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

O presente manual tem como intenção constituir um guia para uma disciplina introdutória de filosofia da linguagem. Foi elaborado a partir da leccionação da disciplina de Filosofia da Linguagem I na Faculdade de Letras da Universidade do Porto desde 2001. A disciplina de Filosofia da Linguagem I ocupa um semestre lectivo e proporciona aos estudantes o primeiro contacto sistemático com a área da filosofia da linguagem. Pretende-se que este manual ofereça aos estudantes os instrumentos necessários não apenas para acompanhar uma (...) iniciação ao campo da filosofia da linguagem mas também para o estudo e a investigação autónomos posteriores. Para isso é percorrido um trajecto que conduz das intuições pré-teóricas acerca de linguagem, de que todos dispomos, até um conhecimento disciplinar específico, histórico e temático, da filosofia da linguagem. Em termos práticos, são considerados como precedentes da disciplina de Filosofia da Linguagem I – mesmo se, pelo existem actualmente precedências em sentido estrito – as disciplinas de Lógica I e II e de Filosofia do Conhecimento I e II. Os programas dessas disciplinas nos últimos anos estiveram presentes por trás da elaboração do manual. (shrink)

By an incomplete sentence we shall understand a declarative sentence that can be used, without variation in its meaning, to make different statements in different contexts. Although the point deserves supporting argument, which we will not provide, sentences whose grammatical subjects are indexical expressions or demonstratives are obvious, plausible examples of incomplete sentences. Uttered in one context the sentence ‘He is ill’ may be used to make one statement, for example, that George is ill, while in another context the very (...) same sentence may be used to make a quite different statement, for example, that Paul is ill. (shrink)

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates (...) Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain. (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)

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)

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

Adviser: Professor Stefan Baumrin In the first chapter I introduce the distinction between metaethics and normative ethics and argue that metaethics, properly conceived, is a part of cognitive science. For example, the debate between rationalism and sentimentalism can be informed by recent empirical work in psychology and the neurosciences. In the second chapter I argue that the traditional view that one’s theory of semantics determines what one’s theory of justification must be is mistaken. Though it has been the case that (...) there are ‘typical’ combinations of semantic and justificational theories this is by no means forced on one. In the third chapter I examine two current kinds of expressivism; that of Blackburn and Copp. Each gives us an example of different combinations of semantic and justificatory theory. In Blackburn’s case he combines a use theory of meaning with a classic emotivist theory of justification, In Copp’s case it is a neo-Gricean philosophy of language with a realist’s theory of justification. I find both of these wanting as they ultimately collapse into relativistic subjectivism. In the fourth and fifth chapter I turn to developing Emotive Realism. The basic idea behind this view is that when someone says ‘x is wrong/right’ that person has (a) expressed a moral emotion about x and at the same time (b) expressed the belief that the emotion in (a) is the correct one to have. The belief expressed in (b) will be true or false depending on one’s theory of justification. In the fourth chapter I argue that we need separate semantic theories for thoughts and sentences. In the fifth chapter I fill in the details of Emotive Realism as I see it. (shrink)

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...) I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

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

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)

In this article, we study the prehistory of type theory up to 1910 and its development between Russell and Whitehead's Principia Mathematica ([71], 1910-1912) and Church's simply typed λ-calculus of 1940. We first argue that the concept of types has always been present in mathematics, though nobody was incorporating them explicitly as such, before the end of the 19th century. Then we proceed by describing how the logical paradoxes entered the formal systems of Frege, Cantor and Peano concentrating on Frege's (...) Grundgesetze der Arithmetik for which Russell applied his famous paradox and this led him to introduce the first theory of types, the Ramified Type Theory (RTT). We present RTT formally using the modern notation for type theory and we discuss how Ramsey, Hilbert and Ackermann removed the orders from RTT leading to the simple theory of types STT. We present STT and Church's own simply typed λ-calculus (λ → C) and we finish by comparing RTT, STT and λ → C. (shrink)

Anscombe raises a difficulty for the very idea of quotation. Davidson seeks to dissolve this difficulty. But the difficulty is real. And its lesson is that, in quotation, language takes itself as its topic in a non-objectifying manner. The idea of a non-objectifying manner of being a topic is crucial, not merely for understanding quotation, but for understanding the distinctive form of sensory consciousness in which language is perceived.

Augustine famously claims every word is a name. Some readers take Augustine to thereby maintain a purely referentialist semantic account according to which every word is a referential expression whose meaning is its extension. Other readers think that Augustine is no referentialist and is merely claiming that every word has some meaning. In this paper, I clarify Augustine’s arguments to the effect that every word is a name and argue that ‘every word is a name’ amounts to the claim that (...) for any word, there exist tokens of that word which are autonymous nouns. Augustine takes this to be the result of universal lexical ambiguity or equivocity and I clarify how Augustine’s account of metalinguistic discourse, which is one of the most detailed to have survived from antiquity, differs from some ancient and modern theories. (shrink)

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I (...) argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning. -/- (Note for readers: the paper's brief discussion of uniform reflection and omega inconsistency is misleading. The imagined interlocutor's argument makes an assumption about the PA-provability of provability generalizations that, while true for the Godel sentence's instances, is unjustified, in general. This means my position is stronger against this objection than the paper suggests, since omega inconsistent theories are not automatically inconsistent with their uniform reflection principles, you also need to assume the arithmetically true Pi-2 sentences.). (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)

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)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (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)

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)

The strategy of this paper is twofold: First, we carry out a systematic investigation of the question of what specific kind of meaning quotation marks contribute to the overall meaning of an utterance. We consider the following kinds of meaning: literal meaning (§ 2.1), conventional implicature (§ 2.2), presupposition (§ 2.3), and conversational implicature (§ 2.4). We present arguments in favor of a pragmatic analysis of quotation marks, claiming that the notion of conversational implicature seems to be the most promising (...) alternative: All general features of this kind of meaning are met by quotational constructions. Nonetheless, an approach based on conversational implicatures faces some problems when taking direct and pure quotations into account, namely effects on truth-conditions and, allegedly, on grammaticality. Thus, our second aim is to propose acceptable solutions to these criticisms in § 3. Finally, in § 4, we consider how a radical pragmatic account of quotation could be integrated into a Neo-Gricean architecture of the semantics/pragmatics-interface. (shrink)

The first Ukrainian translation of the most famous Quine’s article (1951), which became one of the classic texts of Analytical Philosophy.

O presente artigo busca debater a posição de Charles Sanders Peirce e dos primeiros estudantes peirceanos de Lógica (Christine Ladd e O. H. Mitchell nos Studies in Logic, 1883) dentro do debate inspirador da visão da linguagem dentro da Filosofia Analítica, conhecido como “Lingua Universalis contra Calculus Ratiocinator”, cujos primórdios podem ser traçados desde a filosofia de Gottfried Leibniz. Para isso, comparamos esse campo do pensamento peirceano com o debate crucial entre a conceitografia de Gottlob Frege (Begriffsschrift, 1879) e a (...) lógica algébrica de George Boole (An investigation of the Laws of Thought on which are founded the mathematical theories of Logic and Probabilities, 1854). O nosso objetivo principal é observar que esse momento da filosofia peirceana pode ser comparado com o pensamento wittgensteiniano, especialmente em sua nova vertente, chamada New Wittgenstein, que tenta superar a tradicional divisão entre Tractatus Logico-Philosophicus e Investigações Filosóficas. Pela comparação entre pensadores influenciados por C. S. Peirce e a filosofia de Ludwig Wittgenstein, pretendemos abrir caminhos na compreensão do conceito de jogo de linguagem, especialmente em sua gramática e em seus operadores simbólicos, através da observação das funções de verdade [truth functions] e as tabelas de verdade [truth tables] enquanto lógica algébrica. (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)

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.

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...) contextualism, and pluralism. Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. One rather conspicuous example is that the process of refining logical terminology has been productive. Future logic students will no longer be burdened by obscure terminology and they will be able to read, think, talk, and write about logic in a more careful and more rewarding manner. Closely related is increased use and study of variable-enhanced natural language as in “Every proposition x that implies some proposition y that is false also implies some proposition z that is true”. Another welcome development is the culmination of the slow demise of logicism. No longer is the teacher blocked from using examples from arithmetic and algebra fearing that the students had been indoctrinated into thinking that every mathematical truth was a tautology and that every mathematical falsehood was a contradiction. A fifth welcome development is the separation of laws of logic from so-called logical truths, i.e., tautologies. Now we can teach the logical independence of the laws of excluded middle and non-contradiction without fear that students had been indoctrinated into thinking that every logical law was a tautology and that every falsehood of logic was a contradiction. This separation permits the logic teacher to apply logic in the clarification of laws of logic. This lecture expands the above points, which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”. (shrink)

We are pleased to release this edition of Ralph Johnson’s The Rise of Informal Logic as Volume 2 in the series Windsor Studies in Argumentation. This edition is a reprint of the previous Vale Press edition with some typographical errors and other minor mistakes corrected. The prime motive for gathering Ralph H. Johnson’s essays under one cover is their clear articulation of the goals, concerns and problems of the discipline of informal logic. To my knowledge all of the published articles, (...) even of the 1980s, are still in print. But some are obtainable only by special request of a journal back issue. Their availability, even their existence, is not nearly widely enough known, and this volume is dedicated to remedying that disservice to those currently working in the field of informal logic, critical thinking, argumentation, and practical reasoning. Three of these sixteen pieces appear here in print for the first time. The previously published pieces have appeared from 1980 to 1992 as chapters in collective works or as articles in journals, and these in turn published in Canada, USA, The Netherlands and Belgium. It is hoped that gathering this hitherto scattered material under one cover will contribute to a greater understanding of what informal logic is, and to an enhanced sense of the impact of Johnson’s ideas. A discipline of informal logic might exist today without the writings of Johnson and his frequent co-author, J. Anthony Blair. But it would almost certainly be quite different from what it actually is. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (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)

1. Deductive and Inductive Inference. Within the traditional treatments of scientific method, e.g., in and, it was customary to divide scientific inference into two parts: deductive and inductive. Deductive inference was taken to mean the activity of deducing theorems from postulates and definitions, whereas inductive inference represented the activity of constructing a general statement from a set of particular “facts.” Deductive inference was relegated to the mathematical sciences, and inductive inference to the empirical sciences. As a consequence, the whole of (...) science was split into two quite distinct parts: deductive science was conceived to start with precise axioms, postulates, and definitions, and its method consisted in drawing inferences from these “givens” in such a way that if the original assumptions are taken as true, then the theorems must be taken as true also. The obligation behind this “must” of the mathematical sciences was an obligation based on strict rules of deductive inference; in the earlier analyses, it was supposed that these rules were all aspects of the general theory of the syllogism, as it was described in an almost complete form in but in later work the rules have been formalized in more general terms. Inductive inference, on the other hand, was supposed to start with observed facts; these facts, or “data,” were presumably given by the senses, and described particular aspects of the external world. If the facts were given in a certain way, then the empirical scientist could “infer” a generalized description; this generalization had the characteristic that if it were granted as true, then all the facts could be deduced as consequences. The inductive process admittedly does not lead to unique generalizations, and the philosopher of science searched for other defining characteristics of good inference, such as “simplicity” and “convenience.” These empirical generalizations were taken to be “descriptions of the phenomenal world of the scientist”; a further inductive step might be taken by constructing a set of very general principles out of the more specialized generalizations within specific research problems. These “higher” inductive inferences were regarded as “theories,” which could be studied by themselves within the method of deductive inference. The scientist was then described as “checking” theory by determining whether or not the predicted consequences deduced from theory actually hold in the phenomenal world. (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 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)

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

Arnold Cusmariu ABSTRACT: The Cogito formulation in Discourse on Method attributes properties to one conceptual category that belong to another. Correcting the error ends up defeating Descartes’ response to skepticism. His own creation, the Evil Genius, is to blame. Download PDF.

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)

The unification argument, usually regarded as the main argument for predicativism about proper names, has recently been attacked by Robin Jeshion. According to Jeshion, the unification argument is based on the assumption of the literality of predicative uses of proper names in statements such as “There is one Alfred in Princeton.” In such a use, a proper name ‘N’ is used predicatively to denote those, and only those, objects called N. As Jeshion argues, however, there are many other examples in (...) which a proper name ‘N’ is used predicatively to denote objects which are not called N. Based on such cases, Jeshion challenges the predicativist to provide a justification for assuming that the original predicative use of proper names, to which the predicativist appeals in the unification argument, is literal. My aim in this paper is to defend predicativism by arguing that the predicativist’s assumption is well motivated. To this end, I first present the unification argument for predicativism and Jeshion’s challenge to it. Then, I argue that the answer provided by Delia Graff Fara to Jeshion’s challenge is unsatisfactory. Finally, I meet Jeshion’s challenge by extending the phenomena highlighted in Jeshion’s examples to the referential uses of proper names. (shrink)

Greg Ray (2014) believes he has discovered a crucial oversight in Donald Davidson’s semantic programme, recognition of which paves the way for a novel approach to Davidsonian semantics. We disagree: Ray’s novel approach involves a tacit appeal to pre-existing semantic knowledge which vitiates its interest as a development of the Davidsonian programme.

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)

This paper proposes a reading of the history of equivalence in mathematics. The paper has two main parts. The first part focuses on a relatively short historical period when the notion of equivalence is about to be decontextualized, but yet, has no commonly agreed-upon name. The method for this part is rather straightforward: following the clues left by the others for the ‘first’ modern use of equivalence. The second part focuses on a relatively long historical period when equivalence is experienced (...) in context. The method for this part is to strip the ideas from their set-theoretic formulations and methodically examine the variations in the ways equivalence appears in some prominent historical texts. The paper reveals several critical differences in the conceptions of equivalence at different points in history that are at variance with the standard account of the mathematical notion of equivalence encompassing the concepts of equivalence relation and equivalence class. (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)