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This chapter gives a survey of the field of philosophy where (1) the philosophical foundations of modern logic were discussed and (2) where such themes of logic were discussed that were on the borderline between logic and other branches of the philosophical enterprise, such as metaphysics and epistemology. The contributions made by Gottlob Frege and Charles Peirce are included since their work in logic is closely related to and also strongly motivated by their philosophical views and interests. In addition, the chapter pays attention to a few philosophers to whom logic amounted to traditional Aristotelian logic and to those who commented on the nature of logic from a philosophical perspective without making any significant contribution to the development of formal logic.

Traditional formal logic as developed by Fred Sommers is compared and contrasted with the modern quantified predicate logic that we owe to Gottlob Frege and Bertrand Russell; the latter is argued to be implicitly committed to a two-category ontology of particulars and universals. A system of sortal logic is described, which exhibits some features of traditional formal logic and some of modern quantified predicate logic, such as its deployment of a symbol for identity. It is argued that this system represents more perspicuously than other systems the ontological distinctions of the four-category ontology, and that this counts as a distinct advantage in its favour.

This chapter formulates the main question to be addressed in the first three chapters of the book, the question of what holds the constituents of propositions together. It considers the answers Gottlob Frege and Bertrand Russell offered to this question. These answers are rejected, motivating the search for a new answer.

This chapter explores Gottlob Frege's contribution to logic. Frege has been called the greatest logician since Aristotle, but he failed to gain influence on the mathematical community of his time and the depth and pioneering character of his work was acknowledged only after the collapse of his logicist program due to the Zermelo–Russell antinomy in 1902. Frege, by proving his theorem χ without recourse to Wertverläufe, exhibited an inconsistency (or at least an incoherence) in the traditional notion of the extension of a concept. He prompted our awareness of a situation the future analyses of which will hopefully not only deepen our systematic control of the interplay of concepts and their extensions but also improve our understanding of the historical development of the notion of “extension of a concept” and its historiographical assessment.

This introductory chapter begins with a brief discussion of how Gottlob Frege's name and work remain unknown to the wider intellectual public. It then describes Frege's contributions to philosophy, including concentration on language in the expression of knowledge and a recognition of the power of logic to illuminate the structure of language and its contribution to the expression of knowledge. It shows how Frege's positivist successors used his innovations against a background of philosophical attitudes that Frege did not share. They differed with him, in absolutely fundamental ways, about both meaning and knowledge. The chapter make some more specific philosophical remarks about Frege's contributions, as discussed in these three parts: truth, structure, and method; sense and cognitive value; and rationalism.

The formal ontological concept of an object is explicated and contrasted with that of a property. F. P. Ramsey’s objections to this distinction are challenged. The sense in which objects possess an individuality not exhibited by entities of certain other types is discussed. The object/property distinction is distinguished from that between universals and particulars. The ontological status of events and processes, and that of abstract entities such as numbers, are examined. Gottlob Frege’s treatment of number and his object/concept distinction are criticized, and an alternative account of the ontological status of concepts is advanced.

This chapter works out an interpretation of Immanuel Kant's theory of syntheticity. More precisely, it sketches the basics of Kant's theory of syntheticity in relation to Gottlob Frege's theory, and, in the course of so doing, offers good historical and philosophical reasons for challenging the vigorous anti-intuitionism that generally characterizes the analytic tradition after Frege and right up to Willard Van Orman Quine. This chapter discusses the argument's three stages. According to Kant, a true proposition is synthetic if and only if it is consistently deniable and its truth and meaning are intuition-dependent. In turn, an intuition is an immediate, sensibility-related, thought-prior, singular, object-dependent (existential, actual) means of semantic reference. Thus, the fundamental feature of Kantian syntheticity and intuition alike is their essential indexicality.

In his contribution, Burge contrasts the use Kant and Frege make of the a priori in their work. Burge argues that for Kant, the conscious states of pure intuition are states that entitle a subject to make judgements of geometrical principles and provide a justification that is independent of perceptual experience. This conception Burge contrasts with Frege's philosophical explication of the a priori in The Foundation of Arithmetic.

The history of analytic philosophy from Gottlob Frege to Willard Van Orman Quine is the history of the rise and fall of the concept of analyticity, whose origins and parameters both lie in Immanuel Kant's first Critique. This chapter also has a broader Kantian moral that might be summarized as follows. All creatures minded are compelled to think via concepts. Otherwise put, concepts are cognitively indispensable because they are the proper outputs of the natural activation of the discursive side of our psychological constitution. Since concepts are cognitively indispensable, philosophy must admit the legitimacy of the concept CONCEPT. However, the concept CONCEPT leads directly to the idea of a conceptually necessary truth — the analytic proposition. The function of an analytic truth is to express intrinsic features of the form and content of the several concepts included within our total conceptual repertoire. Therefore, this admits the legitimacy of the concept of analyticity. Analyticity is a genuine concept which philosophy is better off with.

This chapter discusses the foundations of philosophical semantics, covering the work of Gottlob Frege and Bertrand Russell. Frege, along with Russell, did more than anyone else to create the subject. The development of symbolic logic, the analysis of quantification, the application of logical ideas and techniques to the semantics of natural language, the distinction between sense and reference, the linking of representational content to truth conditions, and the compositional calculation of the contents of compound expressions from the semantic properties of their parts are all due to Frege and Russell. Philosophy of language, as we know it today, would not exist without them.

This chapter investigates Austin’s conception of truth, comparing it with Frege’s. Of central importance is the relation between the conceptual and the non‐conceptual, and, in particular, how to understand the generality that characterizes the conceptual. Frege thinks of it in terms of a function mapping objects onto truth‐values, such that once the function is determined it will not be left open how to apply it in a particular case. Austin rejects the very idea of such determinacy. For him, a concept does determine something, but what it determines leaves its application in particular cases negotiable. Still, he retains many of Frege’s central insights, such as the indefinability of truth, the shareability of content, and the notion of a fundamental distinction between the generality of the conceptual and particularity of the non‐conceptual. Frege’s and Austin’s views might even be fully reconcilable, given the different purposes for which they were proposed.

Looks at the work of Gottlob Frege on truth and composition. It investigates Frege's idea that a sentence refers to a truth‐value, his Principle of Composition, and his abandonment of what Donald Davidson calls ‘semantic innocence’. Neale explains what kinds of slingshotian considerations prevented Frege from accepting facts as denotations of sentences and made him see sentences rather as names of truth‐values. The three sections of the chapter are: Reference and Composition; Innocence Abandoned; and The Reference of a Sentence.

This chapter considers Gottlob Frege as the founder of contemporary logic through his little book Begriffsschrift that came out in 1879. The name stands for something like “writing for concepts,” in the sense of a notation, and there is a long subtitle that specifies the notation as “a formula language of pure thinking, modeled upon that of arithmetic.” The actual notation in Frege's book made a rather bizarre impression on many, and no one else ever used it. Luckily he had Bertrand Russell among his few readers; some 25 years after the Begriffsschrift, Russell rewrote Frege's formula language in a style, adopted from Giuseppe Peano, that later evolved into the standard logical and mathematical notation we have today.

This chapter examines the role of language theory and unity of thought on the contradictions in the limits of thought. It is natural for a theory of language to have implications about what can and what cannot be expressed, and modern theories of language always seem to render important things beyond the limit of expression. This chapter analyses philosopher Gottlob Frege's postulates on the existence of concepts, and suggests that his claims about them are beyond the limit of the expressible. It also evaluates Ludwig Wittgenstein's notion of form, and suggests that his account for unity of thought is beyond the expressible.

The present chapter is organised as follows. First, the unity problem will be presented as it struck Bertrand Russell in 1903. Russell’s articulation of the problem is a useful and traditional starting place. Second, it will be argued that there are in fact two unity problems. The first is what I call the interpretive problem, which bears on how we can compositionally describe what a given unity means. This problem presupposes that there are unities around; the problem is how to specify their content in the appropriate way. Although historically deep, the basic problem here is resolvable in a fairly straightforward way. The second unity problem I call the combinatorial problem. This problem does not presuppose that there are unities, but asks how there can be unities at all, or, as it is often put, what’s the difference between a sentence and a list. The remainder of the present chapter and the next one will argue that none of a range of entertained solutions to the combinatorial problem is satisfactory. The arguments to be presented will be based upon three desiderata on an adequate solution. Chapter 5 will attempt something like a solution that meets the three desiderata, and chapters 6 and 7 will clarify and defend the solution.

This chapter discusses the methodology that guided logico-linguistic analysis from Gottlob Frege’s 1879 Begriffsschrift to Rudolf Carnap’s 1934 The Logical Syntax of Language. In the first four decades of this period, culminating with Bertrand Russell’s 1918–19 lectures on The Philosophy of Logical Atomism, analysis was viewed as an increasingly powerful tool employed in the service of solving traditional philosophical problems. The logicist reduction of arithmetic to what was taken to be logic was the driving force, providing the exemplar of philosophical analysis and the model for extending it beyond the philosophy of mathematics. The methodology is indicated by the role played by A2 in answering Frege’s guiding philosophical questions Q1 and Q2.

This book has two intimately intertwined topics. First, it is an interpretive study of Immanuel Kant's massive and seminal Critique of Pure Reason; but secondly and equally, it is a critical essay on the historical foundations of analytic philosophy from Gottlob Frege to Willard Van Orman Quine. By Kant's own reckoning, the first Critique is an extended reflection on a single question: ‘Now the real problem of pure reason is contained in the question: how are synthetic a priori judgements possible?’. Translated out of Kant's jargon, this question raises a deep and broadly applicable philosophical difficulty: how can the same judgement be at once necessarily true, referred to the real or natural world in a substantive way, yet cognizable by creatures minded like us apart from all sense experience? For easy reference, the chapter calls this ‘the Modal Problem’.