AMERICAN PHILOSOPHICAL QUARTERLY Volume 16, Number 3, July 1979

IV . MEANING, R E F E R E N C E A N D S U B J U N C T I V E C O N D I T I O N A L S

J. N. H A T T I A N G A D I

T H E q uestion has been raised whether during a scientific revolution a change in the meaning of

words creates a logical gap between old and new conce~tians in a science. Can there be a rational choice when one chooses not only a view but the style of a rg~menta t ion?~ Unfortunately, the dis- cussion of this auestion has not been carried out with any clear, let alone rigorous, theory of meaning in mind. The net result has been less than satisfactory from an intellectual point of view.2 We must first satisfv ourselves thai when fundamental theories change, meanings do also, and to state precisely in what way.

Let every extant expression of English which may be a predicate expression in some sentence of the language be called an "atomic predicate" (of Eng- lish). This is a finite list. We could use the Oxford English Dictionary, for example, as the lexicon. Consider every predicate which is atomic or which can be defined by using atomic predicates (a "molar" predicate). The class of molar predicates will include at least all the truth-functional defini- tions of more complex predicates, so that it is at least denumerablv infinite. Other methods of definition. which we cannot specify in a natural language, may also generate molar predicates. Let us call the class of molar predicates of English which is closed under all definitional operations at time t, the "semantic field" of English at t. The semantic field of English at time t, then, is a class of meaningful predicates of the language. But is the class of meaningful predi- cate expressions of English greater than the semantic field?

Let us call all predicate expressions which fall outside of the semantic field "problematic expres- sions." Then we can study the question of meaning change more precisely by asking if there is any reason to believe that (a) there are problematic expressions which are meaningful and (b) they arise in the con-

text of theorizing. Since the class of molar predicates has not been adequately determined, because we have allowed unspecified definitional operators in the definition of a semantic field, it may be im- possible to say of any given concept at time t whether it is a molar predicate or a problematic expression. A discussion of cases is therefore of no value. We can, however, use some abstract con- siderations to guide us.

Languages presuppose social convention^.^ If we understand each other to any degree of sophistica- tion, then it is because we share the conventions (e.g., the "idiom") of some linguistic tradition. The argument for believing that social conventions are necessary for language, in some sense of the word L C convention," lies in the existence of a diversity of languages. These languages are not genetically determined in us. A child ofone language community can learn to speak the language of another com- munity, with proper exposure. Moreover, learning a new language involves at least learning how others communicate--that is to say, learning the conven- tions of that community. A great many conventions have to be mastered over a period of years before one acquires that facility in a new language which one has in one's mother tongue. So the semantic field at oneTs command depends upon the social conventions that one has learnt.

Social conventions, being socially and not geneti- cally determined, must have a beginning in time. The reason is that according to the neo-Darwinian conception of the descent of man, man had a beginning in time, and therefore, so must have had human social conventions. I t follows, that the seman- tic field of English has grown gradually to its present proportions. Since this can only happen if the se- mantic field at time ti is smaller than the field at time ti+,, for some i, it follows that new expressions are added from time to time to the semantic field.4

P. K. Feyerabend, Agaimt Method (London, 1g75), ch. 17 .

' P. K. Feyerabend, op. cit., ch. 17, p. 255. D. K. Lewis, Convention (Cambridge, Mass., 1969). ' The reason why this must be "from time to time" or gradually is because one can only fall back on existing language to make

oneself understood, and so if change is too sudden, it would not be accepted or understood.

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At the time of addition, a new expression to be added is problematic. Moreover, it is meaningful, since, when added, we get a larger semantic field. This shows that meaningful problematic expressions must exist from time to time as languages develop.

Since problematic expressions must exist, we may ask, do they arise in the context of theorizing? It is plausible that they do. A problematic expression is introduced into language presumably because one cannot say within a semantic field what one would like to express. Since theorizing often involves new theories of the universe which have not been thought of before, it is not unreasonable to suppose that as our ideas improve we are obliged to introduce problematic expressions into our language. With usage they soon become unproblematic, and get integrated into the semantic field.

But we have a paradox. We use language to com- municate. A new expression acquires meaning only in the context of its use in a language. How can a problematic expression change the semantics of the very language which gives it its meaning?

The paradox can be solved only if we allow that there is something besides usage which gives mean- ings to words.6 Though usage gives meanings to words, it is not only usage which gives them meaning. Moreover, the meanings that usage gives to words is not the usage itself, but must be something else. If meaning were usage, language would stagnate. We cannot approach the problem of meaning change with reference alone, which is a possible a l te rna t i~e .~ The reference of a word may be quite different from what one imagines it to be. Suppose I believe that the sky is a dome over the flat earth, and the stars are jewels set in this dome. If meaning is reference, then I truly do not understand what the word "star" means, for its reference is not what I take it to be. How can I find out my mistake? Perhaps by doing astronomy. But checking astronomical hypotheses would be impossible unless I knew what the expres- sions "earth," "sky" and "stars" mean well enough to make a start at astronomy. An expression must have some meaning of an epistemic nature other than usage and reference.

The central thesis of this paper is that the meaning of any expression of some semantic field is a set of theories.? To put it picturesquely, a meaning is a crystallization of theories, where theories include expectations, beliefs, attitudes, tacit assumptions and the like, in addition to explicit theorie~.~ Semantic change, then, is the following general process. Some new theory is proposed which contra- dicts a theory implicit in the meaning of an old word. As a result, the word must change its meaning, if we are to continue to speak coherently in the new intellectual context. Semantic change can therefore be represented logically.

The hypothesis that the meaning of an expression is a set of theories, however, has one prima facie difficulty. In resolving it, we shall see that the hypothesis is capable- of generating a complete theory of meaning, reference and subjunctive conditionals.

A universal statement is always about the whole universe. A statement of the form (Vx) (Fx 3 Gx) is not only about F's, but also about G's; or, perhaps, everything can equally be regarded as the s u b j e ~ t . ~ But if the meaning of a word is a set of theories, how could we ever use words to refer to things, as we do every day? If I say "Please pass the salt," and the word "salt" has for its meaning some universal theories, how can they help me locate the salt, which is what is needed? Let us try to cash out the theories which are part of the meanings of expres- sions. Since a great many will be needed, we can call this an expansion of the meaning of an expres- sion. If I expand my meaning of an expression F, each of my expansion sentences would have the following properties: ( I ) I would be sayin@ some- thing about F things. (2) I would believe that they would be true of all F things. (3) I would not say that it is part of the meaning of F that something or the other happens to be F, but only that any F thing would have certain (general) characteristics.

We can say that an expansion sentence of an expression F is a subjunctive conditional of universal form in which Fx is the antecedent and (6x is some simple or complex predicate as consequent with x as its only free variable. Further-

5 As against Ludwig Wittgenstein's Philosophical Imestigationr (Oxford, 1958). W. V. 0 Quine, Word and Object (Cambridge, Mass., 1959) is an attempt to get by with as little as possible besides reference,

following Russell's lead. P. K. Feyerabend and W. V. 0 . Quine have argued for the close relationship between theories and meanings. I propose to

define meanings entirely within theories. The theories which together constitute the meaning of a word are not to be contrasted with observation statements. Rather,

by "theory" one means to include the content of any statement whatsoever, however trivial, and even if it is only acted upon by u's and never made explicit.

@ C. G. Hempel, "Studies in the Logic of Confirmation," in Aspa& of Scimhjk Explanation (New York, 1965).

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more, if this is to represent what I mean by the word, believe. But "(Vx) ( - Red x ~ x is not attacked by then it must be something that I believe, (or consider as a a bull)" may not be believed, since bulls may be hypothesis.) I t is important not to limit expansions believed to attack a great many other things. Now of meanings to beliefs, even if they include tacit the set B defined by those "-4's" which are in ones. To understand "phlogiston" one must enter- expansion sentences of "- H" may not in fact tain certain discredited hypotheses about com- exclude members of the class A defined by the "4's." bustion and calcination. To the extent that I do When there is not enough known about H, if our understand it, I "make believe." It is only in this understanding of it is vague, then A and B will not be weaker sense that beliefs are involved in my concept mutually exclusive. The second possibility is that the of "phlogiston." expansion sentences of an expression give us contra-

The symbol 'a' will be used as a convenient dictory beliefs. In this case we have an ambigous notation for subjunctive implication reminding us that if "(Vx) (FxaGx)" is true then so is "(Vx (Fx3x)"-though its truth might be vacuous. The former can be read "If any x's should be F they would be G," and would expand part of what is meant by 'F.' Thus "(VX) (Red x ~ x will be attacked by a nearby bull)" is an expansion of what I mean by "red." No matter that bulls are colour blind, it is only necessary that I believe it of bulls. For another person "(Vx) (Red x a x will absorb all light except that of some characteristic wave- lengths)" might be an expansion sentence. The meaning of an expression however is not the set of expansion sentences, but the theories expressed by them.

If we are given a list of all the expansion sentences yielding the meaning of any expression F (and it is perhaps a denumerably infinite list), then the reference of F for me can be defined as follows :-F refers to the set theoretical intersection of the sets referred to by each ofthe 4s which occur in the list. Let us see why this works. If something is F, it must be 4 according to my beliefs. Consequently, the class of things to which F refers must be included in the class of b's. If we take all the 4 sets and find their intersectidns, we are bound to find all our F's there. If there are enough 4's, hoepfully only F's will be in the inter- section. But how many 4's are "enough" to give the reference of a predicate? They are enough pro- vided F is not vague and F is not ambiguous.

Here is the test for vagueness in a new expression, 'H.' Suppose the set of 4's generates a set A such that every He A. Now I can ask the following question. Which negation of the "4's" can also be used to give me the reference of " - H" (the nega- tion of 'H')? Naturally, not every '4' will have a corresponding " - 4" such that (VX) (- Hx cc 4x) will be an acceptable hypothesis. Thus (VX) (Red x a x is attacked by a bull)" may be something I

expression. By dividing the expanded meaning, with some expansion sentences in common, two different meanings of the original expression may be dis- tinguished. otherwise the expression is unaccept- able. We can avoid both difficulties by laying down a criterion of acceptabili ty of a problematic expression as follows: " - F" has a satisfactory meaning if and only if the reference which its expansion sentences determine (by the set theoretical intersection of the "4's") is the set theoretical complement of the reference of "QF" determined by the " -4's"' in the expansion sentences of " - F." Equivalently we may say that a problematic expression 'F' is accept- able if and onlv if 'F' and " - - F" have the same reference. When we accept such a criterion we are laying down, in effect, that the only laws necessary for monitoring the growth of language are the laws of classical logic. o n e may note,however, that the meaning of expressions remains "constructive" or "intuitionistic," since 'F' and " - - F" do not mean the same thing, though the reference structure is entirely classical.

Our theory of reference has also incidentally given us a criterion for the acceptability of a new expres- sion. Ifa new expressionis incompatible with theories embedded in language, of course, then a great many other expressions may have to change their mean- ings first before the new expression can be coherent with them. Let us note, moreover: ( I ) A language cannot acquire reference by itself. Since each expres- sion depends on other expressions for its reference, some expressions must acquire reference by acquaint- ance. (2) I t is not necessary that the knowledge by acquaintance that is required for the determination of the referential system of a language be the same for each of us. Each of us may use his acquaintances to build up his own system of reference. But if we have the same basic beliefs about the world, we will eventually get the same references.1° (3) It follows

10 Bertrand Russell, "Knowledge by Acquaintance and Knowledge by Description," in Mysticism and b g u (London, 1950); and Thc Problem of Philosophy (London, 1946).

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that neither knowledge by acquaintance nor know- ledge by description is primary. Knowledge by acquaintance is necessary, but it acquires its deter- minate function only in the context of a descriptive language. (4) Finally we can define the true reference of expressions, and also their intended reference. We can define the true reference of 'F' as that class of objects which is the set theoretical intersection of all the objects truly referred to by all the 'v" in those expansion sentences which happen to be true. The intended reference of "F" will be the set theoretical intersection of the intended reference of all the 4 classes in expansion sentences which are believed but may be false.

This can be extended to the case of relations as follows:-A relation Rxj will yield expansion sentences with 4's which have at most x, or y or both x and y as free variables; (Vx) (Vy) (Mother (x, y) a x is female), (Vx) (Vy) (Mother (x, y) a y has a date of birth), (Vx) (Vy) (Mother (x, y) a x is older than y) are all expansions of "mother of." Then the reference of "mother o f ' will be the set of ordered pairs determined as follows. Consider all the 4's which have only x as the free variable. For each object which satisfies 4 consider the set of ordered pairs (x, zi) where zi is each object in the domain in turn. Similarly, we can associate ordered pairs with each 4 which has only y as the free variable. If now we take all the sets of ordered pairs so produced, and the set of ordered pairs of 4(x, y) their intersection is the reference of "mother of."

These considerations regarding meanings and reference bring us to the crucial question for this approach: If meanings are crystallizations of theories, there would almost certainly be a problem of communication. It is very unlikely that two people will share exactly the same hypotheses about the world, in which case there would be no shared meanings, and so all communication would seem to break down. If "Fa" and "-Fa" are each asserted by two people respectively, but each means something different by 'F,' how can they contradict each other? Let us review our situation. Most of the expectations that we have of our world are bio- logically determined in us. If some of these are modified, and other expectations added to them, most of the rest are socially accepted fairly univer- sally at least within a linguistic community. Of the rest, there are bound to be many theories that are shared by virtue of our being educated and talked at in similar environments. So the vast majority of the expansion sentences of common words, such as colour words, for example, is liable to be the same for

any two of us. Nevertheless, there is room for dif- ference. One person may be an artist and know about the emotional impact of blue colours, whereas another may be a physicist who knows something about characteristic wavelengths. If the meaning of an expression is a set of theories, then the word "blue" would "mean" different things to these people. Given any word it is likely that some expansion sen- tence or other is not shared by two people. The hypothesis that meanings are theories would imply a breakdown in communication only if we assume and tacitly conjoin to it a certain principle--namely, that two people must mean exactly the same thing by the same words in order to communicate. But this principle can be replaced by a better one.

The new principle that needs to be stated here involves another kind of meaning which words have, in addition to the "total meanings" so far dis- cussed. which mav be called "restricted meanincs." A " restricted meaning of an expression F for a person is a property 4 which has the following character- istics : ( I ) '4' occurs as the consequent of an expan- sion sentence of F, or is a conjunction of such predicates. (2) The person concerned believes (Vx) (FXS~X) (3) (Vx) ( F X ~ ~ X ) or (VX) ( 4 x 3 Fx) are not theorems of the predicate calculus.

Thus, 4 is part of the meaning of F, and is taken to be co-extensive with F by the speaker concerned, and moreover the co-extension is not trivial. The reason for condition (3) is to rule out such cases as " - - F" as a restricted meaning of 'F.'

Let us note a few attributes ofrestricted meanings, before I illustrate them. ( I ) They are not expansion sentences, but only predicates which occur in expan- sion sentences. (2) There may be more than one restricted meaning for any predicate. (3) Knowing the meaning of an expression does not automatically show us how to get a restricted meaning, because we may not have a non-trivial biconditional at hand. i (4) Restricted meanings are also, like total meanings, - not free of theoretical content. But a restricted mean- ing is a very small part of theoretical content which r is by itself sufficient to characterize the reference of the expression in question. Now we can state the principle for communication :-

Fa and -F'a are contradictbus if and only if b l e s there is a G which is a restricted meaning of F, and of F'. Let us consider an example from geometry.

"Parallel lines" could be defined in one of two ways : ( I ) a//b iff a, b are straight lines on a plane and a does not intersect b. (2) a//b iff a, b are straight lines on a plane and a keeps a constant distance from b. Let us

MEANING, R E F E R E N C E A N D S U B J U N C T I V E C O N D I T I O N A L S 20 I

imagine that the second is taken as the restricted meaning of "parallel lines" and someone discovers for the first time that a transversal cuts two parallel lines in such a way that the alternate angles are equal. Now this may change the meaning of "parallel lines," but it leaves the restricted meanings intact. Because every pair of straight lines in Euclidean plane geometry which are cut by a transversal with equal alternate angles are parallel to each other, we could get a third restricted meaning of "parallel lines" in terms of alternate angles.

The interesting point is that restricted meanings are chosen ad hoc or ad homines, for the purposes of an argument. Artists arguing about light can take light as characterized by a different restriction on mean- ing than would physicists. When we have an argu- ment, then for that argument we can use a restricted meaning which is neutral. Suppose we wanted to know whether or not our space is Euclidean. Then we would choose a restriction which would be such that "parallel lines" would be characterized by some predicate which would be adequate in both Eucli- dean and in non-Euclidean geometry. Using a characteristic like this we could show that in Euclidean geometry each line has one and only one line on a plane parallel to a given straight line, but in some non-Euclidean geometries this is not so. If we take "parallel lines" as those which do not meet, then in some geometries they do not have equal alternate angles. In a dispute between Euclidean and non-Euclidean conceptions of space all that is necessary is to find some characteristics which are satisfactory to each of the parties (i.e., which for each is a restricted meaning of "parallel lines"). All the other properties can then be regarded as matters of fact, or matters of dispute. The reason for this is that in each geometry, we can take one definition and treat the other restricted meanings of it as theorems. The difference in different geometrical theorems about the world can then be tested by whatever means we have at our disposal.

What we see, therefore, is that restricted meanings, where available, allow "Fa" and " - F'a" to be contradictories even though 'F' and "F"' have different total meanings. Perhaps the difference be- tween total and restricted meaning can be brought out by means of derived notions of synonymy and analyticity.ll ( I ) 'F' and 'F"' are strictly synonymous if and only if 'F' and "F'" have the same expansion sentences. (2) 'F' and "F'" are loosely synonymous

in a debate or with respect to an argument if and only if there is 'C' which is neutral to the debate or adequate for the argument and such that 'G' is a restricted meaning of 'F' and of "F"'.

Now the interesting thing is that strict synonymy is transitive, but only obtains very rarely, usually in the case ofa predicate and itself. But loose synonymy, which is commonly found, is intrann'tive. F may have a restricted meaning G, and G may have a restricted meaning H, but F may not have H as a restricted meaning since in each case the debate or argument which is the context, may be different. When there is a debate between parties who find that what they mean by a critical word is not the same thing, they can use a common equivalent expression to charac- terize the reference of the word, and reduce the difference of meanings to a matter of fact. In this way, instead of talking at cross purposes, they can disagree over facts. In other words, borrowed from Kripke, the expression works as a rigid designator by means of a restricted meaning which gives us the extension of the expression.12

So far it has been shown that every predicate-like expression has a meaning, a reference, and con- sequently the possibility of a device to restrict its meaning in such a way that the expression functions in some context as a rigid designator. The same analysis also holds for the case of proper names, even though it is true that when a proper name is first attached to a referent, it may beattached not because it is appropriate, but only as a means of identifying the object. It is tempting to think that a name has only reference, and no meaning. But this is a mis- take. For when someone gets his name, the name also gets a meaning. In when an expression acquires a reference, it becomes part of our system of reference and thereby acquires meaning. The difference between proper names and predicates, then, is only a difference ofhistory. As a general rule, proper names acquire meaning derivatively, but most predicates acquire reference derivatively, though exceptions to both rules abound.

Proper names can also be given restricted mean- ings. These are usually in the form of d$nite descrip- tions. Such a description does not define or delimit the meaning of the proper name. In a given context it designates rigidly. In a similar vein, a physicist in the nineteenth century could treat "force" as (implicitly) defined by "proportional to mass times acceleration." Note, here, that if there were a debate

Another derived notion of the analytic (which is also aposkrion) is the inclusion of the expansion ofFin that of G (e.g. "Red things are colored").

Saul Kripke, "Naming and Necessity," in Semantics of Natural Language, ed. by D. Davidson and G . Harman (Dordrech, 1972).

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in Newton's day between a Newtonian and a Car- tesian, such an implicit definition would be value- less. For Descartes had suggested that force is proportional to the quantity ofmotion, or mass times velocity. One can hardly discuss the truth of this claim fairly by defining "force" in a Newtonian manner. In a debate with Cartesians. we must find an expression which is co-extensive with "force" for each side in the debate, (e.g., "that which changes the state of motion of any body" because for both theoretical systems this is an adequate way of' characterizing the reference of "force").

In general, then, whether a name or a predicate designates rigidly m not is not a characteristic of it, butjust its function within a context. Consequently, while a proper name can be used to designate its reference, it can also be used descriptively, just like a predicate. The expression "Nixon," for example, can function non-rigidly: ( I ) "If Nixon were not Nixon, the Watergate Scandal would not have grown to such proportions." (2) "Carter is no Nixon, so we can expect lower interest rates, more civil rights legisla- tion and a more expansionary monetary policy." Or, for other proper names:-($ "The very star which is Hesperus in some evenings of the year travels around the ecliptic and is Phosphorus just before dawn at other times of the year." (4) "And this is Professor Quine." In all these cases, the proper name designates non-rigidly.

Rigid designation is a use made of expressions, but it is worth noting, however, that it is only because expressions have referents that we can use them to designate rigidly. An interesting use of language, largely neglected among logicians, is the use of expressions to rigidly-not-designate. A metaphorical use of an expression is a use which is rigidly non- designative. Interpreted descriptively, for example, Tennyson's lines are nonsense : "His honour rooted in dishonour stood, and faith unfaithful made him falsely true." But these lines do capture the con- flicting loyalties of a medieval knighi in an unusual situation. This is possible only because we can use words deliberately not to indicate their reference, but a part of their meaning. In a pun, or a play on words, on the other hand, a word rigidly indicates its own sound, and neither its meaning nor its reference.

One difficulty of everything said so far is that we have relied upon subjunctive conditionals, and there is as yet no satisfactory way to express them in logic. Subjunctive conditionals cannot be given a truth-

functional, or any purely extensional analysis. Many unsuccessful attempts have been made to find a more complex analysis. Let me briefly indicate two approaches.

One of these is in terms of possible worlds.13 A subjunctive conditional is said to be true if it is true in the nearest possible world(s) to our own in which the antecedent is fulfilled. Now the trouble with this is not only that we have no way of knowing if there is such a nearest possible world, and that we have no way of checking whether some statement is true in it. These problems are bad enough. But it is true be- sides that any two worlds which differ maximally with respect to the antecedent must differ with respect to exactly a denumerably infinite number of statements. The reason is that any statement has a denumerable number of nontrivial consequences, and the two worlds must differ with respect to them if they differ on anything. If the nearest world is necessarily so far away, then even if it exists, in some logical heaven, and if we can divine that the con- sequent is true in it, it seems irrelevant to the truths of our world. What does nearness prove if the near- ness is always so far away? What consolation that other worlds are supposedly even farther away?

Another difficulty is the holistic character of a possible world. A possible world is an integrated system of reference. If we translate a subjunctive conditional into terms of a "possible world" we are immediately thrown into abstract questions of what a world would be like if the antecedent were true. which have no relevance whatsoever to the subjunc- tive conditional. Thus: "If there were an elephant in the room it would be crowded" is said to be true of a world which is the nearest possible world in which there is an elephant in this room. But what our world would be like if an elephant were to find its way here is very complex. Would it be an ele- phant from the circus, and what would happen when they discovered it missing? What means of transporting it here? How would it get in through the narrow doorway? The point is that all these are irrelevant to the truth of the subjunctive conditional. Insofar as possible-world talk brings in these red herrings, the whole approach is suspect. We may restrict features of the possible world to those of significance, of course, but even if this can be done with some measure of accuracy, the point of invok- ing possible worlds when the world-like character is then subtracted seems to be going the long way around. Finally the ideal of "nearness" of possible

13 D. K. Lewis, CounferfactuaLs (Cambridge, Mass., 1973). R. C. ditional Logic," Thoria, vol. 36 ( 1 9 7 0 ) ~ pp. 23-41.

, Stalnaker and R. H. Thomason, "A Semantic Analysis of Con-

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worlds, or that of maximal similarity between worlds is peculiar. Normally when two things are said to be similar, they are so in some respect. If no such clause seems necessary, it is because a contexthally clear point of view is presupposed. It is hard enough to say whether Galileo is more similar to Plato than to Archimedes. Lewis' approach expects us to say this of two worlds which are separated by a denumerably infinite number ofstatements. Having done so, there are, of course, different "intuitions" of what simi- larity consists in, and what may count as "plausible." But if this is all that we are left with in our theory of subjunctives, it seems that we are far better off without the theorv.

Another much more promising line is taken by Quine.14 Quine notices a close relation between dis- positions and subjunctive conditionals. "To say that an obiect is soluble at time t is to sav that if it were in water a t time t it would dissolve at t." But having noticed this relationship between the predicate "soluble" and the subiunctive conditional above. ., Quine goes on to use the subjunctive conditional to paraphrase "solubility" into statements about what dissolves. Since subiunctive conditionals can- ., not be naturally translated by using the horse-shoe of material implication, Quine looks for another way of dealing with subjunctives.

Solubility, he notices, seems to come with a theory of subvisible structure. The solubility of something is due to some structure which makes it liable to dissolve. "What we have seen dissolve in water had, according to the theory, a structure suited to dissolv- ing and when we speak of some new dry sugar lump as soluble, we may be considered merely to be saying that it, whether destined for water or not, is similarly structured." Using this insight of similarity in struc- ture, Quine invokes a relative term M corresponding to the word "alike in molecule structure" in some appropriate sense. Thus "x is soluble" is para- phrased as "(3y) [ M ( x , y) and y dissolves]." (This may be written "(3y) [M ( x , y) and y is put in water and y dissolves]" to be less ambiguous.)

Let us now see if we can find a general method of treating subjunctive conditionals this way. Consider Elmer, the largest mammal that ever lived, which was a giant whale. Now we may discover a new hor- monewhich, if injected, increases the size of any mammal by a percentage above its actual weight. I could say "If Elmer were injected with this serum he would have been even larger," a perfectly plaus- ible statement. But translated by Quine's method

of paraphrasing it, we invoke a relation M of similarity, and it becomes "(3y) [M (Elmer, y), and y is injected, and y is larger than Elmer]" which is false for trivial reasons, since Elmer is the largest mammal ever. This shows us that using the existen- tial quantifier and hunting for another object of similar structure is not a general way of proceeding with the paraphrase of subjunctive conditionals. Quine himself makes it clear, of course, that his method is not a general one. But Quine believes that for the purposes of science it will do. Let us consider an example from science. We can proceed with a Newtonian analysis of the motion of Mars as follows: "If there were no force on Mars at time t it would move in a straight line. But there is a gravitational force on it, so it takes on the following direction . . ." and so on. Now the first sentence "If there were no force on Mars at time t it would move in a straight line" invoking a relation M, would have to be translated as follows :

(3y) [M (Mars, y), and y has no force actipg upon it, and y travels in a straight line]

But this statement is trivially false in Newton's theory of the solar system, in which there can be no body without some gravitational force upon it, however small. Even for the restricted case of science, it seems, Quine's approach breaks down. But there is an insight in Quine's approach which we can disentangle from his attempted solution, and make it into a general theory of subjunctive conditionals.

Quine's requirements for a theory of subjunctive conditionals can be divided into two. First, he requires that dispositional predicates be eliminated in favor of manifest predicates. Thus, "soluble" should be translated into terms of what does and does not dissolve. Secondly, Quine requires that a subjunctive be translated by invoking a new predi- cate which is hinted at. Thus, "soluble" should be understood in terms of a subvisible structure M. Let us call the first of these the principle ofpredicate- elimination and the second the principle of predicate- construction. If we accept a generalized form of the principle of predicate-construction only, we shall have as general and complete a theory of subjunc- tive conditionals as possible.

Let me begin by arguing against predicate elimin- ation. Quine wants to eliminate dispositional predi- cates in favor of manifest ones. His reasons are not germane to the issue, so we need not go into it here. I t is worth noting that this is a reasonable procedure

" W. V. 0. Quine, Zbid.

A M E R I C A N P H I L O S O P H I C A L Q U A R T E R L Y

only if the predicates of English are at least partially ordered with respect to their dispositional and non- manifest character. If we have a set of predicates A then there must be a subset B of A which are uni- formly less dispositional than the others if we are to eliminate some of the ~redicates in favour of others. Suppose this were not so, and each predicate F is reduced to another, and the other to a third and so on, and in the end one of the reduced predicates is reduced back to F. We can then see that Quine's programme of elimination becomes pointless, since nothing will be eliminated.

This, however, is exactly what happens. Let us take the case of the predicate "soluble."l5 There are many dispositions true of a soluble object: one of these is that it dissolves when ~ u t in water. Another perhaps, that it has the subvisiblestructure imagined by Quine. A third would be that it does not form a com~ound when in contact with water and so on. Let us take the most obvious subjunctive conditional. "If x is soluble, then if x were put in water it would dissolve." Let us now take the word "dissolve." Many things can be said of any dissolved object. Among others, that it has not formed a chemical compound with water. How do we check to see that it has not? By resolving it, of course, by distillation perhaps. "If x is dissolved in water, then if the solu- tion should be distilled, x would resolve." Thus, we can find that "dissolves" is a disposition that involves the "manifest" ~redicate "resolves." Now we can ask what is true of x being resolved. Obviously, x must be the same substance which was originally dissolved. For example, if I put a salt in water, stir it, then distill the solution, and get a new salt, this would not be a resolution, but another chemical process. But how do I check to see that the same substance is produced by distillation? Clearly by finding out if the precipitate has the same properties as the original substance x. Among these properties is the solubilitv of the substance. We could hardlv call something a resolution ifwhat is produced is an insoluble substance. Thus we see that solubility is a manifestation of resolution.

Now we have seen that solubilitv is manifested in dissolution, dissolution in resolution, and resolution in solubility. In general, "what would be true" for each word, when fully stated, shows our language to be unordered in terms of manifestation. In a very obvious way, this is already what the notion of C' expansion sentences" implies.

Quine's second principle, however, can be generalized-let me state this most generally: A subjunctive conditional is a possibly incomplete directive for the construction ofa predicate. We can obtain a com- plete theory of subjunctive conditionals from this principle. Let us consider the subjunctive condi- tional "If Mars were to occupy positions p,, p,, p,, not in a straight line at time t,, t,, and t,, then for any t, it would occupy position p, at t,." This states that given three points of the orbit of Mars we can predict its orbit completely. Since this is satisfied only in the case where Mars moves in a circle, the above subjunctive conditional has the meaning : "Mars moves in a circular orbit," which has the form "Fa."

Now the subiunctive conditional does not mention circles. I t is just that with our knowledge ofgeometry we can construct the predicate "moves in a circular orbit" to capture the conditional completely. We might say that the subjunctive conditional has given a recipe for constructing the predicate. In this case, of course, the predicate to be constructed was com- pletely specified by the subjunctive conditional. This is usually not the case. Usually, a subjunctive conditional gives us an incomplete directive, a partial recipe for a predicate. Thus "If this match were struck it would light" might be a partial recipe for a property which we might call "friction- inflammable." This property is ascribed of this match, in a sentence whose logical form is "Fa."

Since a subjunctive conditional only gives an incomplete recipe for a predicate, it follows that the meaning of the conditional is not entirely deter- mined by its form. This is a well-known phenomenon which has been noted in the literature regarding subjunctive conditionals.16 It should be obvious that this hypothesis about subjunctive conditionals is the converse of my theory of meaning. Meanings were earlier cashed out in expansion sentences. Now I suggest that subjunctive conditionals be regarded as expansion sentences of some unspecified predicate.

The main novelty of this suggestion is that it reverses a general trend in the search for the logical form of expressions. Generally, such things as num- bers, operators, definite descriptions, and so on have been given an adequate logical form by specifying more structure than was first apparent. In the case of subjunctive conditionals, however, the attempt to specift a greater structure has led to nothing be- cause of their non-extensional character. Well, sub-

l6 K. R. Popper, Th bgic of Scient$c D~covely (London, ~gsg), p. 440. la R. M. Chisholm, "The Contrary-to-Fact Conditional," Mind, vol. 55 (1946), pp. 289-307, and N. Rescher, Hypothetical

Reasoning (Amsterdam, 1964).

MEANING, R E F E R E N C E A N D S U B J U N C T I V E C O N D I T I O N A L S

junctive conditionals are not extensional, they are the stuff of pure intension. The correct translation into logic is therefore not to look for more structure, but less. In general, a subjunctive conditional is itself a more elaborate way of saying something which is logically speaking much simpler. Why, it might be asked, do we use a more complex form of expression when we could be speaking more simply? Most of the time when we use subjunctive con- ditionals it is because we cannot find a predicate that applies simply. It is in the absence of a predicate F, which we could use to say "Fa" that we resort to the circumlocution "Ifa were G it would be H." In order for this to be adequate, the unspecified 'F' must have as its expansion sentence "(Vx) ( F x a ( - Gx v Hx))." But this by itself does not determine the reference of 'F' unless - G v H happens to be co- extensive with F. Hence it is that a subjunctive conditional has an indeterminate character.

A subjunctive conditional hints at a predicate which is dispositional, which mangests itself as the consequent Efthe antecedent obtains. The predicate hinted at, however, is ambiguous. "Had Muskie been nominated by the Democratic Party for the Presi- dential Election of 1972, Nixon would still have won a landslide victory." What does this assert? Its message is ambiguous. I t could mean that no matter who was put up by the Democratic Party, Nixon would have won as he did. Or else it could mean that Muskie in particular could not have done any- thing about it. In a given context, one may not be able-to judge what i s meant. And if one cannot judge what is meant, you could ask "Do you mean that there was nothing the Democratic Party could have done to stop Nixon?" And if the answer is "Yes, incumbent Presidents who have just terminated a war cannot be beaten," then it is obvious that the import was universal. If on the other hand the reply is "No, what I was getting at is the fact that McGovern's and Muskie's policies were not that far apart." Now we see that the subjunctive ascribes some property to Muskie as a politician. In the latter case we could translate the subjunctive as "Muskie held unpopular policies in 1972," and in the former case, "Nixon was invincible in 1972." Note thegreat difference in the two messages. In each case, however, some object is described in terms of a predicate, which is only hinted at in the subjunctive. The logical form is: "Gm" and "Hn" respectively,

where 'G' ="held unpopular policies in 1972" and 'H7= L ' ~ a ~ invincible in 1972," and m stands for Muskie, n for Nixon.

There is another kind of ambiguity that is worth noting, namely between subjunctive conditionals of particular or universal import. For example, "If Hitler had not invaded Russia he would not have lost the war" could either mean "Hitler had a winning strategy," or it could mean "No European power can invade Russia and win a European war." In the first case, the logical form is "Fa," in the second case " (Vx) (Gx 3 Hx) ."

If we compare this treatment of subjunctive conditionals with, let us say, Russell's theory of definite descriptions, we find one striking difference. Russell's theory gives a simple algorithm for trans- lating definite descriptions. There is no algorithm in this analysis oflogical form. This might be thought to be a defect of my views. But is it? The fact is that subjunctive conditionals are ambiguous, and depend upon context to convey what is intended. This is a fact we have to face, and no analysis which does not take account of ambiguity can be successful. Yet, the logical form of any interpreted sentence cannot be ambiguous, since in classical logic we wish to preserve the principle that every statement is either true or false but not both.

More philosophically speaking, a subjunctive con- ditional is used precisely because the predicate in- volved cannot be formulated. It is the very paucity ofone's language that makes us resort to them. Their use is a constant reminder that our lexicon is inadequate to say even very ordinary things that we would like to say in our everyday life. Of course such conditionals may also be used when a perfectly good predicate is available, for emphasis, or to be polite, or as a joke.

While there is no algorithm for reducing sub- junctive conditionals to logical form, there are guidelines we can lay down for it.

Given any subjunctive of the form AccC, the logical form is either Fa, or (Vx) (Hx3 Gx) (or some more complex form which I need not elaborate) where F has as one of its expansion sentences (Vx) (Fxcc ( -Ax v Cx)) and H has as one of its ex- pansion sentences (Vx) (Hxcc (Gx 3 ( - Ax v Cx) ) ). Beyond this, we have to use the context, and possibly further questions, to elicit what is being suggested by a subjunctive conditional."

York University Received June 20, 1978

l7 This paper received support from Canada Council, in the form of a Leave Fellowship in 1975-76, during which time the paper underwent major revisions.