The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

Standard compositionality is the doctrine that the semantic content of a compound expression is a function of the semantic contents of the contentful component expressions. In 1954 Hilary Putnam proposed that standard compositionality be replaced by a stricter version according to which even sentences that are synonymously isomorphic (in the sense of Alonzo Church) are not strictly synonymous unless they have the same logical form. On Putnam’s proposal, the semantic content of a compound expression is a function of: (i) the (...) contentful component expressions; and (ii) the expression’s logical form. Kit Fine recently expanded and modified Putnam’s idea into a sweeping theory in philosophy of language and philosophy of mind. The present paper is a detailed critique of Fine’s “semantic relationism.” Fine’s notion of coordination is explained in terms of the familiar pragmatic phenomenon of recognition. A serious error in Fine’s formal disproof of standard Millianism is exposed. It is demonstrated furthermore that Church’s original criticism of Putnam’s proposal can be extended to Fine’s semantic relationism. Finally, it is also demonstrated that the positive position Fine proffers to supplant standard Millianism is in fact exactly equivalent to standard Millianism, so that Fine’s overall position not only does not displace standard Millianism but is in fact inconsistent. (shrink)

A new philosophical analysis is provided of the notorious Sleeping Beauty Problem. It is argued that the correct solution is one-third, but not in the way previous philosophers have typically meant this. A modified version of the Problem demonstrates that neither self-locating information nor amnesia is relevant to the core Problem, which is simply to evaluate the conditional chance of heads given an undated Monday-or-Tuesday awakening. Previous commentators have failed to appreciate the significance of the information that Beauty gains upon (...) waking, and which is relevant to the conditional chance of heads: de re acquaintance with the awakening itself and the non-locating knowledge that it is an experimental awakening. David Lewis and company are committed to several unjustifiable and unacceptable probability assessments. Previous commentators have in effect confused the information that Beauty undergoes this particular experimental awakening for the information that she undergoes some experimental awakening or other. Lewis in particular thereby illegitimately tips the scales both in favor of heads and in favor of Monday. The Sleeping Beauty Problem is equivalent to a ball-in-urn word problem in elementary probability theory. (shrink)

University of California, Santa Barbara.

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that there is no effective procedure for ascertaining whether a given procedure is effective. This (...) result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (shrink)

Although Professor Schiffer and I have many times disagreed, I share his deep and abiding commitment to argument as a primary philosophical tool. Regretting any communication failure that has occurred, I endeavor here to make clearer my earlier reply in “Illogical Belief” to Schiffer’s alleged problem for my version of Millianism.1 I shall be skeletal, however; the interested reader is encouraged to turn to “Illogical Belief” for detail and elaboration. I have argued that to bear a propositional attitude de re (...) is to bear that attitude toward the corresponding singular proposition, no more and no less. If this is right, then according to Millianism every instance of the following modal schema is true. (shrink)

Quine’s criterion of theoretical ontological commitment is subject to a variety of interpretations, all of which save one yield incorrect verdicts. Moreover, the interpretation that yields correct verdicts is not what Quine meant. Instead the intended criterion unfairly imputes ontological commitments to theories that lack those commitments and fails to impute commitments to theories that have them. Insofar as Quine’s criterion is interpreted so that it yields only correct verdicts, it is trivial and of questionable utility. Moreover, the correct criterion (...) invokes analyticity, a notion that Quine spent most of his life tirelessly combating. This yields a dilemma for Quinean philosophy: Either his criterion of ontological commitment is incorrect, or else Quine is committed to a traditional philosophical notion that he emphatically rejected as disreputable. (shrink)

Alonzo Church famously provided three principal competing criteria for “strict synonymy,” i.e., sameness of semantic content. These are his Alternatives (0), (1), and (2)—numbered in order of increasing course-grainedness of content. On Alternative (2), expressions are deemed strictly synonymous iff they are logically equivalent. This criterion seems hopeless as an account of the objects of propositional attitude. On Alternative (1), expressions are deemed synonymous iff they are λ-convertible. Alternative (1) also evidently conflicts with discourse about the attitudes. On Alternative (0), (...) expressions are deemed strictly synonymous iff they are “synonymously isomorphic” in Church’s sense. On Alternative (0), semantic content is so fine-grained that not even “Romeo loves Juliet” and “Juliet is loved by Romeo” qualify as strictly synonymous. A fourth alternative, here called “Alternative (3),” deems expressions strictly synonymous iff they are co-intensional, i.e., they have the same semantic extension with respect to the same possible worlds. This criterion’s notion of content is even more course grained than that of Alternative (2). Several objections to Alternative (3) are considered. (shrink)

We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on which the (...) purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs. (shrink)

A sequel to the author’s book /Frege’s Puzzle/ (1986).

Kit Fine has replied to my criticism of a technical objection he had given to the version of Millianism that I advocate. Fine evidently objects to my use of classical existential instantiation in an object-theoretic rendering of his meta-proof. Fine’s reply appears to involve both an egregious misreading of my criticism and a significant logical error. I argue that my rendering is unimpeachable, that the issue over my use of classical EI is a red herring, and that Fine’s original argument (...) commits the straw-man fallacy. I argue further that contrary to Fine’s gratuitous attribution, what Kripke’s Pierre lacks and a typical bilingual has is not knowledge of a “manifest-making” premise, but the capacity to recognize London when it is differently designated. Fine’s argument refutes a preposterous theory no one advocates while leaving standard Millianism unscathed. The failure of his argument threatens to render Fine’s central notion of “coordination” redundant or empty. (shrink)

In Frege’s Puzzle (1986), Salmon analyzed ‘a withholds believing p’ in terms of a ternary relation BEL of x believing a proposition p under a guise g. The proposed analysis is the following: There is a proposition guise g such that a grasps p by means of g but a does not stand in BEL to p and g. Sean Crawford has made a proposal for Millians to evade propositional guises through second-order belief. Specifically, in effect, Crawford’s proposes to (...) analyze the crucial notion of withheld belief instead as believing that one does not believe: a believes that a does not believe p. Crawford’s clever proposal thus avoids explicit quantification over guises. However, it is shown that the proposal is inadequate to avoid guises. The resulting notion is too weak to capture the relevant notion of withheld belief. (shrink)

In this candid autobiographical essay, Nathan Salmon recounts and assesses the impact of various philosophers and events on his philosophical development.

Nathan Salmon; XII*—How to Measure the Standard Metre, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 193–218.

A puzzle concerning fractional and mixed numbers of things (e.g., two and a half oranges) is examined.

A thorough critique (extracted from the author’s 1979 doctoral dissertation) of Kripke’s purported derivation, in footnote 56 of his philosophical masterpiece /Naming and Necessity/, of nontrivial modal essentialism from the theory of rigid designation.

My title is meant to suggest a continuation of the sort of philosophical investigation into the nature of language and modality undertaken in Rudolf Carnap’s Meaning and Necessity and Saul Kripke’s Naming and Necessity. My topic belongs in a class with meaning and naming. It is demonstratives—that is, expressions like ‘that darn cat’ or the pronoun ‘he’ used deictically. A few philosophers deserve particular credit for advancing our understanding of demonstratives and other indexical words. Though Naming and Necessity is concerned (...) with proper names, not demonstratives, it opened wide a window that had remained mostly shut in Meaning and Necessity but that, thanks largely to Kripke, shall forevermore remain unbarred. Understanding of demonstrative semantics grew by a quantum leap in David Kaplan’s remarkable work, especially in his masterpiece “Demonstratives” together with its companion “Afterthoughts.” In contrast to the direct-reference propensities of these two contemporary figures, Gottlob Frege, with his uncompromisingly thoroughgoing intensionalism, shed important light on the workings of demonstratives in “Der Gedanke”—more specifically, in a few brief but insightful remarks from a single paragraph concerning tense and temporal indexicality. (shrink)

Jeffrey King's principal objection to the direct-reference theory of demonstratives is analyzed and criticized. King has responded with a modified version of his original argument aimed at establishing the weaker conclusion that the direct-reference theory of demonstratives is either incomplete or incorrect. It is argued that this fallback argument also fails.

On Kripke’s intended definition, a term designates an object x rigidly if the term designates x with respect to every possible world in which x exists and does not designate anything else with respect to worlds in which x does not exist. Kripke evidently holds in Naming and Necessity, hereafter N&N (pp. 117–144, passim, and especially at 134, 139–140), that certain general terms – including natural-kind terms like ‘‘water’’ and ‘‘tiger’’, phenomenon terms like ‘‘heat’’ and ‘‘hot’’, and color terms like (...) ‘‘blue’’ – are rigid designators solely as a matter of philosophical semantics (independently of empirical, extra-linguistic facts). As a consequence, Kripke argues, identity statements involving these general terms are like identity statements involving proper names (e.g., ‘‘Clark Kent=Superman’’) in that, solely as a matter of philosophical semantics, they express necessary truths if they are true at all. But whereas it is reasonably clear what it is for a (first-order) singular term to designate, Kripke does not explicitly say what it is for a general term to designate. General terms are standardly treated in modern logic as predicates, usually monadic predicates. There are very forceful reasons – due independently to Church and Godel, and ultimately to Frege – for taking predicates to designate their semantic extensions. But insofar as the extension of the general term ‘‘tiger’’ is the class of actual tigers (or its characteristic function), it is clear that the term does not rigidly designate its extension, since the class of tigers in one possible world may differ from the class of tigers in another. What, then, is it for ‘‘tiger’’ to be rigid? (shrink)

A thesis (“weak BCP”) nearly universally held among philosophers of probability connects the concepts of objective chance and metaphysical modality: Any prospect (outcome) that has a positive chance of obtaining is metaphysically possible—(nearly) equivalently, any metaphysically impossible prospect has zero chance. Particular counterexamples are provided utilizing the monotonicity of chance, one of them related to the four world paradox. Explanations are offered for the persistent feeling that there cannot be chancy metaphysical necessities or chancy metaphysical impossibilities. Chance is objective but (...) contrary to popular opinion it is also largely epistemic. Chancy necessities are analogous to necessary a posteriori truths. Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 644-662, November 2019. (shrink)