Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical (...) monism is called for. I review the possible forms of logical pluralism and render them more plausible. I thus arrive at logical dynamism, a synthesis of various pluralisms and monism focused on how logic develops. (shrink)

Logical pluralism is the view that there is more than one correct logic. This very general characterization gives rise to a whole family of positions. I argue that not all of them are stable. The main argument in the paper is inspired by considerations known as the “collapse problem”, and it aims at the most popular form of logical pluralism advocated by JC Beall and Greg Restall. I argue that there is a more general argument available that challenges all variants (...) of logical pluralism that meet the following three conditions: that there are at least two correct logical systems characterized in terms of different consequence relations, that there is some sort of rivalry among the correct logics, and that logical consequence is normative. The hypothesis I argue for amounts to conditional claim: If a position satisfies all these conditions, then that position is unstable in the sense that it collapses into competing positions. (shrink)

From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic logic) lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation (...) of intuitionistic logic is in terms of preservation of constructive proof; of paraconsistency is in terms of preservation of evidence. In this paper, we explain and defend the epistemic approach to paraconsistency. We argue that it is more plausible than dialetheism and allows a peaceful and fruitful coexistence with classical logic. (shrink)

In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style ofPrincipia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics of (...) axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition (Carnap and Tarski) and two proponents of the first-order tradition (Gödel and Hilbert), we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory. (shrink)

I propose a way of thinking aboout content, and a related way of thinking about ontological commitment. (This is part of a series of four closely related papers. The other three are ‘On Specifying Truth-Conditions’, ‘An Actualist’s Guide to Quantifying In’ and ‘An Account of Possibility’.).

According to some philosophers, the Liar paradox arises because of a mistaken theory of truth. Its lesson is that we must reject some instances of the naive propositional truth-schema \It is true that \ if and only if \\. In this paper, I construct a novel semantic paradox in which no principle even analogous to the truth-schema plays any role. I argue that this undermines the claim that we ought to respond to the Liar by revising our theory of truth.

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th (...) century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

Jaakko Hintikka points out the power of Skolem functions to affect both what there is and what we know. There is a tension in his presupposition that these functions actually extend the realm of logic. He claims to have resolved the tension by “reconstructing constructivism” along epistemological lines, instead of by a typical ontological construction; however, after the collapse of the distinction between first and second order, that resolution is not entirely satisfactory. Still, it does throw light on the conceptual (...) analysis Hintikka proposes. (shrink)

Sellars [1960, ‘Grammar and existence: A preface to ontology’] argues that the truth of a second-order sentence does not incur commitment to there being any sort of abstract entity. This paper begins by exploring the arguments that Sellars offers for the above claim. It then develops those arguments by pointing out places where Sellars has been unclear or ought to have said more. In particular, Sellars's arguments rely on there being a means by which language users could come to understand (...) sentences of a second-order language wherein the truth of second-order existential sentences do not require there to be abstract entities. In addition to this, as Sellars [1979, Naturalism and Ontology] notes, a formal account of quantification is required that does not make use of the apparatus of sequences. Both such a translation of and a formal account of quantification are provided in this article. (shrink)

This paper is about the putative theoretical virtue of strength, as it might be used in abductive arguments to the correct logic in the epistemology of logic. It argues for three theses. The first is that the well-defined property of logical strength is neither a virtue nor a vice, so that logically weaker theories are not—all other things being equal—worse or better theories than logically stronger ones. The second thesis is that logical strength does not entail the looser characteristic of (...) scientific strength, and the third is that many modern logics are on a par—or can be made to be on a par—with respect to scientific strength. (shrink)

Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings clarity (...) to a debate in which opponents frequently talk past one another. With the two views stated precisely, our investigation reveals the dependence of the mereologists’ ontological commitments on the semantics of plural quantifiers. Though we discuss the debate with respect to a simplified and idealized model, the insights provided will make more complex debates on composition more productive and deflationist criticisms of the debate less substantial. (shrink)

I offer an analysis of the sentence "the concept horse is a concept". It will be argued that the grammatical subject of this sentence, "the concept horse", indeed refers to a concept, and not to an object, as Frege once held. The argument is based on a criterion of proper-namehood according to which an expression is a proper name if it is so rendered in Frege's ideography. The predicate "is a concept", on the other hand, should not be thought of (...) as referring to a function. It will be argued that the analysis of sentences of the form "C is a concept" requires the introduction of a new form of statement. Such statements are not to be thought of as having function--argument form, but rather the structure subject--copula--predicate. (shrink)

We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show (...) that some of these logics are non-degenerate. (shrink)

We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.

This essay argues that deflationism is incompatible with the phenomenon of referential indeterminacy. This puts the deflationist in the difficult position of having to deny the possibility of what otherwise seems like a manifest and theoretically important phenomenon. Section 1 provides background on deflationism. Section 2 considers an intuitive argument by Stephen Leeds to the effect that deflationism precludes RI; the essay argues that this argument does not succeed. The rest of the essay presents its own, distinct argument for the (...) incompatibility of deflationism and RI. Section 3 argues that direct RI—RI that is not simply a derivative of some other, nonreferential instance of indeterminacy—is strictly incompatible with deflationism. Section 4 considers a couple of different ways the deflationist might try to achieve indirect RI—via indeterminate identity and indeterminate synonymy—and argues that each is unsatisfactory. (shrink)

First-order logic haslimitedexistential import: the universalized conditional ∀x[S(x) → P(x)] implies its corresponding existentialized conjunction ∃x[S(x) & P(x)] insome but not allcases. We prove theExistential-Import Equivalence:∀x[S(x) → P(x)] implies ∃x[S(x) & P(x)] iff ∃xS(x) is logically true.The antecedent S(x) of the universalized conditional alone determines whether the universalized conditionalhas existential import: implies its corresponding existentialized conjunction.Apredicateis a formula having onlyxfree. Anexistential-importpredicate Q(x) is one whose existentialization, ∃xQ(x), is logically true; otherwise, Q(x) isexistential-import-freeor simplyimport-free. Existential-import predicates are also said to beimport-carrying.How (...) widespread is existential import? How widespread are import-carrying predicates in themselves or in comparison to import-free predicates? To answer, let L be any first-order language with any interpretation INT in any [sc. nonempty] universe U. A subset S of U isdefinable inLunderINT iff for some predicate Q(x) in L, S is the truth-set of Q(x) under INT. S isimport-carrying definableiff S is the truth-set of an import-carrying predicate. S isimport-free definableiff S is the truth-set of an import-free predicate.Existential-Importance Theorem: Let L, INT, and U be arbitrary. Every nonempty definable subset of U isbothimport-carrying definableandimport-free definable.Import-carrying predicates are quite abundant, and no less so than import-free predicates. Existential-import implications hold as widely as they fail.A particular conclusion cannot be validly drawn from a universal premise, or from any number of universal premises.—Lewis-Langford, 1932, p. 62. (shrink)

Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonably thorough (if not (...) exactly comprehensive) overview of the structure and content of Hale’s book and, second, to a limited extent, to engage Hale’s book philosophically. I approach these tasks more or less sequentially: Parts I and 2 of the review are primarily expository; in Part 3 I adopt a somewhat more critical stance and raise several issues concerning one of the central elements of Hale’s account, his essentialist theory of modality. (shrink)

Take a correct sequent of formal logic, perhaps a simple logical truth, like the law of excluded middle, or something with premises, like disjunctive syllogism, but basically a claim of the form \.Γ can be empty. If you don’t like my examples, feel free to choose your own, everything I have to say should apply to those as well. Such a sequent attributes the properties of logical truth or logical consequence to a schematic sentence or argument. This paper aims to (...) answer the question of how beliefs in such attributions are justified, on both its descriptive and normative interpretations; I aim to say when we generally take ourselves to be justified in forming such beliefs, and to make it plausible that beliefs formed this way really are justified.We can ask such questions about many domains but there are special difficulties for answering them in logic. Some of the difficulties stem from the fact that logic is thought t.. (shrink)

The notion of strict identity is sometimes given an explicit second-order definition: objects with all the same properties are identical. Here, a somewhat different problem is raised: Under what conditions is the identity relation on the domain of a structure first-order definable? A structure may have objects that are distinct, but indiscernible by the strongest means of discerning them given the language (the indiscernibility formula). Here a number of results concerning the indiscernibility formula, and the definability of identity, are collected (...) and a number of applications discussed. (shrink)

There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...) the philosophy of language, I suggest that i functions like a parameter in natural deduction systems. This may require some rethinking of the role of singular terms, at least in mathematical languages. (shrink)

Amongst those views sometimes attributed to the later Wittgenstein are included both a deflationary theory of truth, as well as a non-factualism about certain regions of discourse. Evidence in favor of the former attribution, it is thought, can be found in Wittgenstein’s apparent affirmation of the basic definitional equivalence of ‘p’ is true and p in §136 of his Philosophical Investigations. Evidence in favor of the latter attribution, it might then be presumed, can be found in the context of the (...) so-called ‘private language argument’, wherein Wittgenstein provides an expressivist treatment of first-person present tense sensation utterances. In this paper, by contrast, I will argue that Wittgenstein’s later philosophy is best understood as endorsing neither a non-factualism about sensation utterances, nor a deflationism about truth. Wittgenstein should instead be understood as offering a ‘mixed’ view of sensation utterances according to which some while not others are apt for expressivist treatment. Moreover, he should be thought of as identifying truth-conditions with semantic ‘correctness-conditions’, and thus truth with semantic ‘assertibility’. (shrink)

In this paper, I use the cases of intuitionistic arithmetic with Church’s thesis, intuitionistic analysis, and smooth infinitesimal analysis to argue for a sort of pluralism or relativism about logic. The thesis is that logic is relative to a structure. There are classical structures, intuitionistic structures, and (possibly) paraconsistent structures. Each such structure is a legitimate branch of mathematics, and there does not seem to be an interesting logic that is common to all of them. One main theme of my (...) ante rem structuralism is that any coherent axiomatization describes a structure, or a class of structures. If one weakens the logic, then more axiomatizations become coherent. (shrink)

Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such as the (...) aforementioned validity of attitude-report inferences. It then shows that the notion of a predication act-type, which remains importantly Russellian in spirit, is sufficient to explain the range of propositional phenomena in question, in particular the validity of attitude-report inferences. The paper concludes with a discussion of whether predication act-types are really just propositions by another name. (shrink)

Recently, in the debate about the ontology of quantum mechanics some authors have defended the view that quantum particles are individuals in a primitive sense, so that individuality should be preferred over non-individuality (the alternative option). Primitive individuality involves two main claims: (1) every item is identical with itself and (2) it is distinct from every other item. Non-relativistic quantum mechanics is said to provide positive evidence for that position, since in every situation comprising multiple particles there is a well-defined (...) number of them to begin with, and so they must be distinct from each other. We argue that the link between a well-defined number of items and the relation of identity that is being claimed to hold is not imposed by quantum mechanics, but rather by a metaphysical view. Formal evidence is advanced in favor of the thesis that counting may be performed for items without identity (non-individuals), so that quantum mechanics needs not be viewed as endorsing an ontology of individuals. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...) Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

This paper argues for an account of the relation between thought ascription and the explanation of action according to which de re ascriptions and de dicto ascriptions of thought each form the basis for two different kinds of action explanations, nonrationalizing and rationalizing ones. The claim that de dicto ascriptions explain action is familiar and virtually beyond dispute; the claim that that de re ascriptions are explanatory of action, however, is not at all familiar and indeed has mostly been denied (...) by philosophers. I explain how de re ascriptions enter into non-rationalizing explanations of action and how attention to their distinctive explanatory nature reveals flaws in an alternative “dual-component” view about action explanation. (shrink)

Dans la première partie de cet article, je presente une thèse parapluie — la thèse de l'«exhaustion» — qui cerne bien l'élément central des diverses positions déflationnistes au sujet de la vérité : l'idée que le contenu du prédicat de vérité s'épuise entièrement dans le contenu de ce à quoi le prédicats'applique. Je soutiens que cette thèse n'est supportée que d'une manière triviale par l'idée courante que la vérite résiste à une analyse substantielle, car les prédicats en général ne se (...) prêtent guere à ce genre d'analyse. J'examine ensuite deux élaborations positives de la thèse de l'exhaustion; et je soutiens que ni l'une ni l'autre ne commence même à montrer que la thèse en question soit explicativement adéquate. (shrink)

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...) the focal point is the categorical syllogism. (shrink)

In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically invariant (...) and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing. (shrink)

In his 1993 article George Bealer offers three separate arguments that are directed against the internal coherence of empiricism, specifically against Quine’s version of empiricism. One of these arguments is the starting points argument (SPA) and it is supposed to show that Quinean empiricism is incoherent. We argue here that this argument is deeply flawed, and we demonstrate how a Quinean may successfully defend his views against Bealer’s SPA. Our defense of Quinean empiricism against the SPA depends on showing (1) (...) that Bealer is, in an important sense, a foundationalist, and (2) that Quine is, in an important sense, a coherentist. Having established these two contentions we show that Bealer’s SPA begs the question against Quinean empiricists. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...) epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, based on (...) a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible. (shrink)

The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized similarly is a natural generalization of Tarski’s thesis, due to Sher, in terms of bijections between domains. My main (...) objections are that on the one hand, the Tarski-Sher thesis thus assimilates logic to mathematics, and on the other hand fails to explain the notion of same logical operation across domains of different sizes. A new notion of homomorphism invariant operation over functional type structures (with domains M0 of individuals and {T, F} at their base) is introduced to accomplish the latter. The main result is that an operation is definable from.. (shrink)

In addition to the distinction between species as a category and speciesas a taxon, the word species is ambiguous in a very different butequally important way, namely the temporal distinction between horizontal andvertical species. Although often found in the relevant literature, thisdistinction has thus far remained vague and undefined. In this paper the use ofthe distinction is explored, an attempt is made to clarify and define it, andthen the relation between the two dimensions and the implications of thatrelation are examined. (...) Using Darwin's analogy of language evolution forspeciesevolution, and by appealing to a major change in the conception of languagebetween 19th- and 20th-century linguistics, it is argued that the horizontaldimension has priority (pragmatic, epistemological, logical, and ontological)over the vertical dimension. This has immense ramifications for the modernspecies problem. Fundamentally, it favors horizontal species concepts oververtical ones. In so doing it places species realism on a much more securefoundation and largely undercuts species pluralism. In addition it raises aserious problem for the increasingly popular family of phylogenetic speciesconcepts, which generally suffer from a dimensionality confusion. However,thereis a recent trend within this family that attempts to restore the priority ofthe horizontal dimension. It is concluded that this trend should be affirmedandthat the species-as-individuals view should be abandoned. (shrink)

Since the early part of this century there has been a considerable amount of discussion of the question 'Does time pass?'. A useful way of approaching the debate over the passage of time is to consider the following thesis: The space-time thesis (SPT): Time is similar to the dimensions of space in at least this one respect: there is no set of properties such that (i) these properties are possessed by time, (ii) these properties are not possessed by any dimension (...) of space, and (iii) in virtue of time's possession of these properties it is true to say that time passes. Those who say that time does not pass generally want to affirm something like SPT. But those, on the other hand, who say that time does pass generally want to deny SPT. Of course, SPT is, as it stands, a mere skeleton of a thesis. It needs to be fleshed out. What could the relevant properties be? Why exactly would it be that in virtue of time's possession of these properties it is true to say that time passes? What exactly would it mean to say that time passes? These are all matters that require considerable discussion. The aim of this paper, however, is to take up some linguistic issues that have been considered central to the debate over the passage of time. There are two main reasons why I think it is appropriate to discuss these linguistic issues independently of the relevant metaphysical issues. The first reason is historical: many of the writers who have taken up the issue of whether or not time passes have begun their discussions by focusing on linguistic.. (shrink)

We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

The arguments of Fodor, Garret, Walker and Parkes [(1980) Against definitions, Cognition, 8, 263-367] are the source of widespread skepticism in cognitive science about lexical semantic structure. Whereas the thesis that lexical items, and the concepts they express, have decompositional structure (i.e. have significant constituents) was at one time "one of those ideas that hardly anybody [in the cognitive sciences] ever considers giving up" (p. 264), most researchers now believe that "[a]ll the evidence suggests that the classical [(decompositional)] view is (...) wrong as a general theory of concepts" [Smith, Medin & Rips (1984) A psychological approach to concepts: comments on Rey, Cognition, 17, 272], and cite Fodor et al. (1980) as "sounding the death knell for decompositional theories" [MacNamara & Miller (1989) Attributes of theories of meaning, Psychological Bulletin, 106, 360]. I argue that the prevailing skepticism is unmotivated by the arguments in Fodor et al. Fodor et al. misrepresent the form, function and scope of the decompositional hypothesis, and the procedures they employ to test for the psychological reality of definitions are flawed. I argue, further, that decompositional explanations of the phenomena they consider are preferable to their primitivist alternatives, and, hence, that there is prima facie reason to accept them as evidence for the existence of decompositional structure. Cognitive scientists would, therefore, do well to revert to their former commitment to the decompositional hypothesis. (shrink)

The theory of mental models and its computer implementations have led to crucial experiments showing that no standard logic—the sentential calculus and all logics that include it—can underlie human reasoning. The theory replaces the logical concept of validity (the conclusion is true in all cases in which the premises are true) with necessity (conclusions describe no more than possibilities to which the premises refer). Many inferences are both necessary and valid. But experiments show that individuals make necessary inferences that are (...) invalid, e.g., Few people ate steak or sole; therefore, few people ate steak. Other crucial experiments show that individuals reject inferences that are not necessary but valid, e.g., He had the anesthetic or felt pain, but not both; therefore, he had the anesthetic or felt pain, or both. Nothing in logic can justify the rejection of a valid inference: a denial of its conclusion is inconsistent with its premises, and inconsistencies yield valid inferences of any conclusions whatsoever including the one denied. So inconsistencies are catastrophic in logic. In contrast, the model theory treats all inferences as defeasible (nonmonotonic), and inconsistencies have the null model, which yields only the null model in conjunction with any other premises. So inconsistences are local. Which allows truth values in natural languages to be much richer than those that occur in the semantics of standard logics; and individuals verify assertions on the basis of both facts and possibilities that did not occur. (shrink)

This paper examines the conceptions of logic from Leibniz, Hume, Kant, Frege, Wittgenstein and Ayer, and regards the six philosophers as the representatives of logical exceptionalism. From their standpoints, this paper refines the tenets of logical exceptionalism as follows: logic is exceptional to all other sciences because of four reasons: (i) logic is formal, neutral to any domain and any entities, and general; (ii) logical truths are made true by the meanings of logical constants they contain or by logicians' rational (...) insight to consequence relations; (iii) logical truths are analytical, a prior and necessary, so not‐revisable; and (iv) logical laws are normative for how to correctly think. However, logical exceptionalism has encountered difficult open problems: What are logical constants? How to justify basic laws of logic? How are logical laws accessible to us? How to explain the reasonability of rival logics and select from them? How to explain the universal applicability of logical laws? How to explain the normativity of logical laws for correct thinking? This paper concludes that logical anti‐exceptionalism is more hopeful to successfully answer these questions than logical exceptionalism. (shrink)

There are two main parts to this article: (1) Quine's view of truth is substantive in a way that is not generally recognized. There are elements in the view of deflationism, minimalism, and of course disquotationalism to be sure, but from Quine's perspective the capacity for generalization - ascribing truth not to explicitly given sentences but to kinds of sentences - requires a full-bore Tarskian apparatus. This is necessary in order for truth to play what for Quine are its vital (...) roles in science, philosophy (epistemology and those parts of metaphysics that Quine recognizes), and crucially in logic itself. (These points have not been made with adequate care in the literature). (2) But is Tarskianism sufficient for playing all of those roles? Contrary to an interesting article by Lars Bergström - I argue that it is indeed sufficient, at least from Quine's point of view, and to see the point is to appreciate how thoroughgoing and powerful the notion of truth is, despite its being, 'in itself', only a device of sentential generalization. This dovetails with Quine's famous naturalism, a connection which I bring out at the end. (shrink)

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...) logic. Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest. (shrink)

Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...) frames. This unfashionable strategy has been accused of counterfeiting, since the meaning of the concept of existence would be incompatible with its relativization. Therefore, existence could only be relativistically invariant. In this paper, I shall examine whether such an accusation hits its target, and I will do this by examining whether the different criteria of existence that have been suggested by the Philosophical Tradition from Plato onwards imply that existence cannot be relativized. (shrink)

Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, or indeed objects at all. Instead, I argue (...) that realists should follow Prior (1971) and others in treating higher-order quantification (e.g. quantification into predicate or sentence position) as a genuine form of quantification in its own right, and so in particular, not to be analysed in terms of first-order quantification over abstract objects. I argue that from this ‘higher-orderist’ perspective, there is a relatively straightforward answer to the question of how possible worlds-as-propositions succeed in representing possibilities. (shrink)

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

Compared to the extensive amount of literature on various themes of W.V.O. Quine’s philosophy, his immanent concept of truth remains a relatively unexplored topic. This relative lack of research contributes to a persistent confusion on the deflationary and inflationary details of Quine’s truth. According to a popular reading, Quine’s disquotational definition of the truth predicate exhausts the content of truth, thus amounting to a deflationary view. Others promote opposing interpretations. I argue that by relying on Tarski’s semantic conception of truth, (...) Quine’s disquotational account inherits a commitment to classical correspondence intuitions. Based on this, Quine posits a firm constitution for truth as an intermediary between language and the world. From this constitution claim follows that the disquotational account proves incompatible with both the general deflationary thesis and, more specifically, the minimalist account, which deny any constitution for truth past what is given by the preferred deflationary schema. This reading is significant for refuting the widespread misrepresentations of Quine as a prominent deflationist. (shrink)

Constructivism is frequently met with objections, criticism and often equated with nihilism or relativism. Sometimes even blamed for what some would randomly picture as unwanted side effects of radicalism or of a progressivist era: such misconceptions are not only due to an imprecise grasp of the premises shared by the constructivist family of systems. The structure of media, political systems, and economic models, still up today impel societal understandings of knowledge on neo-positivistic grounds. The first part of this essay outlines (...) such pressures while sketching how language and worldviews play critical roles in our knowledge construction. Focusing on recent mediatic events, this work advances displaying some essential limits regarding the construction of human knowledge. Though unavoidable, some of the distinguishing aspects regarding the nature of our narratives are then critically reviewed. Later, it is shown how a special kind of self-denial that certain sub-stories implicitly hold about their own narrative nature leaves us with clashing worldviews that eventually collide onto crisis. Finally, it’ll be argued that it’s precisely in this scenario where a constructivist depiction of social discourses may move us away from any adolescent intent of elucidating absolutes within mere heuristics, to the pragmatic need of arriving on satisfactory agreements between parties (DOI: 10.4236/ojpp.2022). (shrink)