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

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)

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)

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)

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 Russellian notion of what it is for a proposition to be “directly about” something in particular is defined. Various strong and weak, and mediate and immediate, Russellian notions of general aboutness are then defined in terms of Russellian direct aboutness. In particular, a proposition is about something iff the proposition is either directly, or strongly indirectly, about that thing. A competing Russellian account, due to Kaplan, is criticized through a distinction between knowledge by description and denoting by description. The (...) epistemological significance of Russellian aboutness is assessed. A Russellian substitute for de re propositional attitude is considered. (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.

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

A new argument is offered which proceeds through epistemic possibility (for all S knows, p), cutting a trail from modality to Millianism, the controversial thesis that the semantic content of a proper name is simply its bearer. New definitions are provided for various epistemic modal notions. A surprising theorem about epistemic necessity is proved. A proposition p can be epistemically necessary for a knowing subject S even though p is /a posteriori/ and S does not know p. The identity relation (...) is well-behaved in metaphysically possible worlds but can go rogue in epistemically possible worlds. Whereas it can be epistemically possible that Lewis Carroll is not Charles Lutwidge Dodgson, this is not epistemically possible in the manner that anti-Millianism requires. (shrink)

This article offers an interpretation of a controversial aspect of Frege’s The Foundations of Arithmetic, the so-called Julius Caesar problem. Frege raises the Caesar problem against proposed purely logical definitions for ‘0’, ‘successor’, and ‘number’, and also against a proposed definition for ‘direction’ as applied to lines in geometry. Dummett and other interpreters have seen in Frege’s criticism a demanding requirement on such definitions, often put by saying that such definitions must provide a criterion of identity of a certain kind. (...) These interpretations are criticized and an alternative interpretation is defended. The Caesar problem is that the proposed definitions fail to well-define ‘number’ and ‘direction’. That is, the proposed definitions, even when taken together with the extra-definitional facts, fail to fix unique semantic extensions for ‘number’ and ‘direction’, and thereby fail to fix unique truth-values for sentences like ‘Caesar is a number’ and ‘England is a direction’. A minor modification of the criticized definitions well-defines ‘0’, ‘successor’ and ‘number’, thereby avoiding the Caesar problem as Frege understands it, but without providing any criterion of number identity in the usual sense. (shrink)

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.

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)

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).

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)

The topic is time travel of the sort depicted in H. G. Wells’ classic novel, The Time Machine—Wellsian time travel. The range of proper applicability of the concept of Wellsian time travel is investigated. The results of this investigation are applied to provide a new argument against the metaphysical possibility of time travel in absolute time. Alternatively, the argument is against the possibility of Wellsian time travel relative to a single temporal frame of reference. The argument leaves open the prospect (...) that an object nontrivially moves relative to one temporal reference frame from one time to another relative to another temporal reference frame. The argument does not turn on closed timelike curves or “causal loops” of any kind. It does however invoke the prospect of backward causation—a consequence of backward time travel in conjunction with common sense—but it invokes this possibility only in the weak sense of mere logical consistency. (shrink)

University of California, Santa Barbara.

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.

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

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)

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)

The theory that Kit Fine calls 'semantic relationism' replaces standard semantic compositionality with an alternative according to which statements of the form '... A … A ...’ and ‘... A … B ...’ (e.g., ‘Cicero admires Cicero’ and ‘Cicero admires Tully’) differ in semantic content—even where the two terms involved are exactly synonymous—simply in virtue of the recurrence that is present in the former statement and absent from the latter. A semantic-relationist alternative to standard compositionality was first explicitly proffered by (...) Hilary Putnam in 1954 and later by others in the latter part of the 20th Century. However, semantic relationism had already been implicitly rejected in Frege’s 1892 landmark masterpiece "Über Sinn und Bedeutung" (“On Sense and Reference”). The present compilation of three previously published essays cuts through the hype and thoroughly rebuts semantic relationism, particularly Fine’s more developed version (2007). A fatal fallacy is exposed in Fine's high-flown purported formal disproof of Millianism with standard compositionality. Standard Millianism does not implode; Fine's overzealous attempt to demolish it does. The failure of his purported disproof renders Fine's central notion of coordination either redundant or empty. So-called coordination is non-semantic if it is anything real. (shrink)

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.