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)

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)

A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified theory of types (...) is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed. (shrink)

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

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 no effective procedure is possible for ascertaining whether a given procedure is effective. This (...) undecidability 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)

This is a non-technical version of "The Decision Problem for Effective Procedures." The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that the effectively calculable functions on natural numbers are exactly the general recursive functions), cannot be proved. However, it is logically provable from the notion of an (...) effective procedure--without reliance on any (partially) mathematical thesis or conjecture concerning effective procedures, such as the Church–Turing thesis--that the class of effective procedures is undecidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. The proof does not appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of such a procedure. Though this undecidability result itself 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 is, in fact, a decision procedure, i.e., effective—for example, that it invariably terminates with the correct verdict. (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. (This article is wholly contained within the author’s more definitive essay, “Singular Concepts”.). (shrink)

An English translation of Pierre Bayle's posthumous last book, Entretiens de Maxime et de Themiste (1707), in which Bayle defends his skeptical position on the problem of the evil. This book is often cited and attacked by G.W. Leibniz in his Theodicy (1710). Over one hundred pages of original philosophical and historical material introduce the translation, providing it with context and establishing the work's importance.

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.

University of California, Santa Barbara.

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)

Four accounts, three of them Kantian, of true sentences of the form “ exists” are contrasted. Russell’s theory that such sentences are meaningless is contrasted with two other Kantian theories that are analogous to one another: Frege’s semantic-ascent theory and the Frege-inspired ungerade (indirect, “oblique”) theory. Frege’s objection to the semantic-ascent account of identity is applied, ironically with equal force, against his account of existence. A second argument favoring the ungerade theory is offered. The argument is then refuted through an (...) application of a general strategy suggested by Kripke. A fourth theory, the deeply anti-Kantian existence-as-predicate theory, fully accommodates these results. (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.

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)

Paradoxes of nested modality, like Chisholm’s paradox, rely on S4 or something stronger as the propositional logic of metaphysical modality. Sarah-Jane Leslie’s objection to the resolution of Chisholm’s paradox by means of rejection of S4 modal logic is investigated. A modal notion of essence congenial to Leslie’s objection is clarified. An argument is presented in support of Leslie’s crucial but unsupported assertion that, on pain of inconsistency, an object’s essence is the same in every possible world. A fallacy in the (...) argument is exposed. Alternative interpretations of Leslie’s objection are provided and are found to involve equivocation between different notions of “essence.” A material artifact’s modal essence, as distinct from its quiddity essence, could have been different than it is. (shrink)

A distinction is drawn among predicates, open sentences (or open formulas), and general terms, including general-term phrases. Attaching a copula, perhaps together with an article, to a general term yields a predicate. Predicates can also be obtained through lambda-abstraction on an open sentence. The issue of designation and semantic content for each type of general expression is investigated. It is argued that the designatum of a general term is a universal, e.g., a kind, whereas the designatum of a predicate is (...) a class (or its characteristic function) and the designatum of an open sentence is a truth-value. Predicates and open sentences are therefore typically non-rigid designators. It is argued further that certain general terms, including phrases, are invariably rigid designators, whereas certain others (general definite descriptions) are typically non-rigid. Suitable semantic contents for predicates, open sentences, and general terms are proposed. Consequences for the thesis of compositionality are drawn. (shrink)

Expressions are synonymous if they have the same semantic content. Complex expressions are synonymously isomorphic in Alonzo Church’s sense if one is obtainable from the other by a sequence of alphabetic changes of bound variables or replacements of component expressions by syntactically simple synonyms. Synonymous isomorphism provides a very strict criterion for synonymy of sentences. Several eminent philosophers of language hold that synonymous isomorphism is not strict enough. These philosophers hold that ‘Greeks prefer Greeks’ and ‘Greeks prefer Hellenes’ express different (...) propositions even if they are synonymously isomorphic. They hold that the very recurrence (multiple occurrence) of ‘Greeks’ contributes to the proposition expressed something that indicates the very recurrence in question. Kit Fine argues that this thesis, which he labels semantic relationism calls for a radically new conception of semantics. I have argued that the relevant phenomenon is wholly pragmatic, entirely non-semantic. Here I supplement the case with a new argument. No cognition without recognition—or almost none. With this observation, standard Millianism has sufficient resources to confront Frege’s puzzle and related problems without injecting pragmatic phenomena where they do not belong. (shrink)

Theoria, Volume 88, Issue 2, Page 434-437, April 2022.

Alonzo Church provided three criteria for “strict synonymy”, i.e., sameness of semantic content: Alternatives (0), (1), and (2)--in order of increasing course-grainedness of content. On (2) expressions are strictly synonymous iff they are logically equivalent. (1) is a significant improvement over (2). On (1) expressions are synonymous iff they are lambda-convertible. Even on (1), assuming the Millian account of proper names, ‘Tully admires Cicero’ is deemed synonymous with ‘Cicero is self-admiring’. On (0) expressions are strictly synonymous iff they are “synonymously (...) isomorphic” in Church’s sense. A fourth alternative, here called ‘(3)’, has been maintained by several philosophers. On (3) expressions are strictly synonymous iff they are co-intensional. In particular, sentences are strictly synonymous iff they are true with resect to the same possible worlds. This criterion’s notion of content is even more course grained than that of (2). Several objections to (3) are considered. (shrink)

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