§7.1: Two maps of the terrain
The aims of this final chapter are, first, to summarize the constitutive a priori orientation as an answer to Plato’s problem, and, second, to consolidate and extend some main points about the nexus at which epistemology overlaps with both the philosophy of language and the metaphysics of modality.
At a bit more length: this chapter is structured around two related maps. The first map will be developed in §§7.2–4. It concerns the following table, which charts eight possible permutations of the three key notions of immunity to counterexample—necessity, analyticity, and a priority.
Table 7.1
That is, for example, row #3 represents the circumstance that something might be metaphysically necessary and knowable a priori, and yet fail to be analytically true; row #5 represents the circumstance that something could be analytic and a priori, and yet fail to be necessary; and so on.
Rows #1 and #8 should be the least controversial, and the most familiar, roughly corresponding to Hume’s ‘Relations of Ideas’ and ‘Matters of Fact,’ respectively. (Or, if you like, Plato’s Parmenidean side and Plato’s Heraclitean side, respectively.) The strongest candidates for row 1 would include fundamental truths of mathematics and logic, such as [1] and [2]:
1. No proposition is at once both true and not true.
2. Two is a factor of every even number.
Again, even these are not completely unanimous, as paraconsistent logics reject [1], and certain varieties of constructivism may balk at the claim that there is anything metaphysically necessary about [2]. Still, the claim that these belong in row 1 is rather orthodox, probably as close as one can get to unanimity in philosophy. For present purposes, I am content with the qualified claim that these are the strongest candidates, and orthodox picks, for row 1, and avoid the arguments and counterarguments on this point.1 As for row 8, candidates are mundane and ubiquitous—for example, ‘There are ten provinces in Canada,’ ‘Jupiter has more moons than Neptune,’ etc.
What, then, of the other six rows? The controversies over those regions, as they look through the lens of a constitutive a priori orientation, will occupy us for the next three sections.
These issues will be approached down a slightly different avenue in §7.5. Here the discussion will be structured around evaluating the following six conditionals:
1. N→A
2. N→AP
3. A→N
4. A→AP
5. AP→N
6. AP→A
That is, to endorse [1] is to hold that that all metaphysical necessities are analytic truths; to endorse [6] is to assert that everything knowable a priori is analytically true; and so on. The aim of this part of our investigation is to consolidate what has been learned about the plausibility of any such conditionals, especially in the wake of Quine’s challenge of revisability and Kripke’s externalist challenge.
Finally, §7.6 will consist of summarizing our results, drawing out some generalizations, and looking back over some of the perennial themes which have woven through the book.
§7.2: can analyticity vary independently?
Getting back to our first map, then:
Table 7.2
Perhaps the least likely contenders on the table are the rows which allow analyticity to vary independently—that is, 3 [N+, A-, AP+] and 6 [N-, A+, AP-]. Could there be an analytic truth that is neither necessary nor knowable a priori? In the other direction, could something be necessarily true and knowable a priori, and yet fail to be an analytic truth?
Let us take row 6 first. The very idea of an analytic truth that is neither knowable a priori nor necessary seems jarring, to say the least—perhaps, again, due to the distinctive geography of the semantic, constituting as it does a bridge between mind and world. Analyticity, it seems, cannot stand on its own, but rather needs to be co-instanced with (and further, perhaps, grounded in) at least one of the requisite metaphysical furniture or the requisite epistemic relations. To deny that row 6 has any denizens is to assert the following conditional:
[A→ AP v N] If something is an analytic truth, then it is either knowable a priori or necessarily true.
I can think of no counterexamples to this, nor of any philosopher who has even implicitly transgressed this conditional.
In contrast, row 3 [N+, A-, AP+] does have some historical precedent. In particular, (given Kant’s presumption that necessity is a criterion for a priority) Kant’s putative synthetic a priori judgments might be thought to belong in row 3. If so, then the fate of row 3 may be tied to some rather huge issues, within (and well beyond) epistemology. (For example, as cited in §1.4 above, both BonJour [1998] and Aune [2008] hold that the fate of rationalism itself rests on the coherence of the synthetic a priori.)
However, among the major problems to be ironed out before we should concede that certain Kantian candidates belong in row 3 is that Kant gives no firm and comprehensive criterion for analyticity.2 Further, I believe that many of Kant’s specific candidates for synthetic a priori status have been more or less conclusively refuted. (I have in mind here especially the mathematical and logical examples, falling prey to the careful distinctions and counterarguments of especially Frege.) To be sure, the same cannot be said of all of Kant’s candidates, such as the following:
1. Every event has a cause.
(Assume for present purposes that [1] is true, and is known to be true.3) In my view, this is among the most plausible candidates for synthetic a priori status. It seems at once not obviously constitutive of the concept ‘event’—that is, an uncaused event would hardly be a contradiction, as would, say, a five-sided square—and hence it is synthetic; while at the same time there is some inclination to hold that one’s grounds for believing [1] are non-empirical. (It feels more solid than a typical black-swannable inductive generalization.)
However, I take the decisive problem at this juncture to be Kant’s presumption that necessity is a criterion for a priority. That is, the inclination to count [1] as a priori stems, in large measure, from the intuition of its necessity. If [1] is true, then there are grounds to deny that it could be so by contingent happenstance. It is plausible to think that, if it is true, what makes it true must be some deep, fixed, basic features of objective mind-independent reality. So, Kripke’s (1971, 1972) guiding intuition of the form ‘IF P is true, then it is necessarily true,’ which plays a key role in motivating the notion of the necessary a posteriori, seems applicable to [1].4 Given that, and since reasons have subsequently emerged to doubt that necessity is a criterion for a priority, Kant’s case for the a priority of [1] is considerably weakened.
My own view is that [1] is, if true, a Kripkean necessary a posteriori. Justification is not merely non-empirical, in such a case, and so it belongs in row 4 [N+, A-, AP-], not in row 3 [N+, A-, AP+]. (These claims will be bolstered in the next section.)
The reasons to doubt Kant’s presumption that necessity is a criterion for a priority leave us without a positive reason to populate row 3, now conjoined with a standing inclination to hold that analyticity cannot fall on its own, any more than it can stand on its own. If, accordingly, we close off row 3, then we assert the following conditional:
[AP & N→A] If something is both knowable a priori and necessary, then it is an analytic truth.
If both the requisite metaphysical furniture and the requisite epistemic relations are in place, then the relevant semantic relation is bound to be instanced. (See note 7 below for potential qualification.)
To take stock: Rows 1 and 8 are the least problematic, while rows 3 and 6 are quite problematic. That leaves rows 2, 4, 5, and 7 as open questions.
Table 7.3
I will divide up these four remaining open rows into the Kripke cases (i.e., rows 2 & 4) and the indexical cases (i.e., rows 5 & 7).
§7.3: the Kripke cases
By ‘the Kripke cases’ I mean certain varieties of what Kripke (1971, 1972) argued should be understood as necessarily true but nonetheless only knowable a posteriori. Key here are the cases in which it is plausible to hold that the essence of a natural phenomenon has been scientifically discovered. Candidates include:
2. Heat is the motion of molecules.
3. Gold is the element with atomic number 79.
On the one hand, it is arguable that these are necessary truths, in that any possible phenomenon which satisfies the subject also and thereby satisfies the predicate, and vice versa. On the other hand, these can only be known a posteriori—armchair reflection on the subject-concepts will not suffice; but, rather, lots of empirical evidence is required.
Now, to be sure, there have been considerable objections to Kripke’s arguments, which I will not try to comprehensively address here.5 (To cite just one example, the argument in favor of their necessity relies on a premise of the form ‘IF P is true, then it is necessarily true’; that premise is surely a priori, which may go some way to undermine the intuition that this should be counted as a posteriori knowledge.) Further, many of Kripke’s putative candidates are more controversial than [2]–[3].6 Nonetheless, to the extent that: (i) one of the goals of scientific inquiry is to discover the essences of natural phenomena, and (ii) scientific findings are, by and large, a posteriori, then there can be overlap between the categories of necessary truth and a posteriori knowledge. I take [2] and [3] to be fairly uncontentious cases, which are enough to show that at least one of either rows 2 or 4 is occupied.
So, then, do these cases belong in row 2 or 4? That is, are these necessary a posteriori truths analytic or synthetic? As ‘analyticity’ is defined above, [2] and [3] are clearly not analytic, because to judge them false may be mistaken, but is surely not a contradiction. (Heat without molecular agitation would be a significant and surprising discovery, but would be nothing along the lines of the discovery of a five-sided square!) Alternatively, one could be competent with their subject-terms without having any opinion as to the truth of [2] or [3], and so they are not true in virtue of the meanings of their constituent terms. So, [2]–[3] belong in row 4 [N+, A-, AP-]. In other words, the relevant extensions may stand in necessary relations; but, given the degree of deference appropriate to the use of a natural kind term, there is no transparent analytic or a priori access to their so-standing. (Again, though, as discussed in Part III, such cases might become analytic necessities, as a function of conceptual evolution. But they would thereby also become knowable a priori, and hence row 1 cases. Migration from row 4 to row 1 is possible, and may well happen over a few generations for a case like ‘Whales are mammals’.)
Row 2 [N+, A+, AP-], it seems, is bound to end up empty. It is, to say the least, hard to see how something could be both necessary (i.e., could not fail to be) and analytic (i.e., roughly, true in virtue of meaning) but not knowable a priori (i.e., roughly, justified non-empirically); and I cannot think of much in the way of plausible counterexamples nor historical precedent to the contrary.7 So, then, here is where the investigation of the Kripke cases leaves us:
Table 7.4
§7.4: the indexical cases
Now to what I am calling ‘the indexical cases’—that is, certain putative candidates for rows 5 and 7. While denizens of this terrain have played important roles in philosophy since at least Descartes (1641), it is arguable that there were no sophisticated maps of this area until the 1960s and 70s. During that period, there occurred the development of multi-dimensional logics in which the effects of the context of utterance on content semantically expressed can be neatly distinguished from the effects of the context of evaluation on whether that content is true or false.8 For example, consider the exact sense in which the following is immune to counterexample:
6. I am here now.
Following Kaplan (1989), among others, it is not acceptable to count this as a necessary truth. For any utterance of [6], the indexicals are saturated by relevant aspects of the context of utterance, and the content expressed is constitutively tied to a specific individual, place, and time (e.g., Arthur is in his kitchen at 7:00 am). Clearly, that expressed content (or any similarly specific expressed content) is contingent, for had accidents gone otherwise I could have been in my car or on a plane at that instant. At the same time, though, [6] is a good candidate for both analyticity and a priority. It is a good candidate for analyticity because it is precisely the semantic contents of its constituent bits that ensure that what it expresses is, even though contingent, nonetheless guaranteed to be actually true. It is a good candidate for a priority because the kind of justification one would give for one’s confidence that an utterance of [6] expresses a truth would not be empirical. (I would hardly have to investigate as to exactly where I was, before I felt justified in believing that [6] expresses a truth.) So, row 5 it is. [6], among some other cases,9 is [N-, A+, AP+]:
Table 7.5
[§]
The last remaining open question, as to the fate of row 7, turns on how strictly we construe the term ‘experience’ in defining a priori knowledge. (Recall that these matters were delved into, in considerable depth, in §4.2 above.) Is the relevant sense of ‘experience’ limited to sensory perception, or ought non-sensory introspection to also count as experience? How one approaches that question will determine whether ‘I exist,’ or ‘I am conscious,’ or perhaps even ‘I am hungry,’ will turn out to be justifiable a priori. They are independent of perceptual experience, to be sure, but hardly independent of experience tout court, in every philosophically interesting sense of the term.
I will not get into the matter of trying to adjudicate which of these options has in its favor the greatest philosophical precedent. (To a large extent, the exciting action has not been focused on this question, due to such factors as: (i) insofar as perceptual beliefs are the paradigm for the a posteriori case, the question of whether there can be non-perceptual a posteriori beliefs does not arise, and (ii) insofar as, over a broad range of paradigm cases, the a priori/a posteriori distinction lines up neatly with the distinction between beliefs whose content is general [or universal, or necessary] and beliefs whose content is singular [or local, or contingent], the question of whether there can be a priori but singular [local, contingent] beliefs does not arise.) Instead, I will first describe the fate of row 7 [N-, A-, AP+] on a narrow construal of ‘experience,’ and then describe the situation on a broad construal of ‘experience.’
First, if we construe ‘experience’ narrowly, such that only perceptual experience counts, then a belief is justified a priori iff its justification is independent of perceptual experience. Second, if we go with a broader sense of ‘experience,’ then something is justified a priori iff its justification is independent of experience tout court. I will call the first, narrow sense ‘APn,’ and the second, broad sense ‘APb.’ Thus, the likes of ‘I exist,’ ‘I am conscious,’ and perhaps even ‘I am hungry,’ count as APn but not APb.
For the case of APn, then, there are some fairly plausible candidates for row 7 [N-, A-, AP+], such as:
7. I am conscious.
[7] is clearly not a necessary truth. Yet it is APn, for its justification is not constitutively tied to sensory evidence—for I could be justified in believing [7] while not receiving, or attending to, any perceptual inputs. However, unlike [6], it is not analytically true. The analyticity of [6] rests on the point that the meaning of ‘I’ plus the meaning of ‘am’ plus the meaning of ‘here’ plus the meaning of ‘now’ suffice to ensure that a truth is expressed. No such point holds for the case of [7]. (I am, if you like, semantically guaranteed to be here now, but not semantically guaranteed to be conscious.) So, for the case of APn, the table looks as follows.
Table 7.6
Here we have some Cartesian comfort for Kantians—that is, a sense in which there is synthetic a priori knowledge. (Cold comfort it is, though, because the link to necessity has been severed. Kantians would presumably say that it is just not the same.)
[§]
Turning now to the case of APb, it seems that the above sorts of case cannot arise. In this case, [7], along with ‘I exist,’ ‘I am hungry,’ etc. will come out as a posteriori, because the justification for such cases does constitutively depend on some relevant senses of ‘experience’ (even if it is independent of current perceptual experience). That is, the explanation for why [7] is immune to counterexample, say, ineliminably involves an appeal to subjective qualitative feel, to the characters or qualities of experiences (which need not be perceptual). This broad construal of experience yields a more symmetrical table.
Table 7.7
APb, then, entails at least one of analyticity or necessity, while APn, in contrast, can stand on its own (e.g., ‘I am conscious’ is APn but not analytic). Thus, conjoining that point with earlier results, we get a biconditional between analyticity and APb:
but only a conditional between analyticity and APn:
Neither construal of a priority, though, is conditionally linked to necessity.
Whether you want to call that a consequence of Kant’s (1781) status-orientation on a priority, or of Kripke’s (1972) clear distinction between satisfying the conditions for a priority and for necessity (or both, perhaps among other things [e.g., Poincare, Reichenbach, Wittgenstein, Carnap, etc., might also be cited as having provided key pieces of this puzzle]), on the constitutivist picture there is no immediate inference back or forth between necessity and a priority.
§7.5: consolidating the entailment relations
An alternative map of this same terrain, on a constitutive a priori view, will result from evaluating these six conditionals:
1. N→A
2. N→AP
3. A→N
4. A→AP
5. AP→N
6. AP→A
It is an important legacy of mid-twentieth-century philosophy—starting with the development of rigorous semantics for modal logics in the 1950s, and gaining strength with the detection of fallacies and confusions in several varieties of argument against the coherence of metaphysical necessity10—that [1] and [2] are not terribly plausible. Given even a rather minimal degree of metaphysical realism, it becomes awfully difficult to conclusively establish that something is a necessary truth, and no epistemic or semantic conclusions are directly entailed by the claim that something is a necessary truth. (Again, this point is driven home most starkly by the externalist challenge, especially as it pertains to natural kind terms.) Metaphysical necessity lies beyond the control of thought or language. And so we are down to at most four conditionals:
1. N→A
2. N→AP
3. A→N
4. A→AP
5. AP→N
6. AP→A
It seems that [3] and [5] are also off the table. What I above refer to as ‘the indexical cases’ show that something can satisfy either the definition of ‘a priori’ (i.e., roughly, justifiable non-empirically) or of ‘analytic’ (i.e., roughly, true in virtue of meaning) without satisfying the definition of ‘necessary’ (i.e., roughly, could not possibly fail to be). This leaves us with at most two conditionals:
1. N→A
2. N→AP
3. A→N
4. A→AP
5. AP→N
6. AP→A
On an understanding-based orientation, [4] is the most firmly grounded of the six possible conditionals. Semantic intuition provides justification for at least a broad sub-class of what traditional rationalists have wanted out of rational intuition. All analytic truths are knowable a priori. Note well, though, that it is a conditional—that is, it has not really been a direct aim of the present work to conclusively counter all of the arguments against the intelligibility of the notion of analytic truth.11 Nonetheless, if there is such a thing as analytic truth, the present considerations suggest that it will play an important role in any adequate map of the a priori.
As for the fate of [6], see the close of the last section—that depends on whether one takes the relevant notion of a priority to be APb or APn. APb entails analyticity, but APn can stand on its own.
§7.6: immunity to counterexample and Plato’s problem
A point of departure for this inquiry is the intuition that one central thing that the concepts of necessity, analyticity, and a priority have in common—and which, to a large extent, accounts for why they are of such deep and enduring philosophical interest—is that all are tightly linked, in some way or other, to what we might call immunity to counterexample. Throughout, we have distinguished between three different types of immunity to counterexample—one metaphysical, one semantic, and one epistemic. A proposition may be necessarily immune to counterexample in virtue of the nature of the mind-independent facts of the matter (e.g., no two solid objects can simultaneously occupy the same spatial location); a statement may be analytically immune to counterexample in virtue of the meanings of its constituent parts and the way in which they are arranged (e.g., no grandmothers are childless); a piece of knowledge may be a priori immune to counterexample in virtue of one’s justification for believing it being independent of experience (e.g., one cannot steal one’s own property).
The externalist challenge shows up a potential wedge between meaning and extension (at least for certain sorts of cases—especially natural kind terms in their typical deferential use by non-experts); relatedly, there is a gap between metaphysical necessity on the one hand, and the semantic and epistemic modalities on the other. The counterexamples to the traditional semantic internalist idea that meaning determines extension run parallel to the related point, on a different level, that no semantic or epistemic conclusions follow per se from the claim that a certain proposition is necessary.
It is also quite closely related that the challenge of revisability turns out to not apply to metaphysical modality, but to prompt important revisions to the semantic and epistemic cases.12 The notion of the framework-relative constitutive a priori promises to be a good way to absorb the shocks to the modal world-order prompted by these two challenges, and to afford an adequate and non-obscure answer to Plato’s perennial question about the contents of our knowledge outstripping the limits of our particular experiences.
As there exist deep constitutive links between the epistemic and semantic cases (between our beliefs and the meanings of which they are composed), similar points will also apply to the notion of analytic truth. Analyticity is also a framework-relative notion, and hence subject to revision over time in cases of conceptual evolution. Nonetheless, there remains on this stance a clear and substantive sense in which the status of a priority, and the property of analyticity, constitute a kind of immunity to counterexample. The meaning-to-extension links, and hence [UJ] connections, are still evident in a broad range of cases.
However, conceivability does not entail possibility, on this constitutive a priori orientation, because of the deep fissure separating the semantic and epistemic modalities, on the one hand, from metaphysical modality, on the other. Conceivability is a main source of evidence for possibility, but it can founder on coldly indifferent metaphysical rocks. Judgments of conceivability tell us about frameworks of meaning, not about extensions.
Necessity, analyticity, and a priority are one and all indispensable elements of the philosophers’ toolkit. Some crucial differences between then which have emerged are key defining features of this constitutive a priori view.
[§]
Next then to a quick recap and summary. We have distinguished, in the course of our investigation, two distinct types of metaphysical necessity. There is the row 1 type (i.e., N+, A+, AP+), and the row 4 type (i.e., N+, A-, AP-). And note again that there seems to be some possibility for gradual migration from row 4 to row 1, in certain kinds of cases of conceptual evolution. For example, ‘whales are mammals’ was initially a row 4 case, and remained such for generations after its discovery. However, it may well become a row 1 case, provided that we reach a point at which we would want to say that anyone who doubts whether whales are mammals thereby does not share our concept of ‘whale.’ (Certainly, ‘cats are animals’ feels solidly row 1 to me—even if it is conceivable that cats turn out to be Martian spies, that doesn’t make it possible! And so presumably ‘whales are mammals’ could get there. Both contrast with ‘Water is H2O,’ which is a less plausible candidate for migration to row 4 because of its relative technicality.)
We have also distinguished two sub-varieties of analytic truth. In addition to the row 1 cases, there are also the row 5 cases (i.e., N-, A+, AP+). On this front, developments in the semantics of indexicality have shown that strong modal status on the semantic (and epistemic) front does not entail metaphysical immunity to counterexample. Significantly, on this understanding-based, constitutive a priori orientation, all analytic truths are knowable a priori. (Anything guaranteed by semantic intuition is already sufficiently well-grounded, before we need to get into difficult questions about rational intuition.)
Given the complexities attendant upon the different senses of ‘experience’ which might be pertinent to fleshing out ‘independent from experience,’ detailed above in §§5.2 and 7.4, a priority is the most complex case of the three for registering simple generalizations. There are, again, row 1 a priorities (i.e., N+, A+, AP+), as well as row 5 a priorities (i.e., N-, A+, AP+). Further, if we construe ‘experience’ narrowly, then there will also be row 7 a priorities (i.e., N-, A-, APn+)—such as ‘I exist’ or ‘I am conscious.’
As for the great Kant, the constitutive a priori orientation is in many deep ways indebted to his work. Kant offers one of the most original, insightful, and seminal answers to Plato’s problem in the history of Western philosophy. However, many reasons for departing from the letter of Kant’s doctrines have been detailed herein. My two principle objections to Kant’s synthetic a priori are: (i) Kant’s account of the analytic/synthetic distinction is deeply flawed, and (ii) that Kant’s presumption that necessity is a criterion for a priorityis not warranted. As the discussion of the ‘Every event has a cause’ case in §7.2 illustrates, many of Kant’s putative synthetic a priori cases survive in this present map as Kripkean necessary a posteriori row 4 cases (i.e., N+, A-, AP-). Once we absorb the shocks to the modal world-order in the latter half of the twentieth century, that seems to be a more appropriate classification for the informative discoveries which Kant placed at the center of his philosophy.
[§]
I come next to some remarks in response to a claim made by both BonJour (1998) and Aune (2008), cited above—that is, that the fate of rationalism itself rests on the coherence of the synthetic a priori. I am initially inclined to disagree with this claim, on the grounds that the fate of rationalism rests more squarely on whether there is a priori knowledge. That would be enough to keep rationalists gainfully employed; they do not require the further claim that at least some of that a priori knowledge cannot be, in any sense, analytic. However, still, surely BonJour and Aune are onto something here—if, say, Hume (1748) or Ayer (1936) are right that all a priori knowledge is analytic, then in a fairly clear sense there is no work to be done by rational intuition. And what remains of rationalism, without rational intuition?
Well, one line of response is suggested by the above finding that APn is distinct from analyticity. That is enough to prove that these concepts differ not only intensionally but extensionally, and hence that there can be substantive differences between approaching a claim via the question ‘Is this analytic?’ and approaching it via the claim ‘Is this a priori?’
More deeply, though, while the conjecture that all necessary truths are analytic feels more like an attempt to explain away, rather than to explain, metaphysical modality—at least arguably, embodying a reductive, positivistic meta-philosophy—in contrast, the conjecture that all analytic truths are knowable a priori is a substantive theory of the a priori. It need be no part of this latter view that a priority is an illusion, or that a priority has been systematically mis-categorized (as is, say, the idea that linguistic conventions are the real source of what we mistakenly take to be our intuitions of metaphysical necessity). This is, rather, an attempt to explain or to ground a priority.
So, whereas to appeal exclusively to meanings in answering metaphysical questions is a deeply problematic restriction, in contrast, meanings are integrally engaged with, and largely constitute, the data to be explained by epistemology. Semantics cannot be relied on to do any heavy lifting in metaphysics (given the minimal dose of realism which has been assumed herein), but—given the deep evident constitutive connections among meanings, concepts, beliefs—we cannot get very far in epistemology without engaging with semantics. Here again we return to a point from which we began in the Preface, for which this whole book aspires to serve as testament—namely, that twentieth-century philosophy of language is the site of so many significant steps in the maturation of this ancient discipline. Work by Wittgenstein, Carnap, Quine, Kripke, and Kaplan has been marshalled into an argument that the constitutive a priori provides a strong compelling stance on Plato’s ancient and epochal problem.
NOTES
1. Again, many would also hold that certain moral principles (e.g., one ought to keep one’s promises) are also at once knowable a priori, analytically true, and metaphysically necessary. However, it is fair to say that these latter claims are more controversial than [1] or [2], since they presuppose a degree of metaphysical realism about social and moral phenomena that many philosophers reject.
2. This was extensively discussed in §3.2. For example, Kant’s talk of ‘containment’ in defining analyticity (i.e., a judgment is analytic if the predicate is contained in the subject) seems to presuppose a quite outdated and untenable picture of concepts.
3. It has been objected to me that radiative decay, or events in the quantum void, afford counterexamples to [1], but I am not so sure that they should be conceded.
4. This principle says that, for certain privileged propositions P, if they are true, then they must be necessarily true. As discussed above in §4.3—see especially the quote from Kripke (1972: 159) reproduced there—Kripke argues that this principle holds for cases where essences are scientifically discovered (e.g., ‘Heat is the motion of molecules’, ‘Gold is the element with atomic number 79’). There will be further discussion of such cases when we get to rows 2 & 4 in §7.3 below.
Could [1] be true but contingently so? Whether the laws of nature are in some sense contingent is one of the bones of contention between those who identify physical with metaphysical necessity and those who hold that physical necessities are a proper subset of the metaphysical necessities (cf. §3.1). Not to presuppose anything contentious on that front; the essential point here is just that no metaphysical conclusions follow from the point that there is no contradiction between the concepts of ‘event’ and ‘uncaused’. (The fact that we might be able to conceive of the laws of nature being otherwise than they actually are does not yet show that other non-actual laws are metaphysically possible.)
5. Cf., e.g., Soames (2011), Casullo (2012).
6. For example, Kripke argues that the following are also necessary a posteriori:
4. Hesperus is Phosphorus.
5. Water is H2O.
However, as first came up in chapter 2, the proper semantic analysis of the propositions expressed is quite controversial, and so I am steering clear of such cases.
7. That said, I acknowledge that there are many fine semantic distinctions available on the market, which would yield several distinct senses of the term ‘analytic’ (cf., e.g., Russell [2008]). Perhaps on some such precisification, there may be a sense in which at least some of [1]–[3] should be understood as [N+, A+, AP-]. A direct-reference sort of semantic externalist (e.g., Salmon [1986], Soames [2002]) might even be inclined to try to classify [4] or [5], from note 6, as [N+, A+, AP-]. Hence, row 2 may have some defenders. I take it, though, that even if so, for the reasons given, then they would be a small unorthodox minority. (Some of these possibilities are explored in depth, from a different direction, in Sullivan [2010].)
8. Cf. §2.3. Kaplan (1989) and Stalnaker (2001) are among the seminal sources here; cf. Chalmers (2006) for an overview. Kripke’s (1972) provocative discussions of ‘contingent a priori’ truth are also deeply relevant here; though, akin to note 6, I will avoid such examples as ‘meter’ and ‘Neptune’, as (i) in terms of the big picture, they do not add any challenge that is not already raised by the indexical cases, and (ii) I cannot do these examples any justice without getting into controversial theses within the philosophy of language that are not crucially relevant to the big modal picture. (For discussion of such cases see Soames [2003, Vol.II: Ch. 16].)
9. Other candidates for row 5 include examples involving the ‘actuality’ operator, such as ‘If P is true, then it is actually true’. One classic source of the indexical approach to actuality is Lewis (1970); several variants have been developed.
10. See §3.3, and also Kripke (1972, 41–53; 1980, 15–20), for elaboration.
11. For a variety of arguments for the intelligibility of analyticity, cf. Grice & Strawson (1956), Fine (1994), Boghossian (1997), Katz (1997), Jackson (1998), Sober & Hylton (2000), Gertler (2002), Russell (2008), and Sullivan (2008).
12. Recall from §3.1 that there are some distinctive sorts of relativity, or context-shiftiness, to metaphysical modal claims. The key point is that it is rather distinct from the kind of framework-relativity that both the semantic and epistemic cases instance.