Gottlob Freg was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of languageand philosophical logic. He is generally seen as one of the fathers of the analytic method, which dominated philosophy in English-speaking (...) countries for most of the twentieth century. His work is studied today not just for its historical importance, but also because many of his ideas are relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research. (shrink)

Frege's life and character -- The project -- Frege's new logic -- Defining the numbers -- The reconception of the logic, I-"Function and concept" -- The reconception of the logic, II- "On sense and meaning" and "on concept and object" -- Basic laws, the great contradiction, and its aftermath -- On the foundations of geometry -- Logical investigations -- Frege's influence on recent philosophy.

Frege begins Die Grundlagen der Arithmetik, the work that introduces the project which was to occupy him for most of his professional career, with the question, 'What is the number one?' It is a question to which even mathematicians, he says, have no satisfactory answer. And given this scandalous situation, he adds, there is small hope that we shall be able to say what number is. Frege intends to rectify the situation by providing definitions of the number one and the (...) concept of number. But what, exactly, is required of a definition? Surely it will not do to stipulate that the number one is Julius Caesar - that would change the subject. It seems reasonable to suppose that an acceptable definition must be a true statement containing a description that picks out the object to which the numeral '1' already refers. And, similarly, that an acceptable definition of the concept of number must contain a description that picks out precisely those objects that are numbers - those objects to which our numerals refer. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of '1' and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of ‘1’ and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. There is, as we shall see shortly, a great deal of evidence that Frege’s definitions are not intended to pick out objects to which our numerals already refer. But if this is so, how can these definitions teach us anything about our science of arithmetic? And what criteria must these definitions satisfy? To answer these questions, we need to understand what it is that Frege thinks we need to learn about the science of arithmetic. (shrink)

What is the number one? How do we know that 2+2=4? These apparently simple questions are in fact notoriously difficult to answer, and in one form or other have occupied philosophers from ancient times to the present. Gottlob Frege's conviction that the truths of arithmetic, and mathematics more generally, are derived from self-evident logical truths formed the basis of a systematic project which revolutionized logic, and founded modern analytic philosophy. In this accessible and stimulating introduction, Joan Weiner traces the development (...) of Frege's thought from his invention of a powerful new logical language in Begriffsschrift, through his explication of his project in the Foundations of Arithmetic and famous papers such as 'On Sense and Reference', to the brilliant, but ultimately doomed, presentation of the system in Basic Laws of Arithmetic. At each stage, she discusses Frege's motivations in a way which enables the modern reader to appreciate the originality, clarity, and profundity of his thought. Past Masters is a series of concise, lucid, authoritative introducitons to the thought of leading intellectual figures of the past whose ideas still influence the way we think today. (shrink)

Does Frege have a metatheory for his logic? There is an obvious and uncontroversial sense in which he does. Frege introduces and discusses his new logic in natural language; he argues, in response to criticisms of Begriffsschrift, that his logic is superior to Boole's by discussing formal features of both systems. In so far as the enterprise of using natural language to introduce, discuss, and argue about features of a formal system is metatheoretic, there can be no doubt: Frege has (...) a metatheory. There is also an obvious and uncontroversial sense in which Frege does not have a metatheory for his logic. The model theoretic semantics with which we are familiar today are a post-Fregean development. The question I address in this paper is, does Frege have a metatheory in the following sense: do his justifications of his basic laws and rules of inference employ, or even require, ineliminable use of a truth predicate and metalinguistic variables? My answer is ‘no’ on both counts. I argue that Frege neither uses, nor has any need to use, a truth predicate or metalinguistic variables in his justifications of his basic laws and rules of inference. Quine's famous explanation of the need for semantic ascent simply does not apply to Frege's logic. The purpose of the discussions that are typically understood as constituting Frege's metatheory is, rather, elucidatory. And once we see what the aim of these particular elucidations is, we can explain Frege's otherwise puzzling eschewal of the truth predicate in his discussions of the justification of the laws and rules of inference. (shrink)

Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings (...) — interpretations on which these claims receive a very different reading. In Frege on Knowing the Third Realm, Tyler Burge attempts to undermine this trend. Burge argues that Frege is the very Platonist most have thought him — that revisionist interpretations of Frege's Platonism, mine among them, run afoul of the words on Frege's pages. This paper is a response to Burge's criticisms. I argue that my interpretation is more faithful than Burge's to Frege's texts. (shrink)

Why did Frege look for the foundations of arithmetic in logic? Robin Jeshion has argued against several proposed answers, mine among them, and offered one of her own. In response, I argue that (i) Jeshion's own interpretation does not work: it is unsupported by the text and fails to answer the question; (ii) while it is not my view that Frege is motivated solely by philosophical concerns, his motivation cannot be divorced from his belief that foundations for science must show (...) whether its truths are analytic or synthetic, a priori or a posteriori; (iii) it must (for Frege) be evident from the content of a primitive truth to which of these categories the truth belongs. (shrink)

I argued that Frege does not have a metatheory in the following sense: the justifications he offers for his basic laws and rules of inference neither employ nor require a truth-predicate or metalinguistic variables. In ‘Does Frege Use a Truth-predicate in his "Justification" of the Laws of Logic?’, Dirk Greimann disputes this. As Greimann interprets Frege, (i) Frege's remarks commit him to giving a metatheoretic justification of the basic laws and rules of his logic, and (ii) Frege actually gives such (...) a justification in the early sections of Grundgesetze—although the truth-predicate that Frege employs is a non-standard one: it is neither a predicate that holds of all and only true sentences nor a predicate that holds of all and only true thoughts. I argue that Greimann's interpretation is not, in the end, true to the text, and that his non-standard view of what is required of a Tarskian truth-predicate is ultimately not viable. CiteULike Connotea Del.icio.us What's this? (shrink)

It is widely assumed that the methods and results of science have no place among the data to which our semantics of vague predicates must answer. This despite the fact that it is well known that such prototypical vague predicates as ‘is bald’ play a central role in scientific research (e.g. the research that established Rogaine as a treatment for baldness). I argue here that the assumption is false and costly: in particular, I argue one cannot accept either supervaluationist semantics, (...) or the criticism of that semantics offered by Fodor and Lepore, without having to abandon accepted, and unexceptionable, scientific methodology. (shrink)

This book is an expanded version of Joan Weiner's introduction to Frege's work in the Oxford University Press ‘Past Masters’ series published in 1999. The earlier book had chapters on Frege's life and character, his basic project, his new logic, his definitions of the numbers, his 1891 essay ‘Function and concept’, his 1892 essays ‘On Sinn and Bedeutung’ and ‘On concept and object’, the Grundgesetze der Arithmetik and the havoc wreaked by Russell's paradox, and a final brief chapter on Frege's (...) influence. To this, Weiner has added two further chapters on Frege's dispute with Hilbert on the foundations of geometry and on the three late essays of his ‘Logical investigations’. There is little change to the content of the earlier chapters, but they have been divided into sections, each with its own heading, which makes it easier to find one's way around.With the two additional chapters, the book provides an excellent introduction to Frege's work from his earliest Begriffsschrift, which gives the first presentation of his new logic, to his three late essays, which expound his views on logic, truth, and thought. As in the earlier version, the focus is on the logicist project that dominated Frege's career: the attempt to demonstrate that arithmetic is reducible to logic. In all her writings on Frege, Weiner has been particularly sensitive to the philosophical …. (shrink)