We discuss the semantical categories of base and object implicit in the Curry-Howard theory of types and we derive derive logic and, in particular, the comprehension principle in the classical version of the theory. Two results that apply to both the classical and the constructive theory are discussed. First, compositional semantics for the theory does not demand ‘incomplete objects’ in the sense of Frege: bound variables are in principle eliminable. Secondly, the relation of extensional equality for each type is definable (...) in the Curry-Howard theory. (shrink)

The mereological predicate ‘is part of’ can be used to define the predicate ‘is identical with’. I argue that this entails that mereological theories can be ideologically simpler than nihilistic theories that do not use the notion of parthood—contrary to what has been argued by Ted Sider. Moreover, if one accepts an extensional mereology, there are good philosophical reasons apart from ideological simplicity to give a mereological definition of identity.

This paper presents syntactic and semantic rules for a fragment of English with mixed quotation. The fragment shows that quotation has a recursive and compositional structure. Quoted expressions turn out to denote characters, so the semantics of quotation simulates the pragmatics of speech, including dependence on utterance contexts and reference to mental entities. The analysis also accommodates varieties of unquotation, pure quotation, and causal reference.

Nexuses such as exemplification are the fundamental ties that structure reality as a whole. They are “formal” in the sense of constituting the form, not the matter of reality and they are “transcendental” inasmuch as they transcend the categorial distinctions between the denizens of reality, including that between existents and non-existents. I shall advocate a moderately particularist view about (external) nexuses and argue that it provides not only the best solution to Bradley’s regress, but also an elegant account of symmetrical (...) relations (both formal and material), as well as of temporal and modal change. These advantages are illustrated by the reconstruction of an Aristotelian ontology of exemplification involving substances, kinds and material attributes. (shrink)

Neo-Fregeans take their argument for arithmetical realism to depend on the availability of certain, so-called broadly syntactic tests for whether a given expression functions as a singular term. The broadly syntactic tests proposed in the neo-Fregean tradition are the so-called inferential test and the Aristotelian test. If these tests are to subserve the neo-Fregean argument, they must be at least adequate, in the sense of correctly classifying paradigm cases of singular terms and non-singular terms. In this paper, I pursue two (...) main goals. On the one hand, I show that the tests’ current state-of-the-art formulations are inadequate and, hence, cannot subserve the neo-Fregean argument. On the other hand, I propose revisions that are adequate and, hence, can subserve this argument. (shrink)

We consider certain predicative classes with respect to their bearing on set theory, namely on its semantics, and on its ontological power. On the one hand, our predicative classes will turn out to be perfectly suited for establishing a nice hierarchy of metalanguages starting from the usual set theoretical language. On the other hand, these classes will be seen to be fairly inappropriate for the formulation of strong principles of infinity. The motivation for considering this very type of classes is (...) a reasonable philosophy of set theory. Familiarity is assumed only with basic concepts of both set theory and its philosophy. (shrink)

We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postulates for quantifiers and the comprehension schemata of ZF and other set theories. We prove that it is consistent in any finite Boolean subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti, and others, and discuss the relationship of the system to other set-theoretic (...) systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order quantification and abstraction, and then very briefly discuss the application of one of these methods to areas of mathematics outside of logic. (shrink)

The text of Sophist 237-9 is aporetic and shares with many other dialogues this structure: A question is asked and an answer, given in a single sentence, is reached and accepted by the interlocutor. The the interlocutor is examined further and his assent undermined. I argue that the Stranger does not share Theaetetus' perplexity and holds the rejected answer. I explain the Stranger's behavior by appealing to his pedagogy.

The sentence setting the stage for the philosophical investigation within the Philebus is, naively translated, “He says that to enjoy is good.” Instead of the predicate adjective “good,” most interpreters prefer to translate with a definite description, “the good,” with consequences that affect the interpretation of the dialogue as a whole. Part one defends the naïve translation, both in the context of Socrates’ first seven speeches and viewing the dialogue as a whole. Part two considers and rejects the reasons given (...) against the naïve translation on the basis of grammar, idiosyncratic Platonic style, immediate context, and later restatements. (shrink)

Il y a un dilemme de la philosophie scientifique, limitée ici pour simplifier à la philosophie scientifique des sciences, assez évident dans lequel Carnap se trouve pris, mais auquel ni lui ni, sauf erreur de ma part, ses successeurs et commentateurs n’ont cru devoir s’arrêter : Ou bien la philosophie en question est scientifique au même sens que les autres sciences, c’est-à-dire ici qu’elle est elle-même l’une des sciences qu’elle a pour objets. On se demande alors à quoi pourrait ressembler (...) plus précisément une telle philosophie scientifique, à supposer qu’elle fût possible. Ou bien la philosophie en question n’est pas scientifique au sens des autres sciences, c’est-à-dire ici qu’elle est la seule qui puisse les prendre toutes pour objets, mais la seule aussi qu’elle ne puisse prendre pour objet. La prétendue philosophie scientifique des sciences n’est alors pas la philosophie de toutes les sciences, c’est seulement une philo­sophie des sciences non philosophiques. Ce dilemme vaut pour la philosophie scientifique en général et pour celle de Carnap en particulier, pour laquelle il prend une forme assez tranchante pour qu’on puisse en discuter sérieusement, surtout si l’on s’en tient à la philosophie scientifique des sciences identifiée par Carnap, à l’époque de la Syntax, à l’étude syntaxique, ou syntaxe, du Langage de la science. La réponse négative, savante et incontestée qu’il conviendrait alors d’apporter à la question cruciale de la première branche est connue : non, une syntaxe adéquate du Langage de la science dans ce Langage même est impossible, à moins que celui-ci ne soit inconsistant. Dans le présent article, on propose une formulation et une esquisse de démonstration inhabituelles de cette impossibilité, ne mobilisant aucun codage, gödélien ou autre, de la syntaxe élémentaire du Langage de la science dans ce Langage même ; et l’on remet en cause le critère d’adéquation impliqué dans la démonstration de l’impossibilité en question, rouvrant ainsi la possibilité de sortir par le haut d’un dilemme dont Carnap s’est cru obligé, ou du moins s’est conduit comme s’il était obligé, de sortir par le bas. (shrink)

Il y a un dilemme de la philosophie scientifique, limitée ici pour simplifier à la philosophie scientifique des sciences, assez évident dans lequel Carnap se trouve pris, mais auquel ni lui ni, sauf erreur de ma part, ses successeurs et commentateurs n’ont cru devoir s’arrêter : Ou bien la philosophie en question est scientifique au même sens que les autres sciences, c’est-à-dire ici qu’elle est elle-même l’une des sciences qu’elle a pour objets. On se demande alors à quoi pourrait ressembler (...) plus précisément une telle philosophie scientifique, à supposer qu’elle fût possible. Ou bien la philosophie en question n’est pas scientifique au sens des autres sciences, c’est-à-dire ici qu’elle est la seule qui puisse les prendre toutes pour objets, mais la seule aussi qu’elle ne puisse prendre pour objet. La prétendue philosophie scientifique des sciences n’est alors pas la philosophie de toutes les sciences, c’est seulement une philo­sophie des sciences non philosophiques. Ce dilemme vaut pour la philosophie scientifique en général et pour celle de Carnap en particulier, pour laquelle il prend une forme assez tranchante pour qu’on puisse en discuter sérieusement, surtout si l’on s’en tient à la philosophie scientifique des sciences identifiée par Carnap, à l’époque de la Syntax, à l’étude syntaxique, ou syntaxe, du Langage de la science. La réponse négative, savante et incontestée qu’il conviendrait alors d’apporter à la question cruciale de la première branche est connue : non, une syntaxe adéquate du Langage de la science dans ce Langage même est impossible, à moins que celui-ci ne soit inconsistant. Dans le présent article, on propose une formulation et une esquisse de démonstration inhabituelles de cette impossibilité, ne mobilisant aucun codage, gödélien ou autre, de la syntaxe élémentaire du Langage de la science dans ce Langage même ; et l’on remet en cause le critère d’adéquation impliqué dans la démonstration de l’impossibilité en question, rouvrant ainsi la possibilité de sortir par le haut (en restant sur la première branche) d’un dilemme dont Carnap s’est cru obligé, ou du moins s’est conduit comme s’il était obligé, de sortir par le bas (en se repliant sur la seconde). (shrink)

Ce bel ouvrage, clair, aéré et spacieux, se caractérise à la fois par sa volonté de simplicité d’accès, et son ambition, puisqu’on y trouve notamment une démonstration de la complétude d’un certain système déductif S1 pour la logique classique des prédicats, ainsi qu’une version synoptique du théorème de Gödel, selon lequel toute théorie du premier ordre complète axiomatisable est décidable, d’où il s’ensuit que l’arithmétique, c’est-à-dire l’ensemble des énoncés du premier ordre vrais dans, n’est pas axiomatisable; ce qu’on exprime souvent (...) en disant que tout système formel pour l’arithmétique est incomplet, au sens où il y a des énoncés vrais qui ne sont pas des théorèmes du système. (shrink)

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of (...) the strength of the theory. I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental. (shrink)

Carnap's system of inductive logic has very often been criticized on the ground that “degree of confirmation” is defined only for languages which are extremely over-simplified. Allegedly, it would be very difficult—and perhaps impossible—to define it adequately for languages formalized within the higher predicate calculi, or languages equivalent to these in richness, and it is such languages that would be needed were we ever to formalize the language of empirical science as a whole. Thus, this criticism bears not only on (...) Carnap's work, but on all attempts to construct an exact analysis of induction from this particular standpoint; that is, from the standpoint of “logical measure functions.”. (shrink)

Sometimes two expressions in a discourse can be about the same thing in a way that makes that very fact evident to the participants. Consider, for example, 'he' and 'John' in 'John went to the store and he bought some milk'. Let us call this 'de jure' coreference. Other times, coreference is 'de facto' as with 'Mark Twain' and 'Samuel Clemens' in a sincere use of 'Mark Twain is not Samuel Clemens'. Here, agents can understand the speech without knowing that (...) the names refer to the same person. After surveying many available linguistic and pragmatic tools (intentions to corefer, presuppositions, meanings, indexing, discourse referents, binding etc.) I conclude that we must posit a new semantic primitive to account for de jure coreference. (shrink)

In the first exposition of the doctrine of indeterminacy of translation, Quine asserted that the individuation and translation of truth-functional sentential connectives like 'and', 'or', 'not' are not indeterminate. He changed his mind later on, conjecturing that some sentential connectives might be interpreted in different non-equivalent ways. This issue has not been debated much by Quine, or in the subsequent literature, it is, as it were, an unsolved problem, not well understood. For the sake of the argument, I will adopt (...) Quine's background assumption that all the semantic features of a language can be reduced to the speakers' dispositions toward assent and dissent, as far as only the truth-conditional core of the meaning of sentences is concerned. I will put forward an argument to the effect that the speech dispositions of most, if not all, English (French, Italian, etc.) speakers constrain a unique translation of their connectives. This argument crucially relies on an empirical conjecture concerning the behaviour of these operators. (shrink)

In this paper I revisit R. M. Martin’s logic of belief. As with much of Martin’s work, his formal studies into belief and belief reports have gone largely unnoticed. However, in my article I suggest reasons for thinking that these studies warrant revisiting. One reason is that Martin adopted an account of the notion of belief which was more comprehensive than that employed by most rival theorists. Another reason is that Martin couched his theory in a formal pragmatics which utilised (...) a pragmatical meta-language. This method resulted in a rather novel approach which may turn out to be more enlightening than many popular alternative accounts. Martin was a constructivistic nominalist whose approach to philosophical analysis was characterised by a commitment to first-order extensional systems. Yet in the statement of his theory of belief he employed a platonistic syntax simply for the reason that this kind of syntax is a little easier to implement than one which is nominalistic. However Martin also supposed that a fully nominalised version of his theory could be developed. In my article I investigate whether it can. I do this by sketching an inscriptional pragmatics, where this pragmatical system presupposes an inscriptional semantics of the kind developed by Martin himself. While further work is required, I think that a nominalisation of Martin’s logic of belief may be developed. (shrink)

Starting from the familiar observation that no straightforward treatment of pure quotation can be compositional in the standard (homomorphism) sense, we introduce general compositionality, which can be described as compositionality that takes linguistic context into account. A formal notion of linguistic context type is developed, allowing the context type of a complex expression to be distinct from those of its constituents. We formulate natural conditions under which an ordinary meaning assignment can be non-trivially extended to one that is sensitive to (...) context types and satisfies general compositionality. As our main example we work out a Fregean treatment of pure quotation, but we also indicate that the method applies to other kinds of context, e.g. intensional contexts. (shrink)

According to quotational theory, indirect ascriptions of propositional attitudes should be analyzed as direct ascriptions of attitudes towards natural-language sentences specified by quotations. A famous objection to this theory is Church's translation argument. In the literature several objections to the translation argument have been raised, which in this paper are shown to be unsuccessful. This paper offers a new objection. We argue against Church's presupposition that quoted expressions, since they are mentioned, cannot be translated. In many contexts quoted expressions are (...) used and mentioned simultaneously, and the quotational analysis of propositional-attitude ascriptions is such a context. Hence the translation argument is unsound. (shrink)

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

Neo-Russellianism, which incorporates both Millianism (with regard to proper names) and the thesis of singular Russellian propositions, has widely been defended after the publication of Kripke's Naming and Necessity. The view, however, encounters various problems regarding empty names, names that do not have semantic referents. Nathan Salmon and Scott Soames have defended neo-Russellianism against such problems in a novel way; to account for various intuitions of competent and rational speakers regarding utterances of sentences containing empty names, Salmon and Soames appeal (...) neither to entities similar to Fregean senses, e.g. propositional guises or modes of presentation, nor to Gricean implicatures. In this paper, however, I argue that their view slips into neo-Meinongianism; it is committed to nonexistent objects, assigns various properties to them, and allows quantifiers range over such entities. This, I conclude, makes Salmon and Soames' view less appealing, if not implausible. (shrink)

Concept originalism, recently introduced and defended by Sainsbury and Tye, Tye, and Sainsbury, holds that “atomic concepts are to be individuated by their historical origins, as opposed to their semantic or epistemic properties”. The view is immune to Gareth Evans’s “Madagascar” objection to the Causal Theory of Reference since it allows a concept to change its reference over time without losing its identity. The possibility of reference-shift, however, raises the problem of misleading belief reports. S&T try to tackle the problem (...) by strengthening the sufficient condition for a truthful belief report. We will argue that, first, their solution fails, second, and more importantly, their diagnosis of the root of the problem is misguided, third, two initially appealing ways out of the problem fail, and fourth, the prospect of finding a solution to the problem within CO is dim. The view opens the Pandora’s box of reference-shift, in a wide range of cases, without providing the necessary semantic means to take care of them. (shrink)

In his “Wissenschaftslogik: The Role of Logic in the Philosophy of Science,” Michael Friedman argues that Carnap’s philosophy of science “is fundamentally anti-metaphysical—he aims to use the tools of mathematical logic to dissolve rather [than] solve traditional philosophical problems—and it is precisely this point that is missed by his logically-minded contemporaries such as Hempel and Quine”. In this paper, I take issue with this claim, arguing that Quine, too, is a part of this anti-metaphysical tradition. I begin in section I (...) with Russell’s account of scientific philosophy, focusing on its critique of metaphysics and its reliance on logical constructions. I then argue that each of Carnap and Quine take up this call to scientific philosophizing but that they both find Russell’s account of logic wanting. In section II, I first provide an account of Carnap’s critique of metaphysics and its reliance on developments in logic. This is followed by a discussion of his appeal to the analytic/synthetic distinction so as to improve upon Russell’s account of logic. Section III follows this same structure but focuses on Quine. In the end, though, Quine turns not to the analytic/synthetic distinction but to holism to provide an account of logic suitable to scientific philosophy. Carnap had claimed to be “more Russellian than Russell,” and in this final move by Quine I argue that he is “being more Carnapian than Carnap.” I conclude by showing how, contrary to Friedman’s view, Quine’s rejection of the analytic/synthetic distinction does not yield a return to the kind metaphysics that he, Carnap, and Russell all objected to. (shrink)

Mi objetivo es discutir las principales dificultades que Frank P. Ramsey encontró en Principia Mathematica y la solución que, vía el Tractatus Logico-Philosophicus, propuso al respecto. Sostengo que las principales dificultades que Ramsey encontró en Principia Mathematica están, todas, relacionadas con que Russell y Whitehead desatendieron la forma lógica de las proposiciones matemáticas, las cuales, según Ramsey, deben ser tautológicas.

This is a lively, provocative book and many of its arguments are convincing. In this critical study I summarize the book, then discuss some of the authors’ claims, dwelling on three issues: their objections to the view of François Recanati on “pre-semantic” effects; the relation between their theory of quotation and the Tarskian “Proper Name Theory,” which they reject; and their treatment of mixed quotation, which rests on the claim that quotation expressions are “syntactic chameleons.” I argue that the objections (...) to Recanati don’t expose any problem with his view, and that the “Proper Name Theory” has all the virtues of their own proposal. Finally I raise some queries about the technical apparatus of syntactic chameleonism. (shrink)

I defend a Deferred Ostension view of quotation, on which quotation-marks are the linguistic bearers of reference, functioning like a demonstrative; the quoted material merely plays the role of a demonstratum. On this view, the quoted material works like Nunberg’s indexes in his account of deferred ostensión in general. The referent is obtained through some contextually suggested relation; in the default case the relation will be … instantiates the linguistic type __, but there are other possibilities. In this way, the (...) deferred ostension view deals with a problem I pointed out for the identity proposal in my earlier work, that we do not merely refer with quotations to expression-types, but also to other entities related in some way to the relevant token we use: features exhibited by the token distinct from those constituting its linguistic type, features exhibited by other tokens of the same type but not by the one actually used (as when, by using a graphic token, we refer to its phonetic type), or even other related tokens (see the examples on p. 261 of García-Carpintero 1994). (shrink)

Peter Geach's puzzle of intentional identity is to explain how the claim ‘Hob thinks a witch has blighted Bob's mare, and Nob wonders whether she killed Cob's sow’ is compatible with there being no such witch. I clarify the puzzle and reduce it to the familiar problem of negative existentials. That problem is a paradox of representations that seem to include denials of commitment , to carry commitment to what they deny commitment to, and to be true. The best proposed (...) solutions can be understood through this paradox; I evaluate them, and defend a new solution. (shrink)

Pure quotation, as in ‘cat’ has three letters, is a linguistic device designed for referring to linguistic expressions. I present a uniform recon struction of the four classic philosophical accounts of the phenomenon: the proper name theory, the description theory, the demonstrative theory, and the disquotational theory. I evaluate the strengths and weaknesses of each proposal with respect to fundamental semantic properties like compositionality, productivity, and recursivity.

Jim Mackenzie; Authority, Journal of Philosophy of Education, Volume 22, Issue 1, 30 May 2006, Pages 57–65, https://doi.org/10.1111/j.1467-9752.1988.tb00177.x.

This paper is about the mode of being of names. The paper begins by explaining why the joke is on commentators who see Lewis Carroll's White Knight as applying the use/mention distinction. Then it argues that the real problem with the distinction is that the idea that names are used to mention what they name depends on mistakenly conceiving of language as existing autonomously; and that philosophers have this conception because they fail to appreciate what they are doing when they (...) philosophise about language. This failure also explains why philosophers mistakenly think of any manifestation of a name as a (physical) token. (shrink)

What formulas are tense-logically valid depends on the structure of time, for example on whether it has a beginning. Logicians have investigated what formulas correspond to what physical hypotheses about time. Analogously, we can investigate what formulas of modal logic correspond to what metaphysical hypotheses about necessity. It is widely held that physical hypotheses about time may be contingent. If so, tense-logical validity may be contingent. In contrast, validity in modal logic is typically taken to be non-contingent, as reflected by (...) the general acceptance of the so-called “rule of necessitation.” But as has been argued by various authors in recent years, metaphysical hypotheses may likewise be contingent. If, in particular, hypotheses about the extent of possibility are contingent, we should expect modal-logical validity to be contingent too. Let “contingentism” be the view that everything that is not ruled out by logic is possible. I shall investigate what the right system of modal logic is, if contingentism is true. Given plausible assumptions, the system contains the McKinsey principle, and is thus not even contained in S5. It also contains simple and elegant iteration principles for the contingency operator: something is contingent if and only if it is contingently contingent. (shrink)

This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how to extend his (...) method to a subset of first-order formulas, namely, formulas that do not contain dyadic sentential connectives within the scope of any quantifier. (shrink)

The paper offers a historical survey of the emergence of logical formalization in twentieth-century analytically oriented philosophy of religion. This development is taken to have passed through three main ?stages?: a pioneering stage in the late nineteenth and early twentieth centuries (led by Frege and Russell), a stage of crisis in the 1920s and early 1930s (occasioned by Wittgenstein, logical positivists such as Carnap, and neo-Thomists such as Maritain), and a stage of rehabilitation in the 1930s, 1940s, and 1950s (led (...) by the Cracow Circle and Quine). (shrink)

The paper surveys two contrasting views of first‐order analyses of classical theistic doctrines about the existence and nature of God. On the first view, first‐order logic provides methods for the adequate analysis of these doctrines, for example by construing ‘God’ as a singular term or as a monadic predicate, or by taking it to be a definite description. On the second view, such analyses are conceptually inadequate, at least when the doctrines in question are viewed against the background of classical (...) theism’s doctrine of divine simplicity, for first‐order analyses presuppose an ontological complexity on the part of the propositions which they analyze, which fits ill with this doctrine. (shrink)

In Reason and Analysis, Prof. Brand Blanshard criticises the logical empiricist view regarding necessary statements, including the laws of logic. He distinguishes four component these of this view: (I) Necessary statements--here, the laws of logic--are resolutions or reports of linguistic usage. (II) They are conventions. (III) They are analytic (tautologies). (IV) They say nothing about the world. In this paper I first show that Prof. Blanshard is essentially right in his criticisms of (I), (II), and (IV); but that he has (...) done nothing to show that (III) is incorrect with regard to the laws of logic. Then, second, I attempt to show that even though (I), (II), and (more importantly) (IV) are false, (III) is true. That is, the laws of logic are tautologies, and yet, in a sense to be distinguished, they say something about the world. (shrink)

Can rational communication proceed when interlocutors are uncertain which contents utterances contribute to discourse? An influential negative answer to this question is embodied in the Stalnakerian principle of uniformity, which requires speakers to produce only utterances that express the same content in every possibility treated as live for the purposes of the conversation. The principle of uniformity enjoys considerable intuitive plausibility and, moreover, seems to follow from platitudes about assertion; nevertheless, it has recently proven controversial. In what follows, I defend (...) the principle by developing two arguments for it based on premises reflecting the central aims and assumptions of possibility-carving frameworks for modeling inquiry—that is, frameworks which describe the evolution of individuals’ attitudinal states in terms of set-theoretic operations defined over a domain of objects representing possibilities. (shrink)