Kit Fine (1994. “Essence and Modality”, Philosophical Perspectives 8: 1-16) argues that the standard modal account of essence as de re modality is ‘fundamentally misguided’ (p. 3). We agree with his critique and suggest an alternative counterfactual analysis of essence. As a corollary, our counterfactual account lends support to non-vacuism the thesis that counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are not always vacuously true.
I. Non-Trivial Counterpossibles On Lewis’ account, a subjunctive of the form ‘if it were the case that p, it would be the case that q’ (represented as ‘p → q’) is to be given the following rough meta-linguistic truth-conditions1.
Lewis/Stalnaker semantics has it that all counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are vacuously true. Non-vacuism, by contrast, says the truth-values of counterpossibles are affected by the truth-values of the consequents. Some counterpossibles are true, some false. Williamson objects to non-vacuism. He asks us to consider someone who answered ‘11’ to ‘What is 5 + 7?’ but who mistakenly believes that he answered ‘13’. For the non-vacuist, (1) is false, (2) true: (1) If 5 + 7 were 13, x (...) would have got that sum right (2) If 5 + 7 were 13, x would have got that sum wrong Williamson is not persuaded by the initial intuitiveness of such examples: ... they tend to fall apart when thought through. For example, if 5 + 7 were 13 then 5 + 6 would be 12, and so (by another eleven steps) 0 would be 1, so if the number of right answers I gave were 0, the number of right answers I gave would be 1. (2006) That’s the whole argument—much of it implicit. Alan Baker’s critique (2007) of Brogaard and Salerno (2007) prompts us to say something less abbreviated about a less abbreviated form of Wiliamson’s argument. Then we further develop our (2007) counterfactual analysis of essense. (shrink)
Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another justification (...) derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds. (shrink)
The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to argue (...) against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. The result has also been used to draw more general lessons about the limits of human knowledge. Still others have taken the proof to be fallacious, since it collapses an apparently moderate brand of anti-realism into an obviously implausible and naive idealism. (shrink)
It is widely agreed that contraposition, strengthening the antecedent and hypothetical syllogism fail for subjunctive conditionals. The following putative counter-examples are frequently cited, respectively.
The paradox of knowability threatens to draw a logical equivalence between the believable claim that all truths are knowable and the obviously false claim that all truths are known. In this paper we evaluate prominent proposals for resolving the paradox of knowability. For instance, we argue that Neil Tennant’s restriction strategy, which aims principally to restrict the main quantifier in ‘all truths are knowable’, does not get to the heart of the problem since there are knowability paradoxes that the restriction (...) does nothing to thwart. We argue that Jon Kvanvig’s strategy, which aims to block the paradox by appealing to the special role of quantified epistemic expressions in modal contexts, has grave errors. We offer here a new proposal founded on Kvanvig’s insight that quantified expressions play a special role in modal contexts. On an articulation of this special role provided by Stanley and Szabo, we propose a solution to the knowability paradoxes. Introduction.. (shrink)
Does a factive conception of knowability figure in ordinary use? There is some reason to think so. ‘Knowable’ and related terms such as ‘discoverable’, ‘observable’, and ‘verifiable’ all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn’t say that we were. A’s remarks (...) sound contradictory. In this context the factivity of ‘someone might discover that’ explains this fact. So there is some reason to believe that knowability and related modalities are factive in ordinary use. For factive treatments of knowability in the context of epistemic theories of truth, compare Tennant (2000: 829) and Wright (2001: 59-60, n. 17). (shrink)
In his presidential address to the APA, ‘‘How to be an Anti-realist’’ (1982, 64–66), Alvin Plantinga argues that the only sensible way to be an antirealist is to be a theist.1 Anti-realism (AR) in this context is the epistemic analysis of truth that says, (AR) necessarily, a statement is true if and only if it would be believed by an ideally [or sufficiently] rational agent/community in ideal [or sufficiently good] epistemic circumstances. Plantinga demonstrates, with modest modal resources, that AR entails (...) that necessarily, ideal epistemic circumstances obtain. It is a contingent matter whether ideal epistemic circumstances obtain for worldly agents and communities. Hence, the lesson, according to Plantinga, is that an anti-realist should be a theist. In the present paper we evaluate whether anti-realism entails that necessarily ideal epistemic circumstances obtain. A more careful analysis of Plantinga’s argument appears in section 1. We notice that Plantinga’s interpretation of anti-realism harbors an ambiguity of quantifier scope and that only on the less plausible placement of the quantifiers does AR obviously entail that necessarily ideal epistemic circumstances obtain. In section 2 we evaluate an alternative version of Plantinga’s argument developed by Michael Rea. Rea’s argument gets the quantifiers straight, but depends on logical resources that the anti-realist has independent reason to reject. After evaluating Rea’s argument we conclude that an anti-realist need not be a theist and is not committed to the necessary existence of.. (shrink)
Tr(A) iff ‡K(A) To remedy the error, Dummett’s proposes the following inductive characterization of truth: (i) Tr(A) iff ‡K(A), if A is a basic statement; (ii) Tr(A and B) iff Tr(A) & Tr(B); (iii) Tr(A or B) iff Tr(A) v Tr(B); (iv) Tr(if A, then B) iff (Tr(A) Æ Tr(B)); (v) Tr(it is not the case that A) iff ¬Tr(A), where the logical constant on the right-hand side of each biconditional clause is understood as subject to the laws of intuitionistic (...) logic.2 The only other principle in play in Dummett’s discussion is (+) A iff Tr(A), which, as he notes, the anti-realist is likely to accept. (shrink)
Michael Dummett’s realism debate is a semantic dispute about the kind of truth conditions had by a given class of sentences. According to his semantic realist, the truth conditions are potentially veriﬁcation-transcendent in that they may obtain (or not) despite the fact that we may be forever unable to recognize whether they obtain. According to Dummett’s semantic anti-realist, the truth conditions are of a different sort. Essentially, for the anti-realist, that the truth conditions obtain (whenever they do) is a matter (...) that is always recognizable by us in principle. On this view, truth cannot outrun all possible human knowledge. Unsurprisingly, the outcome of the debate is sometimes said to hinge on whether all truths are knowable.1 More carefully the point of contention is the following.. (shrink)
A primary challenge from the relativist to the contextualist about epistemic modals is to explain eavesdropping data—i.e., why the eavesdropper is inclined to judge the speaker as having uttered an epistemic modal falsehood (when she is so inclined), even though the speaker’s utterance is true according to reasonable contextualist truth conditions. The issue turns in large part on the strength and shape of the data, both of which are in dispute. One complaint is that an eavesdropper’s truth value judgments fluctuate (...) with variations of non- epistemic fact (even after the relevant epistemic/information states are determined). The project here is to strengthen and reframe this complaint in a debate-neutral way, and to show how a sober contextualism can uniformly accommodate it and the standard eavesdropping data. Along the way we reject John Hawthorne’s danger-theoretic explanation of these subtleties. (shrink)
Epistemic modals in consequent place of indicative conditionals give rise to apparent counterexamples to Modus Ponens and Modus Tollens. Familiar assumptions of fa- miliar truth conditional theories of modality facilitate a prima facie explanation—viz., that the target cases harbor epistemic modal equivocations. However, these explana- tions go too far. For they foster other predictions of equivocation in places where in fact there are no equivocations. It is argued here that the key to the solution is to drop the assumption that (...) modal claims are inherently relational (i.e., that they ex- press a logical relation between a prejacent and a premise-set) in favor of a view that treats them as inherently quantificational. In particular it is suggested that modals are mass noun descriptions of information. We demonstrate how this approach unlocks the equivocation problem. (shrink)