthen it is not true that for every concept U-(U + U) represents the universal concept and (U. U) the null-concept. This is so only if U is exact.3 3. Linked concepts and determinables. If an object a resembles another object b with respect to the property U and also with respect to the property V, and if in addition U is a species of V in the sense that either U V or U? V, then U will here be called, in conformity with an established philosophical usage, a " determinate under V ". If, in the conceptual system under consideration, V itself is not a determinate under some other property, then V will be called a " determinable " of the system. (Example: 'green' is a determinate under the determinable 'coloured'.) Before these notions can be used in clarifying various types of resemblance, they themselves must be clarified. This will be done by defining them in terms of relations which hold between inexact concepts only, in particular of exclusionoverlap. (Whenever possible I shall use 'P ', 'Q', 'R ', 'C1' ' C,' for signs of inexact concepts.) Let us say that a concept P is linked with another concept Q if, and only if, either (i) P O Q or (ii) in the conceptual system under consideration there are available concepts C1, C2,.... Cn such that P O C1, C, O C2... C, 0 Q.* Whether or not a concept * In framing some of the definitions of this and the following sections I have profited from discussion with Dr. P. Feyerabend and Dr. C. Lejewski. * Added after reading Mr. Searle's paper : If any link in this exclusionoverlap chain is (or is equivalent to) a conjunction of concepts, then it must not be possible to drop any of them without breaking the chain.

8 ON DETERMINABLES AND RESEMBLANCE 131 is available in a system depends on the rules-prescriptive, proscriptive or permissive-governing the formation of its concepts. Most of the following examples are chosen from a conceptual system of a type which is widely adopted and is implicit in customary ways of speaking. (It is a system of the second of the types discussed in section 4.) If, as we shall assume throughout, with every concept its absolute complement is also available, the first condition above is redundant: If P O Q then P and P have not only the same neutral candidates but share some of them with Q. We have P 0 P, P O Q. If the first condition is fulfilled the second is eo ipso also fulfilled. (Example: Since 'green' is linked with ' blue', ' green' is linked with ' not-green' and ' not-green' with 'blue '.) The relation of linkage between two inexact concepts is symmetrical. If P is linked with Q then Q is linked with P. It is transitive. If P is linked with Q, and Q with R, then P is linked with R. And it is reflexive. In view of P o P, any inexact concept is linked with itself via its absolute complement I.e., P 0 P and P 0 P. Linkage is thus exemplified by any system which contains at least one inexact concept and its complement. Conceptual systems are conceivable in which every concept would be linked with every other. But this is not in general so. (Example: Consider the concept 'green' and its absolute complement 'not-green'. Although 'green' is linked with ' not-green ', it is not linked with all its species- being a species of P if either T < P P. Thus we shall assume that ' green' is not linked with ' romantic ', ' angry', etc. and not of course with any exact concept such as 'being a prime number'. Unless we postulate "links" between any two inexact concepts we can easily provide examples of unlinked inexact concepts.) In order to define the notion of a determinable we must first, mainly in terms of linkage, define a stronger relation. Let us say that a concept P is fully linked with a concept Q if and only if, every species n of P is linked with every species K of Q. Since 12

9 132 s. KiRNER P is a species of P, and Q a species of Q, full linkage implies linkage; while the converse is not true. (Example: ' green' is fully linked with ' yellow or red ' but not with ' yellow or angry ', since' angry '-a species of ' yellow or angry '-is not linked with ' green '.) It follows from the definition of full linkage that the relation is symmetrical and transitive. Thus, if a concept is fully linked with another, it is also-via this concept-fully linked with with itself. (Examples:' green' if fully linked with ' red' and vice versa; ' green ' is fully linked with ' blue ', ' blue ' with' red ' and therefore ' green' with ' red '; ' green ' is fully linked with ' red ', ' red' with ' green ' and, therefore, ' green' with 'green'.) The notion of a determinable can now be defined. A concept Q is a determinable of a concept P if, and only if, (i) P is a species of Q, but not also Q a species of P. (ii) Q is the sum of all concepts which are fully linked with P. It follows that every concept can have at most one determinable. (Example: 'Coloured' is the determinable of 'green'.) But not every concept has a determinable. (Examples: No exact concept has a determinable since, having no neutral candidates, it is not linked with any concept. Again 'green or angry' has no determinable: For assume that D is the determinable. Then in view of condition (i) D must have a species 8 which is not a species of 'green or angry ', but fully linked with it. This implies that 8 if fully linked with 'green' and with 'angry'. From the full linkage between ' green ' and 8 on the one hand and 8 and ' angry' on the other it follows that ' green' is fully linked with 'angry'. But-according to the example of the last paragraph but one-the two concepts are not even linked.) When we say that an object is not green we sometimes mean that it is not even coloured. At other times we mean that it is not green but coloured. In the first case the object is a positive or neutral candidate of the absolute complement of ' green ', in the second case it is a positive or neutral candidate of what may be called the determinate complement of 'green'. A concept Q is the determinate complement of a concept P if, and only if, Q has the same species as the determinable of P, with the exception of P and its species. Writing Det (P) for the determinable of P

10 ON DETERMINABLES AND RESEMBLANCE 133 the definition is briefly: Q = Det (P) - P. (Example: ' green ' and 'not green, but coloured' are determinate complements of each other.) It follows that a concept, if it has a determinate complement at all, can have at most only one; and that a concept has a determinate complement only if it has a determinable. We shall write P' for the determinate complement of P. If a concept P has a determinate complement P' then the determinate complement of P' is P, i.e., (P ')' = P. (See last example.) If P has no determinate complement we may identify P' with the nullconcept, i.e., P '= O. In general we shall have P ' P although in some conceptual systems the absolute and the determinate complement may be identical i.e., P' = P. (Example: Consider a conceptual system containing only colour-concepts. In such a system 'not-green' and 'coloured, but not green' are identical.) If P and Q are any two species of the same determinable, say D, then by the definitions of 'determinable' and 'determinate complement' (P + P ') = (Q + Q ') = Det (P) = Det (P ') = Det (Q) = Det (Q ') = D. That is to say all these expressions represent the same concept, or are different labels which are assigned or refused to objects in accordance with the same rules. (Example: "(blue + blue')" = "(green + green')" = Det (green) -... = 'coloured '.) Two determinables, say P and Q, are identical if every species z of the one is fully linked with every species K of the other. They are different if some species 7r of one is not fully linked with some species K of the other. (Example: ' coloured' and 'having shape' are different determinables although, in various senses of the term "imply ", they imply each other.) I am prepared to admit that the definitions of linkage, full linkage, determinable and determinate complement could be improved and, perhaps, stand in need of improvement. But I do not at present doubt that the procedure of defining them in terms of exclusion-overlap and thus within the framework of the logic of inexact concepts is on the right lines. 4. Exact and inexact determinables. The determinates a

11 134 s. Ki0RNER under the determinable D (8 < D or D, but not vice versa) are necessarily inexact, since their inexactness is a necessary condition of linkage between them. The determinable itself, however, may be exact or inexact. It is obvious (i) that D is inexact if, and only if, D 0 D and (ii) that D is exact if, and only if, DID. For (i) if D is inexact the rules governing its assignment or refusal admit of neutral candidates. D has by definition of the absolute complement the same neutral candidates as D; moreover the positive and negative candidates of D are respectively the negative and positive candidates of D. This implies D o D. On the other hand D 0 D implies the inexactness of D. Statement (ii) is shown to be true in the same way. A statistical enquiry among English-speaking people might, for all I know, show that most of them use, say, the determinable " coloured " as an exact concept. On the other hand, to use it as an inexact concept by no means commits one to any great or unreasonable modification. Imagine, for example, a blue windowpane becoming gradually more and more transparent in the sense of affecting less and less the colours of the objects behind it, until in the end it becomes invisible, though, of course, remaining tangible. Should we, at every stage of the process, say of the window-pane that it is a positive or that it is a negative candidate of 'coloured', and never that it is a neutral candidate of this determinable? Few people can have pondered this question; even fewer can have decided it. Those who are not aware of having made a previous decision can decide the question either way. They may so arrange their language that at one stage of the process of becoming invisible the window-pane is a neutral candidate of 'coloured' and therefore, of ' not-coloured '. In this case ' coloured' 0 'not coloured' and the determinable is inexact. On the other hand they could decide that a fully transparent window-pane has by definition the colour of the objects behind it and make further arrangements to ensure the exactness of 'coloured'. Similar examples could be given showing that determinables may be both exact or inexact. The conceptual systems embodied in most natural languages

12 ON DETERMINABLES AND RESEMBLANCE 135 include, as far as one can judge from one's limited knowledge, exact and inexact concepts and exact and inexact determinables. It is nevertheless instructive to consider some " pure " types of conceptual system, namely, (1) systems in which all concepts are exact; (2) systems which contain only exact determinables, their species and the sums, pruducts and absolute complements of these species; (3) systems which contain only inexact determinables, their species and the sums, products and absolute complements of their species. The first type of system is exemplified by every theory of pure mathematicso far constructed. Every concept, here, is exact and has only exact species. To distinguish this thorough-going exactness of mathematical concepts from the exactness of a determinable, whose species are inexact, one might call the former "purely exact ". An inquiry into the relations, and lack of relations, between inexact and purely exact concepts is, I think, important to the philosophy of mathematics. (See references in footnote 1.) It is sometimes assumed that all empirical concepts are organized in systems of the second type-those which contain only exact determinables. In such a system every empirical concept is an exact determinable or a conjunction of such determinables, a determinate under an exact determinable, or a sum or product of such determinates. A good case might be made in support of the view that Locke's system of empirical knowledge and the systems of his empiricist successors are of this type. Part of what Wittgenstein shows by the construction of various " language games " is that languages or conceptual systems of the second type are by no means the only possible or "proper" ones. Systems of the third type might possibly throw some light on certain prominent features of Hegelian dialectic and of dialectic in general. These are: No category is sharply separated from any other. On the contrary, all categories are connected with each other. Hegelian negation leads allegedly in a unique manner from one category, the thesis, to another category, the antithesis, which is not the absolute complement of the thesis. The thesis and the antithesis combine into a third category the synthesis

13 136 S. KiRNER which includes them both. (Hegel, as is well known, is fond of using the German word "aufheben" in describing dialectical reasoning, because in its various senses it suggests negation, preservation, and lifting to a higher level.) The process-or rather the non-temporal structure exhibited by the process-is complete when the last synthesis is reached. This is the Idea or Absolute which includes within itself all the preceding theses, anitheses and syntheses. Although Hegel begins the process with the category of Being-in his view the most reasonable starting point-this category being the emptiest-he holds, as did Fichte before him-that it could start with any category. Even a pure system of the second type conforms to some of the foregoing principles, as can be seen by re-naming the terms used in the definitions of section 3: We call determinables " categories (or syntheses) of first level "; their proper species " categories of level zero "; the determinate complement of a category its "antithesis"-so that the antithesis of an antithesis is the original thesis. Now clearly every thesis (of a category of level zero) uniquely determines its antithesis; and their sum, a synthesis of first level, includes both thesis and antithesis. If all syntheses or categories of first level (all determinables) are exact, " dialectical reasoning " from thesis to antithesis to synthesis must stop at the first level. If the categories of first level are inexact, exclusion-overlaps and linkages between them become possible. We can then define second-level syntheses between theses and antitheses of first level. This is done, if in the definitions of section 3, we replace " determinable " by "category (or synthesis) of second level ", and replace "proper species of a determinable" by "proper species which are categories of first level ". We can then "reason dialectically" from first-level thesis to first-level antithesis and second-level synthesis and so on, until after a finite or infinite number of steps we reach a synthesis which has no antithesis-the Absolute. Every synthesis includes the preceding synthesis and more species of zero level than its predecessor; the last synthesis includes (under certain specifiable conditions) all of them. Thus all the above-mentioned principles can be satisfied by a pure system of the third type.-this analogy could be

14 ON DETERMINABLES AND RESEMBLANCE 137 elaborated in more detail and with greater precision. But I fear that in merely drawing attention to it I may already have angered both Hegelian and anti-hegelian philosophers. To exhibit the structure of various types of conceptual systems, however pedestrian or fanciful, is not to raise the question of their adequacy. To say that "reality" is best described by one of these types, and that one should therefore be preferred to all the others is to defend a metaphysical view or, as I understand it, a general programme for the construction of conceptual systems. 5. Resemblance. Determinables are respects in which objects resemble each other. Once the notion of a determinable is clear the notion of resemblance can be defined without difficulty. If D is exact then an object a and an object b resemble each other with respect to D if a and b are positive candidates of D. If D is inexact then a and b resemble each other also if one or both are neutral candidates of D. (See the example of the windowpane at the beginning of the preceding section.) This relation is transitive, reflexive and symmetrical: for clearly 'D(a) and D(b)' and' D(b) and D(c)' imply' D(a) and D(c)'; 'D(a) and D(a)' implies 'D (a) and D(a)'; ' D(a) and D(b)' implies ' D(b) and D(a) '.-An object a resembles an object b, if a and b resemble each other with respect to one of a number of D's. This relation is obviously intransitive, reflexive and symmetrical. There is nothing new in these statements except that the term " respect of resemblance " is no longer undefined. There are, however, weaker notions of resemblance which do not fit these definitions. These are now often called "family resemblances ", a notion which is central to Wittgenstein's philosophy and is applied by him in particular to "language games ". In a customary sense of " family resemblance "-for instance, when speaking, say, of the resemblance between the members of the Habsburg family-one uses the term to indicate that any two members of the family are positive candidates for one at least of a limited number of determinables. But this Wittgenstein rejects as mere verbiage and as tantamounto saying that " something"

15 138 S. KiRNER runs " through a thread which we have twisted fibre upon fibre, namely the continuous overlapping of these fibres ".4 But if Wittgenstein's family resemblance is not resemblance with respect to determinables, what is it? From his remarks, and in particular his references to Frege's rejection of inexact concepts, two things seem to emerge: first, that family resemblance between objects cannot be defined in terms of exact concepts, second, that the concepts in terms of which it can be defined must admit of common neutral candidates. Family resemblances can, it would thus appear, be stated only in a language-conceptual system-some of whose concepts are linked with each other through exclusion-overlaps. Sometimes, and not only in poetical moods or when speaking in metaphors, we do assert of two objects which do not fall under the same determinable that they resembleach other. (Examples: In calling the colour of some red objects " warm " we imply a connexion between 'red' and 'warm' without implying that these two concepts are determinates under a common determinable. Again, one might still say that red objects would resemble blue ones in colour even if there were a " discontinuity " in one's colour-conceptsuch that ' blue' and ' red' were not either fully linked or even linked.) The question arises when do we, or are we to, say of objects under concepts which are not fully linked-i.e. of objects under' concepts which are not determinates under a common determinable-that they resemble each other? No clear-cut answer, can be given. All that can be said is that the modification necessary to introduce full linkage between the concepts, i.e., to replace the concepts by suitable determinates under a common determinable, must not be too great. I am not very confident that this definition of "family resemblance " in terms of a set of inexact concepts partly linked by exclusion-overlap and more or less easily modifiable into a set of fully linked concepts, fairly represents Wittgenstein's metaphorically expressed position. But the notion does justice to ' Wittgenstein, Philosophical Investigations Oxford 1953, esp.??

16 ON DETERMINABLES AND RESEMBLANCE 139 many weak senses of resemblance by defining them, at least partly, in terms of clear notions. And this, in any case, is desirable. 6. Analytic propositions involving inexact concepts. I wish now to indicate very briefly in conclusion how in terms of the preceding discussion the structure of analytic propositions involving inexact concepts can be understood. I believe it can be understood in the same manner and to the same extent as the structure of the more familiar analytic propositions belonging to exact systems. This may be seen from two simple examples, by use of some wellknown terms from semantics as developed in particular by Tarski.5 The analytic character of e.g. the statement ' The class of even numbers is included in the class of even numbers ' is explained by the meta-statement: If a is a class-variable then the statementform 'a C a' is satisfied by every model derived from it through replacing the variable by the name of a class. It is in particular satisfied by our example. The analytic character of e.g., the statement '(The concept 'green' is included in the concept 'coloured')' is similarly explained by the meta-statement: If P is an inexact-conceptvariable then the statement-form P < (P + P ') is satisfied by every model derived from the statement through replacing the variable by the name of an inexact concept. It is in particular satisfied by our example if the constant 'green' has a determinate complement, since 'coloured' and " (green + green') " are then names of the same concept. If on the other hand in the system under consideration the constant inexact concept substituted for the variable has no determinate complement, the substitution-instance for P' represents the null-concept and the resulting model again satisfies the statementform. Indeed the meta-statement remains true if it is generalized by permitting P to be any concept-variable and permitting 6 Tarski, Logic, Semantics, Metamathematics, Oxford 1956, e.g., Chapter XVI.

17 140 S. K6RNER substitutions of it by the name of any concept, exact or inexact. A more systematic treatment of so-called " analytic but not L-true " statements, by finding them their proper home in an explicitly formulated logic of inexact concepts does not seem to present any very great difficulty. But it lies beyond the limits of this paper.

18 II.-By JOHN R. SEARLE THE notion of determinables and the relation of determinate to determinable was first introduced into modern philosophy by Johnson in the following words: "I propose to call such terms as colour and shape determinable in relation to such terms as red and circular which will be called determinates..." Professor K6rner's paper is mainly concerned with defining this distinction-or at any rate a related distinction-in terms of the notion of an inexact concept. I wish to state at the outset that it does not seem to me that the problem of elucidating the distinction between determinates and determinables has any special connexion with the problem of inexact concepts, nor is it clear to me why Professor Kbrner thinks it has. The relation of determinates to their determinables is the same whether or not the determinates are exact or inexact. Since the notion of inexact concepts seems to me irrelevant I shall attack this problem in a way quite different from Korner. First a word about terminology. In what follows I shall speak not only of determinate and determinable words but also of classes, concepts, and properties: I shall employ the expression " term" to cover all of these indifferently. I shall employ the expression " the determinable relation " to mean the relation in which any determinate and its determinable stand to each other. I. The Distinction between the Determinable Relation and the Genus-Species Relation In elucidating the relation of determinates to determinables the first consideration which springs to mind is that the determinate term is more specific than the determinable. But clearly not any two terms which stand in the relation of greater to less specificity eo ipso stand in the relation of determinate to determinable: " yellow " is in some sense more specific than " yellow or angry " but it is not a determinate of " yellow or angry " in the sense in which it is a determinate of " colour ". Furthermore " human" is specific relative to " animal " but " human" and

19 142 JOHN R. SEARLE " animal" stand in the relation of species to genus not determinate and determinable. This last point might seem more doubtful and I shall begin by elucidating the distinction between the determinable relation and the genus-species relation. What are these two relations and how do they differ? A species is marked off within a genus by means of differentia. Thus e.g., the class of humans (species) is included within the class of animals (genus) but marked off from other classes within that class in that each human possesses other properties-forty-eight chromosomes, a certain shape, etc. (Philosophers always say that the differentia is rationality. It is not of course but for shorthand let us suppose it is)-which constitute the differentia. And it is the possession of these differential properties as well as membership of the genus which entails of each human that it is human. No analogous specification of a species via differentia exists for the relation of determinates to determinables.1 Both species and determinates are included within genus and determinable respectively-all humans are animals and all red things are coloured-but whereas we can say " all humans are animals which are rational ", how could we fill the gap left for a differentia in " all red things are coloured things which are...."? The only word which presents itself as a candidate is " red " itself! Perhaps our failure to find a differentia is due to the fact that colour terms do not admit of verbal definitions, so let us invent a verbal definition for red. Let us say that all red things are coloured things which are "rouge ". But is "rouge " a differentia of "coloured" in the way that " rational " is a differentia of " animal " determining the species human? Some determinates do admit of verbal expansions, so let us consider one of these e.g., anything spherical has a shape and has each point on its surface equidistant from a common centre. But in both of these cases the candidate for the differentia seems to mean the same as the candidate for the species and 1 Cf. A. N. Prior, "Determinables, Determinates, and Determinants", Mind, 1949.

20 DETERMINABLES AND THE NOTION OF RESEMBLANCE 143 hence falls necessarily under the genus. For what can " rouge " mean if not " red ", and we know that " has each point equidistant..." just means " spherical ". But this is quite unlike our standard species-genus examples, for "rational" is not synonymous with " human" nor does it entail " animal ". What these examples show can be stated in two ways: first, in order for some property to be a genuine differentia of a species within a genus, it must be logically possible that entities outside the genus could have that property, i.e., the differentia must be logically independent of the genus. For example, even if humans are in fact the only rational things it is at least logically possible that calculating machines, spirits, etc., could show signs of rationality. But it is not logically possible that things without shape could have all points on their surface equidistant from a common centre. Secondly: where two properties stand as determinate to determinable nothing can fulfil the function of a differentia, for anything which in conjunction with the determinable entailed the determinate would (with exceptions to be discussed later) have to entail the determinable. In short, a species is a conjunction of two logically independent properties-the genus and the differentia. But a determinate is not a conjunction of its determinable and some other property independent of the determinable. A determinate is, so to speak, an area marked off within a determinable without outside help. These two relations can be illustrated graphically: species determinable determinate genus differentia The species is determined by the intersection of two logically independenterms, but anything which marked off the determinate could not be independent of the determinable.

21 144 JOHN R. SEARLE II. The First Criterion: Specificity Using the materials from this discussion we can now lay down a criterion for deciding of any two terms whether or not they stand in the determinable relation. In constructing our criterion we shall employ only the notions of term and entailment between terms. Let us first review the conditions any such criterion (or definition) must satisfy: what characteristics of the relation must it elucidate? 1. It must show that any determinable is a more specific form of its determinable. This is a basic feature of the criterion and most of its other features will be designed to eliminate pairs of terms which stand in this relation but which have other features rendering them unlike pairs of terms standing in the determinable relation. 2. It must enable us to distinguish the determinable relation from the genus-species relation. 3. It must enable us to distinguish the determinable relation from the relation of a determinable to a conjunction of one of its determinates with some independent terms-e.g., we need to distinguish the way " red " stands to " colour " (or "red thing " to "coloured thing ") from the way "red rose" stands to "colour " (or " coloured thing "). 4. It must enable us to distinguish the determinable relation from the relation of some arbitrary disjunction (sum) of terms to one of its members-e.g., we must be able to distinguish the relation of " colour " to " yellow " from the relation of " yellow or angry " to " yellow ". 5. It would help also if we could distinguish the way " red" is a determinate of " colour " from the way " scarlet " is a determinate of " red ". In some sense one wants to say that both these pairs stand in the determinable relation, yet the relation of either " red " or " scarlet " to " colour " seems more fundamental than the relation of " scarlet " to "red ". Furthermore one

22 DETERMINABLES AND THE NOTION OF RESEMBLANCE 145 would like some way of showing that e.g., " red " and " yellow " are on the same level as determinates of " colour " whereas " scarlet " is on a different and lower level. 1. Let us say of any two terms A and B: A is a specifier of B if and only if A entails B, but B does not entail A. In applying this criterion we shall tacitly assume that the necessary syntactical adjustments are made throughout; e.g., strictly speaking " is spherical" entails " has a shape " but we shall say for short " spherical " entails " shape ".2 This criterion is of course very weak as it stands. In the context of another problem Aycr has tried to strengthen it by adding the qualification that A must not be a component of B.3 But this qualification is worthless since the notion of a component is unexplicated: presumably A is a component of B if the word expressing A is also used to express B. (What else could it mean?) But then we can always eliminate componency by using a different word. Thus e.g., " yellow " is a component of " yellow or angry " only until we introduce a different word, say " yengry " to mean " yellow or angry ". Let us therefore abandon this terminology of componency and simply say: A is a specifier of B if and only if A entails B, and B does not entail A. (In symbols, letting "S " mean " is a specifier of " and " -" mean " entails ": ASB -- df. A B. (B -, A).) A necessary condition of A's being a determinate of B is that A is a specifier of B. 2. If A is a specifier of B then A and B will not stand in the relation of species to genus if there is no term C such that the conjunction of B and C entails A, but not C by itself entails B, that is, there must not be any differentia which taken with the genus entails the species but which does not by itself entail 2 Later we shall see that it is more accurate to say " spherical " presupposes rather than entails "' shape " and we shall have to make a slight revision in our criterion accordingly. 3 A. J. Ayer, " Negation ', Philosophical Essays. K

23 146 JOHN R. SEARLE the genus. Any specifier which satisfies this condition I shall call an " undifferentiated specifier ". For example " negro " is a specifier of "man" but not an undifferentiated one since " black " and " man " entail " negro ", but " black " does not by itself entail " man ". But " spherical " is an undifferentiated specifier of " shape ": though " has all points equidistant from a common centre " taken together with " has a shape " entails " spherical ", "has all points equidistant from a common centre " entails " has a shape ". It is a necessary condition of A's being a determinate of B that A is an undifferentiated specifier of B. This criterion still suffers from a serious defect for it does not so far allow us to say that " scarlet " is a determinate under "red ". This can be shown as follows: suppose that beside scarlet there are three other shades which along with " scarlet " exhaust the term " red ". Then" scarlet " is not an undifferentiated specifier of " red " because " neither one nor two nor three but red " entails " scarlet ". And " neither one nor two nor three " does not entail " red ". However, as " neither one nor two nor three " is clearly logically related in some way to " red " since its negation entails " red ", we can remedy the criterion by amending it to read, rather long-windedly, A is an undifferentiated specifier of B if and only if A is a specifier of B and there is no term C such that though C and B entail A, neither C nor its negation entails B. This admits " scarlet " as an undifferentiated specifier of "red ", "eighteen years old " as an undifferentiated specifier of " under thirty years old ", etc., but excludes genus-species terms. (In symbols, letting "U " mean " undifferentiated ", then: AUSB = df. ASB.3. (I C) [(C. B--> A).e (C ->- B v C - B)].) 3. Satisfying our third condition is a bit awkward but absolutely essential. After all, so far we are not even in a position to show how the relation of " red'" to " colour" differs from that of " red rose " to " colour ", since " red rose " is an undil'iere-ntiated specifier of " colour ". However, one would like to exclude " red rose ", because it is a conjunction of

24 DETERMINABLES AND THE NOTION OF1 RESEMBLANCE 147 a determinate of " colour " with a term not a determinate of " colour ". How do we do this without circularity, i.e., without using the notion of determinate which we are trying to define? We can exploit the logical consequences of the fact that " red rose " is a conjunction of terms one of which is a determinate of " colour " and one of which is not. The one which is not, " rose ", though it may entail " colour ", is neither a determinate of " colour" nor synonymous with "colour" and therefore must be equivalent to a conjunction of terms some of which are logically independent of "colour" e.g., " has a smell ". Thus, our original term " red rose " is equivalent to a set of terms some of which do not entail " colour " and we build our definition on this feature. We eliminate this class of cases by requiring that if A is a specifier of B then A must not be equivalent to a set of terms such that one (or more) of them entails B while the others do not. Let us say of any A and B satisfying this relation that A is a non-conjunctive specifier of B. Recalling our problem with " red " and " scarlet ", we must amend the criterion to read: A is a non-conjunctive specifier of B if and only if A is a specifier of B, and A is not equivalent (entails and is entailed by) to any set of terms C, D, E, etc., such that one or more of them C entails B but of some others of them D, neither D nor its negation entails B. Being non-conjunctive entails being undifferentiated, so this criterion satisfies both requirements 2 and 3 in one fell swoop. It is a necessary condition of A's being a determinate of B that A is a non-conjunctive specifier of B. (In symbols letting "N " mean "non-conjunctive ", and " -" mean "equivalent " : ANSB - df. ASB. N (~ C, D) [(A = C. D). (C ->- B).r (D B v D -->- B)].) 4. It might seem that we could satisfy the fourth requirement by insisting that " yellow " was not a determinate of " yengry " since non-conjunctive specifiers of " yengry " are not separated by a single fundamentun divisionis the way non-conjunctive specifiers of " colour " are. The instinct here is sound but the difficulty lies in formulating the point as a criterion in a way that will not render it too circular or question-begging to be useful. It will not do to say simply that there must be a single fundamnenitun K2

25 148 JOHN R. SEARLE divisionis, for how do we decide if there is one? Nor will it do to say that all determinates under a given determinable have something in common, for what is it that e.g., all colours have in common that makes them colours? Any answer must be circular.4 We can however formulate a non-circular criterion by reminding ourselves of certain features of determinates alluded to earlier. Genuine determinates under a determinable compete with each other for position within the same area, they are, as it were, in the same line of business, and for this reason they will stand in certain logical relations to each other. Johnson supposed that all determinates under a determinable were mutually exclusive; but this is not quite accurate, " green " excludes " red ", but " scarlet " does not exclude " red ", it is a specifier of it, yet all three are determinates of " colour ". Let us say of any two terms that they are logically related if either entails the other or either entails the negation of the other. (In symbols, letting "R" mean "is logically related ", ARB = df. (A ->- B) v (B -+ A) v (A ->- B).) It is a necessary condition of any two terms A and B being determinates of a third term C that A and B are logically related. (We can of course expand this definition to include pairs of inexact concepts, i.e., concepts with a common vague boundary.) Ignoring for a moment the fifth condition, we can now state a criterion for the determinable relation: For any two terms A and B, A is a determinate of B if and only if A is a non-conjunctive specifier of B, and A is logically related to all other non-conjunctive specifiers of B. (In symbols, letting "dt." mean "is a determinate of ", A dt. B = df. ANSB. (C) (CNSB D ARC).) Let us pause for a moment to consider the nature of this criterion. Our essential condition for the determinable relation 4 Cf. D. F. Pears, " Universals ", in Flew, Logic and Language, Second Series.

26 DETERMINABLES AND THE NOTION OF RESEMBLANCE 149 is specificity, but we need to exclude pairs of terms which stand in the relation of specificity but which do not stand in the determinable relation. These fall into four classes: where the specifier is a conjunction of the specified with some other term (this is the genus-species situation), where the specifier is a conjunction of a determinate of the specified with some other term, where the specified is a disjunction of the specifier and some other term, and where the specified is a disjunction of a determinable of the specifier and some other term. (In symbols, letting " A " stand for a determinable and " a " for one of its determinates and "b" for some independent term, the cases of specificity we wish to eliminate are: a. bsa, a. bsa, asavb, asavb.) The first two cases are climinated by conditions two and three, the last two by condition four. K6rner, incidentally, makes no provision for eliminating the first two. and his criterion suffers thereby as we shall see. 5. Once we have a basic criterion for the determinable relation the fifth condition is easily satisfied. Two terms A and B are same level determinates of C if and only if they are both determinates of C and neither is a specifier of the other. Thus " yellow " and " red " are same level determinates of " colour ", as are also " red " and " not red ", but " red " and " scarlet " are not same level determinates. The more fundamental position which " colour" occupies vis a vis both " red " and " scarlet " is shown by the fact that the predication of " red " " not red ", " scarlet" or " not scarlet" of any object presupposes that "coloured" is true of the object. A term A presupposes a term B if and only if it is a necessary condition of A's being either true or false of an object x, that B must be true of x. For example, as we ordinarily use these words, in order for it to be either true or false of something that it is red, it must be coloured. Both " red" and " scarlet " then presuppose their common determinable "coloured ". But "scarlet" does not presuppose its determinable "red", and we may generalise this point as a criterion: B is an absolute determinable of A if and only if A is a determinte of B, and A presupposes B. Thus "coloured " is an

27 150 JOHN R. SEARLE absolute determinable of " red "'. but " red " is not an absolute determinable of scarlet. Presupposition is not a kind of entailment, e.g., it does not follow the same rule for contraposition which entailment follows, so having introduced the notion of presupposition we shall have to revise our previous definitions to include both entailment and presupposition. Where before we had e.g., "A entails B ", we must read "A entails or presupposes B " throughout.5 The notion of an absolute determinable is relevant to the traditional problem of categories: every predicate carries with it the notion of a kind or category of entities of which it can be sensibly affirmed or denied. For example, " red" is sensibly affirmed or denied only of objects which are coloured-this is part of what is meant by saying that "red" presupposes "coloured ". Absolute determinables then provide us with a set of category terms. With the addition of criteria for " same level determinate " and " absolute determinable ", our criterion now satisfies the five conditions we set for it. It is worth emphasising that the aim of the five conditions and the resulting criterion is not simply to pick out terms standing in the determinable relation-for the paradigms at least we know what pairs to look for before we even begin our investigation-but to cast light on the nature of the relation. The philosophical tradition bequeathes us pairs of terms that look similarly related: " colour " and " red", " number " and " seventeen "," temperature " and " 30 degrees", etc. But exactly how are these pairs similar and how do they differ from other pairs of terms? The criterion is an attempt to answer these questions and it seems to me a merit of this criterion as against Professor Kirner's that it provides us with the beginnings of a philosophical elucidation of the relation. The weakness of this approach on the other hand lies in the inappropriateness of attacking certain areas of ordinary language 5 This was pointed out to me by Mr. P. F. Strawson, who also made other valuable criticisms of this paper.

28 DETERMINABLES AND THE NOTION OF RESEMBLANCE 151 with such crude weapons as entailment, necessary and sufficient conditions, etc., and. the consequent air of unreality surrounding any such approach. Part of Wittgenstein's point in his discussion of family resemblance is simply to cast doubt on any general philosophical method of this sort, for not all terms admit of clear cut analyses of the required kind. We cannot, e.g., say exactly what terms entail and are entailed by " game ". The criterion then must be taken as an ideal model and not a description of the way language actually works. III. The Second Criterion: Resemtblance with Respect to. If a criterion like the foregoing is of any serious philosophic importance, if it really marks a division that is important in our conceptual scheme, then it is likely that ordinary language has some way of its own for making the same distinction. It seems to me that ordinary speech does mark off tle de ei ninable relation-though in a rather rough and ready way-through certain variations on the notion of resemblance. The most important and the most frequent observation made about " resemblance " (and its brother notions, " likeness " and " similarity ") is that they are in some sense incomplete predicates. One has not been given any information, or at any rate only very minimal information, about two entities if one is merely told that they resemble each other. For to be told that two objects resemble each other is to be told that they have some property in common, but it is not so far to be told what property they have in common, and since any two entities will have some property in common, it is not so far to be told anything. The statement A resembles B thus invites the question "how?"-it invites completion. What has been less frequently noticed is that it admits of at least two distinct kinds of completion. These two kinds are marked grammatically by such locutions as " resembles in that " and "resembles with respect to ". Two red objects resemble each other in that they are are both red, but that they are both red entails that they resemble each other (are alike, are exactly alike) with respect to (in respect of) colour. And these latter locutions seem to me to provide us with another criterion for

29 152 JOHN R. SEARLE the determinable relation. If to say of any two objects x and y that they have the property A entails that they resemble each other (are alike, are exactly alike) with respect to (in respect of) B, then-with qualifications to emerge later-a is a determinate of B. In the light of this criterion consider the following list of pairs of determinably related terms; the paradigms are near the top, less paradigmatic cases near the bottom: A spherical 108 degrees F. blue 3 ft. wide 18 years old worth?1 10s. Od. pint false scarlet male decrepit drunk shatters easily B shape temperature colour width age value volume truth value redness sex physical condition degree of sobriety degree of brittleness. Each of these pairs satisfies both criteria for the determinable relation. Yet we need to make some qualifications to the application of the second criterion: whenever two entities satisfy the same A term precisely, we are more inclined to say that they are of the same (have the same) B, reserving the locution " resembles with respect to " for cases where the two objects do not resemble each other exactly. That is, we move from "are exactly alike with respect to colour, shape ", etc., to " have the same colour, shape ", etc. I state my criterion in terms of the former rather than the latter, for though the latter is the more natural form, the former is not incorrect, and it has greater sortal powers, in particular it excludes certain genus-species terms (e.g., " silver " and " metal ") the latter would include. The most important class of counter-examples which the

30 DETERMINABLES AND THF NOTION OF RESEMBLANCE 153 second criterion allows are cases where the A term is a conjunction of a determinate of the B term with one or more unrelated terms. (These counter-examples are those discussed under condition 3 of the first criterion.) For example, if two dogs are both cocker spaniels, then they resemble each other with respect to but " cocker shap-,: spaniel " is not a determinate of " shape ". With these qualifications and exceptions the second criterion gives an interesting if not very precise test for the determinable relation drawn from ordinary language. One of its merits is that it excludes genus-species examples: we do not, e.g., say of two humans that they " resemble each other with respect to animality ". Upon scrutiny of the lists A and B in terms of the two criteria, several questions present themselves. On the second criterion, A terms (determinates) are characteristically adjectives and adjective-like expressions, B terms (determinables) are characteristically abstract nouns. Why? Is this connected with the fact that species terms are characteristically nouns, and the second criterion excludes pairs of species-genus terms? Why do the two criteria give similar results at all'? Perhaps the following consideration will give us the beginnings of answers to such questions. First let us introduce two new expressions: by the expression " individuating term" I shall mean a term which provides a principle of individuation, a principle of counting, e.g., " man " is an individuating term, as it allows " one man", " three men ", etc. By the expression " characterising term" I shall mean a descriptive term which does not provide by itself a principle of counting, e.g., " red " is a characterising term. Individuating terms are characteristically nouns, characterising terms characteristically adjectives and verbs.6 Paradigm species terms are conjunctions of separately specifiable terms, some of which are called the genus, other the differentia. Paradigm individuating terms are used to individuate the paradigm individuals, material objects. But any material 6 For a similar distinction see P. F. Strawson, Individuals.

31 154 JOHN R. SEARLE object will admit of description by several terms, not all of them individuating terms. The concept formation of any individuating term, then, is likely to involve a conjunction of several terms not all of them individuating terms (cf. Locke on nominal essence) e.g., we learn to discriminate horses from the rest of our environment and to form the concept horse, but since any horse is describable by several terms, not all of which are individuating, the concept horse will be analysable into other terms not all of which are individuating. We thus develop at least two distinct kinds of terms, individuating terms, which divide the world and which are in some sense conjunctions, i.e., they admit of some sort of " definition ", and characterising terms which describe the world in ways which cut across the divisions set up by the individuating terms and which are not characteristically conjunctions of other terms. These two kinds of terms proliferate two different conceptual hierarchies: because the relation of species to genus just is the relation of a conjunction to one of its components, the individuating terms, being conjunctions, proliferate a genus-species hierarchy. But characterising terms, " brown ", " rough ", etc., do not admit of any such analysis and hence do not admit of a genus-species hierarchy. We invent a term (e.g., "colour ", " texture ", " shape ") to cover a whole range of characterising terms which are all in the same line of business. But this higher order term (determinable) is not part of an analysis of the lower order terms, it is just a name for the line of business they are all in. Thus we see the start of a growth of a connexion between the determinable relation and characterization on the one hand, and the genus-species relation and individuation on the other. Roughly speaking individuating terms are characteristically conjunctions of determinates and hence admit of genus-differentia analysis, but paradigm characterising terms are not such conjunctions. Perhaps this point will be clearer if we consider a prominent class of counter-examples. Names of shapes often serve as both characterising and individuating terms e.g., " is spherical" and "is a sphere ". This is because shapes provide a convenient

32 DETERMINABLES AND TIHE NOTION OF RESEMBLANCE 155 principle of individuation without the help of any other term. But they are unlike most individuating terms in this respect; the term " horse " for instance includes not only the notion of a certain shape, but several other characteristics as well. Note also that the determinable expression often provides, or has cognates which provide, a (rather weak) principle of individuation, not of objects, but of its determinate terms. Thus, e.g., besides the characterising expression " is coloured" we have the individuating expression " is a colour ". These abstract noun forms of the determinable term neatly fit the syntactical requirements for list B of the second criterion. Near the bottom of list B we seem to run out of abstract nouns. Why? Wherever we have only two or three expressions competing in the same area, language is less likely to provide us with an abstract noun to cover the whole area than if we have several. Thus we do not have an abstract noun collecting " drunk " and " sober" as " temperature " collects our elaborate terminology for degrees of heat. In such cases we have to fabricate " degree of sobriety " or some such expression. If we had an elaborate terminology for degrees of sobriety we should most likely have a word corresponding to "temperature ". " Male" and " female " we do collect under " sex ", but we do not have a word collecting " dead ' and " alive ". The foregoing suggests an explanation why the two criteria give similar results: the first relies on the fact that determinates compete for position without outside help within an area covered by the determinable. The second relies on the fact that language provides us with abstract nouns, or the possibility of forming abstract nouns, to cover the range of such characterising universals, and it ties certain possible completions of the incomplete predicate " resembles " to such abstract nouns. IV. Professor K5rner's Approach. My attack on this problem has been rather different from Professor K6rner's. Indeed I am not quite sure I have understood exactly what his aims are. Perhaps I can best emphasize our difference of approach and expose any misunderstanding I

33 156 JOHN R. SEARLE may have of his paper by stating in a crude form the objections I have to it. 1. His definition excludes any exact concept as a possible candidate for a determinate. Thus no numerical concept can be a determinate and any concept we care to define exactly ceases to be a determinate. He accepts these consequences with more equanimity than seems to me justified. For surely it must restrict the philosophical interest of any definition enormously if it excludes vast areas of what are usually taken as paradigmatic terms standing in the determinable relation, with no justification or explanation offered. Indeed any such definition must be positively misleading if-as I have suggested-the exact concepts share the essential features of the determinable relation along with the inexact. 2. Leaving aside the question of exact concepts, whatever relation Kbrner defines, it is not the determinable relation as ordinarily understood, not even the determinable relation between inexact concepts. Now of course, it is open to anyone to define his terms as he likes, but Professor K6rner insists that his definition is " in accordance with established philosophical usage ". That it is not is shown conclusively by the fact that his definition provides no way of distinguishing the determinable relation from the genus-species relation. But part of Johnson's point in introducing the notion, and he after all established the "philosophical usage" in question, was to distinguish the determinable relation from the genus-species relation. 3. Even if we ignore both problems raised in my first two objections the criterion breaks down. Professor K6rner only offers us one example, " colour ", of how it is supposed to work, but it does not seem to me to work even for that one example. He inadvertently offers us a proof of this in his discussion of the example of the blue window pane: imagine a blue window pane growing progressively more transparent until it reaches one hundred per cent transparency, i.e., invisibility. At some point "the window pane is a neutral candidate of coloured and therefore

34 DETERMINABLES AND THE NOTION OF RESEMBLANCE 157 of not coloured" i.e., invisible. But precisely at that point, I should like to add, it is also a neutral candidate of " blue " and " invisible ". Thus " blue " and " invisible " are fully linked. But the definition of the determinable relation stipulates that the determinable must be the sum of all concepts fully linked with any determinate. Hence, by the definition, if " blue " is a determinate of " colour " so is " invisible ", which is absurd. Other empirical concepts can be made to run off the rails in the same way. " Shape " for instance will go via the extensionless point. "Human" and "animal" will not qualify since " human " is linked to plant concepts; " human " and " organism " will have no hope since the organic and the inorganic are similarly linked. Furthermore the criterion provides no way of excluding arbitrary conjunctions (products) of terms only one of which is a genuine determinate. Thus " blue monkey ", " red horse ", and " yellow cow " would all count as determinates of" colour ". On the criterion as stated I do not see how these difficulties can be avoided cannot think he means exactly what he says in his definition of " resemblance ". He says as part of his definition that two objects resemble each other with respect to a determinable D if they are both positive candidates of D. Thus on the definition, a brown object and a blue object must be said to resemble each other with respect to colour since they both are coloured (both are positive candidates of " coloured "); a midget and a giant would resemble each other with respect to size since they both have a size. This is clearly not what is ordinarily meant by " resembles with respect to ". 5. I am puzzled by the definition of inexactness. One ordinarily thinks of inexact concepts as those which have borderline cases (though I should prefer some other term such as " vague " to " inexact "). But on the proposed definition this is not sufficient for inexactness. It is also necessary that the borderline cases should have borderline cases, the borderline cases of' the borderline cases should have borderline cases, and

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