Frege's essay "Der Gedanke.Eine logische Untersuchung" was first published in the Beitrage zur Philosophie des Deutschen Idealismus for 1918-1919 and is one of three related logical studies published as a complete work by Gunther Patzig entitled Logische Untersuchungen in Gottingen, 1966 .

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

Forthcoming in Darren Bradley (ed.), Carnap and Contemporary Philosophy. -/- This paper is centered on Carnap’s views on rationality. More specifically, much of the focus is on a puzzle regarding Carnap’s view on rationality that Florian Steinberger has recently discussed. Not only is Steinberger’s discussion of significant intrinsic interest: his discussion also raises general questions about Carnap interpretation. As I have discussed in earlier work, there are two very different ways of interpreting Carnap’s talk of “frameworks” – and, relatedly, different (...) ways of interpreting Carnap’s principle of tolerance. Carnap can be interpreted as either a relativist or as what I call a language pluralist. Steinberger’s puzzle arises given the relativist interpretation; I believe the language pluralist interpretation is correct. Most of the discussion will concern the correct interpretation of Carnap, and what this means for Steinberger’s puzzle. While I will not here mount a full defense of the language pluralist interpretation, I will pause to discuss Vera Flocke’s recent criticism of it. Towards the end, I will describe a puzzle regarding rationality different from Steinberger’s. The puzzle that I describe does arise already for the language pluralist. (shrink)

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different categories, (...) on the one hand, and the way in which the realm of Bedeutungen stratifies into logical categories, on the other hand. A proper understanding of this internality reveals how Frege's conception of the relation between language and the world is neither a form of realism nor a form of linguistic idealism. To come to understand Frege's conception of the logical categories, is to come to understand both these forms of internality by coming to understand how they hang together. (shrink)

Analytic philosophy has been perhaps the most successful philosophical movement of the twentieth century. While there is no one doctrine that defines it, one of the most salient features of analytic philosophy is its reliance on contemporary logic, the logic that had its origin in the works of George Boole and Gottlob Frege and others in the mid‐to‐late nineteenth century. Boolean algebra, the heart of Boole's contributions to logic, has also come to represent a cornerstone of modern computing. Frege (...) had broad philosophical interests, and his writings on the nature of logical form, meaning and truth remain the subject of intense theoretical discussion, especially in the analytic tradition. Frege's works, and the powerful new logical calculi developed at the end of the nineteenth century, influenced many of its most seminal figures, such as Bertrand Russell, Ludwig Wittgenstein and Rudolf Carnap. (shrink)

In this extended essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of detailed (...) evidence that there are numerous (over a hundred) and extensive parallels both in formulation and --more importantly-- in content between the Stoics and Frege, parallels so plentiful that one would be hard pressed to brush them off as coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope. -/- (Corrigendum: At school, Frege likely had seven, not ten, years of intensive Latin and four years of intensive ancient Greek courses.). (shrink)

This work addresses the critical discussion featured in the contemporary literature about two well-known paradoxes belonging to different philosophical traditions, namely Frege’s puzzling claim that “the concept horse is not a concept” and Gongsun Long’s “white horse is not horse”. We first present the source of Frege’s paradox and its different interpretations, which span from plain rejection to critical analysis, to conclude with a more general view of the role of philosophy as a fight against the misunderstandings that come from (...) the different uses of language (a point later developed by the “second” Wittgenstein). We then provide an overview of the ongoing discussions related to the Bai Ma Lun paradox, and we show that its major interpretations include—as in the case of Frege’s paradox—dismissive accounts that regard it as either useless or wrong, as well as attempts to interpret and repair the argument. Resting on our reading of Frege’s paradox as an example of the inescapability of language misunderstandings, we advance a similar line of interpretation for the paradox in the Bai Ma Lun: both the paradoxes, we suggest, can be regarded as different manifestations of similar concerns about language, and specifically about the difficulty of referring to concepts via language. (shrink)

The volume assembles thirteen essays on logic, language and meaning, and is preceded by an introduction by Paul Gochet. Most of the papers were published between 1981 and 2000 in European journals such as Dialectica, Logique et Analyse, and Erkenntnis. The papers stand alone, yet throughout the book an overarching view of the relationship between pragmatics and semantics transpires clearly. Callaway defends a midway position between American analytic philosophy and American pragmatism. The result is a blend of Quine's scientific (...) philosophy and Dewey's social pragmatism. In addition other thinkers such as Frege, Peirce, Davidson, Putnam, Fodor and Haack are critically discussed. (shrink)

Meaning without Analyticity draws upon the author’s essays and articles, over a period of 20 years, focused on language, logic and meaning. The book explores the prospect of a non-behavioristic theory of cognitive meaning which rejects the analytic-synthetic distinction, Quinean behaviorism, and the logical and social-intellectual excesses of extreme holism. Cast in clear, perspicuous language and oriented to scientific discussions, this book takes up the challenges of philosophical communication and evaluation implicit in the recent revival of the (...) pragmatist tradition—especially those arising from its relation to prior American analytic thought. This volume continues the work of Callaway’s 1993 book, Context for Meaning and Analysis, building on the “turn toward pragmatism.” . (shrink)

In this dissertation I offer a global and detailed reconstruction of the logic developed by Gottlob Frege throughout his career. Even though Frege's logic suffered profound modifications from his initial formulation in Begriffsschrift to its revised version in Grundgesetze, the significant differences between these two works have been rarely taken at face value. I not only argue that these differences exist, but I also explain how they should be understood in the light of the evolution of Frege's thought. First, (...) I suggest a new reconstruction of Begriffsschrift's logic, which amounts to a completely novel reading of its formal system—one that contradicts the core of modern historical studies. In particular, I defend that this logic is not—as it has been repeatedly said—a second-order logic and provide the following reasons. (1) The language is not properly a formal language. (2) In Begriffsschrift there is only one sort of quantification: quantification over arguments. (3) Begriffsschrift's logic does not have a semantics in the modern sense. Second, I offer an explanation of the reasons that drive the evolution of Frege's logic. The transition from Begriffsschrift to Grundgesetze has been seldom addressed and never fully explained. According to my historical analysis, the switch from Frege's position concerning logic in Begriffsschrift to his later conception—finally established in Grundgesetze—can be articulated through the adoption of the distinction between concept and object as the basic element of the formal system. This leads to a formalisation of the notion of concept, which in the end drives to Grundgesetze's notion of function. Finally, I put forward a global analysis of Grundgesetze's logic. In this work, Frege develops a formal system that resembles in many relevant ways a second-order one. I suggest a reconstruction of this formal system that allows us to compare it with Begriffsschrift's. In particular, I formulate precisely every rule of inference proposed by Frege and especially focus on the rules of substitution. Moreover, I reflect on several meta-logical results that can be drawn from this reconstruction. (shrink)

The paper deals with the main contribution of the Finnish logician Jaakko Hintikka: epistemic logic, in particular the 'static' version of the system based on the formal analysis of the concepts of knowledge and belief. I propose to take a different look at this philosophical logic and to consider it from the opposite point of view of the philosophy of logic. At first, two theories of meaning are described and associated with two competing theories of linguistic competence. In a (...) second step, I draw the conclusion that Hintikka's epistemic logic constitutes a sort of internalisation of meaning, by the introduction of epistemic modal operators into an object language. In this respect, to view meaning as the result of a linguistic competence makes epistemic logic nothing less than a logic of unified meaning and understanding. (shrink)

In this paper, I aim to reconstruct and discuss Stanley Cavell’s interpretation and critique of analytic philosophy. Cavell objects to the tradition of analytic philosophy that, in its eagerness to provide abstract, theoretical reconstructions, it has failed to understand the importance of “the human voice” for philosophy. First, I outline Cavell’s retelling of the history of analytic philosophy from Frege and Russell to ordinary language philosophy. Second, I turn to Cavell’s reading of Kierkegaard and Wittgenstein in order to show what (...) the suppression of the human voice is supposed to mean and entail. Central to Cavell’s account is a particular view of language according to which no structure can explain our capacity for sense-making. Third, I exemplify Cavell’s approach by analyzing his debate with Kripke. Kripke sees the absence of “rails” determining meaning as a skeptical problem and calls for a communal solution. Cavell, by contrast, accepts the absence of rails while highlighting the need for individual responsiveness. In the conclusion I contrast the analytic interest in theory, structure, and abstraction with what I see as Cavell’s humanism. While respectful of key aspects of the analytic tradition such as its commitment to rigor and transparency, Cavell wished to bring the human subject back into philosophy. (shrink)

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical (...) forms of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory. (shrink)

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, (...) logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its (...) cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L: syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science. (shrink)

Analytical philosophy is ruled by the alliance of logic, linguistics and mathematics since its beginnings in the syllogistic calculus of terms and premises in Aristotle's Analytica protera, in the theories of medieval logic that dealt with what are Proprietatis Terminorum (significatio, suppositio, appellatio), in the theological apologetics of argumentation with the combinatorics of symbols by Raymundus Llullus in the work Ars Magna, Generalis et Ultima (1305-08), in what is presented as Theologia Combinata (cf. Tomus II.p.251) in Ars Magna Sciendi sive (...) Combinatoria by Athanasius Kircher (1669), in analytical combinatorics based in Leibniz's dissertation Ars Combinatoria (1666), where language is understood as a lingua characteristica and as a calculus ratiocinator, in the combinatorics of classes that have the meanings 1 or 0 given in the idea of Boolean functions (1854), in Frege's work Begriffschrift, eine der arithmeticeschen nachgebildete Fomelsprache des reinen Denkens (Concept letter, the language of formulas of pure thought made according to the model in arithmetical language), in Cantor's study of set theory / Grundlagen einer allgemeinen Mannigfaltigkeitstheorie (1883) and up to algorithms of fuzzy logic as a "means of approximate thinking that is in the human prior" (Zadeh, 1990) and fuzzy linguistics in computer semantics (Burghard B. Rieger, 1993). These are all the philosophical ideas of mathematicians and logicians that founded what we call logical pragmatism here as a demand that logic be absolutely used in every way in which it will dominate the grammar of language until logic itself becomes the philosophical grammar of the mind!!! (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell (...) and others are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its (...) various roles in conversation. This communicative turn in semantics raises historical questions: Why was truth-conditional semantics dominant in the first place, and why were the phenomena now driving the communicative turn initially ignored or misunderstood by truth-conditional semanticists? I offer a historical answer to both questions. The history of natural-language semantics—springing from the work of Donald Davidson and Richard Montague—began with a methodological toolkit that Frege, Tarski, Carnap, and others had created to better understand artificial languages. For them, the study of linguistic meaning was subservient to other explanatory goals in logic, philosophy, and the foundations of mathematics, and this subservience was reflected in the fact that they idealized away from all aspects of meaning that get in the way of a one-to-one correspondence between sentences and truth-conditions. The truth-conditional beginnings of natural- language semantics are best explained by the fact that, upon turning their attention to the empirical study of natural language, Davidson and Montague adopted the methodological toolkit assembled by Frege, Tarski, and Carnap and, along with it, their idealization away from non-truth-conditional semantic phenomena. But this pivot in explana- tory priorities toward natural language itself rendered the adoption of the truth-conditional idealization inappropriate. Lifting the truth-conditional idealization has forced semanticists to upend the conception of linguistic meaning that was originally embodied in their methodology. (shrink)

The idea that thought and language can be clarified through logical methods seems problematic because, while thought and language are not always exact, logic (by its very nature) must be. According to Kuusela, ideal (ILP, represented by Frege and Russell) and ordinary language philosophy (OLP, represented by Strawson) offer opposed solutions to this problem, and Wittgenstein combines the advantages of both. I argue that, given Kuusela’s characterisation of OLP, Strawson was not an OLP’er. I suggest that, instead of seeing ILP (...) and OLP as opposed to one another, it is better to regard OLP as an extension of ILP. (shrink)

In this article I present some characteristics of logics and semantics of an uncertain world. I confront two-valued and fuzzy logic. I use Kafka’s novel Process as an example, which is designed as an uncertain context with words which are rigid designators without rigid meaning. That produces an uncertain world of logical and semantical relations. In presentation of problems I introduce basic concepts of Frege’s, Wittgenstein’s, Tarsky’s, Searle’s, Quine’s and Davidson’s philosophy of language. I differ the logical and semantical (...) identification of identity. I differ reference and inference, or representation and identification as two components which are fundamental for the identification of identity. I found this difference on the role of logical unification and granulation of predicates in the structure of thought and semantical unification and granulation of attributes in the structure of statements and their relation to ontology of context. Through the confrontation of the logical and semantical unification and granulation I find that the limits of logic are not also the limits of language. The semantical unification goes over the highest genre and below the lowest species. That enables the extra-logical, non-scientifical, con-fessional, pro-phetical, artistic, and ordinary use of language. (shrink)

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of logic contains many interesting thoughts that (...) have gone widely unnoticed. (shrink)

My title is meant to suggest a continuation of the sort of philosophical investigation into the nature of language and modality undertaken in Rudolf Carnap’s Meaning and Necessity and Saul Kripke’s Naming and Necessity. My topic belongs in a class with meaning and naming. It is demonstratives—that is, expressions like ‘that darn cat’ or the pronoun ‘he’ used deictically. A few philosophers deserve particular credit for advancing our understanding of demonstratives and other indexical words. Though Naming and Necessity (...) is concerned with proper names, not demonstratives, it opened wide a window that had remained mostly shut in Meaning and Necessity but that, thanks largely to Kripke, shall forevermore remain unbarred. Understanding of demonstrative semantics grew by a quantum leap in David Kaplan’s remarkable work, especially in his masterpiece “Demonstratives” together with its companion “Afterthoughts.” In contrast to the direct-reference propensities of these two contemporary figures, Gottlob Frege, with his uncompromisingly thoroughgoing intensionalism, shed important light on the workings of demonstratives in “Der Gedanke”—more specifically, in a few brief but insightful remarks from a single paragraph concerning tense and temporal indexicality. (shrink)

Gottlob Frege’s conception of works of art has received scant notice in the literature. This is a pity since, as this paper undertakes to reveal, his innovative philosophy of language motivated a theoretically and historically consequential, yet unaccountably marginalized Wittgenstinian line of inquiry in the domain of aesthetics. The element of Frege’s approach that most clearly inspired this development is the idea that only complete sentences articulate thoughts and that what sentences in works of drama and literary art express (...) are ‘mock thoughts’ (Schiengedanken). The early Wittgenstein closely followed Frege’s lead on this theme. One sees this, for example, in the Tractatus, where Wittgenstein announces that only sentential propositions model (‘picture’) states of affairs whereas works of art are objects we perceive sub specie aeternitatis (1961, 83). By the 1930s, however, Wittgenstein began to revise his view beyond his initial Frege-inspired standpoint. He came to insist that works of art can convey thoughts as well, but that thoughts do not model (picture) the world of facts and hence do not convey information about measurable objects and events. Rather, his contention was that aesthetically configured thoughts that artworks communicate impart information about our perspective on reality and reconfigure our view of life. To be more explicit, successful (gelungene) or ‘good’ works of art (ibid.), in Wittgenstein’s view, can supply aesthetically instructive ‘gestures’ that open to living experience promising new ways of being. It is in this respect, he held, that artists ‘have something to teach’ (1980, 36). (shrink)

Analytical philosophy defines mathematics as an extension of logic. This research will restructure the progress in mathematical philosophy made by analytical thinkers like Wittgenstein, Russell, and Frege. We are setting up a new theory of mathematics and arithmetic’s familiar to Wittgenstein’s philosophy of language. The analytical theory proposed here proves that mathematics can be defined with non-logical terms, like numbers, theorems, and operators. We’ll explain the role of the arithmetical operators and geometrical theorems to be foundational in mathematics. Our position (...) states that mathematical operators and theorems are tautologies. Here numbers are arbitrary signs of magnitudes whose meaning is arbitrated by the mathematical operator. We will prove that set theory in mathematics doesn’t form a branch of logic and operators arbitrarily form sets into units. Herein are the foundations of numbers. (shrink)

The paradox of the concept horse has often been taken to be devastating for Frege’s ontological distinction between objects and concepts. I argue that if we consider how the concept-object distinction is supposed to account for the unity of linguistic meaning, it transpires that the paradox is in fact not paradoxical.

In this article I present some characteristics of logics and semantics of an uncertain world. I confront two-valued and fuzzy logic. I use Kafka’s novel Process as an example, which is designed as an uncertain context with words which are rigid designators without rigid meaning. That produces an uncertain world of logical and semantical relations. In presentation of problems I introduce basic concepts of Frege’s, Wittgenstein’s, Tarsky’s, Searle’s, Quine’s and Davidson’s philosophy of language. I differ the logical and semantical (...) identification of identity. I differ reference and inference, or representation and identification as two components which are fundamental for the identification of identity. I found this difference on the role of logical unification and granulation of predicates in the structure of thought and semantical unification and granulation of attributes in the structure of statements and their relation to ontology of context. Through the confrontation of the logical and semantical unification and granulation I find that the limits of logic are not also the limits of language. The semantical unification goes over the highest genre and below the lowest species. That enables the extra-logical, non-scientifical, con-fessional, pro-phetical, artistic, and ordinary use of language. (shrink)

A presentation and discussion of Gottlob Frege's understanding of language, both natural and artificial, with close attention to his texts.

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every (...) one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

I provide a critical survey of some of the major findings of Wittgenstein and Searle on the logical structure of intentionality(mind, language, behavior), taking as my starting point Wittgenstein’s fundamental discovery –that all truly ‘philosophical’ problems are the same—confusions about how to use language in a particular context, and so all solutions are the same—looking at how language can be used in the context at issue so that its truth conditions (Conditions of Satisfaction or COS) are clear. The basic problem (...) is that one can say anything but one cannot mean (state clear COS for) any arbitrary utterance and meaning is only possible in a very specific context. I begin with ‘On Certainty’ and continue the analysis of recent writings by and about them from the perspective of the two systems of thought, employing a new table of intentionality and new dual systems nomenclature. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

By means of a reductio argument, Wittgenstein’s Tractatus calls into question the very idea that we can represent logical form. My paper addresses three interrelated questions: first, what conception of logical form is at issue in this argument? Second, whose conception of logic is this argument intended to undermine? And third, what could count as an adequate response to it? I show that the argument construes logical form as the universal, underlying correlation of any representation and the reality it represents. (...) I further show that the argument seeks to undermine core commitments of Frege’s and Russell’s. But the reductio, as I read it, is not intended to establish the falsity of any of their specific assumptions. Rather, its aim is to make manifest the indeterminacies that underlie the language in which these assumptions are framed, and establish the need for a transformation of that language. So understood, Wittgenstein’s argument exemplifies his idea that philosophy is not a theory, but an activity of elucidation. The interpretation I propose bears on one of the central debates in the literature, namely how we should understand Wittgenstein’s contention that his elucidations succeed despite being nonsensical. (shrink)

I provide a critical survey of some of the major findings of Wittgenstein and Searle on the logical structure of intentionality (mind, language, behavior), taking as my starting point Wittgenstein’s fundamental discovery –that all truly ‘philosophical’ problems are the same—confusions about how to use language in a particular context, and so all solutions are the same—looking at how language can be used in the context at issue so that its truth conditions (Conditions of Satisfaction or COS) are clear. The basic (...) problem is that one can say anything but one cannot mean (state clear COS for) any arbitrary utterance and meaning is only possible in a very specific context. I begin with ‘On Certainty’ and continue the analysis of recent writings by and about them from the perspective of the two systems of thought, employing a new table of intentionality and dual systems nomenclature. (shrink)

In what follows, the difference between Frege’s and Schröder’s understanding of logical connectives will be investigated. It will be argued that Frege thought of logical connectives as concepts, whereas Schröder thought of them as operations. For Frege, logical connectives can themselves be connected. There is no substantial difference between the connectives and the concepts they connect. Frege’s distinction between concepts and objects is central to this conception, because it allows a method of concept formation which enables us to form concepts (...) from the logical connectives alone. Schröder in contrast unifies the distinction between concepts and objects, but keeps the distinction between logical connectives and what they connect. It will be argued that Frege’s particular way of perceiving logical connectives is crucial for his foundational project. (shrink)

I provide a critical survey of some of the major findings of Wittgenstein and Searle on the logical structure of intentionality (mind, language, behavior), taking as my starting point Wittgenstein’s fundamental discovery –that all truly ‘philosophical’ problems are the same—confusions about how to use language in a particular context, and so all solutions are the same—looking at how language can be used in the context at issue so that its truth conditions (Conditions of Satisfaction or COS) are clear. The basic (...) problem is that one can say anything but one cannot mean (state clear COS for) any arbitrary utterance and meaning is only possible in a very specific context. I begin with ‘On Certainty’ and continue the analysis of recent writings by and about them from the perspective of the two systems of thought, employing a new table of intentionality and new dual systems nomenclature. (shrink)

I investigate why Frege rejected the theory of types, as Russell presented it to him in their correspondence. Frege claims that it commits one to violations of the law of excluded middle, but this complaint seems to rest on a dogmatic refusal to take Russell’s proposal seriously on its own terms. What is at stake is not so much the truth of a law of logic, but the structure of the hierarchy of the logical categories, something Frege seems to neglect. (...) To come to a better understanding of Frege’s response, I proceed to investigate his conception of the nature of the logical categories, and how it differs from Russell’s. I argue that, for Frege, our grasp of the logical categories cannot be severed from our grasp of the Begriffsschrift notation itself. Russell, on the other hand, attaches no such importance to notation. From Frege’s point of view, Russell has not succeeded in presenting an alternative conception of the logical hierarchy, since such a conception must go in tandem with the development of a notation. Moreover, Frege has good reasons to think that Russell’s proposal does not admit of a suitable notation. (shrink)

Between the end of the nineteenth century and the first twenty years of the twentieth century, stimulated by the impetuous development of logical studies and taking inspiration from Leibniz's idea of a characteristica universalis, the three founding fathers of the analytic tradition in philosophy, i.e., Frege, Russell, and Wittgenstein, started to talk of a logically perfect language, as opposed to natural languages, all feeling that the latter were inadequate to their (different) philosophical purposes. In the second half of the twentieth (...) century, however, the very idea of a logically perfect language ceased for various reasons to seem attractive to analytic philosophers. Thus, it might appear that this idea could be classified together with the many other bizarre ideas that from time to time surface in the history of philosophy-an idea that perhaps had a beneficial impact on the development of twentieth century logic, but which can now be put to rest. In this brief note, I contend that this conclusion may be too hasty. Indeed, if a well-known empirical hypothesis advanced in 1975 by Jerry Fodor turns out to be true, then there is a logically perfect language, after all. More precisely, I argue that, if it exists, Fodor's language of thought possesses the main characteristics a logically perfect language is required to have. (shrink)

Gottlob Frege maintained that two name-containing identity sentences, represented schematically as a=a and a=b,can both be true in virtue of the same object’s self-identity but nonetheless, puzzlingly, differ in their epistemic profiles. Frege eventually resolved his puzzlement by locating the source of the purported epistemic difference between the identity sentences in a difference in the Sinne, or senses, expressed by the names that the sentences contain. -/- Thus, Frege portrayed himself as describing a puzzle that can be posed prior (...) to and independently of any particular theoretical position regarding names, and then resolving that puzzle with his theory of Sinn and Bedeutung. In this paper, I suggest that Frege’s presentation is problematic. If attempt is made to characterize the epistemic status of true identity sentences without appeal to Frege’s theoretical commitments, then what initially seemed puzzling largely dissolves. It turns out that, in order to generate puzzlement, Frege must invoke the theoretical account that he uses the puzzle to establish the purported necessity of. (shrink)

As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing (...) the development of his views in the forties have recently begun to be published, as well as careful philosophical studies of, for instance, the evolution of his key doctrine that mathematical and logical truth are continuous with, not divorced from, the truths of natural science. But one central text has remained unexplored: Quine's Portuguese-language book on logic, his 'farewell for now' to the discipline as he embarked on an assignment in the Navy in WWII. Anglophone philosophers have neglected this book because they could not read it. Jointly with colleagues, I have completed the first full English translation of this book. In this accompanying paper I draw out the main philosophical contributions Quine made in the book, placing them in their historical context and relating them to Quine's overall philosophical development during the period. Besides significant developments in the evolution of Quine's views on meaning and analyticity, I argue, this book is also driven by Quine's indebtedness to Russell and Whitehead, Tarski, and Frege, and contains crucial developments in his thinking on philosophy of logic and ontology. This includes early versions of some arguments from 'On What There Is', four-dimensionalism, and virtual set theory. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and (...) functions. Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

Husserl’s theory of fulfilment conceives of empty acts, such as symbolic thought, and fulfilling acts, such as sensory perceptions, in a strict parallel. This parallelism is the basis for Husserl’s semantics, epistemology, and conception of truth. It also entails that any true proposition can be known in principle, which Church and Fitch have shown to explode into the claim that every proposition is _actually_ known. I assess this logical challenge and discuss a recent response by James Kinkaid. While Kinkaid’s proposal (...) saves one direction of the parallel for semantics, it gives up the parallelism for truth. I spell out a different response which meshes naturally with Husserl’s account of meaning. If the parallelism is restricted to a class of basic propositions, the truth of non-basic propositions can be defined inductively, without leading to the paradox. I then discuss objections that have been raised against a similar proposal by Dummett. The result is that exegetically plausible and popular interpretations of Husserl’s correlationism are indeed challenged by Church and Fitch. But when taking into account the ‘logical adumbration’ of propositional blindspots, truth and possible fulfilment can be connected without paradox. (shrink)

Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue (...) that for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)

This book provides a concise overview, with excellent historical and systematic coverage, of the problems of the philosophy of language in the analytic tradition. Howard Callaway explains and explores the relation of language to the philosophy of mind and culture, to the theory of knowledge, and to ontology. He places the question of linguistic meaning at the center of his investigations. The teachings of authors who have become classics in the field, including Frege, Russell, Carnap, Quine, Davidson, and Putnam (...) are critically analyzed. I share completely his conviction that contemporary Anglo-American philosophy follows the spirit of the enlightenment in insisting on intellectual sincerity, clarity, and the willingness to meet scientific doubts or objections openly. --Professor Henri Lauener, Editor of Dialectica. (shrink)

An investigation of what Frege means by his doctrine that functions (and so concepts) are 'unsaturated'. We argue that this doctrine is far less peculiar than it is usually taken to be. What makes it hard to understand, oddly enough, is the fact that it is so deeply embedded in our contemporary understanding of logic and language. To see this, we look at how it emerges out of Frege's confrontation with the Booleans and how it expresses a fundamental difference between (...) Frege's approach to logic and theirs. (shrink)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which LTL has (...) helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

This paper is a critique of coercive theories of meaning, that is, theories (or criteria) of meaning designed to do down ones opponents by representing their views as meaningless or unintelligible. Many philosophers from Hobbes through Berkeley and Hume to the pragmatists, the logical positivists and (above all) Wittgenstein have devised such theories and criteria in order to discredit their opponents. I argue 1) that such theories and criteria are morally obnoxious, a) because they smack of the totalitarian (...) linguistic tactics of the Party in Orwell’s 1984 and b) because they dehumanize the opposition by portraying them as mere spouters of gibberish; 2) that they are profoundly illiberal since if true, they would undermine Mill’s arguments for free speech; 3) that such theories are prone to self-contradiction, pragmatic and otherwise; 4) that they often turn against their creators including what they were meant to exclude and excluding what they were meant to include; 5) that such theories are susceptible to a modus tollens pioneered by Richard Price in his Review Concerning the Principle Questions of Morals(1758); and 6) that such theories are prima facie false since they fail to ‘predict’ the data that is it their business to explain (or, in the case of criteria, fail to capture the concept that they allegedly represent). The butcher’s bill is quite considerable: some of Hobbes, a fair bit of Locke, half of Berkeley, large chunks of Hume, Russell's Theory of Types, verificationism in its positivist and Dummettian variants, much of pragmatism and most of Wittgenstein - all these have to be sacrificed if we are to save our souls as philosophic liberals. (shrink)

In this paper I will discuss Dummett’s interpretation of Frege’s “On sense and reference” that takes place in his Frege: Philosophy of Language, where he attributes a notion of meaning to Frege that is not explicit on the text of “On sense and reference”. I believe that this attribution is incompatible with what Frege is really saying in the article and with the partition of the notion that Dummett himself exposes.

Wittgenstein’s mention of the term “phenomenology” in his writings from the middle period has long been regarded as puzzling by interpreters. It is striking to see him concerned with that philosophical approach, generally regarded as foreign to the tradition of Russell and Frege, in which Wittgenstein’s thought is commonly taken to have primarily developed. On the basis of partially unpublished material from Wittgenstein’s Nachlass, the thesis provides a reconstruction of the rationale and fate of his conception of phenomenology, which he (...) advances after his return to Cambridge in 1929. On the one hand, that conception is tributary to his longstanding task to philosophically clarify the workings of language. On the other hand, Wittgenstein’s concern with phenomenology develops against the background of his reconsideration of the resources for clarification provided by his early philosophy. His 1929 paper “Some Remarks on Logical Form” is elucidatory in this respect. The paper expresses a dissatisfaction with the Tractarian account of logical grammar and pleas for a “logical investigation of the phenomena themselves”. That plea echoes Wittgenstein’s notion of a “phenomenological language” in the manuscripts from the same period. The thesis addresses the intricacies of that notion and the reasons for Wittgenstein’s coming to criticize it. By contrast to the prevalent view in the literature, it turns out that he did not fully endorse for a definite period, and then suddenly abandoned, the idea of phenomenological language. Wittgenstein rather attempts to develop a viable means of clarification and of philosophical expression through phenomenological language, while critically exploring the assumptions and implications of that attempt at the very same time. (shrink)

Logical reflection in early modern philosophy (EMP) is marked by the instability of the period, although it is more lasting (the Port-Royal Logic was nevertheless used as a handbook in philosophy courses until the end of the nineteenth century). It started in the sixteenth century and ended in the nineteenth century, a period of 300 years during which there were deep transformations in the conceptions of authority and scientific method. For the history of twentieth-century philosophy, it was the period of (...) “classical logic,” which lasted from the Renaissance to the linguistic turn conducted by Gottlob Frege. The period was used to be thought of as centuries of little or no original contribution to logic, in which conceptions of logic were tainted by rhetoric, epistemology, and psychologism in the worst sense (Kneale and Kneale 1962; Michael 1997). From the last decades of the twentieth century, however, scholars began to regard this period more accurately with respect to reflection and changes in logic and semantics. It has recently become a promising field for historical and conceptual research; today we can say that the legacy of early modern logical reformism has a philosophical, logical, and semantic value in itself. (shrink)

The paper gives an overview of key themes of twentieth century philosophical treatment of the language of science, with special emphasis on the meaning variance of scientific terms and the comparison of alternative theories. These themes are dealt with via discussion of the topics of: (a) the logical positivist principle of verifiability and the problem of the meaning of theoretical terms, (b) the postpositivist thesis of semantic incommensurability, and (c) the scientific realist response to incommensurability based on the (...) causal theory of reference. (shrink)