All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.

In this paper we argue, from an inferential approach, that the inferential role played by a model, during modeling practice, is independent of the notion of representation engaged with the chosen modeling approach. Indeed, we believe that the notion of surrogative reasoning is neither subsidiary nor founded on the notion of representation and that it will only find its foundations in logic itself. Neither the notion of representation is an inferential notion nor FIM is a type of representation-based thinking.

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...) an inter-weaving of methodological and epistemological considerations. The latter aspect illustrates how philosophical concerns can grow out of mathematical practice, as opposed to being imposed on it from outside. It also sheds new light on the legacy and the lasting significance of logicism today. (shrink)

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)

After describing the philosophical background of Kerry's work, an account is given of the way Kerry proposed to supplement Bolzano's conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege's work and Kerry's views were then attacked by Frege.The following two issues were central to this controversy: (a) the relation between the content of a concept and the object of a concept; (b) the logical roles of the definite article. Not only (...) did Frege in 1892 offer an unconvincing solution to Kerry's puzzle concerning 'the concept horse' but he also overlooked the many criticisms levelled by Kerry against the notion of an (indefinite) extension on which his own definition of number was based. (shrink)

The idea underlying the Begriffsschrift account of identities was that the content of a sentence is a function of the things it is about. If so, then if an identity a=b is about the content of its contained terms and is true, then a=a and a=b have the same content. But they do not have the same content; so, Frege concluded, identities are not about the contents of their contained terms. The way Frege regarded the matter is that in an (...) identity the terms flanking the symbol for identity do not have their ordinary contents, but instead have themselves as their contents. In ?Uber Sinn und Bedeutung? Frege became convinced that if an identity a=bis about the signs aand b, then it expresses no proper knowledge. So, since it is evident that many such identities do express proper knowledge, Frege concluded that identities are not about their contained signs. So he became convinced that his Begriffsschrift account was incorrect. What was the error in the argument that led Frege to that account? It was thinking that the content of a sentence is a function of the contents of its constituent signs, that is, the things it is about. (shrink)

We reconstruct Frege’s treatment of certain deducibility problems posed by Boole. It turns out that in his formalization and solution of Boole’s problems Frege anticipates the idea of propositional resolution.

The paper presents an argument against a "metaphysical" conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its (...) a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: "the realm of the natural", constituted by the things of our empirical world, and "the realm of the formal", constituted by the structures that we use as "prisms" to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic. (shrink)

While according to the inferentialists, meaning is always a kind of inferential role, proponents of other approaches to semantics often doubt that actual meanings, as they see them, can be generally reduced to inferential roles. In this paper we propose a formal framework for considering the hypothesis of the.

The concept ofsemantic interpretation is a source of chronic confusion: the introduction of a notion ofinterpretation can be the result of several quite different kinds of considerations.Interpretation can be understood in at least three ways: as a process of dis-abstraction of formulas, as technical tool for the sake of characterizing truth, or as a reconstruction of meaning-assignment. However essentially different these motifs are and however properly they must be kept apart, these can all be brought to one and the same (...) notion of interpretation: to the notion of a compositional evaluation of expressions inducing a possible distribution of truth values among statements. (shrink)

One particular topic in the literature on Frege’s conception of sense relates to two apparently contradictory theses held by Frege: the isomorphism of thought and language on one hand and the expressibility of a thought by different sentences on the other. I will divide the paper into five sections. In (1) I introduce the problem of the tension in Frege’s thought. In (2) I discuss the main attempts to resolve the conflict between Frege’s two contradictory claims, showing what is wrong (...) with some of them. In (3), I analyze where, in Frege’s writings and discussions on sense identity, one can find grounds for two different conceptions of sense. In (4) I show how the two contradictory theses held by Frege are connected with different concerns, compelling Frege to a constant oscillation in terminology. In (5) I summarize two further reasons that prevented Frege from making the distinction between two conceptions of sense clear: (i) the antipsychologism problem and (ii) the overlap of traditions in German literature contemporary to Frege about the concept of value. I conclude with a hint for a reconstruction of the Fregean notion of ‘thought’ which resolves the contradiction between his two theses. (shrink)

The German debates concerning the need for a reform of logic in post-Hegelian times took place under the label “The logical question”, a label introduced by Friedrich Adolf Trendelenburg. The main objective of these debates was to overcome the Hegelian identification of logic and metaphysics without re-establishing the old Aristotelian-scholastic formal logic. This paper presents the positions developed by Friedrich Adolf Trendelenburg, Otto Friedrich Gruppe, and Carl v. Prantl, each of whom advocated the importance of language in logic in order (...) to introduce a more dynamical element into the alleged static character of formal logic. (shrink)

How does your information change when you learn that something might be the case, where the modal “might” is epistemic? On the orthodox view, a proposition is added to your information base; on the view defended here, no propositions are added to your information base but some are removed from it. I argue that Stephen Yablo’s recent attempt to define this removal operation as a kind of propositional subtraction fails, offer a definition of my own in terms of the part–whole (...) relations between the truthmakers of the propositions one accepts, and argue that a deontic analogue of this account solves a problem about permission posed long ago by David Lewis. (shrink)

Discussion of Frege’s theory of fiction has tended to focus on the problem of empty names, and has consequently missed the truly problematic aspect of the theory, Frege’s commitment to the view that even fictional sentences that contain no empty names fail to refer. That claim prima facie conflicts with his commitment to the cognitive transparency of sense, and the determination of reference by sense. Resolving this tension compels us to recognize that fiction for Frege is a special kind of (...) force, and that words express a sense capable of picking out a referent only in the presence of the appropriate assertoric force. In effect, Frege’s theory of fiction reveals his commitment to an act-centered rather than an expression-centered semantics. (shrink)

Some Carrollian posthumous manuscripts reveal, in addition to his famous ‘logical diagrams’, two mysterious ‘logical charts’. The first chart, a strange network making out of fourteen logical sentences a large 2D ‘triangle’ containing three smaller ones, has been shown equivalent—modulo the rediscovery of a fourth smaller triangle implicit in Carroll's global picture—to a 3D tetrahedron, the four triangular faces of which are the 3+1 Carrollian complex triangles. As it happens, such an until now very mysterious 3D logical shape—slightly deformed—has been (...) rediscovered, independently from Carroll and much later, by a logician , a mathematician and a linguist studying the geometry of the ‘opposition relations’, that is, the mathematical generalisations of the ‘logical square’. We show that inside what is called equivalently ‘n-opposition theory’, ‘oppositional geometry’ or ‘logical geometry’, Carroll's first chart corresponds exactly, duly reshap.. (shrink)

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably (...) infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. -/- Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects. (shrink)

This paper concerns the formal semantic analysis of imperative sentences. It is argued that such an analysis cannot be deferred to the semantics of propositions, under any of the three commonly adopted strategies: the performative analysis, the sentence radical approach to propositions, and the (nondeclarative) mood-as-operator approach. Whereas the first two are conceptually problematic, the third faces empirical problems: various complex imperatives should be analysed in terms of semantic operators over simple imperatives. One particularly striking case is the Dutch pluperfect (...) imperative. It is argued that this construction should be analysed as a genuine counterfactual imperative. On the constructive side, in the last part of the paper a formal semantic analysis of imperatives is presented, in the framework of Update Semantics. On this analysis, imperatives are sui generis semantic entities, on a par with propositions. The analysis also includes an account of the counterfactual imperatives. (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)

Dylemat Jörgensena długo stanowił dla logiki zagadkę. Do jego rozwiązania okazało się konieczne dokonanie pewnych rozstrzygnięć filozoficznych. Artykuł podaje te rozstrzygnięcia i omawia sposób rozwiązania dylematu.

The dilemma mentioned in the title have long been a puzzle to logic. To solve it, it was necessary to make some philosophical decisions. The article provides these decisions and discusses the way to solve the problem.

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...) assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​. (shrink)

A constant of Frege’s writing is his rejection of indeterminate predicates as found in natural language. This paper follows Frege’s remarks on vagueness from the early "Begriffsschrift” to his mature works, drawing brief parallels with the main contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness in his mature ontology is mainly due to heuristic rules of thumb which Frege took as essential, not to a deep (...) problem in his fundamental apparatus. (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)

I propose to reconsider Gilbert Ryle’s thesis in 1956 in his introduction to The Revolution of Philosophy that “the story of twentieth-century philosophy is very largely the story of this notion of sense or meaning” and, as he writes elsewhere, the “preoccupation with the theory of meaning is the occupational disease of twentieth-century Anglo-Saxon and Austrian philoso- phy.” Ryle maintains that this preoccupation demar- cates analytic philosophy from its predecessors and that it gave philosophy a set of academic credentials as (...) a rigorous discipline with its own domain and method. I will maintain that Ryle, with some minor qualifica- tions, was correct in his assessment of the nature of analytic philosophy at that time, and I will argue that the next 50 years continued to be, very largely, the story of meaning, exemplified by the groundbreaking work of Rawls and Kripke. However, I argue that this work also contains the seeds that contributed to the emergence of philosophies that represent a significant departure from analytic philosophy. (shrink)

Un trait du langage qui menace de saper la sûreté de la pensée est sa tendance à former des noms propres auxquels aucun objet ne correspond. [...] Un exemple particulièrement remarquable de cela est la formation d’un nom propre selon le schéma «l’extension du concept a», par exemple «l’extension du concept étoile». À cause de l’article défini, cette expression semble désigner un objet; mais il n’y a aucun objet pour lequel cette expression pour-rait être une désignation appropriée. De là les (...) paradoxes de la théorie des ensembles, qui ont porté un coup mortel à la théorie des ensembles elle-même. J’étais moi-même sous cette illusion quand afin de fournir une fondation logique aux nombres, j’ai tenté de construire les nombres comme des ensembles. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...) forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

Over the past thirty years, it is been common to hear the mind likened to a digital computer. This essay is concerned with a particular philosophical view that holds that the mind literally is a digital computer (in a specific sense of “computer” to be developed), and that thought literally is a kind of computation. This view—which will be called the “Computational Theory of Mind” (CTM)—is thus to be distinguished from other and broader attempts to connect the mind with computation, (...) including (a) various enterprises at modeling features of the mind using computational modeling techniques, and (b) employing some feature or features of production-model computers (such as the stored program concept, or the distinction between hardware and software) merely as a guiding metaphor for understanding some feature of the mind. This entry is therefore concerned solely with the Computational Theory of Mind (CTM) proposed by Hilary Putnam [1961] and developed most notably for philosophers by Jerry Fodor [1975, 1980, 1987, 1993]. The senses of ‘computer’ and ‘computation’ employed here are technical; the main tasks of this entry will therefore be to elucidate: (a) the technical sense of ‘computation’ that is at issue, (b) the ways in which it is claimed to be applicable to the mind, (c) the philosophical problems this understanding of the mind is claimed to solve, and (d) the major criticisms that have accrued to this view. (shrink)

The traditional use of the expression 'pseudoproblem' is analysed in order to clarify the talk of pseudoproblems and related phenomena. The goal is to produce a philosophically serviceable terminology that stays true to its historical roots. This explicative study is inspired by and makes use of the method of logical reconstruction. Since pseudoproblems are usually expressed by pseudoquestions a formal language of questions is presented as a possible reconstruction language for alleged pseudoproblems. The study yields an informal theory of pseudoproblems (...) whose presuppositions are critically investigated right away. At least one result remains: Claims of pseudoproblemship and their refutations must not be voiced casually - they are to be relativized and need substantial interpretive effort. (shrink)

A crítica de Frege ao psicologismo evoluiu ao longo do tempo. O ponto principal desta evolução é a passagem da crítica do psicologismo em “Fundamentos da aritmética” àquela das “Leis básicas da aritmética”. O papel determinante nesta passagem se dá a partir da crítica que Frege recebeu de Kerry.

In our introduction we make some remarks on the main topics of this issue: assertion and proof. We briefly describe how each of the papers in the present publication has contributed from either different or complementary perspectives to the logical reflection on assertion and proof, while also specifying the relation between them.

Some central philosophical issues concern the use of mathematics in putatively non-mathematical endeavors. One such endeavor, of course, is philosophy, and the philosophy of mathematics is a key instance of that. The present article provides an idiosyncratic survey of the use of mathematical results to provide support or counter-support to various philosophical programs concerning the foundations of mathematics.

“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science, (3) Formal (...) systems in the sense of Hilbert, Curry and the formalist school, (4) Symbolic logic, a science using symbols, such as Venn diagrams, (5) Mathematical logic, a mathematical approach to reasoning. We argue that these five meanings are independent and that the meaning (5) is the one which better characterized modern logic, which should therefore not be called “formal logic”. (shrink)

In the philosophical debate on lying, there has generally been agreement that either the speaker believes that his statement is false, or he believes that his statement is true. This article challenges this assumption, and argues that lying is a scalar phenomenon that allows for a number of intermediate cases – the most obvious being cases of uncertainty. The first section shows that lying can involve beliefs about graded truth values (fuzzy lies) and graded beliefs (graded-belief lies). It puts forward (...) a new definition to deal with these scalar parameters, that requires that the speaker asserts what he believes more likely to be false than true. The second section shows that statements are scalar in the same way beliefs are, and accounts for a further element of scalarity, illocutionary force. (shrink)

Translated from: W.V.O.Quine, W. H. O. (1986): Philosophy of Logic. Second Edition. Harvard University Press. Cambridge, Massachusetts and London, England, 47-61.

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)