This chapter is dedicated to increasing some prerequisite technical precision when it comes to certain points about concepts, thought, and language which will be important for our ongoing project. In particular, I mentioned in §1.3 that there have been many leaps forward in semantics and the philosophy of language in twentieth-century philosophy, which are pertinent to a refined understanding of a priority. It will prove worthwhile to chart some of this territory, before turning to critical work on the varieties of immunity to counterexample, in Part II.
§2.1: some important terms and concepts
First up: There is considerable diversity in the literature, when it comes to the question: To what, precisely, should the terms ‘necessary,’ ‘analytic,’ and ‘a priori’ be attributed? (This is especially true of the term ‘a priori,’ as we will see in §4.1. Truths, propositions, concepts, inferences, knowledge, and justification are among the many things which are commonly labeled a priori.) I will begin this section with discussion of two common and central candidates: truths and propositions.
‘Necessary truth,’ ‘analytic truth’ and ‘a priori truth’ are all common locutions in philosophy. All three of these terms target special categories of truth, truths not limited to specific people, times, or places. Like many much-discussed philosophical concepts, ‘truth’ tends to be employed rather variously. One hears that truth is culturally constructed, that truth is power, truth is historical, truth is whatever the rich say it is, and so on. One is apt to encounter the sentiment that you have your notion of truth, I have mine, and no one is in a position to comparatively evaluate them.
Although not without motivation, these sentiments are, as stated, rather sloppy and misleading. ‘Truth’ in the above sentiments stands not for the content of the concept truth, but rather for the set of things that are taken to be true. It is the set of things that are taken to be true that varies from culture to culture, that the rich and powerful have a disproportionate say in dictating, and so on. You may well be free to take as true whatever you see fit, and no one else has authority to decree otherwise, but none of that touches the one constant content of the concept of truth. It would be rash to conclude from these wide variations in what is taken to be true that the content of the concept of truth varies widely. Quite the contrary: disagreements about which things are true depend upon agreement about what the term ‘truth’ means.
In this book I will adopt a deflationary stance concerning the content of the concept ‘truth.’1 Strictly speaking, truth is a simple, elementary concept. One cannot learn a language, or tell a lie, without manifesting a grasp on it. ‘Truth’ names a basic relation between linguistic expressions and what they are about, on which three-year-olds have a decent purchase, and with which we are all thoroughly competent long before adolescence. There are all manner of difficult philosophical and political questions about who gets to say what is to be counted as true, about how what is taken to be true varies across perspectives, and so on; but these debates presuppose, rather than call into question, the one constant content of the concept of truth. In the Metaphysics, Aristotle makes the earth-shaking assertion that truth consists of saying of what is that it is, and of saying of what is not that it is not. Two and a half millennia later, after the rise and fall of some much more sophisticated theories of truth, that’s about where matters stand. As Quine (1992: 82) puts it: ‘One who puzzles over the adjective “true” should puzzle rather over the sentences to which he ascribes it. “True” is transparent.’
One conclusion that is fairly well supported by the many failed attempts to give a non-circular, substantive definition of truth is that it probably cannot be done. Truth cannot be reduced to any other terms. This elementary status should not be all that surprising, and is hardly a defect—very few concepts can be reduced to others without remainder. (Potential examples of concepts that can be so reduced include ‘snowball’ [= made of snow + shaped like a ball] or perhaps ‘bachelor’ [= unmarried + man]). It is now widely recognized that, in this respect, these concepts are in the minority. Just try to break down ‘freedom,’ ‘happiness,’ ‘good,’ or ‘art,’ say, into self-evident, discrete factors! In general, this inability to factor out discrete and exhaustive constituents of a concept is not a sufficient reason to hold that that renders the concept suspect, or second-rate.2
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I depart from Quine (1992: 82) in taking the things for which the question of truth or falsity arises to be not sentences, but rather the propositions that sentences are used to express (in context). So, in calling something a ‘truth,’ I mean that the proposition expressed by the given sentence is true. The term ‘proposition’ is introduced to have one to denote what is in common among, for example, uses (in context) of the following sentences:
1. Aristotle is now sitting.
2. I am now sitting. (said by Aristotle)
3. You were sitting, yesterday at this time. (said to Aristotle, in 24 hours)
4. Aristote est assis, maintenant. (said in Quebec)
[1]–[4] describe the same situation, express the same information, or say exactly the same thing. Henceforth, I’ll say that they express the same proposition. Propositions are more abstract than sentences—the same proposition can not only be believed or doubted by different speakers, but can be expressed by means of different sentences, in different languages, and so on.
So, first and foremost, the term ‘proposition’ is a useful one in this kind of inquiry, because it allows one to categorize various thoughts and utterances into equivalence classes, based on their representational properties, or information content. Over and above that point about usefulness, though, some such abstract term as ‘proposition’ is essential in this kind of inquiry, because it is only at this level of information content that questions of truth or falsity—and, a fortiori, question about immunity to counterexample—arise.
Propositions are means of categorizing attitudes and assertions into equivalence classes. Within the philosophy of language, there are many complex debates about the precise nature, contents, and individuation conditions of propositions. It would be tangential to our present project to delve very deeply into these waters, but some pertinent refinements will be explored in this chapter. For example, prior to—and deeply pertinent to—the question of whether ‘Water is H2O’ is necessary, analytic, or a priori is the question of how precisely to individuate the content of the proposition expressed; and on that question, there are many distinct options.3
In addition to ‘sentence’ and ‘proposition,’ I also sometimes avail of the notion of ‘statement’ below—where a statement is a particular dated use of a sentence to express a proposition.
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I next consider some miscellaneous notes on some terms in the neighborhood of our core notions of necessity, analyticity, and a priority which have some currency, but which will not play a role in this book.
One such term is ‘epistemically necessary,’ which is used to mean something like ‘necessitated by one’s antecedent beliefs’ or ‘entailed by things one holds true.’ As I use the terms in this book, ‘epistemic necessity’ is not well-formed—since ‘necessity’ is not an epistemological concept. To speak of such explicitly epistemic concerns, I will use explicitly epistemic vocabulary.
Consider next the common terms ‘conceivable’ and ‘conceptual truth.’ As above, given my above setup, this is a kind of hybrid that vaguely straddles distinct philosophical sub-terrains of necessity, analyticity, or a priority. Most specifically: I take ‘conceptual truth’ to typically mean a certain semantic/epistemic hybrid—that is, ‘knowable a priori because it is analytically true.’ In any case, by Part IV, I will have come down firmly against the metaphysical import of anything like ‘conceptual truth’; for conceivability tells us about our concepts, as opposed to about the mind-independent objects which make up the extension of (most of) our concepts.
Another such term is ‘logically necessary,’ which may or may not be broader than metaphysical necessity (just as metaphysical necessity is broader than physical4). Logical possibility is supposed to include everything conceivable, anything that is not precluded by the laws of logic, where these are understood to be distinct from, and perhaps more inclusive than, the laws of metaphysics. I shall not make use of this notion here, either. I am not sure that this distinction between metaphysical and logical laws could be drawn in a clear and comprehensive way, let alone what pertinence this notion of logical necessity would have for our ongoing discussion anyway, in addition to the three notions of metaphysical necessity, analytic truth, and a priori knowledge. Anyway, nothing which follows either presupposes or further investigates any distinction between logical and metaphysical necessity.
I will have little to say that is directly about certain other important, nearby notions of logical truth, entailment, validity, etc. First and foremost, these notions pertain to relations between propositions; whereas my primary interest here lies more at the level of properties of propositions. While logic and the philosophy of logic are relevant to parts of our ongoing discussion (cf., e.g., §6.2), for the most part, they will not be directly engaged in a sustained way. (And, even there, it is a case study in epistemology, as opposed to logic or the philosophy of logic per se, which is our focus.)
§2.2: the arbitrary nature of linguistic conventions
It is important to examine at a bit more length the arbitrary nature of linguistic conventions. Let us start with some candidates for necessity, analyticity, or a priority:
1. 2+ 2 = 4.
2. One cannot steal one’s own property.
3. All bachelors are unmarried men.
For present purposes, it is crucial to hold linguistic conventions fixed, because what is at issue is not the identity or nature of the symbols, but rather what the symbols express. The claim that [1] is necessary, or that [2] is knowable a priori, say, is not in tension with the fact that our linguistic conventions are, in some sense, arbitrary. We came up against this matter in §1.2, in considering the claim that [1] is necessary: there it was stated that we might have spoken a language in which the sentence ‘2+2=4’ meant something different, but that is not relevant to the modal status of [1]. The claim that [1] is necessary would not be falsified if that sequence of squiggles were to be put to some other use; rather, it would be falsified only if—regardless of which kinds of objects you consider, or in which order you count them—two of anything added to two of anything failed to yield four of them. This distinction between symbols and what they are used to express is absolutely fundamental here, and so I should elaborate it a bit further. (As we will soon see below, and again in §3.3, some skeptical arguments about the very idea of immunity to counterexample founder on cautious distinctions in this neighborhood.)
Given the distinction between sentences and propositions, the point is that there is nothing necessary about sentences; it is only at the level of propositions that the question of necessity arises. (This might seem so basic as to not need pointing out; but especially when we come to certain arguments against the coherence and worth of analyticity, these basic points will prove their worth.) The claim that [1] is necessary, or that [2] is knowable a priori, say, is consistent with the fact that our linguistic conventions are, in some sense, arbitrary. The claim is not that these sentences could not possibly have been used to mean something false, or that they might not express contingencies in another possible language. It is rather that, holding linguistic conventions fixed, what [1] means could not possibly be false, and that [2] can be known to be true without performing experiments or taking polls, but rather just by reasoning things through. In considering these claims of immunity to counterexample, we must first fix on the proposition expressed by the sentence; and then we consider whether that could possibly be false (in the case of questions of necessity), whether it is true in virtue of meaning (for questions of analyticity), or whether it can be known to be true without empirical investigation (in the case of a priority).
The relation between any linguistic expression and its meaning is somewhat arbitrary—that is, in no case is it necessary that any particular sound or symbol (e.g., ‘2,’ ‘no,’ or whatever) has the particular meaning that it does. These symbol-sound-meaning conventions are historical accidents, contingent facts set by the evolution of our language. As a consequence, there is something arbitrary about the relation between sentences and the propositions that they express—since historical accidents play a role in the meanings of all the constituent parts of, say, ‘One cannot steal one’s own property,’ the link between sentence and proposition is also a complex conventional historical accident. So, as linguistic conventions vary, which proposition is expressed by a given sentence will vary. If ‘steal’ meant what ‘sell’ actually does, then [2] would express a different proposition; if ‘property’ meant what ‘orangutan’ actually does, then [2] would express a different proposition; and so on.
Hence, if we did not hold linguistic conventions fixed, all would be (trivially) contingent—it is in no case necessary that any given sentence express the particular proposition that it does. Crucially, though, necessity, analyticity, and a priority have nothing to do with alternative possible linguistic conventions. Rather, they have to do with the meaning that is expressed with a given utterance or inscription of a sentence. As Kripke (1972: 77) puts it:
One doesn’t say ‘two plus two equals four’ is contingent because people might have spoken a language in which ‘two plus two equals four’ meant that seven is even.
To bring up alternative possible meanings, in adjudicating our questions (of a priority, necessity, and analyticity), is to change the subject.
The issue of precisely how we determine which meaning is expressed with a given sentence is quite complex. The crucial point for now is that claims of analyticity, like necessity and a priority, are not claims about other possible linguistic conventions, and so cannot be undermined by appeal to them.5
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These above distinctions pertaining to linguistic conventions are most crucial when it comes to certain lines of attack on the notion of analytic truth. Consider for example the following possible interpretation of ‘analytic truth’—that is, way to understand exactly what ‘truth in virtue of meaning’ comes to—described by Boghossian (1997: 336): ‘Our meaning p by S makes it the case that p,’ where ‘S’ stands for a sentence, and ‘p’ stands for the proposition it expresses.6 This sort of view would take our meaning-conventions to have some supernatural magical potency. It reads the ‘in virtue of’ in ‘truth in virtue of meaning’ as a causal connection. The idea seems to be that our meaning-conventions have the power to move things about in mind- and language-independent reality, to change the nature of the things about which we think and talk.
Boghossian (1997) clearly rejects this conception of analyticity. I, too, want nothing to do with this strange view. (As far as I can tell, no one ever held this view.) The claim that [1] or [2], say, is analytic is not the claim that linguistic conventions caused the relevant mind- and language-independent facts to fall into place.
[1] 2 + 2 = 4.
[2] Murder is wrong.
Rather, if our meaning-conventions determine that ‘+’ and ‘four’ (or that ‘murder’ and ‘wrong’) express certain concepts, and if it is plausible that the relations between these concepts are immune to counterexample, then there will be statements such that grasp of their meaning is sufficient for recognition of their truth.
Here we see the importance of the above distinctions between conventional links between S and p and truth-conditions of p. First, it is a contingent conventional accident that such symbols as ‘square’ or ‘four-sided’ are used to express the concepts that they in fact express; second, it still yet may be immune to counterexample that all squares are four-sided. Given that some relations among concepts are not vulnerable to refutation by contingent happenstance, it would be awfully odd if we were somehow barred from making statements whose role is to express such exceptionless relations.
There is, however, an incontrovertible point in the neighborhood of the above straw conception of analyticity. The straw conception has it that:
[S] Our meaning p by S makes it the case that p.
In contrast, the distinct, more refined point is that:
[Si] Our meaning p by S makes it the case that, if p is impossible, then what S expresses is false in every possible circumstance.
[Sii] Our meaning p by S makes it the case that, if p is contingent, then what S expresses is true in some circumstances and false in some circumstances.
[Siii] Our meaning p by S makes it the case that, if p is necessary, then what S expresses is true in every possible circumstance.
The key difference is that [Si–iii] explicitly separate out two very different factors which are relevant to the question of a statement’s truth-value—that is, first, there is the conventional link between S and p; and second, there is p’s truth-condition.
Again, if we did not hold linguistic conventions fixed, in the course of our present inquiry, all would be trivially contingent—since all links between sentences and propositions are contingent. Crucially, though, necessity, analyticity, and a priority have nothing to do with alternative possible linguistic conventions. Those notions concern what statements express, not what they might have expressed. To bring up questions about alternative meanings, in these kinds of discussion, is to change the subject.
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Perhaps not surprisingly, given his naturalistic agenda, Quine was prone to run roughshod over this distinction between the conventional link between S and p, on the one hand, and the truth-conditions of p, on the other. Consider, for example:
The statement ‘Brutus killed Caesar’ would be false if the world had been different in certain ways, but it would also be false if ‘killed’ had the sense of ‘begat.’ (1951: 36)
There are enormous relevant differences between the two conditions cited by Quine. If the world had been different in certain ways, then Brutus might not have killed Caesar, but if ‘killed’ had the sense of ‘begat,’ then the sentence ‘Brutus killed Caesar’ would express a rather different proposition. If we uncritically sweep the contingencies of linguistic conventions together with the contingencies of language-independent facts, in this way, then the trivial, misleading pseudo-conclusion that all is contingent quickly follows.
To the contrary, whereas Quine treats these two separate truth-value-determining factors (i.e., the conventional link between S and p, and the truth-conditions of p) as if they were of the same sort, these factors are operative at different levels. Linguistic conventions have to be settled first, and held fast, so that we can fix on a particular p; after which point linguistic conventions are entirely irrelevant to modal questions about p. On this point, Stalnaker articulates a clear advance beyond Quine (1951):
[W]hen a statement is made, two things go into determining whether it is true or false. First, what did the statement say: what proposition was asserted? Second, what is the world like; does what was said correspond to it? (1972: 177)
Stalnaker’s first question is the conventional one, whereas our ongoing focal questions (about necessity, analyticity, and a priority) only pertain at the level of the second question, subsequent to settling on answers to the first question. (We’ll pick up and build on this shortly, in the next section.)
So, insofar as Quine’s point was merely that ‘in general, the truth of statements depends obviously on both language and upon extralinguistic fact’ (1951: 41), then well and good—I completely agree. However, that by no means entails that there is no such thing as immunity to counterexample in virtue of meaning:
[1] No grandmother is childless.
[2] Every even number is divisible by two.
While it is awfully hard to draw a firm boundary around the set of analytic truths, there clearly are paradigm cases. What would you say to someone who thought it an open question whether all grandmothers are women who are or were previously mothers, thought that we should do a poll or conduct experiments before we could confidently claim that [2] is true? The conclusion that they simply do not understand the meanings of the relevant terms is compelling if not inevitable; and it will be grounded within a sophisticated framework, below in Parts III and IV.
There is nothing obscure or magical at work here; the only requisite ingredients are (i) conventional relations between expressions and properties, and (ii) necessary relations among properties. (We will get into putative analytic truths which are not necessary in due course.) Of course, both metaphysical necessity and the determinacy of meaning raise hard questions. The present point is just that anyone who accepts both the notions of necessity and of meaning has already purchased all the ingredients for analytic truth; since analytic truth is widely held to be such a far cry more contentious that either metaphysical necessity or the determinacy of meaning, the point is worth making here.
§2.3: meaning, extension, indexicality, modality
Up to this point I have occasionally availed of a fairly uncritical, intuitive notion of ‘meaning,’ and have said just a little bit about the indispensable notion of a ‘proposition’ (i.e., basically, equivalence classes of sentence-sized meanings). The next business here is to increase the technical precision when it comes to these two notions, particularly when it comes to the ways in which developments in the semantics of indexicality and of modality (among other related developments) have altered the terrain.
The first basic refinement to ‘meaning’ is as follows: I use the term ‘extension’ to designate the thing or set of things to which a given expression refers, or correctly applies. For example, the extension of ‘persimmon’ is a certain bunch of fruit; the extension of ‘the richest woman in Europe’ is the person who satisfies the condition specified; and the extension of ‘midnight blue’ might be taken to be the scattered and diverse collection of spatial regions which instance the relevant shade.
Although we sometimes say such things as ‘“Persimmon” means that kind of fruit right there,’ or ‘“Midnight blue” means that shade right there,’ I will never use ‘meaning’ in this way here. The term ‘extension’ will be used exclusively for this sort of job.
‘Meaning,’ in contrast, will be used to designate the significance or connotation of an expression. The meaning is what a dictionary aims to record; it is the conceptual condition that must be grasped in order to understand the expression. So the extension of ‘persimmon’ is a bunch of fruit, but its meaning is the conceptual condition that picks out all and only that fruit. To know the meaning is to grasp that condition. This meaning/extension distinction is starkly illustrated by the case of definite descriptions, such as ‘the richest woman in Europe.’ If one understands all the constituent words, and is competent with the grammar of English, then one grasps its meaning; but knowing who its extension is goes beyond linguistic competence. One must actually know which person happens to satisfy the relevant condition. It is easy to generate definite descriptions whose meaning we all grasp but whose extension probably none of us do (e.g., the biggest fish in the Indian Ocean, the tallest left-handed Mexican in Finland).
There is obviously a close connection between meaning and extension—that is, the meaning specifies the conditions that must be satisfied in order to qualify for membership in the extension. Meaning, in context, imposes constraints on what can count as the extension. To know the meaning is, very roughly, to be able to identify the extension (in normal contexts), to distinguish between the extension and its complement.
Now, a part of why we need to be as clear as possible about such semantic matters is that the notion of synonymy (i.e., sameness of meaning) is crucially important to, first and foremost, analyticity, and, subsequently, to a priority as well. Sameness of extension is clearly a necessary condition for synonymy.7 If, say, someone thought that ‘persimmon’ and ‘pomegranate’ were synonyms, but then became convinced that there was an object to which only one of those terms correctly applied, then that person would have to reject the previously held hypothesis about the terms’ synonymy.
Throughout the history of theorizing about logic and language, many have also wanted to hold that sameness of extension is a sufficient condition for synonymy. In that case, meanings would be relatively easy to incorporate into a naturalistic world-order. Meanings would obey set-theoretic axioms of extensionality, as well as other intuitive principles of extensional logic. (Key ones include the substitutivity of co-referential terms salva veritate [i.e., if a=b and Fa, then Fb] and existential generalization [i.e., if Fa, then ∃xFx].) Talk of meaning could be translated into, or transparently reduced to, well-understood set theory. The meaning could be identified with the extension; and hence otherwise obscure questions about sameness of meaning would be transformed into relatively clear questions about whether distinct sets do or do not have the same members.
However, meanings do not seem to be so simple. It appears that distinct expressions may differ in meaning even while being co-extensive. Classic cases include ‘renate’ (or: organism with kidneys) and ‘cordate’ (or: organism with a heart). While clearly the conditions for membership in these sets differ, these conditions determine exactly the same members. That is, as a matter of fact, all and only renates are cordates. Hence, at least prima facie, these terms are co-extensive but not synonymous. Other related types of examples include distinct terms with null extension, which do not seem to be thereby synonymous (e.g., ‘phlogiston’ vs. ‘perpetual motion machine’ vs. ‘frictionless plane,’ and so on). Frege famously argued that the same phenomenon occurs in the case of proper names (e.g., ‘Hesperus’ vs. ‘Phosphorus’), but while this claim that such co-extensive names differ in meaning is plausible and has been influential, it is too controversial to rest much upon, without the kind of extensive further analysis of the semantics of proper names which will not be undertaken in this present work.
In any case, I take the renate/cordate cases to at least strongly suggest that more than just extension seems to be involved, when it comes to questions of meaning. Hence, talk of meaning cannot obviously be translated or reduced to talk of extensions. This situation is deplored by naturalists such as Quine (1956), who laments that meanings are ‘obscure … creatures of darkness’. A comprehensive theoretical account of human beings must appeal to and incorporate a theory of meaning, but as of yet meanings have not been naturalistically, seamlessly incorporated into a scientific world-order.8
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Next to move from individual-expression-meanings to sentence-sized meanings (i.e., propositions). In what Kaplan (1975) calls ‘the Golden Age of Pure Semantics,’ the links between individual atomic meanings and propositional molecules were taken to be simple and transparent. Every independently significant linguistic expression was taken to have a context-independent meaning. Semantic competence requires pairing expressions with their meanings. When expressions are put together into an intelligible sentence, those meanings and their mode of composition determine the content of the proposition expressed. Propositions themselves were then complex sentence-sized meanings which constitute (among other things) the truth-conditions of an assertoric use of the sentence, and that which must be grasped in order to count as understanding the meaning of the sentence. Some would even go so far as to characterize the semantic enterprise itself via this end of pairing up well-formed sentences with propositions expressed (cf. Lewis [1975]).
The Golden Age is long gone now. (Kaplan himself cites Carnap [1947] as its zenith.) Various different factors have served to show that the relations between atomic meanings and propositional molecules is vastly more complex than that. Key developments here include developments in the semantics of indexicality and modality.9 These developments are very important, for our purposes, since: [1] they complicate various senses in which something might be taken to be immune to counterexample, and [2] they necessitate distinctions which are in any case crucial for an adequate degree of semantic precision.
Indexicals are linguistic expressions whose extension shifts from use to use (e.g., ‘she,’ ‘today,’ ‘here,’ ‘this’). Here we have a common kind of context-sensitivity in which sameness of meaning is compatible with differences in extension. For example, various utterances of ‘Today is rainy’ or ‘She is German’ (in different contexts) can clearly express truth-conditionally distinct propositions. The semantics of indexicality studies the factors which determine the contents of propositions expressed in such cases. Indexicality is clearly in tension with the Golden Age conception of the relations between sentences and propositions; one important question is whether these indexical cases are circumscribed oddballs, or else the thin end of the wedge.10
Modality poses a similar but very different challenge to the Golden Age conception. Modality is an ancient area of philosophical inquiry that centers on concepts like possibility, contingency, and necessity (or, in their more common guises, might, can, and must). Drawing modal distinctions can be seen as a matter of conceiving of and reasoning about non-actual but possible contexts of evaluation. Thus, insofar as we would concede that although Neil Young is not in fact the prime minister of Canada in 2017, he might have been, that is to say that there is a consistent, coherent non-actual situation in which different historical accidents befell Neil Young and he became a successful Canadian politician instead of a folk-rock icon. In contrast, insofar as we would also concede that Neil Young could not have been a coffee cup, that is to say that there is no such consistent coherent scenario in which historical accidents could have conspired to make our actual Neil Young into such an object. Hence, the study of modality involves consideration of distinct non-actual contexts of evaluation.
Now, recall that on the Golden Age conception of things, interchange of co-extensive parts ought to preserve truth-conditions. If all renates are cordates, then ‘All John’s pets are renates’ is true iff ‘All John’s pets are cordates’ is. However, modality provides one fairly clear case in which this Golden Age tenet is subject to counterexample. Suppose actually true anything of the form ‘a = the F’ (e.g., Justin Trudeau is the prime minister of Canada, or Adele is the richest woman in Europe); even still, ‘a is G’ and ‘The F is G’ nonetheless differ in their truth-conditions across various possible contexts of evaluation (e.g., ‘Justin Trudeau is charming’ vs. ‘The Prime Minister of Canada is charming’). There clearly are consistent coherent non-actual situations in which Justin Trudeau is charming but the prime minister of Canada is not, for example, or in which Adele is rolling in the deep but the richest woman in Europe is not.
Hence, the kind of consideration of non-actual contexts of evaluation involved in the study of modality points to another important sort of refinement to the Golden Age. Co-extensiveness of parts is no guarantee of sameness of truth-condition across contexts of evaluation. This is another major complication to the relations between linguistic meaning and propositions expressed, which will be pertinent in what follows. (It is also another reason to be wary of the reduction of meaning to extension.)
It is interesting to consider these complications necessitated by indexicality and modality against the backdrop of a quote from Stalnaker cited in the last section:
[W]hen a statement is made, two things go into determining whether it is true or false. First, what did the statement say: what proposition was asserted? Second, what is the world like; does what was said correspond to it? (1972: 177)
Indexicality is complexity about the relation between linguistic meaning and the first level—factors in the context of utterance can affect which proposition gets expressed. In contrast, modality pertains to the relation between proposition expressed and its conditions of satisfaction, and hence pertains to the second level. Factors in the context of evaluation can affect whether the proposition that is expressed is true or false.
Generally, investigation into indexicality and modality lead to the development of multi-dimensional semantic frameworks in which the effects of the context of utterance on content of the proposition semantically expressed can be neatly distinguished from the effects of the context of evaluation on whether that proposition is true or false (cf. Kaplan [1989], Stalnaker [2001], Chalmers [2006]). These refinements to the relations between the meanings of linguistic expressions and the propositions which are expressed when they are used in context will be crucial to subsequent discussions of immunity to counterexample—first in §3.3, and then throughout Parts III and IV. There will be many significant further appearances by both indexicality and modality.
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Now to move onto propositions per se, that is, the complex meanings of complete sentences. Due in large part to increasing sophistication in our understanding of such phenomena as indexicality and modality, we now distinguish several varieties of sentence-sized semantic entity, each of which is suited to some but not all of the jobs traditionally associated with the term ‘proposition.’ In the course of progress, Golden-Age, canonical propositions (as Frege or Russell conceived of them) have been methodically pulled apart.
The phenomenon of indexicality provides a relatively simple way to illustrate this point. Given a use of ‘I am here now’ (in context), there are (at least) two different sentence-sized semantic entities which must be distinguished, both of which are plausibly thought of as (in some sense or other) semantically expressed by the utterance. There is what Kaplan (1989) calls the ‘character’ (i.e., the information that is identifiable independently of the context of utterance), and then there is what he calls the ‘content’ (i.e., the information that issues once the character becomes saturated by the relevant features of the context of utterance).
To the extent that indexicality is thoroughly prevalent, important differences emerge between character and content. For present purposes, consider just two of the proposition’s main jobs—to constitute that the grasp of which constitutes linguistic competence, and to specify the truth-conditions. As for ‘linguistic competence,’ insofar as we demand of propositions that they be that which is grasped by one who understands the sentence (whether or not they can ascertain all pertinent features of the context of utterance) then it is sentential characters which fit the bill. (Common examples for making this point include receiving a postcard in the mail, with the author’s name and location illegible, that says ‘I am having a great time here’. Linguistic competence gives you the character, but you need to solve for WHO and WHERE to get to the content.) In contrast, insofar as propositions are the bearers of truth-conditions, then here contents are much better suited.11
In this respect, indexicality is just the thin end of the wedge. Things get more and more complicated for poor old golden-age propositions once we recognize the prevalence of context-sensitivity, semantic underdetermination, etc. Even further, much has transpired since the 1970s, when it comes to the various semantic entities associated with sentences; such that by this point there are several other alleged denizens in what Taylor (2007) calls ‘the sub-syntactic basement of the language’—unarticulated constituents, hidden variables, non-classical relativistic parameters, etc. It is not altogether clear exactly how such posits should be taken to affect the individuation conditions for propositions12; though again here we are straying into technical issues within the philosophy of language which lie beyond the scope of our present inquiry.
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For the case of sub-sentential expressions, I am going to stick with the terms ‘meaning’/‘extension,’ as opposed to taking on Kaplan’s ‘character’/‘content.’ There is broad overlap between these contrastive pairs, over a range of paradigm cases; but ultimately Kaplan’s terms are integrally connected to his technical artifice in a way that may not well-suit the scope of this project. (When you pick terms as common and varied as ‘meaning’/‘extension,’ people pay attention to your exact stipulations as to how they are to be used; but when you talk in terms of ‘character’/‘content,’ the boundary between novel research and Kaplanian exegesis gets blurrier.)
One possible drawback to ‘character’/‘content’ is that while it clearly applies to indexical pronouns, it is less clear or obvious how to apply it to various other sorts of expression. When it comes to ‘the richest woman in Europe,’ for example, what exactly is its content? A person? An identifying condition? Something else? The general run of quantified noun phrases (‘a man,’ ‘three thugs,’ ‘everyone’) is illustrative of the possible cases for which (as opposed to ‘she’ or ‘today,’ used in context) it is not clear exactly what the content should be taken to be. From the other direction (and again as opposed to ‘she’ or ‘today,’ used in context), it is not clear what the character of proper names or natural kinds terms, for example (e.g., ‘Aristotle,’ ‘aluminum’), should be taken to be. So, in contrast to the characters versus contents of indexical expressions, as stipulated above, the ‘meaning’/‘extension’ pair has a broader range.
A second reason not to go with ‘character’/‘content’ is that Kaplan’s talk of characters as functions from contexts to contents, though helpful in many respects, has unfortunately helped to engender some oversimplified pictures of the relations between uses of linguistic expressions and the propositions thereby expressed.13 Only in the case of ‘I’ (sometimes called an ‘automatic indexical’) is its character plausibly viewed as a function from contexts to content. Even in cases of other guaranteed-to-refer indexicals such as ‘here’ and ‘now,’ it is clear that characters merely constrain content, and fall far short of determining content. (For example, by ‘here’ do you mean this room? This building? This city? This country? This planet?) This is even more evident with, say, a discourse-initial use of ‘She is German’ in a room in which there are many females (though the speaker has one specific person in mind, whether or not it is contextually obvious to the audience which person that is).
Meanings merely constrain extensions, they do not determine extensions. The possibility of mistaken associations on this point—when it comes to slogans along the lines of ‘characters determine contents,’ or ‘characters are functions from contexts to contents’—amount to another reason to be wary of applying those terms to sub-sentential expressions. (Cf. note 13 for arguments against indexicalism building from exactly this point.)
At the sentential level, though the distinction between sentential characters (i.e., context-independent, compositionally determined, sentence-sized meanings) and sentential contents (i.e., the specific truth-conditions expressed in context) is an indispensable tool which will be availed of at several junctures. The phenomena of indexicality (e.g., ‘Today is rainy,’ ‘She is German’) and modality (e.g., ‘The current Prime Minister of Canada might not have been charming’) drive home the importance of this distinction. Crucially, for our purposes, it is at least an intelligible possibility that, for example, a priority is properly understood as a property of sentential characters while necessity is a property of sentential characters.14
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In addition to the two semantic dimensions of meaning/extension and sentential characters/sentential contents, the externalist challenge necessitates distinguishing another semantic element—that is, the reference determiner. For the externalist challenge challenges precisely any traditional, Golden Age conception of the relations between meanings and extensions. It seems evident that, at least in certain cases, there are mechanisms of reference determination at work which bear little in the way of constitutive connections to the meaning (i.e., to that which needs to be grasped in order to be counted as competent with the relevant linguistic expressions).
The paradigm cases for motivating this distinction between meaning and reference determiner are natural kind terms (e.g., ‘aluminum,’ ‘elm’), particularly in their deferential uses by non-expert speakers. Here it seems that what counts as understanding the meaning falls well short of the ability to decisively delineate the extension. (You don’t need to be able to expertly distinguish elms or aluminum from similar things, in order to be counted as competent with the terms.) Similar points also seem to apply to proper names (e.g., ‘Aristotle,’ ‘Feynman’).
These considerations dovetail with certain lessons learned in the semantics of modality—specifically, when it comes to differences in extension, while meaning is held constant, across contexts of evaluation. Distinctions between meaning, extension, and reference determiner, and their impact on a priority and related notions, will pop up again in §3.2, and will be relevant to various points in Part III.
§2.4: interim overview
We have reached a plateau now, a base camp from which it is worthwhile to stop and look ahead at the climb ahead of us, reflecting on and integrating what we have taken on board in the course of our journey so far.
Our goal is to show that a constitutive a priori orientation can address the challenge of revisability and the externalist challenge, and yield a non-obscure but adequate and comprehensive epistemology. This is an understanding-based, rather than acquaintance-based, approach to the a priori; whether it should be thought of as a variety of moderate rationalism or of moderate empiricism remains to be seen. Many pertinent details are yet to be worked out; the preliminary work executed in this present chapter will prove useful toward those ends.
Next, to draw out some ongoing morals. To ask whether something is necessary is to ask of a proposition whether it could be (or could have been) false, if contingent matters had gone otherwise. For example, provided that there could not possibly be fire without the presence of oxygen, then it is a necessary truth that fire requires oxygen. It is by now a familiar, Kripkean point that (given a minimal dose of realism) metaphysical necessity has nothing to do with anyone’s knowledge of anything. Many consequences of this point will be further unpacked throughout; but now, to begin, here are two important ones.
One corollary worth underlining is that necessity may well be steadfastly indifferent to the challenge of revisability. That which is necessary is not revisable, for it is precisely the things which are most firmly bolted down that that concept is tailored to single out. (Of course, any particular agent’s, or community’s, guesses as to what is necessary may be revised over time, as a function of new evidence, insight, etc.; but that nowhere near entails that the truth-conditions of ‘It is necessary that P’ change over time. Necessity is the hardest of steel.) This is perhaps the central, deep important difference between necessity on the one hand and analyticity and a priority on the other hand—on the kind of understanding-based, constitutive a priori orientation developing here. Meanings can evolve, and what is taken to be self-evident varies widely across agents and communities; but metaphysical necessities are mind- and language-independent matters, steadfastly indifferent to what anyone thinks or says about them.
Secondly, and relatedly, metaphysical necessity is unlike the semantic and epistemic modalities in being in a certain sense vehicle-indifferent. That is, the semantic or epistemic modal status of a given proposition might be sensitive to certain features of the sentences which express it; but this seems to be decidedly less so for the question of necessity. (In other words, sentential contents matter for questions of necessity; and here sentential characters seem to be relatively unimportant. While, in contrast, not only sentential contents but also sentential characters are crucial to questions of analyticity and a priority.) Consider the following pairs:
1a. I am here now.
1b. Arthur is in the A.C. Hunter library at noon on October 18, 2017.
2a. Water contains hydrogen.
2b. H2O contains hydrogen.
3a. All cordates are renates.
3b. All cordates are cordates.
It is controversial exactly how we ought to understand the precise content of the propositions expressed (in these cases as of many others), and it is beyond the scope of this present work to try to conclusively settle such debates within the philosophy of language. However, all that this present point requires is that it is possible that (at least some of) those pairs express the same sentential content but differ with respect to the questions of analyticity or a priority. Most importantly: given that they agree in truth-condition, then either member of each pair is necessary iff both are; but, on the constitutive a priori orientation, no analogous point holds of their status with respect to analyticity or a priority.
So, in this sense, necessity is, while analyticity and a priority are not, vehicle-indifferent. The above pairs of sentences are alike in metaphysical modal status. It is extensions, as opposed to meanings—that is, what the statement is about, as opposed to the way in which it characterizes or determines its extensions—which are crucial, when it comes to metaphysical modality. If a proposition is necessary, then it is so regardless of how it is characterized or expressed. In contrast, in the semantic and epistemic cases, the guises of different sentences can make a difference (even if they still might express the very same proposition).
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Of our three focal notions, analyticity is the least vehicle-indifferent. Even the most slight and subtle difference of sentential character can be relevant here. In particular, in Part IV I will argue that [1a] is analytic while [1b] is not (even though both are true, and their content [in context] are at the very least closely related [if not identical]):
1a. I am here now.
1b. Arthur is in the A.C. Hunter library at noon on October 18, 2017.
As we will see, analogous claims could be defended for several other similar pairs.
To ask whether something is analytic is to ask: Does the meaning of the constituent bits, plus the mode of composition, suffice to ensure that the statement expresses a truth? Alternatively, is the denial of this contradictory? (Could a grandmother be childless? Or a bachelor married?) This is—in part, but centrally—a question about vehicles. One of the levels which it is so important to distinguish, when it comes to questions about analyticity (i.e., the conventional links between a sentence S and the proposition P it is used to express, on the one hand, and the truth-conditions of P, on the other hand) precisely concerns the linguistic vehicle of the expression.
Finally, to ask whether something is knowable a priori is to ask whether one is justified non-empirically in judging it to be true. First and foremost, a priority is a property of the justification for a belief. Can this be known to be true without experience of what it is about? (For example, Could one steal one’s own property?) Can this be known independently of any sensory experience? (For example, Could something think but not exist?)
Here the vehicle is not so clearly the issue, as in the case of analyticity, but it is still definitely relevant. [1a] (i.e., ‘I am here now’) is a relatively strong candidate for a priority, but it is far from obvious that [1b] (i.e., that I am at this—or indeed any—specific location at this—or any—specific time) should be so-classified. The epistemic status of a proposition seems to be relative to not just its intrinsic, truth-conditional content, but also to the guise or specific way in which the proposition is expressed. Hence, epistemic modality is also vehicle-relative; sentential characters clearly matter here too. (Relatedly, and as the externalist challenge drives home, as agents who fall decidedly short of omnipotence and infallibility, it is arguable that we could fail to recognize that what two distinct statements express is truth-conditionally identical. This will be further unpacked below in Parts III-IV; cf. especially §§6.4–5.)
[§]
So, then, on this framework-relative, understanding-based, constitutive a priori view, when it comes to both the issue of revisability, as well as the issue of vehicle-indifference, we have a clear split between metaphysical modality on the one hand and the semantic and epistemic cases on the other hand.
Whereas metaphysical modalities solely concerns extensions, truth-conditions, sentential contents, the semantic and epistemic cases also and essentially concern the dimension of meaning, characters, and the frameworks of meaning which are involved in understanding and communication. This is the root of some core differences, when it comes to revisability and vehicle-dependence, since our frameworks are themselves constantly subject to revision in light of new evidence and unforeseen connections, and concepts themselves (in addition to linguistic conventions pairing them with sounds and/or marks) are subject to a certain distinctive sort of evolution. (For example, what humans have believed about aluminum and metals has changed over time, and it is plausible that the meanings of the terms ‘aluminum’ and ‘metal’ have also evolved, but aluminum itself has remained constant and unconcerned throughout this ongoing process. If it is necessary that aluminum is a metal, this did not become the case as a result of any discovery or conceptual evolution.)
A further important aspect of this situation, also to be developed in depth below, concerns the constitutive ties between the semantic and epistemic cases—that is, between analyticity and a priority. One way into these ties is to consider the relation between what we have been calling ‘semantic intuition’ and ‘rational intuition.’ Though both alleged phenomena are controversial, and both terms are variously employed, there is some reason to think that the terms ultimately target the same underlying thing: that is, understanding of concepts grounding the justification of beliefs. At a minimum, more conservatively, one might hold that semantic intuition is a sub-part of rational intuition; semantic competence is always and essentially a part of a priori justification. Ultimately, our beliefs are constituted by our meanings. The root of the close links between analyticity and a priority lies in the fact that the (epistemic) frameworks which are constitutive of our beliefs are themselves constituted by (semantic) meanings.
These deep, constitutive links between semantic and epistemic immunity to counterexample will amount to some strong reasons to think that all analytic truths are knowable a priori (though not necessarily the converse). Prior to explicitly addressing such questions in Part IV, much more ground needs to be excavated, when it comes to developing the relevant notion of a framework, and related conceptions of understanding-based accounts of the semantic and epistemic modalities.
NOTES
1. See chapters 5 & 6 of Grayling (1997) for extensive discussion of the comparative strengths and weaknesses of various theories of truth. I am not claiming that there are no outstanding technical questions for deflationists (e.g., semantic paradoxes), but they are outside the scope of this present work.
2. There is a related discussion of what Coffa (1991: 9) calls the ‘chemical theory’ of concepts, as it pertains to analytic truth, below in §3.2.
3. Cf., for example, Soames (2002: Ch’s 9–11) for extensive discussion.
4. There is discussion of this distinction in §3.1, and it crops up again in §7.3.
5. Of course, it is perfectly intelligible, and sometimes quite significant, to counterfactually vary linguistic conventions—for example, suppose ‘arthritis’ meant something distinct from what it actually does (cf. Burge [1979]). The present point is just that this latter sort of thought experiment is quite different from the kind of modal inquiry in which our interest is in the expression’s extension—for example, might water have turned out to be composed of XYZ? In these latter cases, it is crucial to hold fixed the meaning of ‘water’.
6. Boghossian calls this a metaphysical conception of analyticity, as opposed to a distinct epistemic conception. There is much more on this issue in §3.2.
7. The exception to this is indexicality (i.e., words like ‘this’ or ‘today’, whose extension changes from use to use, while their meaning nonetheless stays constant), which will be discussed in some depth immediately below.
8. Cf. Loewer (1997) for a good general accounts of this dialectical situation.
9. There are various other important complications to the Golden Age conception of the relation between context-independent meanings and propositions expressed in context—such as context-sensitivity and semantic underdetermination. Indexicality and modality are the most important for our purposes, for reasons to be detailed below, and in any case are sufficient to develop the main departures from the Golden Age. For more on context-sensitivity, cf. Searle (1978), Recanati (2004), and for a discussion of semantic underdetermination cf. Bach (2005).
10. Cf. Stanley (2007) for development of a view generally classified as ‘indexicalism’, which takes indexicality to be a pervasive norm and not a circumscribed, distinctive sub-case.
11. Here see Kaplan (1989: 539): ‘The bearers of logical truth and of contingency are different entities. It is the character … that is logically true [in cases such as “I am here now”], producing a true content in every context. But it is the content … that is contingent or necessary.’
12. See Sullivan (2015a) for an overview.
13. Here I am in broad agreement with Schiffer (2003), Bach (2005), Neale (2007).
14. Cf. note 11, or consider Donnellan’s (1983) talk of the a priori/a posteriori distinction only applying to a proposition through the guise of the various sentences which can (in context) express it.