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 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.

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

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 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)

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)

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

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)

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)

Despite some notable similarities between the scientific realisms of Sellars and Peirce (such as both being anti-representationalist, and future-directed), in his mature work Science and Metaphysics Sellars explicitly critiqued Peirce’s account of truth, as lacking “an intelligible foundation” (Sellars 1968: vii). In this paper, I explore Sellars’ proposed remedy to Peirce’s purported lack, in his complex and enigmatic account of picturing – a non-discursive ‘mapping’ of the world. I argue that although Sellars’ development of this idea is largely sound, much (...) of what he charges Peirce’s philosophy with missing is actually present there. By means of his semiotic icon / index / symbol distinction, Peirce manages to develop a philosophy of language which effectively coordinates the real order and the order of signification within the very structure of the proposition as he understands it, by contrast to Sellars’ claim that the two orders are merely connected by ‘analogy’. I also argue that in between Sellars’ ambitious account of veridicality, which appears to anticipate a form of scientific self-mensuration, and the dismissive ‘anti-truth’ quietism of neopragmatists such as Rorty, Peirce’s “contrite fallibilism” (Peirce CP 1.14) charts a wise middle path. (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.

It is widely held that metaphysical modality is the broadest non-epistemic, alethic modality, and that /a posteriori/ modal essentialist truths, like that gold has atomic number 79, enjoy the necessity of the broadest alethic modality. One prominent argument for these conclusions--given by Cian Dorr, John Hawthorne, and Juhani Yli-Vakkuri--rests upon an extremely dubious premise: that certain pairs of properties—e.g., being gold and being made of atoms containing 79 protons—are one and the very same property. The two properties are seen to (...) be distinct on independent philosophical grounds. Metaphysical modality is in fact a restricted alethic modality. In particular, mathematical modality is broader than metaphysical modality. Arguably, the broadest alethic modality is logical modality, which is distinct from metaphysical modality. Even if it is metaphysically necessary that gold have atomic number 79, there is no logical/analytical inconsistency in the supposition that it does not. (shrink)

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)

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)

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)

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

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

I defend the thesis that friendship can constitutively require epistemic irrationality against a recent, forceful challenge, raised by proponents of moral and pragmatic encroachment. Defenders of the “encroachment strategy” argue that exemplary friends who are especially slow to believe that their friends have acted wrongly are simply sensitive to the high prudential or moral costs of falsely believing in their friends’ guilt. Drawing on psychological work on epistemic motivation (and in particular on the notion of “need for closure”), I propose (...) a different picture of what friendship requires in the doxastic realm. I argue that contrary to what the encroachment strategy suggests, exemplary friends’ belief formation ought not be guided by a concern with accuracy or error avoidance, but instead by a need to avoid a “specific closure” – namely, a need to avoid concluding in their friends’ guilt. I propose that exemplary friendship often generates a defeasible, doxastic obligation to exemplify such a need, despite its inherent corrupting effects on exemplary friends’ epistemic faculties. (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)

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)

This paper addresses some apparent philosophical tensions between realism and enactivism by means of Charles Peirce’s pragmatism. Enactivism’s Mind-Life Continuity thesis has been taken to commit it to some form of anti-realist ‘world-construction’ which has been considered controversial. Accordingly, a new realist enactivism is proposed by Zahidi (_Phenomenology and the Cognitive Sciences,_ _13_(3), 461–475, 2014 ), drawing on Ian Hacking’s ‘entity realism’, which places subjects in worlds comprised of the things that they can successfully manipulate. We review this attempt, and (...) argue that whilst Zahidi rightly urges enactivists towards ‘internal realism’, he cannot sustain a non-negotiable aspect of realism that is crucial for scientific progress – the claim that multiple subjects inhabit _the same world_. We explore Peirce’s pragmatism as an alternative solution, foregrounding his distinction between existence and reality, and his inquiry-based account of cognition. These theoretical innovations, we argue, fruitfully generalize Zahidi’s _manipulation-based_ enactivist realism to a richer, _inquiry-based_ enactivist realism. We explore how this realism’s pan-species monism about truth encourages and supports the investigation of non-human animal cognition, and conclude by considering some implications of our discussion for long-standing realism debates within pragmatism. (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)

Mainstream philosophy has seen a recent flowering in discussions of intellectualism which revisits Gilbert Ryle’s famous distinction between ‘knowing how’ and ‘knowing that’, and challenges his argument that the former cannot be reduced to the latter. These debates so far appear not to have engaged with pragmatist philosophy in any substantial way, which is curious as the relation between theory and practice is one of pragmatism’s main themes. Accordingly, this paper examines the contemporary debate in the light of Charles Peirce’s (...) habit-based epistemology. We argue both that knowing-that can be understood as a particularly sophisticated form of knowing-how, and that all bodily competencies—if sufficiently deliberately developed—can be analysed as instantiating propositional structure broadly conceived. In this way, intellectualism and anti-intellectualism are seen to be not opposed, and both true, although Peirce’s original naturalistic account of propositional structure does lead him to reject what we shall call ‘linguistic intellectualism’. (shrink)

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.

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)

The account of natural kinds as stable property clusters is premised on the possibility of separating the epistemic value of natural kinds from their underlying metaphysics. On that account, the co-instantiation of any sub-cluster of the properties associated with a given natural kind raises the probability of the co-instantiation of the rest, and this clustering of property instantiation is invariant under all relevant counterfactual perturbations. We argue that it is not possible to evaluate the stability of a cluster of properties (...) without taking stock of the metaphysical picture used to account for that stability. Thus, even on the stable property cluster account, the epistemic value of natural kinds remains partly grounded in their metaphysical status. (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)

Wilfrid Sellars’ distinctive scientific realism has lately been gaining ground, but a crucial issue is how it can or should theorize modality. We argue that many interesting questions in this area transcend the usual ‘first-order’ concerns: “Is there an objectivist modal ontology?” and “What modal entities should we posit”? Rather, Sellars invites us to take a fresh look at the relationship between logic and metaphysics through an investigation of ‘second-order’ philosophical categories. This investigation contrasts with both the first-order 'external' ontologising (...) of metaphysicians such as David Lewis and the 'easy' ontologising of metaphysicians such as Amie Thomasson. We argue that Sellars' approach stimulates a more conscious and fruitful examination of our role and methods as philosophers in the modal arena. Moreover, since the notion of metaphysics as a ‘second-order’ activity has recently gained attention in contemporary philosophy of science through the work of David Wallace, we explore both Sellars’ potential contribution to these discussions and the relationship between Sellars’ approach and contemporary ontic structural realist views regarding modal structure, thereby opening up fundamental questions concerning where and how the metaphysics of modality might be integrated with our current best physics. (shrink)

In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or (...) localized a faculty to register them. We defend the perception of necessity against such Humeanism, drawing on examples from mathematics. (shrink)