§1. Truth and Rules of Meaning. The view that the necessities required by induction are real stands in contrast with the view that whatever is necessary is so precisely because it is analytic. Moreover, the necessities important here need not be─as necessities are often supposed to be─a priori. To make the notion of real a posteriori necessity less mysterious requires a fresh look at the interrelation of the notions of the necessary, the analytic, and the a priori.
The necessity of a grain of salt to be water soluble and the necessity of the grain to be the same as itself are not different modalities. As was argued in Chapter II, §1, the necessity of a physical and that of a logical condition are identical. Of course, the conditions that are necessary─the necessities─are not identical, and the propositions─also called the necessities─made true by these conditions are not identical. It is widely thought that analyticity is the nature of the necessity of a logical truth.1 Such a truth holds in all possible situations if and only if it has a form that makes it undeniable. But if the necessity of a physical truth and that of a logical one are not different─that is, if the univocity thesis holds─then analyticity is the nature of the necessity of a physical truth, and thus a necessary physical truth is necessary because it is analytic. In particular, the necessities required by induction are necessary, not because of what entities are, but because of linguistic rules. We cannot avoid this result by abandoning the univocity thesis. For, as we saw in Chapter II, without it one can no longer claim that there is a genuine concept of physical necessity.
To illuminate the notion of real a posteriori necessity will involve two projects. First, to avoid putting analyticity at the basis of physical necessity, I shall try to show that analytic propositions may even be false. Mere form is no guarantee of truth. But if this is so, then analyticity cannot be at the basis of the necessity of a logical truth either.
The chief reason for holding that analyticity is at the basis of logical necessity is that the necessary truths of logic are thought to be vacuous. They are “Vacuous” if there are no specific features that entities must have for them to be true. Now an analytic claim cannot be denied without a violation of rules. But despite this, may not what it claims misdescribe entities? Yet if the claim is vacuous this difficulty is blocked. For then it cannot misdescribe anything. So in view of their vacuity, logical truths can have a necessity whose nature is analyticity. But if analyticity is the nature of logical necessity, then analyticity is at the basis of physical necessity, according to the univocity thesis. An important part of the first project will, then, be to reject the view that logical necessities are vacuous.
Second, if a physical truth is necessary because it is analytic, then physical necessity would be intentional rather than real. The necessity of a physical proposition would imply that it had a certain relation to consciousness and not that the physical condition making it true results from the nature of the entities with that condition. But if the necessity is real, it not only does not come from analyticity but does not imply analyticity. So the view that physical necessity is real seems to commit me to the view that at least some necessary physical truths are synthetic a priori. For it is an old and respected doctrine that the necessary is also the a priori.
The logical empiricist philosopher will predictably recoil from this consequence.2 But whether or not there are persuasive arguments against the synthetic a priori, it is well to point out that the dogma of the a priori nature of necessities is unsupportable. Once we reach this point we see that any one of the unspecified necessities called for by inductive practice may be at once necessary in the way a necessary truth of logic is necessary; synthetic in the way a claim that an entity has a certain definite condition is synthetic; and a posteriori in the way contingent claims about the world are a posteriori.
In carrying out the first project, I need to show that analyticity does not imply truth in the correspondence sense. The fact that it does not imply truth in the correspondence sense is at the basis of Quine’s attack on the analytic-synthetic distinction. If we suppose there is such a thing as a rule of meaning for a term, as opposed to a rule of liturgy or a rule of clean speech, then an “analytic” proposition is one expressed by a sentence that cannot be negated without violating a meaning rule for one of its terms.* Now, by denying that a proposition will be true just because a sentence expressing it cannot be negated without violating a meaning rule for one of its terms, I am denying at least one sort of analytic-synthetic distinction. For I am denying that any proposition is guaranteed correspondence with entities just by its form or by rules for terms used to express it.3
Let us say a proposition is “ontically” analytic if it is expressed by a sentence that cannot be denied without violating a meaning rule and it corresponds to what entities are precisely because it is expressed by such a sentence. But how could linguistic constraints ever suffice for correspondence? Suppose, however, one switched from linguistic to conceptual constraints. An analytic proposition would be one whose denial involved a confusion about the concepts composing it. This does not help since concepts, like words, are inventions that may inadequately reflect the realities they stand for. So neither terms nor concepts can of themselves guarantee truth.
It might be objected that the defenders of analyticity never intended to claim that meaning rules generate truth in a correspondence sense. But if this objection were sound we could expect to find some alternative account of truth for analytic truths put forth by the defenders of analyticity who were attacked by Quine. There is, however, rather general agreement among these defenders that no such account was needed. Indeed, an account along the lines of Tarski’s semantic conception of truth4 was adopted for logical truths, which were deemed the core of analyticity. In this account, the logical truth that either Jones is tall or he is not tall is true since, in this world of ours, Jones has the condition of being tall. Of course, it would also have been true had he been short. But the important thing for the defender of analyticity is that, by virtue of the meaning rules for the logical particles, the proposition is true in the sense that it corresponds to Jones's actual condition. Indeed, by virtue of these meaning rules the proposition would be true in any circumstances and is thus vacuous in the above sense. This does not mean that it corresponds to no condition of Jones. Rather, it means it would correspond to whatever condition─whether it is being tall or being short─Jones would have in any given circumstances.
One who denies a distinction between synthetic propositions and ontically analytic ones─because of denying that there are any ontically analytic propositions─may still hold that indeed there are propositions expressed by sentences that cannot be negated without violating meaning rules. Let us say a proposition is “neutrally” analytic if it is expressed by a sentence that cannot be negated without violating a rule of meaning for one of its terms. Now Quine has suggested a reason for rejecting even an analyticsynthetic dichotomy for neutral analyticity. He has challenged others to give an account of the notion of rule of meaning that does not rest on the notion of ontic analyticity. If the challenge cannot be met, the notion of a meaning rule is essentially empty since there is no ontic analyticity.5 In effect, if by rules of meaning you must mean rules that of themselves can generate truth, there can be no such rules since it is wrong to think that there are truths generated by rules.
The mistake here is the supposition that a rule of meaning must be treated so that it is the sort of truth-generator required by ontic analyticity. Once we see that the role of rules of meaning is to establish fixed points of reference from which progress can be made in conversation and inquiry, the rules cease to depend on the possibility of their generating truth. Quine himself recognizes neutral analyticity and, consequently, rules of meaning in this nontruth-generating sense when he speaks of “analyticity intuitions.”6 Such intuitions, and hence the existence of the neutrally analytic, do not justify a “dichotomy between analytic truths as by-products of language and synthetic truths as reports on the world.”
That there can be no justification for such a dichotomy should be evident from the frequent reminders we have that our language is not fully adequate to deal with the subject matters for which it was developed. We grope our way to more adequate concepts and to less misleading associations for corresponding terms. The following account for getting at this notion of adequacy for a certain subject matter is the basis for my contention that there may be false analytic propositions.
§2. Reference and Inadequate Concepts. Meaning rules, as I have just described them, relate term to term. But any full account of usage must consider the way terms relate to the world. One meaning rule will lay it down that ‘fox’ is not to be denied of anything ‘Vixen’ applies to. Another will lay it down that ‘green’ is not to be affirmed of any surface to which ‘red’ applies to every part. But to what does ‘vixen’ or ‘red’ actually apply? Here one might appeal to other meaning rules; one might say these terms apply precisely where certain other terms apply. But the question of application continues to arise. There must then be an element in the usage of some terms that is independent of the linguistic relations posited by meaning rules. Such an element will enter into the account of how it is that humans use terms consistently, that is, apply them to or withhold them from roughly the same entities. It is part of such an account that the entities to which a term is generally agreed to apply will have similar components.
But this of itself is insufficient, since to account for the consistency of usage one must appeal to the fact that humans interact with some of these entities. Not any kind of interaction will do; it must be one yielding an experience. And the experience must be an experience of a condition of one of the entities to which a term is generally agreed to apply. The condition experienced must be a condition of having a component that is similar to components of the other entities to which the term is generally agreed to apply. But, as was noted in Chapter I, §3, an experience need not be, nor need it involve, a judgment. Thus to appeal to experience in order to account for usage is not to introduce the conceptual apparatus of judgment. In particular, an experience of a condition need not be conditioned by having learned any meaning rules. Rather than involving a judgment, an experience is required to account for consistency in judgments.
This discussion complements that of signification in Chapter III, §3. There the signification of a term was said to be a collection of components of entities to which it applies. ‘Red’ signifies the rednesses of all the red entities. The components in the signification are, then, similar entities. (A fuller account would consider terms whose significations contain components that, though not all similar, all resemble one another in some way.) For simplicity, I shall speak in a Platonizing fashion of the red of all red entities, rather than more correctly of the collection of rednesses, as the signification of ‘red’.
This tells us that the significations are components but not which ones they are. Clearly, a term’s signification has something to do with its consistent usage. Indeed, in applying a term, without relying on inference or habitual expectation, to an entity with which one is presented, one generally experiences the condition of the entity's having the component the term signifies. This component is often a property, but it may be an action or even a physical part. I have not said that one applies the term because one reasons that, if the presented entity has the condition one experiences, then the term applies to that entity. Rather, the experience is part of the very application of the term. It is not a premiss from which the language user infers that the term applies. Similarly, between the objects of such experience, there is a basis for consistent usage of the term. Of course, a term is often applied to entities too far removed to be objects of experience or to entities which, though present, do not reveal all of their conditions directly. Nonetheless, to account for the consistent usage of such a term it will be essential to appeal to an experience of the relevant condition in at least some of the entities with the term's signified property.
Let F be a term and φ and Ψ properties. Now one might apply F directly on experiencing the having of φ Thus F would signify φ But what if one also applies F on experiencing the having of Ψ? If one does this directly, then F signifies, in addition, Ψ But suppose one does it indirectly. That is, suppose one applies F to an entity on experiencing the condition of its having Ψ only because one has the belief that whatever is Ψ is φ. Does F then signify Ψ in addition to φ? Or suppose one applies F to an entity on experiencing the condition of its having Ψ only because one accepts the meaning rule that F, which signifies at least φ, cannot be denied of an entity of which G, which signifies Ψ is affirmed. Experiencing the entity’s condition of being Ψ does not account directly for applying the term F. The application is mediated by transformations depending on general beliefs or meaning rules that relate several properties or several terms. But we want a signified property to be one that accounts for the application directly. The experience of a condition of having the signified property is a facet of consistent usage that involves a relation to the world that is not mediated by beliefs relating several properties or several terms. So in the above case it is φ not Ψ that F signifies.
Ignoring terms with multiple significations, we have:
(1) A component φ is the “signification” of the term F if and only if (i) users apply F to roughly the same entities; (ii) a basis for this consistent usage is that (a) φ is common to those and only those entities to which F would generally be applied and (b) some users of F experience some of these entities’ condition of being φ by interaction with them; and (iii) this experience is not a basis for consistent usage just because the users accept meaning rules for F or have beliefs in regularities for φ.
The signification is not just a common component, for there may be many such components. It is rather a common component that is a basis for consistent usage. Since signification is a matter of the relation of a term to the world and not of a term to other terms, there is nothing paradoxical in the idea that one could vary the meaning rules for a term without varying its signification. Suppose it becomes a violation of usage to say that F applies to that to which the term G─signifying Ψ─applies, whereas previously F and G were unrelated by meaning rules. All that has happened is, doubtless, that a connection between φ and Ψ that was already believed to hold has come to be taken as a settled matter. The property signified has not been replaced by a new one just because the term for it has come to be connected by a rule with another term. This is not to deny that a change of meaning rules can so alter the application of a term that in time it does come to signify a new property. But even when we alter radically our view as to which connections between a property signified by a term and other properties are to be taken as matters beyond further investigation, we may continue to use that term to signify the same property.
If, then, a meaning rule does not contribute to signification, to what does it contribute? I shall say it contributes to intension:
(2) The “intension” of a term is the collection of components of entities signified by the terms to which it is related by meaning rules for it.
The kind property signified by ‘fox’ and the property signified by ‘female’ are members of the intension of ‘vixen’. The intension, though, divides into those properties deemed sufficient for the application of the term, those deemed necessary for its application, and those deemed exclusive of its application. Thus even greenness is in the intension of ‘red’ since ‘green’ cannot apply to that to which ‘red’ applies everywhere.
A term can have an intension without a signification. Suppose it is a recently coined term. Even though its application will involve the judgment that a certain property is present, this application will be indirect since it will depend on a meaning rule leading from the term for this property to the coined term. Until the term becomes familiar, it will not become associated with any property that is its own signification.
Do theoretical terms of science have, then, intension without signification? Nothing in the concept of experience I am using limits us to everyday, non-laboratory experience. The requirement of experience in the definition for signification can be met, in principle at least, for conditions of microparticles. Observing a diffraction pattern obtained by rebounding electrons from a metal grating may in some cases be an experience of the electrons’ having a wave character. Davisson and Germer, who first made this obser־ vation, doubtless reasoned from it back to the wave character of electrons. But the observation of the pattern could become an experience of the wave condition; such an experience need not conceal an inference from a differently described experience by a meaning rule or an assumed regularity.
As regards signification of scientific terms, there are two separate questions. First, it might be wondered whether the consistent usage of scientific terms could be based on nothing more than their connections among themselves and to pre-scientific terms with their own signification. There is no obvious obstacle to saying this should be possible, that is, to saying that their having intensions alone would suffice for their consistent usage. Second, it might be wondered whether the terms, if they lack signification, can be used to make true or false claims that entities in the world have certain conditions. In the next section I shall try to show that without signification of their own these terms could not be used to make true or false claims. Kant expresses this view when he says that “knowledge of an object” requires that the object be signified and that this in turn requires that the object be experienceable.7 “If we abandon the senses, how,” he asks, “shall we make it conceivable that our categories . . . should still continue to signify something, since for their relation to any object more must be given than merely the unity of thought─namely, in addition, a possible intuition to which they may apply.”8
Not only may a term have intension without signification, but it may also happen that a term may have a signification without an intension. It can come into use on the basis of the recognition of an associated property without any rule relating its application to that of other terms with signification. Indeed, two terms might signify different properties but have the same intensions. For, though they have come to be used on the basis of experience, no meaning rules may have been laid down to indicate that, say, the two terms exclude different properties. And even if they are finally differentiated by such rules, they may continue to signify the properties they did before.
Corresponding to the notions of signification and intension are those of reference and extension:
Just as reference is based on signification, extension is based on intension. But some complication is involved in considering the class determined by an intension. I shall mean by the class “determined” by the intension of a term that class of entities in which each member, first, has the components that, according to the meaning rules of the term, are needed for the term’s application; second, lacks those components that, according to the rules, must be absent for it to be applicable; and, third, has any one of the components, if any, that, according to the rules, suffice for its application. So:
(4) The “extension” of a term is the class determined by the intension of the term when the intension provides at least one sufficient condition for the term's application; otherwise, it is the null class.
Clearly, reference and extension will not always coincide, (i) The reference of F might be included within its extension. This might happen when there is a meaning rule saying that whatever the term G applies to the term F applies to. For, in actuality, the presence of the property signified by G may simply not guarantee that of the property signified by F. In short, the meaning rule is misleading as to the real connections among properties, (ii) The reference of F may lie partly outside its extension. This would happen if there were a property that implies that signified by F, but there were no meaning rule taking this to be a settled matter, (iii) The reference of F may lie totally outside its extension. For the meaning rules may posit a necessary condition for F that is, in fact, only thought to be present when the property signified by F is present.
We can grasp the notion of adequate terminology in terms of the notion of signification. To enforce a meaning rule is to attempt to have language users treat a connection involving properties signified by the terms mentioned in the rule as fixed for further inquiry. Here I am assuming that the terms do have signification, for the question of adequacy arises only for such terms. But the meaning rule does not guarantee that the connection holds. I propose, then, a necessary condition for saying that our language for talking about certain aspects of entities is “adequate”: the meaning rules for terms in that part of the language must not conflict with the connections that properties signified by those terms have to other properties. It would be overly demanding to say our Ianguage for a given domain is inadequate unless there is a meaning rule corresponding to each connection between any two properties, each signified by a term in that part of the language. Still, unless there are meaning rules corresponding to some of these connections, the language is, at best, a cumbersome guide.
I set out to show that if there are neutrally analytic propositions it does not follow that there are ontically analytic ones. That is, I set out to show that, even if there are propositions expressed by sentences that cannot be denied without violating meaning rules, there need be no propositions that are true by virtue of the meaning rules for terms in the corresponding sentences. This fact is easily seen to be contained in the fact that there can be inadequate terminology. In view of the distinction between signification and intension, it is clear that a term may signify a property even though this property does not have all the connections with other properties that, according to its intension, it does have. This lack of fit between actual connections and connections according to intension typifies an inadequate terminology. Now it is obvious that, if an analytic proposition is actually true, the connection among components that makes it true will agree with the intensions of the corresponding terms. But since a lack of fit is possible, the connection needed for the analytic proposition to be true need not obtain. In short, an analytic proposition expressed by inadequate terminology may be false.
From the point of view of reference and extension, the same result emerges. When the proposition expressed by all F are G is analytic, the extension of G contains that of F. As we saw, this is compatible with the possibility that the reference of F could fall, partly or entirely, outside the reference of G. So the analytic proposition may be false. And of course if it may be false, analyticity does not imply necessity. Newman captured this idea when he declared that “an alleged fact is not therefore impossible because it is inconceivable, for the incompatible notions, in which consists its inconceivableness, need not each of them really belong to it in that fulness which would involve their being incompatible with each other.”9
As an example, consider the term ‘isotope’. At one time it was reasonable to suppose that chemical inseparability from a given element was a part of the intension of this term. “Elements which are chemically inseparable, but have different atomic weights, were named by Soddy isotopes.”10 Later Urey investigated hydrogen isotopes. There was no serious doubt that the signification of the term was a component of deuterium. Deuterium had the kind property of the kind isotope-of-the-same-element. But Urey found hydrogen and deuterium could be chemically separated; deuterium is set free from oxygen after ordinary hydrogen in the electrolysis of water. The extension of the term ‘isotope’ excluded deuterium; the reference did not. The proposition expressed by ‘Isotopes of the same element are chemically inseparable’ was analytic, but it was false and thus not necessary.
What are the consequences of the alternative to this view? Suppose that meaning rules of themselves determine which properties terms signify. First, this alternative gives no assurance of a common subject matter for an inquiry that undergoes changes of meaning rules. For an inquiry maintains a common subject matter so long as its key terms have the same reference. Yet for this alternative, a change of meaning rules would change the signification and thus make possible a change of reference.
With the enlightenment afforded by the theory of special relativity, one recognizes that nothing satisfies the intension for the temporal term ‘duration’ as it would be used by a Newtonian. For it seems reasonable to say, with some interpreters of classical physics, that part of this term’s intension as it was used by a Newtonian is the invariance of a duration on change of reference frame.11 One would have to conclude, on the alternative view, that Newton spoke about nothing when he spoke about duration. To avoid this absurdity, it suffices to recognize that the component duration is a common signification of the term 'duration' as used by Newton and by the relativist. Nonetheless, this common component is related by each through different meaning rules to quite different properties.
Second, the alternative view, if consistently carried through, destroys any connection between general terms and the world. If to signify a property is merely to have certain conventional relations to other terms of the language, then those other terms will themselves signify properties merely by conventional relations to other terms. But this only produces a web of intralinguistic relations. To break out, we require that some of these terms have a stable use. But then we are back to the point of needing common properties and experiences of the belonging of these properties to entities to account for those uses. And this means the acceptance of terms with significations that have not been determined by meaning rules.
§3. Are Logical Concepts Adequate to Logical Properties? If we apply the preceding views to logical propositions, we arrive at the conclusion that even analytic logical propositions need not be true, and hence need not be necessary. This comes about because the logical properties possessed by entities may have connections among themselves that are not adequately represented by meaning relations between the corresponding terms. But what are logical properties?
Suppose that (Fa → Gb), where, in this section, the → replaces the commonly used if-then. Among the properties of a is the property it has when it is F only if b is G. I wish to suggest that this property is one of the properties in the signification of the →. If (Ga →Ha), then another property in the signification of the → is the property a has when it is G only if it is H. This multiplicity corresponds to the multiplicity of rednesses in the signification of ‘red’. All the properties so far mentioned here belong to entities referred to from the antecedent of a conditional. In addition, there is the property b has when it is G if a is F, and that a has when it is H if it is G. These belong to entities referred to from the consequents of the above conditionals. Thus we can distinguish the signification of “antecedent →” from that of “consequent →.” As before, it is convenient to speak in a Platonic manner of each of these significations as though it were a single property; in fact, each is but a collection of similar properties. I shall call the signification of antecedent → the “antecedent conditionally” property. It, like the “consequent conditionality” property, is a “logical” property.
Likewise, suppose it is true that ~Fa and that ~Gb; the properties of a and b that make these propositions true belong to the signification of ~. That is, the property a has when it is not F and that b has when it is not G belong to the signification of ~. Treated as a single property, this signification can be called the “negation” property. And the property a has when it is F and b is G will be in the signification of the conjunctive connective . Likewise, this signification is to be called the “conjunction” property. Each of these logical properties is also a “complex” property; in describing it a logical connective is used in addition to at least one predicate. But this descriptive mechanism need not imply an ontological complexity.
However, there is one simple logical property, the “component” property. The property a has when it is F and that b has when it is G belong to the signification of the juxtaposition between subject and predicate, that is, to the signification of predication. The properties in this signification are part of what will be called the component property. But how can F be in the signification of both ‘F’ and predication? This would be absurd only if it implied that F alone is signified by a predication involving the predicate ‘G’. But the signification of a predication anywhere involves both properties.
Now if entities have conditionality properties, one may go far wide of the mark in attempting to lay down, by meaning rules, just how these properties are related to other logical properties. Specifically, conditionality properties may have relations to conjunction and negation properties quite different from those expressed by the meaning rules of truth-table logic. Truth-table logic tries to tie the→ down by proposing as a rule that (Fa→ Gb) is not to be denied if ~Fa is affirmed. Thus it becomes analytic that (Fa → Gb) if ~Fa. This analytic proposition may, however, be false since the intensions given by the meaning rules for → and ~ may conflict with the connections between the conditionality properties and the negation property.
It is certain to be objected that the meaning rules of truth-table logic are used to coin terms, not to govern the use of established terms with significations. Thus it is preposterous to hold that a logical claim such as the above, which is analytic by truth-table rules, may be false.
In response, I shall face the objector with a dilemma. If, on the one hand, the terms are merely coined, then there is no basis for the truth, or even the falsity, of the resulting analytic propositions. If, on the other hand, the terms have significations, then if the analytic propositions expressed with them are true, their truth is not due to meaning rules. In either case, analyticity does not imply truth, and hence it does not imply necessity. I need to establish only the first horn of the dilemma, the second having already been dealt with. Grant that it is a rule that (Fa → Gb) is not to be denied when ~Fa is affirmed. This does not make it true that (Fa → Gb) if ~Fa. All one knows is that the rule would be violated by denying the conditional. Indeed, at the times the terms are coined, there is no basis for (Fa → Gb) itself being either true or false. One has agreed to say it is true under certain conditions and false under others. But agreeing to say it is true under those conditions does not mean it is true under those conditions.
Likewise, if I agree not to deny ‘There is an earth goddess under us’ whenever we experience an earth tremor, my utterances of the sentence are still no more than ritualistic until such a time as experiences of earth goddesses become current. For the sentence with → and for the sentence with ‘earth goddess’ to express a truth or a falsehood, what the assertion is must be clear. Merely to agree that it can be asserted or denied when other sentences are asserted or denied is to be given no clue as to what it asserts. Indeed no condition is being asserted by the sentence when key terms lack signification. As determined merely by meaning rules “concepts are empty; through them we have indeed thought, but in this thinking we have really known nothing; we have merely played with representations.”12
Though laying it down that things are true does not make them so, a term with signification can be used to express a true proposition. A term has signification only through widespread consistent usage ultimately based on experience. Logical predicates that can be used to express true propositions will have significations and hence widespread consistent usage based on the experience of entities’ having logical properties. Analytic propositions expressed with such logical predicates may, then, be false. By a logical predicate I mean one, like ‘(F_→ Gb)’, that signifies a logical property. If the logical predicates lack signification, then analytic propositions expressed by sentences involving them will be neither true nor false. A so-called interpreted logical system will, in general, not involve terms whose consistent usage is based on experience; therefore, the system’s terms will lack significance and its analytic propositions will have no truth value.
I have not yet discussed the “universality” property. How could an individual have the universality property, when the very notion suggests that the property transcends individuals? But notice that (x)Fx is equivalent to the conjunction ((x)Fx • Fa), where a is an arbitrary individual in the range of x* The property a has, when both it is F and (x)Fx, is a property in the signification of the universai quantifier. The universality property is this signification. Again, it is not a tautology, but a synthetic claim, that the universality property of entities is accurately represented by an analytic connection laid down for the universal quantifier in a given logiccum- semantics.
Consider ((x)Fx →Fa). This proposition is a logical necessity if, by nature, the connection holds that it asserts between, on the one hand, having the universality property and, on the other hand, having the corresponding component property. The antecedent is equivalent to ((x)Fx • Fb), where b is an arbitrary one of the x’s. Thus the conditional proposition asserts a connection─not between the proposition that (x)Fx, in the antecedent, and the proposition that Fa, in the consequent─but between a condition that any arbitrary individual, b, has and a condition that a has. One need not, then, resort to intentions, such as propositions, to discover the source of the necessity, for logical necessities are natural necessities. The above proposition is a logical necessity provided that, by the nature of b or as well by the nature of a, b’s being such that it is both F and (x)Fx implies a’s being F. That is, ((x)Fx → Fa) is a logical necessity if, by the nature of b or as well by the nature of a, b’s having a property in the signification of the universal quantifier implies a’s having the corresponding property in the signification of predication.*
The so-called universality property and the so-called component property are in reality only collections of properties. So, to say that an entity has the universality property is to say only that it has one of the properties in the signification of the universal quantifier. To say that it has the “corresponding” component property is, then, to say it has that property in the signification of the predication operation that is described using the same predicate. Even the logically true ~(Fa • ~Fa) will be said to assert a connection─in this case, one of exclusion─between logical properties of a. The component property excludes the corresponding negation property.
The fact that variables for propositions are employed in the propositional calculus should not lead us to think that the logical necessities of this calculus are intentional simply because propositions are themselves intentional. Rather, we should consider that the propositions for which variables are employed are ones with references to entities; it is ultimately the natures of these entities that ground logical necessities. These necessities of the propositional calculus are laws of the real and not of the intentional.
§4. The Factual Content of Logical Truths. If logical connectives signify logical properties, meaning rules may be misleading in regard to connections among these properties. Analytic logical propositions may be false. To be true, the logical properties would have to have the connections asserted. Since entities must manifest these connections if there are to be logical truths, logical truths have factual content. There is a condition of an individual corresponding to the logical truth that whatever holds universally holds in an instance. In this case its condition is one of having a connection of implication between having the universality and having the corresponding component property. By requiring this condition in any individual the logical truth is not vacuous.
Opposed to this logical realism is the view that logical truths are vacuous in the sense that no specific conditions of entities need obtain when logical truths hold. They would have factual content if, for them to hold, entities had to have some specific conditions. Even so, vacuous logical truths are thought to be true in a correspondence sense. For, no matter what conditions obtain for entities, it is these conditions that are thought to be the actual basis for the truth of logical truths. If no specific condition is required, then logical properties are not required and they become otiose. But if there are no logical properties, then logical connectives have no significations and are completely characterizable by meaning rules. Logical terminology cannot then be inadequate since there is nothing for it to be adequate to. Analytic logical propositions could not be false.
How might one support the vacuity thesis? Not, certainly, by pointing out merely that logical truths remain true no matter how the truth values of atomic propositions are varied. This only shows that if logical truths do require that entities have certain special conditions, these conditions are not ones that make atomic propositions true. Similarly, it does not suffice to point out that, since logical truths hold in all possible worlds, they are true no matter what properties entities have. For this is true only of properties that it is logically possible to vary. But the properties corresponding to logical truths would be precisely those it would not be logically possible to vary. Of course, to assume there are no properties which it would be logically impossible to vary would be to beg the question of whether there is a specific property that entities must have─say, that b has when it satisfies ((x)Fx • F_) → Fa─if a logical truth is to be true.
To make these arguments for the vacuity thesis work, it is necessary to add to them a premiss indicating precisely when complex properties are to be treated as superfluous. The logical atomist has tried to show that there is a reasonable basis for holding that no specific conditions are needed if logical truths are to hold. Such conditions, and logical properties along with them, are superfluous since they are superfluous in respect to atomic conditions and properties. This view is far from dead13 despite old and unanswered objections to it, which are therefore worth repeating.
First, a word about complex properties. In our ontology, the important distinction as regards properties is that in Chapter V between basic and derived properties. Some basic properties may be complex□\the property signified by the complex predicate ‘(F_→ Gb)’ may well be basic for a─and some simple properties may be derived─where ‘(F_→G_)’ signifies a derivational connec-
tion the simple property G will be derived in, say, a. The notion of a complex property is inevitably relative to a particular system of concepts, perceptions, or terms. Unlike the notion of derived property it is a notion that has import for the intentional rather than the real order. The property signified by ‘(F_→ Gb)’ may belong to something that has neither F nor G. So this property will not be made up of F and G, which is as it should be in the component ontology for which individuals but not properties have components. The atomist says that predicates formed with the primitive ones of a system by the use of connectives do not signify properties. Since the distinction between simple and the rejected complex properties is relative to a system, one might suspect that it cannot have the ontological consequence the atomist wants to derive from it.
The atomist’s argument can be put in the following form:
(i) Let A be a true complex proposition.
(ii) There is then a set of true simple propositions, S՝, sufficient for the truth of A.
(iii) So no more is required for the truth of A than is required for the truth of all the simple propositions of S.
(iv) Hence, there is no complex property such that when one or more entities have it A is true.
In particular, since logical truths are complex propositions, there are no conditions of having complex properties making them true. But they are also true no matter what simple properties entities have. Since, then, their truth does not depend on specific conditions─complex or simple─of entities, they have no factual content.
It is sufficient to consider examples from the propositional logic to see how the argument is flawed. Russell himself was worried about eliminating negative facts, and as regards negation I shall give a modification of his argument.14 Where Fa is a simple proposition, suppose ~Fa is true. What simple propositions are sufficient for the truth of the complex proposition ~Fa? Now let G be a simple property that happens to belong to all and only those things to which the property F does not belong. Then Ga is sufficient for ~Fa. (In place of G we could have had a set of simple properties jointly coextensive with the complement of F.) The crucial question is: In what sense sufficient? If we mean sufficiency in the sense of material implication, then an arbitrary true simple proposition is a sufficient condition for any other true proposition. And thus, by the reasoning of the atomist’s argument, the assumption of any more than one property in the world becomes gratuitous. For an entity’s having any one simple property is a sufficient condition, in this weak sense, for the truth of any true proposition whatsoever.
To avoid this absurdity, ‘sufficient’ in (ii) should be construed in a stronger sense. But for any stronger sense that is not ad hoc, a’s having the property G is not sufficient for ~Fa, since by hypothesis it just happens that the extensions of F and G are complementary. Even if we adopted the different hypothesis that F and G do not just happen to be complementary, disaster would await us. For then there would be a true proposition containing both Fa and Ga for whose truth no simple propositions are sufficient in the stronger sense. So the inference from (i) to (ii) fails unless we accept the absurdity that there is only one property.
Suppose then we admit, over and above simple properties, the negation property, which a has by not being F. Is there now any reason to go one more step and admit properties corresponding to molecular complex propositions? Suppose the truth of Fa and the truth of Ga are sufficient for the truth of (Fa • Ga). If they are sufficient only in the sense of being a conventional basis for saying (Fa • Ga) is true, then indeed there is no point to positing, over and above simple properties, a conjunction property. For as was noted in §3, insofar as we only agree to take (Fa • Ga) as true when Fa is true and Ga is true, (Fa • Ga) is not yet actually true or false. Even so, the sufficient condition itself─the truth of Fa and the truth of Ga─is conjunctive. When this sufficient condition is satisfied, is there not something with a complex property described by the sign for some logical connective? Not, of course, if it too has a conventional basis for satisfaction made up of non-molecular positive or negative facts. We can imagine still higher conventions, each positing conditions that are satisfied without recourse to the realization of complex properties in the world in view of still higher conventions. So to escape complex properties we must agree that any bit of molecular discourse is prepared for by an infinity of conventions.
But there is an alternative to all this. At some point the sufficiency may not be conventional. The truth of certain simple propositions may not be merely a conventional basis for saying something complex, but rather a sufficient condition for something complex being true. The inference from (ii) to (iii) is then blocked, for a non-conventional sufficient condition is often quite distinct from what it conditions. Striking a match might be sufficient for producing a flame, but the flaming and the striking are nonetheless quite different processes.
In view of this failure of՝ the logical atomist’s argument, there remains no serious obstacle to supposing that there are complex properties. But if there are complex properties, there is no objection to saying that the truth condition for a logical truth is that entities have a specific complex property. That is, if there are complex properties, one can hold that logical truths are not vacuous. They have factual content even though they are true under any variation of conditions involving simple properties. The condition that entities must have for a proposition to be a logical truth is one that involves some connection among logical properties. The connections logical properties actually have are not determined by meaning rules for the corresponding logical connectives. Thus a proposition that cannot be denied without violating a meaning rule for a logical connective is not, for that reason, a logical truth. The meaning rules may misrepresent the connections among logical properties.
However, if the atomist is right, there are no logical properties, and hence logical propositions do not assert connections among logical properties. If logical propositions are analytic, there is, then, no room for saying they might misrepresent the connections among logical properties. Since the atomist's argument has been shown to be a failure, the analyticity of a logical proposition is not a guarantee of its truth and is thus not the nature of its necessity. In view of the thesis of the univocity of necessity, it follows that neither a logical nor a physical proposition must be necessary because it is analytic.
An obvious consequence of the atomist’s view is that analytic logical propositions cannot be false for any reason. It might be thought that they could be false even without the conditions of having complex properties playing the role of their truth conditions. For, nonetheless, the possession of simple properties will, by the meaning rules, be their truth conditions. And these rules may give a misleading picture of what these truth conditions are. Such simple properties are not the significations of complex predicates─such as ‘((x)Fx→ F_)’ ─obtained by abstraction from logical sentences. Rather, they are signified by simple predicates.
However, falsity cannot arise under these conditions. Since there are no complex properties, the complex predicates will, in general, have no significations. The link between simple predicates and such complex ones is, then, by meaning rules. The net effect of these rules will be to tell us to take as true of any entity a logical predicate like ‘((x)Fx → F_)’, no matter what simple predicate is true of it. By our earlier reasoning, this means, however, that only simple propositions will actually be true or false. The rest, including logical ones, will be neither true nor false since the sentences expressing them fail to meet the requirement of signification. Atomism then leads to the view that, though logical propositions can be analytic, they cannot be false since they are neither true nor false.
Earlier I granted the possibility that logical truths could be true in a correspondence sense even if they were vacuous. This possibility seemed warranted in view of the semantic conception of truth. But since then I pointed out that truth or falsity requires that terms be significant in a quite demanding sense. Since logical truths are vacuous for the atomist, logical terms within them will not have signification. Thus, for the atomist, nothing in logic can be true in a correspondence sense.
§5. Two Classical Arguments for the Apriority of Necessities. Once having set aside the notion that necessity has its source in analyticity, we have set aside a major obstacle to viewing necessity as real, that is, as being grounded in components of entities rather than in propositions, concepts, or terms about entities. We have shown that being necessary does not follow from being analytic. It is equally clear that the converse is true, that being necessary does not imply being analytic. For there is nothing in the notion that a proposition follows from the fact that an entity has a certain component─a nature─that implies the proposition cannot be denied because of its form. Of course, some necessary propositions are analytic; at best, this is a happy coincidence between natures and rules. We are then led to the view that there can be─and very likely are─synthetic necessities.
Are we thereby committed to the view that there can be─and very likely are─a priori synthetic truths? By an a priori truth, I shall mean one that can be confirmed, up to any degree, by methods other than those that are considered empirical. This description is intentionally schematic; no indication is given of what a non-empirical method might be, and for our discussion none need be given. Intellectual intuition has often been spoken of as a non-empirical method. There is also the method of examining the presuppositions of empirical methods, which I employed in Chapters IV and V.
Now one argument that leads from synthetic necessity to the synthetic a priori is Kant’s argument from confirmation. If a proposition is necessary then presumably one can have a warranted belief that it is necessary. But how can it be warranted? Not, it would seem, through experience. For “experience teaches us that a thing is so and so, but not that it cannot be otherwise.”15 Some other method must be looked for. Only if the proposition can be confirmed by a non-empirical method can we have a warrant for asserting its necessity. According to Kant, using the non-empirical method requires a “faculty of a priori knowledge.”
The validity of Kant’s argument─the strongest and most influential for the apriority of what is necessary─is unquestionable. But the premiss about the limits of what is taught by experience is false. Indeed, if experience confirms any propositions it confirms explicitly modal propositions. For an assumption of necessities is behind all learning from experience. The form of assumption argued for in Chapter V is that the ratio of favorable to over-all possibilities for two of an entity’s properties being necessarily connected is finite. On the basis of this assumption, there is finite support for their being connected necessarily.
Let us say further entities are observed, and they all have the one property if they have the other. Now if additional instances can increase the initial support for a universal claim, then additional instances will increase the initial support for a modal claim. If experience teaches anything, it can teach us something modal. However, this procedure differs from the one Kant mistakenly identified as the only way to learn a modal truth from experience. He thought he had rejected the possibility of learning a modal truth from experience when he rightly rejected the possibility of getting a measure of support for a modal claim only on the basis of experience. Here we have presented another possibility. A modal content is injected from the start into all learning from experience, for there must be the assumption of necessities. It is not then surprising on this basis that experience adds support to modal claims and thus teaches us modal truths.
Modal claims could be unconfirmed by experience only because there is no initial support for them. But if there is no initial support, there could be no chance that there are necessities, and hence no confirmation of non-modal claims either. This is not an ad hoc rebuttal of Kant’s perceptive argument since it is a direct consequence of my argument for necessity as a presupposition of learning from experience. Moreover, it is not to be objected that the modal claims are a priori because the assumption of initial support is not based on experience. For, by our argument, the confirmation of even the most contingent claim involves a non-empirical assumption of necessities. The conclusion would have to be the absurd one that all claims about the unobserved are a priori.
Another argument is Hume’s argument from inconceivability. If a proposition is necessary, Hume wanted to contend, its denial is inconceivable. In the special case of temporal succession, a necessary connection implies “the absolute impossibility for the one object ... to be conceived not to follow upon the other.”16 To determine whether it is conceivable that the connection should fail, we have but to “compare these ideas” of the two objects. This comparison of ideas is a non-empirical procedure, and thus were there necessary connections we would confirm them a priori.
I know of only two ways in which conceivability is important to inquiry. In one way it enters as “weak” conceivability, and then the first premiss of this Humean argument─that necessities have inconceivable denials─is false. The denials of many necessities are weakly conceivable. In the other, it enters as “strong” conceivability, and then the second premiss─that inconceivability is an a priori affair─is false. The denial of a claim is strongly conceivable only if as one conceives of it, a posteriori considerations enter in.
The philosopher is adept at counterexamples that are weakly conceivable. He tells a logically consistent tale containing a counterexample to a certain view and a context for it. Yet when a natural scientist arrives at a counterexample to a theory by a thought experiment, he supposes not only that the story is a logically consistent one but that what happens in it is consistent with the natures of the things making up the context of the counterexample. Such a counterexample is then strongly conceivable. The counterexample typical of the philosopher serves only to show that the logical possibilities have not been exhausted by the view in question.
When only weak conceivability is required, it is false that counterexamples to necessities are inconceivable. At least it is false if there are non-logical necessities, and so far we have no reason to doubt that there are some. The counterexample typical of the natural scientist's thought experiment serves to show that the possibilities afforded by the natures of things have been underestimated by the view in question. But a sense of what the natures of things are rests on information derived from empirical investigation. So when strong conceivability is required, it is false that the inconceivability of the counterexample is an a priori affair. These matters admit of illustration, but hardly of strict definition.
Strawson provides an illustration of the usual way a philosopher puts conceivability to work.17 The illustration concerns vision. Normally, the character of a visual experience depends on the state of the eye, the position of the body, and the direction of the head. Moreover, the dependency is on the eye, the body, and the head of one and the same animal. Now Strawson wants to show that this dependency on a single body is contingent. For, he says, one can imagine that a given visual experience depends on the state of the eye of one body, the position of another, and the direction of the head of yet another. He does not bother to ask how, given what is known about light, the eye, and the brain, factors at such diverse locations manage to come together to form a single visual experience.
The only work done before he claims that it can be imagined is the work done in checking the account of what is imagined for logical consistency. That is, he has checked to see that he does not contradict himself in saying that some visual experience depends for its clarity on the state of the eyes of a body in one room; for its range on a body in another room─only objects in that room are possible objects of the experience; and for its actual object on the direction of the head of a body in a third room─the actual object seen in the second room being selected by the direction of the head in the third. As merely an abstract exercise in not contradicting oneself, the construction of the counterexample fails to indicate─apart from the question begging assumption that all necessities are logical─that visual dependence on a single body is contingent.
To conceive a counterexample in the strong sense, it is not sufficient to juxtapose imagined things arbitrarily; they must be related in a way thought to accord with what they themselves are. There is a notable case where Einstein and Bohr differed on whether this condition was satisfied. Against the claim that definite values of position and momentum cannot simultaneously characterize a physical system, the following situation was imagined.18 Two systems are in interaction up to a certain time; afterwards, they exist separately.
Because of the prior interaction, they are subsequently correlated. For if, after the separation, a position measurement is made on one of the systems, the position of the other system can be inferred. Similarly, if a momentum measurement is made on one, the momentum of the other can be inferred. The measuring device does not interact with the system with inferred values. But if either a definite position or a definite momentum value can be inferred, depending only on the choice of measurement to be made on the other system, then, Einstein concluded, the unmeasured system must have both definite position and momentum values. For if a student can answer correctly either the question “What is 2 plus 3?” or the question “In what country is London?” then even though, after answering the question asked first, the student becomes so confused that he or she cannot answer the other, it would be natural to say that, just before receiving the first question, the student knew the answer to both.
Now Bohr denies that this is a genuine counterexample to the disputed claim.19 The question is whether it conforms to the nature of physical states. This is not just an a priori question, for answering it involves appeal to experimentally based claims about the nature of physical states. Physical states are, for Bohr, relational in that they exist only in relation to the application of some measurement device. The system separated from the one directly measured has, then, no definite position (or momentum) apart from that distant position (or momentum) measurement. Only on the supposition that it does─a supposition Bohr sees as incompatible with the quantum nature of states─is there a counterexample. If necessity were a matter of inconceivability and if Bohr were right that it is strongly inconceivable that position and momentum can simultaneously characterize a system, then the necessity of this incompatibility would not thereby be a priori.
The question of whether there is a synthetic a priori is left unanswered by these criticisms. There may be a synthetic a prioriג but there appears to be no basis for believing that the synthetic necessities called for by the principle of levels of limited variety are a priori. That there must be some necessities is a condition of the reasonableness of action on prior experience. Thus this condition is not first confirmed by inductive practice, since it is required for inductive practice. If whatever is presupposed by human practice is a prioriג then the existence of some necessities is indeed a priori. However, the apriority of this general condition for reasonable practice in no way implies the apriority of any specific necessities. As we saw, experience can confirm the necessity and hence the truth of specific necessities. But from this it does not follow that a priori methods are excluded for the confirmation of these necessities.
* 1 purposely leave open the question of whether, if this is true of one such sentence expressing an analytic proposition, it must be true of any sentence expressing the same proposition. For the only reasonable way for this to be true would require a debatable dependence of propositional sameness on sameness of meaning rules.
* In this case, if this implication holds by the nature of b, it will also hold by the nature of a. This indifference is associated with the fact that the necessity is logical. But as was shown in Chapter III, §2, it does not hold generally where the necessity involves more than one individual.
* If this range is empty, then both conjuncts can reasonably be taken to be truth valueless, and thus the equivalence is not upset.