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 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)

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)

Kripke’s examples of allegedly contingent a priori sentences include ‘Stick S is exactly one meter long’, where the reference of ‘meter’ is fixed by the description ‘the length of stick S’. In response to skepticism concerning apriority Kripke replaced the meter sentence with a more sophisticated variant, arguing that the modified example is more immune to such skepticism. The case for apriority is examined. A distinction is drawn between apriority and a broader notion, “qua-priority,” of a truth whose epistemic justification (...) is dependent on no experience other than that required to justify belief of the deliverances of pure semantics. It is argued that Kripke’s examples are neither a priori nor qua-priori. (shrink)

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

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.

Frege held that the bare demonstrative ‘that’ is incomplete, and that it is the word together with a gesture that serves as the designating expression, and likewise that it is the word ‘yesterday’ together with the time of utterance that designates the relevant day. David Kaplan’s original theory of indexicals holds that Frege’s supplementation thesis is correct about demonstratives but incorrect about ‘yesterday’. Kaplan’s account of demonstratives deviates from Frege’s in treating supplemented demonstratives as directly referential, hence rigid. It is (...) argued here that the gesture or other demonstration that accompanies an utterance of ‘that’ is not part of the designating expression but instead part of the utterance context. (shrink)

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

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.

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)

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)

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)

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)

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.

A detailed interpretation is provided of the ‘Gray's Elegy’ passage in Russell's ‘On Denoting’. The passage is suffciently obscure that its principal lessons have been independently rediscovered. Russell attempts to demonstrate that the thesis that definite descriptions are singular terms is untenable. The thesis demands a distinction be drawn between content and designation, but the attempt to form a proposition directly about the content (as by using an appropriate form of quotation) inevitably results in a proposition about the thing designated (...) instead of the content expressed. In light of this collapse, argues Russell, the thesis that definite descriptions are singular terms must accept that all propositions about a description's content represent it by means of a higher-level descriptive content, so that knowledge of a description's content is always ‘by description’, not ‘by acquaintance’. This, according to Russell, renders our cognitive grip on definite descriptions inexplicable. Separate responses on behalf of Fregeans and Millians are offered. (shrink)

An expanded version of the author’s candid, autobiographical “My Philosophical Education”.

Charles Carlini interviews Nathan Salmón about the philosophical work of his mentor and friend, the late Saul Kripke, one of the foremost philosophers of the 20th Century.

Toward a theory of n-tuples of individuals and concepts as surrogates for Russellian singular propositions and singular concepts. Alonzo Church proposed a powerful and elegant theory of sequences of functions and their arguments as singular-concept surrogates. Church’s account accords with his Alternative (0), the strictest of his three competing criteria for strict synonymy. The currently popular objection to strict criteria like (0) on the basis of the Russell-Myhill paradox is misguided. Russell-Myhill is not a problem specifically for Alternative (0). Rather (...) it is a disproof of unrestricted concept comprehension. Unrestricted comprehension is also inconsistent with facts about sets of properties. It is demonstrated furthermore that the principal rival conception of propositions, as classes of possible worlds, is subject to a fatal philosophical collapse: It follows on that conception, given that each of us is fallible, that everyone believes everything. Although it is far superior to its principal rival conception, Church’s proposed theory is vulnerable under (0) to a version of Russell’s notorious Gray’s /Elegy/ objection. Some amendments to Church’s proposal are proffered that address Russell’s objection, including an amendment first proposed in the present author’s /Frege’s Puzzle/ (1986). Church’s response (personal correspondence) is considered. (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)

A correct observation to the effect that a does not exist, where ‘a’ is a singular term, could be true on any of a variety of grounds. Typically, a true, singular negative existential is true on the unproblematic ground that the subject term ‘a’ designates something that does not presently exist. More interesting philosophically is a singular, negative existential statement in which the subject term ‘a’ designates nothing at all. Both of these contrast sharply with a singular, negative existential in (...) which the subject term is a name from fiction. I argue that such singular, negative existential statements are false. My account of fictional characters differs significantly from Kripke’s. It is shown that an objection to my account rests on a serious misunderstanding. Finally, a crucial aspect of the account is emphasized. (shrink)