Deflationists claim that the truth predicate was introduced into our language merely to full a certain logico-linguistic function. Oddly enough, the question what this function exactly consists in has received little attention. We argue that the best way of understanding the function of the truth predicate is as enabling us to mimic higher-order quantification in a first-order framework. Indeed, one can show that the full simple theory of types is reducible to disquotational principles of truth. Our analysis has important consequences (...) for our understanding of truth. In this paper, we can only touch on one of them: we will argue that the insubstantiality of truth does not imply a conservativity requirement on our best theories of truth. (shrink)

The article is an extended critical discussion of Kevin Scharp’s Replacing Truth. Scharp’s case for the claim that the concept of truth is inconsistent is criticized, and so is his case for the claim that the concept of truth must be replaced because of its inconsistency.

In Replacing Truth, Scharp takes the concept of truth to be fundamentally incoherent. As such, Scharp reckons it to be unsuited for systematic philosophical theorising and in need of replacement – at least for regions of thought and talk which permit liar sentences and their ilk to be formulated. This replacement methodology is radical because it not only recommends that the concept of truth be replaced, but that the word ‘true’ be replaced too. Only Tarski has attempted anything like it (...) before. I dub such a view Conceptual Marxism. In assessing this view, my goals are fourfold: to summarise the many components of Scharp’s theory of truth; to highlight what I take to be some of the excess baggage carried by the view; to assess whether, and to what extent, the extreme methodology on offer is at all called for; finally, to briefly propose a less radical replacement strategy for resolving the liar paradox. (shrink)

In the first part of this paper, I express doubts that Tarski and Carnap were guilty of some confusions about the relations between truth and meaning, attributed to them by Soames. In the second part, I consider Quine's Carrollian argument against conventionalism about logical truth, discussed only briefly and approvingly by Soames, and I explore the question whether some not obviously incorrect forms of conventionalism about logical truth, such as what I call "finitary conventionalism", are immune to Quine's argument.

One of the main problems that Paul Horwich’s Minimalist theory of truth must face is the generalization problem, which shows that Minimalism is too weak to have the fundamental explanatory role Horwich claims it has. In this paper, I defend Horwich’s response to the generalization problem from an objection raised by Bradley Armour-Garb. I also argue that, given my response to Armour-Garb, Horwich’s proposal to cope with the generalization problem can be simplified. -/- L’un des principaux problèmes auxquels la théorie (...) minimaliste de la vérité de Paul Horwich doit faire face est le problème de la généralisation. Horwich soutient que le minimalisme a un rôle explicatif fondamental, mais le problème de la généralisation montre que cette théorie est trop faible pour tenir ce rôle. Dans cet article, je défends la réponse d’Horwich au problème de la généralisation à partir d’une objection soulevée par Bradley Armour-Garb. Je prétends également que ma réponse à Armour-Grab nous permet de formuler d’une manière plus simple la réponse d’Horwich au problème de la généralisation. (shrink)

Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, strong modal force, generality, (...) topic neutrality, basicness, and (quasi-)apriority, (v) the veridicality of logic and its applicability to science, (v) the normativity of logic, (vi) error, revision, and expansion in/of logic, and (vii) the relation between logic and mathematics. The high explanatory power of the truth-theoretic approach does not rule out an equal or even higher explanatory power of the proof-theoretic approach. But to the extent that the truth-theoretic approach is shown to be highly explanatory, it sets a standard for other approaches to logic, including the proof-theoretic approach. (shrink)

In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. (...) I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers. (shrink)

Alfred Tarski’s refinement of an account of truth into a formal system that turns on the acceptance of Convention-T has had a lasting impact on philosophical logic, especially work concerning truth, meaning, and other semantic notions. In a series of studies completed from the 1930s to the 1960s, Arne Næss collected and analysed intuitive responses from non-philosophers to questions concerning truth, synonymy, certainty, and probability. Among the formulations of truth studied by Næss were practical variants of expressions of the form (...) “p’ is true if and only if p’. This paper calls attention to a series of experimental results Næss overlooked in his original study. These data collectively suggest that acceptance of expressions of the form “p’ is true if and only if p’ varies according to what kind of statement p is. (shrink)

A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth (...) based on ᴌukasiewicz infinitely valued logic: PAᴌT. (shrink)

Presented here is an overview from the standpoints of sociology, history of science, philosophy of science and “pure science” of the lingering question of whether sociology is a form of scientific pursuit. The conclusion is drawn that sociology barely meets any of the rigid criteria traditionally associated with the natural sciences. Sociology is viewed as having a position of theory and argument which is labeled “inconoclastic scepticism.”.

Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can (...) then be strengthened to the conclusion that infinitely many things exist. Those things are not just all Gödel codes of sentences but rather all natural numbers. Against this background inclusive negative free logic collapses into noninclusive free logic, which collapses into classical logic. The consequences for ontological deflationism with respect to truth are discussed. (shrink)

Substantivism is a general philosophical methodology advocating a substantive approach to philosophical theorizing. In this article, I present an overview of this methodology with a special emphasis on the field of truth. I begin with a framework for understanding what is at stake in the substantivist–deflationist debate and describe the substantivist critique of deflationism. I then proceed to discuss contemporary substantivism as a positive methodology, present examples of recent substantivist theories of truth, delineate several principles of philosophical substantivism, and connect (...) it to contemporary thought about the nature and methods of philosophy. Due to limitations of space, I am unable to discuss all the forms contemporary substantivism has taken. But I try to give a clear sense of the central principles, challenges, and promise of this methodology. (shrink)

Many of Tarski’s better known papers are either about or include lengthy discussions of how to properly define various concepts: truth, logical consequence, semantic concepts, or definability. In general, these papers identify two primary conditions for successful definitions: formal correctness and material adequacy. Material adequacy requires that the concept expressed by the formal definition capture the intuitive content of truth. Our primary interest in this paper is to better understand Tarski’s thinking about material adequacy, and whether components of his view (...) developed over time. More precisely, we are concerned with how Tarski’s understanding of the content of the common-sense, every-day usage of truth may have developed over time. We distinguish this concern from the character of the extensional criterion of adequacy Tarski proposes: that a materially adequate definition must entail all instances of Convention T. We will develop our reading of Tarski as follows: first, we will review the “Polemical Remarks,” focusing primarily on §§14 and 17, and Tarski’s references to Naess’ empirical research. Next, we will provide a summary and discussion of Naess’ work, especially his findings with respect to Tarski’s definition of truth and his research that suggests there is no single common or everyday concept of truth. Third, we will consider several possible objections to our interpretation of the Tarski–Naess dialectic. We will conclude that Tarski’s conception of material adequacy developed over time, potentially because of what he had learned through his interactions with Naess. (shrink)

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...) and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics. (shrink)

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...) In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (shrink)

The writings of Joseph Henry Woodger (1894–1981) are often taken to exemplify everything that was wrongheaded, misguided, and just plain wrong with early twentieth-century philosophy of biology. Over the years, commentators have said of Woodger: (a) that he was a fervent logical empiricist who tried to impose the explanatory gold standards of physics onto biology, (b) that his philosophical work was completely disconnected from biological science, (c) that he possessed no scientific or philosophical credentials, and (d) that his work was (...) disparaged – if not altogether ignored – by the biologists and philosophers of his era. In this paper, we provide the first systematic examination of Woodger’s oeuvre, and use it to demonstrate that the four preceding claims are false. We argue that Woodger’s ideas have exerted an important influence on biology and philosophy, and submit that the current consensus on his legacy stems from a highly selective reading of his works. By rehabilitating Woodger, we hope to show that there is no good reason to continue to disregard the numerous contributions to the philosophy of biology produced in the decades prior to the professionalization of the discipline. (shrink)

Kotarbiński is one of the leading figures in the Lvov-Warsaw school of Polish philosophy. We summarize the development of Kotarbiński’s thought from his early nominalism and ‘pansomatistic reism’ to the later doctrine of ‘temporal phases’. We show that the surface clarity and simplicity of Kotarbiński’s writings mask a number of profound philosophical difficulties, connected above all with the problem of giving an adequate account of the truth of contingent (tensed) predications. The paper will examine in particular the attempts to resolve (...) these difficulties on the part of Leśniewski. It will continue with an account of the relations of Kotarbińskian reism to the ontology of things or entia realia defended by the later Brentano. Kotarbiński’s identification of Brentano as a precursor of reism is, it will be suggested, at least questionable, and the paper will conclude with a more careful attempt to situate the Brentanian and Kotarbińskian ontologies within the spectrum of competing ontological views. (shrink)

Alfred Tarski’s influence on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is Tarski’s work on the decision procedure for algebra and geometry, the method of elimination of quantifiers, the semantics of formal languages, model-theoretic preservation theorems, and algebraic logic; various connections of each with computer science are taken up.

This book is a survey of the most important developments in Austrian philosophy in its classical period from the 1870s to the Anschluss in 1938. Thus it is intended as a contribution to the history of philosophy. But I hope that it will be seen also as a contribution to philosophy in its own right as an attempt to philosophize in the spirit of those, above all Roderick Chisholm, Rudolf Haller, Kevin Mulligan and Peter Simons, who have done so much (...) to demonstrate the continued fertility of the ideas and methods of the Austrian philosophers in our own day. For some time now, historians of philosophy have been gradually coming to terms with the idea that post-Kantian philosophy in the German-speaking world ought properly to be divided into two distinct traditions which we might refer to as the German and Austrian traditions, respectively. The main line of the first consists in a list of personages beginning with Kant, Fichte, Hegel and Schelling and ending with Heidegger, Adorno and Bloch. The main line of the second may be picked out similarly by means of a list beginning with Bolzano, Mach and Meinong, and ending with Wittgenstein, Neurath and Popper. As should be clear, it is the Austrian tradition that has contributed most to the contemporary mainstream of philosophical thinking in the Anglo-Saxon world. For while there are of course German thinkers who have made crucial contributions to the development of exact or analytic philosophy, such thinkers were outsiders when seen from the perspective of native German philosophical culture, and in fact a number of them found their philosophical home precisely in Vienna. When, in contrast, we examine the influence of the Austrian line, we encounter a whole series of familiar and unfamiliar links to the characteristic concerns of more recent philosophy of the analytic sort. As Michael Dummett points out in his Origins of Analytic Philosophy, the newly fashionable habit of referring to analytic philosophy as "Anglo-American" is in this light a "grave historical distortion". If, he says, we take into account the historical context in which analytic philosophy developed, then such philosophy "could at least as well be called "Anglo-Austrian" (1988, p. 7). Much valuable scholarly work has been done on the thinking of Husserl and Wittgenstein, Mach and the Vienna Circle. The central axis of Austrian philosophy, however, which as I hope to show in what follows is constituted by the work of Brentano and his school, is still rather poorly understood. Work on Meinong or Twardowski by contemporary philosophers still standardly rests upon simplified and often confused renderings of a few favoured theses taken out of context. Little attention is paid to original sources, and little effort is devoted to establishing what the problems were by which the Austrian philosophers in general were exercised -- in spite of the fact that many of these same problems have once more become important as a result of the contemporary burgeoning of interest on the part of philosophers in problems in the field of cognitive science. (shrink)

Meaning involves normativity: a word has a meaning only if some of its uses are correct and some are incorrect. A full understanding of meaning demands an account of the normativity of meaning. One such account has it that the normativity of meaning stems from conventions for the use of words. Donald Davidson argues that communication does not require linguistic conventions. Ian Hacking has objected to Davidson's theory of meaning on the ground that Davidson is unable to allow for the (...) possibility of error, since his conception of communication is too impoverished to supply the requisite normativity. In this paper I describe Hacking's objection and attempt to answer it. (shrink)

Some important ideas in Kelsen's Pure Theory of Law can be traced back to Kantian tradition, which has been very influential in Kelsen's thought, particularly in his early period. Among them we find the distinction between two radically different worlds (the world of facts and the world of norms), the normativity of legal science and the idea of validity as a binding force, based on the famous doctrine of the basic norm. These tenets and, especially, the use of a normative (...) concept of validity prove to be incompatible with Kelsen's positivistic programme of a value‐free legal science. The science of law cannot state that legal norms are obligatory or binding without trespassing the limits of Kelsen's ideal of a legal science; on the other hand, it is possible to define the concept of a legal system without resorting to the basic norm. So, if Kelsen is to be regarded as a consequent positivist, the Kantian ingredients of his theory must be rejected and the descriptive concept of validity as membership must be substituted for the normative notion of validity as a binding force. (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)

The Polish logicians' propositional calculi, which consist in a distinct synthesis of the Fregean and Boolean approaches to logic, influenced W. V. Quine's early work in formal logic. This early formal work of Quine's, in turn, can be shown to serve as one of the sources of his holistic conception of natural language.

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

This paper was written with two aims in mind. A large part of it is just an exposition of Tarski's theory of truth. Philosophers do not agree on how Tarski's theory is related to their investigations. Some of them doubt whether that theory has any relevance to philosophical issues and in particular whether it can be applied in dealing with the problems of philosophy (theory) of science.In this paper I argue that Tarski's chief concern was the following question. Suppose a (...) language L belongs to the class of languages for which, in full accordance with some formal conditions set in advance, we are able to define the class of all the semantic interpretations the language may acquire. Every interpretation of L can be viewed as a certain structure to which the expressions of the language may refer. Suppose that a specific interpretation of the language L was singled out as the intended one. Suppose, moreover, that the intended interpretation can be characterized in a metalanguage L +. If the above assumptions are satisfied, can the notion of truth for L be defined in the metalanguage L + and, if it can, how can this be done? (shrink)

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences, yet not in the scope of negation, the system with the reflection (...) schema for these T-sentences assumes the strength of the Kripke-Feferman theory KF, and thus of ramified analysis up to go. (shrink)

This paper was written with two aims in mind. A large part of it is just an exposition of Tarski’s theory of truth. Philosophers do not agree on how Tarski’s theory is related to their investigations. Some of them doubt whether that theory has any relevance to philosophical issues and in particular whether it can be applied in dealing with the problems of philosophy (theory) of science. In this paper I argue that Tarski’s chief concern was the following question. Suppose (...) a language L belongs to the class of languages for which, in full accordance with some formal conditions set in advance, we are able to define the class of all the semantic interpretations the language may acquire. Every interpretation of L can be viewed as a certain structure to which the expressions of the language may refer. Suppose that a specific interpretation of the language L was singled out as the intended one. Suppose, moreover, that the intended interpretation can be characterized in a metalanguage L +. If the above assumptions are satisfied, can the notion of truth for L be defined in the metalanguage L + and, if it can, how can this be done? Many students of Tarski’s conception will find the above exposition inconsistent with their own views on the essence of Tarski’s conception. On the other hand, as it is argued in this paper, the proposed interpretation of Tarski’s ideas allows one to use Tarski’s theory as a fundamental tool for semantic analyses of various theories, factual theories in particular. More specifically, it is argued that Tarski’s theory of truth allows one to clearly oppose a theory meant to be certain deductive system (a set of accepted sentences, say axioms, and a logical machinery for deducing from them new ones) and a theory meant to be a certain semantic system, i.e a set of sentences that serve to communicate some states of affairs and to use that opposition to explicate and occasionally also define the notion of truth. The opposition in question is of the utmost significance for analyzing some developments in both mathematics and factual sciences. The approach which is concerned with the logical relations between the elements of science such an approach is throughout this paper called analytical is put into question. The growth of science is determined by how well scientific theories are able to account for factual states of affairs. The intuitive notion of truth applied by the scientists does not necessarily correspond in a straightforward way to its Tarskian counterpart. On the other hand, as is claimed in this paper, the Tarskian notion of truth offers as adequate explication of intuitive notion of truth as possible. (shrink)

Philosophical analysis was the central preoccupation of 20th-century analytic philosophy. In the contemporary methodological debate, however, it faces a number of pressing external and internal challenges. While external challenges, like those from experimental philosophy or semantic externalism, have been extensively discussed, internal challenges to philosophical analysis have received much less attention. One especially vexing internal challenge is that the success conditions of philosophical analysis are deeply unclear. According to the standard textbook view, a philosophical analysis aims at a strict biconditional (...) that captures the necessary and sufficient conditions for membership in the relevant category. The textbook view arguably identifies a necessary condition on successful philosophical analyses, but understood as a sufficient condition it is untenable, as I will argue in this paper. To this end, I first uncover eight conditions of adequacy on successful philosophical analyses, some of which have rarely been spelled out in detail. As we shall see, even sophisticated alternatives to the textbook view fail to accommodate some of these conditions. I then propose the concept grounding view as a more promising account of philosophical analysis. According to this view, successful philosophical analyses require necessary biconditionals that are constrained by grounding relations among the concepts involved. Apart from providing a satisfactory account of philosophical analysis in its own right, the concept grounding view is also able to meet the challenge that the success conditions of philosophical analysis are problematically unclear. (shrink)

The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, (...) the paper considers an alternative approach that focuses the blame on antisymmetry but allows us to keep natural supplementation axioms. Third, we look at counterexamples to the idempotency of composition and the associated ‘parts just once’ principle. We explore options for developing weaker mereologies that avoid such commitments. (shrink)

The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].

Formulating my comments I have had difficulties of three kinds. First, I am not at all sure that I have understood Davidson correctly at every point. Secondly, not being aware of how far I may take for granted that Davidson and I share what may be called the same background ...

The paper [Tarski: Les fondements de la géométrie des corps, Annales de la Société Polonaise de Mathématiques, pp. 29—34, 1929] is in many ways remarkable. We address three historico-philosophical issues that force themselves upon the reader. First we argue that in this paper Tarski did not live up to his own methodological ideals, but displayed instead a much more pragmatic approach. Second we show that Leśniewski's philosophy and systems do not play the significant role that one may be tempted to (...) assign to them at first glance. Especially the role of background logic must be at least partially allocated to Russell's systems of Principia mathematica. This analysis leads us, third, to a threefold distinction of the technical ways in which the domain of discourse comes to be embodied in a theory. Having all of this in place, we discuss why we have to reject the argument in [Gruszczyński and Pietruszczak: Full development of Tarski's Geometry of Solids, The Bulletin of Symbolic Logic, vol. 4, no. 4, pp. 481—540] according to which Tarski has made a certain mistake. (shrink)

Bertrand Russell’s 1906 article ‘The Theory of Implication’ contains an algebraic weak completeness proof for classical propositional logic. Russell did not present it as such. We give an exposition of the proof and investigate Russell’s view of what he was about, whether he could have appreciated the proof for what it is, and why there is no parallel of the proof in Principia Mathematica.

Suszko’s problem is the problem of finding the minimal number of truth values needed to semantically characterize a syntactic consequence relation. Suszko proved that every Tarskian consequence relation can be characterized using only two truth values. Malinowski showed that this number can equal three if some of Tarski’s structural constraints are relaxed. By so doing, Malinowski introduced a case of so-called mixed consequence, allowing the notion of a designated value to vary between the premises and the conclusions of an argument. (...) In this article we give a more systematic perspective on Suszko’s problem and on mixed consequence. First, we prove general representation theorems relating structural properties of a consequence relation to their semantic interpretation, uncovering the semantic counterpart of substitution-invariance, and establishing that mixed consequence is fundamentally the semantic counterpart of the structural property of monotonicity. We use those theorems to derive maximum-rank results proved recently in a different setting by French and Ripley, as well as by Blasio, Marcos, and Wansing, for logics with various structural properties. We strengthen these results into exact rank results for nonpermeable logics. We discuss the underlying notion of rank, and the associated reduction proposed independently by Scott and Suszko. As emphasized by Suszko, that reduction fails to preserve compositionality in general, meaning that the resulting semantics is no longer truth-functional. We propose a modification of that notion of reduction, allowing us to prove that over compact logics with what we call regular connectives, rank results are maintained even if we request the preservation of truth-functionality and additional semantic properties. (shrink)

I make a Quinean case that Quine’s ontological relativity marked a wrong turn in his philosophy, that his fundamental commitments point toward the classical view of ontology that was worked out in most detail in hisWord and Object. This removes the impetus toward structuralism in his later philosophy.

In the second Critique, Kant claims that the moral law is given as a fact of reason. In this paper, contra the standard view, I argue that there is a non-dogmatic way of defending this claim. And Kant’s principle of morality is widely taken to be a formal principle. How then can such a formal principle be reconciled with our substantial moral end? In this paper, I also argue that Kant’s principle of morality can be construed as a formal principle (...) in the sense that it provides correctness conditions for moral laws, rather than providing specific moral laws.Dans sa deuxième Critique, Kant affirme que la loi morale se donne comme un fait de raison. Dans cet article, contrairement à la position standard, nous prétendons qu’il existe une autre façon — non dogmatique — de défendre cette affirmation. Par ailleurs, le principe de moralité de Kant est largement considéré comme étant formel. Comment un tel principe formel peut-il être réconcilié avec notre fin morale substantielle? Nous soutenons également que le principe de moralité de Kant peut être interprété comme un principe formel dans le sens où il fournit des conditions d’acceptabilité pour les lois morales, et non des lois morales spécifiques. (shrink)

We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to isolate comparable models for each theory. Relying on the chosen interpretations, we introduce the notion of environment structure, that is, a minimal structure that contains a (sub)structure for each theory. In particular, in the case of mereogeometries, the domain of (...) an environment structure is composed of particular subsets of Rn. The comparison of mereogeometrical theories within these environment structures shows dependencies among primitives and provides (relative) definitional equivalences. With one exception, we show that all the theories considered are equivalent in these environment structures. (shrink)

That reference is inscrutable is demonstrated, it is argued, not only by W. V. Quine's arguments but by Peter Unger's "Problem of the Many." Applied to our own language, this is a paradoxical result, since nothing could be more obvious to speakers of English than that, when they use the word "rabbit," they are talking about rabbits. The solution to this paradox is to take a disquotational view of reference for one's own language, so that "When I use 'rabbit,' I (...) refer to rabbits" is made true by the meaning of the word "refer." The reference relation is extended to other languages by translation. The explanation for this peculiarly egocentric conception of semantics-questions of others' meanings are settled by asking what I mean by words of my language-is to be found in our practice of predicting and explaining other people's behavior by empathetic identification. I understand other people's behavior by asking what I would do in their place. (shrink)

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of Lukasiewicz. For the proof we only use Minkowski's convex body theorem and the rudiments of piecewise linear topology.