Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are constructed out of (...) variable assignments. But this has disquieting consequences, including Fine’s antinomy of the variable and an undue dependence of meanings on language. Here I develop an alternative, Fregean version of predicate logic that uses the traditional quantifier–variable apparatus for the expression of generality, possesses a fully compositional, non-representational semantics, and is not subject to the antinomy of the variable. The advantages of Fregean over Tarskian predicate logic are due to the former’s treating variables not as meaningful lexical items, but as mere marks of punctuation, similar to parentheses. I submit that this is indeed how the variables of predicate logic should be construed. (shrink)

W. V. Quine’s first philosophical monograph, Word and Object, is widely recognized as one of the most influential books of twentieth century philosophy. Notes, letters, and draft manuscripts at the Quine Archives, however, reveal that Quine was already working on a philosophical book in the early 1940s; a project entitled Sign and Object. In this paper, I examine these and other unpublished documents and show that Sign and Object sheds new light on the evolution of Quine’s ideas. Where “Two Dogmas (...) of Empiricism” is usually considered to be a turning point in Quine’s development, this paper redefines the place of ‘Two Dogmas’ in his oeuvre. Not only does Quine’s book project reveal that his views were already fairly naturalistic in the early 1940s ; Sign and Object also unearths the steps Quine had to take in maturing his perspective; steps that will be traced in the second half of this paper. (shrink)

This chapter argues that while quotation marks are polysemous, the thread that runs through all uses of quotation marks that involve reference to expressions is pure quotation, in which an expression formed by enclosing another expression in quotation marks refers to that enclosed expression. We defend a version of the so-called disquotational theory of pure quotation and show how this device is used in direct discourse and attitude attributions, in exposition in scholarly contexts, and in so-called mixed quotation in indirect (...) discourse and attitude attributions. We argue that uses of quotation marks that extend beyond pure quotation have two features in common. First, the expressions appearing in quotation marks are intended to be understood, and that they are intended to be understood is essential to the function that such quotations play in communication, though this does not always involve the expressions contributing their extensional properties to fixing truth conditions for the sentences in which they appear. Second, they appeal to a relation to the expression appearing in quotation marks that plays a role in determining the truth conditions of the sentences in which they appear. (shrink)

The aim of the paper is to show that W. V. O. Quine's animadversions against modal logic did not get the same attention that is considered to be the case nowadays. The community of logicians focused solely on the technical aspects of C. I. Lewis’ systems and did not take Quine's arguments and remarks seriously—or at least seriously enough to respond. In order to assess Quine's place in the history, however, his relation to Carnap is considered since their notorious break (...) was about the status of extensionality and modal logic. Since much of the works about the history of analytic philosophy is centered on the relationship of Quine and Carnap, their break about modality deserves much more attention—it also sheds some light on why should anyone wonder about Quine's early arguments against modal logic. The paper ends with some further considerations regarding the early formation of modal logic and hitherto unconsidered problematic issues. (shrink)

Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous cases all (...) involve referential uses of descriptions (or some variations of such uses), the most effective objection to the uniqueness condition draws on genuine attributive uses. (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.

Sometimes form-meaning mappings in language are not arbitrary, but iconic: they depict what they represent. Incorporating iconic elements of language into a compositional semantics faces a number of challenges in formal frameworks as evidenced by the lengthy literature in linguistics and philosophy on quotation/direct speech, which iconically portrays the words of another in the form that they were used. This paper compares the well-studied type of iconicity found with verbs of quotation with another form of iconicity common in sign languages: (...) classifier predicates. I argue that these two types of verbal iconicity can, and should, incorporate their iconic elements in the same way using event modification via the notion of a context dependent demonstration. This unified formal account of quotation and classifier predicates predicts that a language might use the same strategy for conveying both, and I argue that this is the case with role shift in American Sign Language. Role shift is used to report others’ language and thoughts as well as their actions, and recently has been argued to provide evidence in favor of Kaplanian “monstrous” indexical expressions. By reimagining role shift as involving either quotation for language demonstrations or “body classifier” predicates for action demonstrations, the proposed account eliminates one major argument for these monsters coming from sign languages. Throughout this paper, sign languages provide a fruitful perspective for studying quotation and other forms of iconicity in natural language due to their lack of a commonly used writing system which is otherwise often mistaken as primary data instead of speech, the rich existing literature on iconicity within sign language linguistics, and the ability of role shift to overtly mark the scope of a language report. In this view, written language is merely a special case of a more general phenomenon of sign and speech demonstration, which accounts more accurately for natural language data by permitting more strict or loose verbatim interpretations of demonstrations through the context dependent pragmatics. (shrink)

I argue that Frege Problems in thought are best modeled using graph-theoretic machinery; and that these problems can arise even when subjects associate all the same qualitative properties to the object they’re thinking of twice. I compare the proposed treatment to similar ideas by Heck, Ninan, Recanati, Kamp and Asher, Fodor, and others.

In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. This raises two (...) puzzles. First, as I show in section 2, Quine's mature thoroughly naturalized view has it that logic is simply obvious, and this is explains why we do not typically consider revising it. While Quine presents this naturalized view as a way to make good on his earlier metaphor of centrality in a web of belief, I argue that the resources of Quine's naturalized epistemology cannot adequately explain why we are reluctant to revise logic. And, Quine seems to recognize this point himself. In light of this, I explain in section 3 how Quine can allow that our overall scientific theory has systematic structure in a way that is consistent with his naturalistic strictures. Second, the asymmetrical internal structure of the web of belief seems to be inconsistent with its being a holistic web at all. I defuse this problem in section 4 by showing how Quine distinguishes between structural and confirmational considerations. I close by using this distinction to show how Quine's view can evade Michael Friedman’s criticisms, and allow for important methodological distinctions between areas of the web of belief. (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)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)

semantic minimalism and moderte contextualism.

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

Recent scholarship indicates that Quine’s “Truth by Convention” does not present the radical critiques of analytic truth found fifteen years later in “Two Dogmas of Empiricism.” This prompts a historical question: what caused Quine’s radicalization? I argue that two crucial components of Quine’s development can be traced to the academic year 1940–1941, when he, Russell, Carnap, Tarski, Hempel, and Goodman were all at Harvard together. First, during those meetings, Quine recognizes that Carnap has abandoned the extensional, syntactic approach to philosophical (...) analysis, an approach espoused in Carnap’s 1934 Logical Syntax of Language, and which Quine endorsed his entire career. Second, Tarski presents Quine with a philosophically well-motivated reason to think that an apparently analytic discipline, arithmetic, could be synthetic; this reflects one of the central assertions found in “Two Dogmas” but not in “Truth by Convention.” I use this account of Quine’s development to resolve a dispute between Creath and Mancosu concerning the timeline for Quine’s evolving critiques of analyticity. (shrink)

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)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

"Complexity" is a catchword of certain extremely popular and rapidly developing interdisciplinary new sciences, often called accordingly the sciences of complexity. It is often closely associated with another notably popular but ambiguous word, "information"; information, in turn, may be justly called the central new concept in the whole 20th century science. Moreover, the notion of information is regularly coupled with a key concept of thermodynamics, viz. entropy. And like this was not enough it is quite usual to add one more (...) at present extraordinarily popular notion, namely chaos, and wed it with the abovementioned concepts. It is my aim in this paper to critically analyse this conceptual mess from a logical and philosophical point of view concentrating on the concepts of complexity and information and the question concerning the true relation between them. (shrink)

This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did ...

My main aim is to clarify what we mean by ‘look’ sentences such as (1) below – ones that we use to talk about visual experience: -/- (1) The ball looked red to Sue -/- This is to help better understand a part of natural language that has so far resisted treatment, and also to help better understand the nature of visual experience. -/- By appealing to general linguistic principles I argue for the following account. First, we use (1) to (...) talk about an event. Second, we use the verb ‘look’ to specify the kind of event about which we are talking – it is a looking event. Third, we use the subject ‘the ball’ to specify a stimulus of the event – something that looks some way in the event. Fourth, we use the adjunct ‘to Sue’ to specify an experiencer of the event – someone to whom things look some way in the event. Finally, we use the complement ‘red’ to specify a way of the event – a way in which the event occurs (I take ways of occurring to be properties of events). Which way do we use ‘red’ in (1) to specify? I argue: the maximally specific way w such that the following is generically true: looking events whose stimulus is red occur in way w (it is important that this is understood generically: this is what does much of the work in explaining our use of (1) and other ‘look’ sentences). Putting this together, what we mean by (1) is: there was a looking event whose stimulus was the ball, whose experiencer was Sue, and which occurred in the maximally specific way that looking events occur when their stimulus is red. -/- This account of how we use ‘red’ in (1) is one of the most interesting aspects of my thesis. It extends to an account of how we use ‘proud’ in ‘John walks proud’, ‘as if he is American’ in ‘John talks as if he is American’, ‘like a duck’ in ‘John sounds like a duck’, and so on. In each case we use the expression in question to specify a way: the maximally specific way proud people walk, the maximally specific way American people talk, and so on. So the study of ‘look’ sentences has much to tell us about the functioning of many other English language constructions, and suggests that ways have a significant role to play in the semantics of natural language – a fact that has not yet been sufficiently recognised by linguists or philosophers of language. -/- My thesis also has implications for the philosophy of perception. One of the central questions about perception is: What is the nature of visual experience? What is it, for example, for a ball to look red to Sue? My thesis offers an answer: What it is for the ball to look red to Sue is for whatever it is that we mean by ‘The ball looks red to Sue’ to be the case, and what we mean by ‘The ball looks red to Sue’ is that there is a looking event whose stimulus is the ball, whose experiencer is Sue, and which is occurring in a certain way. It thus delivers an adverbial account of visual experience, one that has the resources to better deal with problems that are traditionally thought to be decisive against adverbial accounts. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

Despite the renown of ‘On Denoting’, much criticism has ignored or misconstrued Russell's treatment of scope, particularly in intensional, but also in extensional contexts. This has been rectified by more recent commentators, yet it remains largely unnoticed that the examples Russell gives of scope distinctions are questionable or inconsistent with his own philosophy. Nevertheless, Russell is right: scope does matter in intensional contexts. In Principia Mathematica, Russell proves a metatheorem to the effect that the scope of a single occurrence of (...) a description in an extensional context does not matter, provided existence and uniqueness conditions are satisfied. But attempts to eliminate descriptions in more complicated cases may produce an analysis with more occurrences of descriptions than featured in the analysand. Taking alternation and negation to be primitive (as in the first edition of Principia), this can be resolved, although the proof is non-trivial. Taking the Sheffer stroke to be primitive (as proposed by Russell in the second edition), with bad choices of scope the analysis fails to terminate. (shrink)

This paper propounds a systematic examination of the link between the Knower Paradox and provability interpretations of modal logic. The aim of the paper is threefold: to give a streamlined presentation of the Knower Paradox and related results; to clarify the notion of a syntactical treatment of modalities; finally, to discuss the kind of solution that modal provability logic provides to the Paradox. I discuss the respective strength of different versions of the Knower Paradox, both in the framework of first-order (...) arithmetic and in that of modal logic with fixed point operators. It is shown that the notion of a syntactical treatment of modalities is ambiguous between a self-referential treatment and a metalinguistic treatment of modalities, and that these two notions are independent. I survey and compare the provability interpretations of modality respectively given by Skyrms, B. (1978, The Journal of Philosophy 75: 368–387) Anderson, C.A. (1983, The Journal of Philosophy 80: 338–355) and Solovay, R. (1976, Israel Journal of Mathematics 25: 287–304). I examine how these interpretations enable us to bypass the limitations imposed by the Knower Paradox while preserving the laws of classical logic, each time by appeal to a distinct form of hierarchy. (shrink)

A common objection to Russell's theory of descriptions concerns incomplete definite descriptions: uses of (for example) ‘the book is overdue’ in contexts where there is clearly more than one book. Many contemporary Russellians hold that such utterances will invariably convey a contextually determined complete proposition, for example, that the book in your briefcase is overdue. But according to the objection this gets things wrong: typically, when a speaker utters such a sentence, no facts about the context or the speaker's communicative (...) intentions single out a particular description-theoretic proposition as the proposition expressed. However, this is an objection only if it is assumed that successful linguistic communication requires the hearer to identify a proposition uniquely intended by the speaker. We argue that this assumption is mistaken. On our view, no proposition, descriptive or referential, is uniquely intended in such a context; thus, no proposition can nor need be identified as the proposition expressed. One significant upshot is that, once the aforementioned assumption is rejected, incompleteness no longer poses a threat to Russell's theory of descriptions. (shrink)

The inclusion problem for theories of gender arises when those theories inappropriately fail to include certain individuals in the gender categories to which they ought to belong. The inclusion problem affects both of the most influential traditions in feminist theorizing about gender: social-position accounts and identity accounts. I argue that the inclusion problem can be solved by adopting a structured theory of gender which incorporates aspects of both social-position accounts and identity accounts. According to the theory I favor, an individual’s (...) gender is determined by their gender identity if they have one; otherwise, it is determined by their social position. My structured approach to gender offers a more direct solution to the gender inclusion problem than alternatives recently advocated by Barnes (2020), Jenkins (2023), and others. It also points the way to a simple solution to inclusion problems that arise at the level of gendered language. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

In this paper we present a solution to Saul Kripke’s Puzzle About Belief Meaning and use, Dordrecht, 1979) based on Kaplan’s metaphysical picture of words. Although it is widely accepted that providing such a solution was one of the main incentives for the development of Kaplan’s theory, it was never presented by Kaplan in a systematic manner and was regarded by many as unsatisfactory. We agree with these critiques, and develop an extension of Kaplan’s theory by introducing the notion of (...) “conservative” word uses, as well as arguing for the restriction of Kripke’s Disquotational Principle only to such uses. This restriction allows us to solve Kripke’s Puzzle by arguing that the assent of the puzzle’s protagonist does not allow disquotation and ascription of corresponding inconsistent belief, as it contains the non-conservative use of a proper name. At the end of the paper, we defend two of Kaplan’s theses that we find essential for our argument to work: that individuation of word tokens involves taking into account the intention of the speaker, and that different uniquely referring proper names of the same shape should be regarded as different homonymous words. (shrink)

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)

Among philosophers, Fregeanism and sententialism are widely considered two of the leading theories of the semantics of attitude reports. Among linguists, these approaches have received little recent sustained discussion. This paper aims to bridge this divide. I present a new formal implementation of Fregeanism and sententialism, with the goal of showing that these theories can be developed in sufficient detail and concreteness to be serious competitors to the theories which are more popular among semanticists. I develop a modern treatment of (...) quantifying in for Fregeanism and sententialism, in the style of Heim and Kratzer, and then show how these theories can—somewhat surprisingly—account for “third readings” on the model of the “Standard Solution” from possible-worlds semantics. The resulting Fregean/sententialist proposal has a distinctive attraction: it treats data related to counterfactual attitudes —which have proven challenging to accommodate in the setting of possible worlds semantics—straightforwardly as third readings. (shrink)

Per il dialeteismo ci sono contraddizioni vere. Questa concezione filosofica ha assunto una forma chiara e definita a partire dal lavoro del filosofo e logico Graham Priest – uno dei suoi padri fondatori, nonché uno dei suoi più strenui difensori. Questo libro intende portare il dialeteismo all’attenzione di un ampio pubblico, che non sia solo quello degli addetti ai lavori. Il volume è suddiviso in due parti. La prima include le cinque lezioni su "Dialeteismo e storia della filosofia" tenute da (...) Priest e Filippo Casati a Padova nel 2016, in occasione del Corso di Eccellenza per il dottorato in filosofia dell’Università di Padova. La seconda contiene quattro contributi sul dialeteismo di autori italiani. (shrink)

This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order logic. Peirce thought his graphs to be “more diagrammatic” than equivalently expressive languages for quantificational logic. The reason of this, he claimed, is that less room is afforded in Existential Graphs than in equivalently expressive languages for different ways of representing the same fact. (...) The reason of this, in turn, is that Existential Graphs are a non-linear, occurrence-referential notation. As a non-linear notation, each graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic that are obtained by permuting those elements that in the graphs lie in the same area. As an occurrence-referential notation, each Beta graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic in which the identity of reference of two or more variables is asserted. In brief, Peirce’s graphs are more diagrammatic than the linear, type-referential notation of first-order logic because the function that translates the latter to the graphs does not define isomorphism between the two notations. (shrink)

Mathematical logic was first introduced to China in early 1920s. Although, the process of introduction was facilitated by the lectures of Bertrand Russel at Peking University in 1921 and continued by China’s most passionate adherents of Russell’s philosophy, the establishment of mathematical logic as an academic discipline occurred only in late 1920s, in the framework of a recently reorganised Qinghua University in Peking. The main aim of this paper is to shed some light on the process of establishment of mathematical (...) logic at the department of philosophy at Qinghua University, between the years 1926 and 1945. In its main line of discussion, the article highlights the curricular developments at the department, connecting them with concrete theoretical endeavours by the leading members of the department. Furthermore, in its later parts, the article summarises the main advances made in the context of studies of modern logic at Qinghua University, from the expositions on the quintessential work Principia Mathematica, to the subsequent integration of criticisms coming from circles of logicians at Harvard University and ground-breaking contributions of Kurt Gödel in the mid-1930s. (shrink)

The principle of compositionality requires that the meaning of a complex expression remains the same after substitution of synonymous expressions. Alleged counterexamples to compositionality seem to force a theoretical choice: either apparent synonyms are not synonyms or synonyms do not syntactically occur where they appear to occur. Some theorists have instead looked to Frege’s doctrine of “reference shift” according to which the meaning of an expression is sensitive to its linguistic context. This doctrine is alleged to retain the relevant claims (...) about synonymy and substitution while respecting the compositionality principle. Thus, Salmon (Philos Rev 115(4):415, 2006) and Glanzberg and King (Philosophers’ Imprint 20(2):1–29, 2020) offer occurrence-based accounts of variable binding, and Pagin and Westerståhl (Linguist Philos 33(5):381–415, 2010c) argue that an occurrence-based semantics delivers a compositional account of quotation. Our thesis is this: the occurrence-based strategies resolve the apparent failures of substitutivity in the same general way as the standard expression-based semantics do. So it is a myth that a Frege-inspired occurrence-based semantics affords a genuine alternative strategy. (shrink)

It is often assumed that two linguistic agents can come to understand one another in part because they use the same words. That is, many philosophical theories of communication posit an intersubjective same-word relation. However, giving an account of this relation is complicated by what I call “The Variation Problem”—a problem resulting from the fact that the same word can be pronounced differently. In this paper, I first argue that previous models of the same-word relation, including Kaplanian and Chomskyan models, (...) fail to escape The Variation Problem. I then propose a new model on which the same-word relation is grounded in a particular kind of social relation that holds between the speaker and the audience. On this model, using the same word requires not that agents make the same sounds, but that they coordinate their internal linguistic representations. (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)

Much contemporary ontological inquiry takes place within the so-called ‘Quinean tradition’ but, given that some aspects of Quine’s project have been widely abandoned even by those who consider themselves Quineans, it is unclear what this amounts to. Fortunately recent work in metaontology has produced two relevant results here: a clearer characterisation of the metaontology uniting the aforementioned Quineans, most notably undertaken by Peter van Inwagen, and a raft of criticisms of that metaontology. In this paper I critique van Inwagen’s Quinean (...) metaontology, finding that certain challenges, supplemented by pressure to reflect more closely Quine’s work, should drive Quineans to adopt a stronger metaontology incorporating more of Quine’s radical views. I conclude that while van Inwagen’s Quineanism is problematic there are prospects for a viable, more wholeheartedly Quinean, metaontology. (shrink)

Dramatic changes or revolutions in a field of science are often made by outsiders or 'trespassers,' who are not limited by the established, 'expert' approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.

The conclusion of this chapter is that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on ad infinitum. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts of the (...) nature of vagueness and definiteness. (shrink)

This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

In a recent paper, Pickel and Rabern (2016) argue that a dynamic Tarskian semantics resolves Fine’s antinomy of the variable without the radical consequences for semantics proposed by Fine (2003, 2007). While Pickel and Rabern’s basic insight—a parameter of discourse context that tracks occurrences of variable-binding expressions—is important, I will argue that their own Tarskian theory faces a destructive dilemma: either their theory does not resolve Fine’s antinomy as they propose, or their theory does not reflect the intuitive motivation for (...) what they call structured meanings. I suggest that in response to this dilemma we should reject one of the principles that generates Pickel and Rabern’s version of the antinomy. Here Pickel and Rabern’s insight has surprising, but salutary, foundational consequences for semantics. (shrink)

Abstract: An indirect report typically takes the form of a speaker using the locution “said that” to report an earlier utterance. In what follows, I introduce the principal philosophical and pragmatic points of interest in the study of indirect reports, including the extent to which context sensitivity affects the content of an indirect report, the constraints on the substitution of co-referential terms in reports, the extent of felicitous paraphrase and translation, the way in which indirect reports are opaque, and the (...) use of indirect reports as pragmatic vehicles for other speech acts such as humor, insult, or irony. Throughout I develop several positions: (i) that a semantic analysis of indirect reports is insufficient, (ii) that the distinction between direct and indirect reports is not clear and that indirect reports are the predominate way of reporting while direct reports may be a para-linguistic variation on them, (iii) that most questions about the semantics and pragmatics of indirect reports will rely on a full understanding of the nature of what is reported and how it gets reported, (iv) that an analysis of reporting requires the pragmatic tools of metarepresentation and a social, inter-personal understanding of relevance and shared knowledge. (shrink)

According to Hume’s principle, a sentence of the form ⌜The number of Fs = the number of Gs⌝ is true if and only if the Fs are bijectively correlatable to the Gs. Neo-Fregeans maintain that this principle provides an implicit definition of the notion of cardinal number that vindicates a platonist construal of such numerical equations. Based on a clarification of the explanatory status of Hume’s principle, I will provide an argument in favour of a nominalist construal of numerical equations. (...) The neo-Fregean objections to such a construal will be examined and rejected. And the implications of the nominalist construal for the use of numerals and for the understanding of ontological questions for the existence of numbers will be spelled out. (shrink)

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.

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)

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...) the method to a generation of philosophers—with an eye to determining what the ‘essential characteristics’ of natural deduction are. (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)