Wittgenstein’s attitude to writing philosophy is an important part of his complex legacy from Frege. Even the frequently misconstrued phrase, “Philosophie dürfte man eigentlich nur dichten”, is part of that legacy. How should we actually render that sentence in English? How is the idea that Dichtung is a necessary aspect of philosophical method rooted in thoughts that ultimately find their way back to Frege? Where do we find Dichtung in the so-called private language argument? How is Wittgenstein’s view (...) of the role of Dichtung in philosophy related to his appreciation of humor in philosophizing? What is the role of humor in Frege’s work? How does Wilhelm Busch in Eduards Traum illustrate the philosophical significance of humorous Dichtung? What is the link between Dichtung and craftsmanship in writing philosophy for Wittgenstein? These are the central issues that the article addresses. (shrink)

Gottlob Frege’s Grundgesetze der Arithmetik (Basic Laws of Arithmetic, Vol. I/II; 1893/1903) is a modern classic. Since the 1930s it has belonged to an exclusive class of only eleven works in the history of symbolic logic, which contain the ‘first appearance of a new idea of fundamental importance’ [Church, 1936, p. 122], and its author is the only one whose other major works — Begriffsschrift (1879) and Die Grundlagen der Arithmetik (1884) — also belong to this distinguished group. Together with (...) the seminal paper ‘Über Sinn und Bedeutung’ these three monographs represent the essential contributions to one of the most fascinating foundational projects in mathematics, then and now. For decades Frege struggled with the question, ‘how are we to apprehend logical objects, in particular, the numbers? What justifies us in acknowledging numbers as objects?’ [Frege, 2013, ‘Afterword’, p. 265]. His favourite answer, for a long time, was that arithmetic is a complex branch of logic. But since there is no logicism without logic, Frege started in Begriffsschrift with the invention of a nearly perfect formalization of higher-order classical predicate logic. To discover how far we can get in arithmetic by analytic means alone, it was even necessary to clarify the semantic character of the concept of number. This was done in a marvellous way by Frege five years later, in Grundlagen. The next step was nothing less than the complete execution of his logicist project, a monumental undertaking; and it is well known that here Frege failed, due to Russell’s derivation of the antinomy in 1902. But, despite the contradiction, Grundgesetze contains Frege’s legacy to logicism, which became more and more attractive. (shrink)

In the preface to the Tractatus Wittgenstein acknowledged ‘Frege's great works’ as one of the two primary stimulations for his thoughts. Throughout his life he admired Frege both as a great thinker and as a great stylist. This much is indisputable. What is disputable is how he viewed his own philosophical work in relation to Frege's and, equally, how we should view his work in this respect. Some followers of Frege are inclined to think that Wittgenstein's work builds (...) on or complements that of Frege. If that were true it would be plausible to suppose that the joint legacy of these two great philosophers can provide a coherent foundation for our own endeavours. But it is debatable whether their fundamental ideas can be synthesized thus. The philosophy of Wittgenstein, both early and late, is propounded to a very large extent in opposition to Frege's. They can no more be mixed than oil and water – or so I shall argue. (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...) of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

Bernard Bolzano (1781-1848) was an original and independent thinker, who left a lasting legacy in several areas of philosophy. Four such areas are singled for special attention: political philosophy, ethics and theology, logics and semantics, and mathematics. In all these areas he was far ahead of his time. He had pioneering ideas in political philosophy and in ethics and philosophy of religion, and he argued for them in a brilliantly clear way. In logic and semantics he anticipated Frege, Carnap (...) and Quine on important points, and he had intriguing, yet to be explored, ideas on intuition and other fundamental philosophical notions. In the foundations of mathematical analysis and the theory of infinite sets he anticipated Weierstrass and Cantor. (shrink)

The philosophy of mathematics has long been an important part of philosophy in the analytic tradition, ever since the pioneering works of Frege and Russell. Richard Dedekind was roughly Frege's contemporary, and his contributions to the foundations of mathematics are widely acknowledged as well. The philosophical aspects of those contributions have been received more critically, however. In the present essay, Dedekind's philosophical reception is reconsidered. At the essay’s core lies a comparison of Frege's and Dedekind's legacies, within and (...) outside of analytic philosophy. While the comparison proceeds historically, it is shaped by current philosophical concerns, especially by debates about neo-logicist and neo-structuralist views. In fact, philosophical and historical considerations are intertwined thoroughly, to the benefit of both. The underlying motivation is to rehabilitate Dedekind as a major philosopher of mathematics, in relation, but not necessarily in opposition, to Frege. (shrink)

Gottlob Frege is one of the founding figures of analytic philosophy, whose contributions to logic, philosophical semantics, philosophy of language, and philosophy of mathematics set the agenda for future generations of theorists in these and related areas. Dale Jacquette's lively and incisive biography charts Frege's life from its beginnings in small-town north Germany, through his student days in Jena, to his development as an enduringly influential thinker. Along the way Jacquette considers Frege's ground-breaking Begriffschrift, in which he formulated (...) his 'ideal logical language', his magisterial Grundgesetze der Arithmetik, and his complex relation to thinkers including Husserl and especially Russell, whose Paradox had such drastic implications for Frege's logicism. Jacquette concludes with a thoughtful assessment of Frege's legacy. His rich and informative biography will appeal to all who are interested in Frege's philosophy. (shrink)

Nine of the papers collected here derive directly from a conference organized by Schirn in Munich in 1991. Seven others, three of them reprinted, have been intelligently chosen to complement the original nine. The collection has no overarching theme, nor is it dominated by any particular approach to Frege’s thought. It is “a mixed selection”, and aims to reflect “the prevailing tendency in current Frege scholarship”. The influence of Dreben is less in evidence than one might expect, but otherwise the (...) collection meets that broad brief pretty well. Some of the collection’s best papers—for example, those by Burge, Boolos, Dummett, Heck, and Terence Parsons—are essential reading. Inevitably, not all the others have that standing. But, excepting only an over-long essay by the editor, each deserves its place. (shrink)

The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. This volume of classic, revised and newly written essays by William Demopoulos examines logicism's principal legacy for philosophy: its elaboration of notions of analysis and reconstruction. The essays reflect on the deployment of these ideas by (...) the principal figures in the history of the subject - Frege, Russell, Ramsey and Carnap - and in doing so illuminate current concerns about the nature of mathematical and theoretical knowledge. Issues addressed include the nature of arithmetical knowledge in the light of Frege's theorem; the status of realism about the theoretical entities of physics; and the proper interpretation of empirical theories that postulate abstract structural constraints. (shrink)

This book is about Gottlob Frege. The guiding thought is that Frege left philosophy a legacy which has been largely ignored, not least of all by his admirers. In order of logical priority, Frege's first concern was to locate the law-like behaviour of truths and falsehoods merely by virtue of their being such. The just-mentioned legacy lies in his first step towards that goal. It consists in winnowing the 'logical' from the 'psychological', the business of being true (...) as such from that of holding, or holding forth as true-and to keep these separate. A first lesson: what belongs to what is thus abstracted cannot be read directly back into what it was abstracted from. This is what is most widely ignored. The book is divided in three parts. The first presents Frege's general picture of the business of being true-of what belongs to the abstraction. The second is primarily concerned with steps Frege takes between 1891 and 1895, to pave the way for what became, after logic itself, his central project, that whose attempted carrying out is contained in Grundgesetze I. The third part concerns views of logic, truth, the inexorableness of logic, which Frege eventually came to hold, and what it might be to study 'The Mind' as opposed to minds. (shrink)

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)

In ‘On Denoting’ and to some extent in ‘Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie’, published in the same issue of Mind (Russell, 1905a,b), Russell presents not only his famous elimination (or contextual defi nition) of defi nite descriptions, but also a series of considerations against understanding defi nite descriptions as singular terms. At the end of ‘On Denoting’, Russell believes he has shown that all the theories that do treat defi nite descriptions as singular terms fall (...) logically short: Meinong’s, Mally’s, his own earlier (1903) theory, and Frege’s. (He also believes that at least some of them fall short on other grounds—epistemological and metaphysical—but we do not discuss these criticisms except in passing). Our aim in the present paper is to discuss whether his criticisms actually refute Frege’s theory. We fi rst attempt to specify just what Frege’s theory is and present the evidence that has moved scholars to attribute one of three different theories to Frege in this area. We think that each of these theories has some claim to be Fregean, even though they are logically quite different from each other. This raises the issue of determining Frege’s attitude towards these three theories. We consider whether he changed his mind and came to replace one theory with another, or whether he perhaps thought that the different theories applied to different realms, for example, to natural language versus a language for formal logic and arithmetic. We do not come to any hard and fast conclusion here, but instead just note that all these theories treat defi nite descriptions as singular terms, and that Russell proceeds as if he has refuted them all. After taking a brief look at the formal properties of the Fregean theories (particularly the logical status of various sentences containing nonproper defi - nite descriptions) and comparing them to Russell’s theory in this regard, we turn to Russell’s actual criticisms in the above-mentioned articles to examine the extent to which the criticisms hold.. (shrink)

Opposing a long-standing orthodoxy of the Western philosophical tradition running from ancient Greek thought until the late nineteenth century, Frege argued that psychological laws of thought--those that explicate how we in fact think--must be distinguished from logical laws of thought--those that formulate and impose rational requirements on thinking. Logic does not describe how we actually think, but only how we should. Yet by thus sundering the logical from the psychological, Frege was unable to explain certain fundamental logical truths, most notably (...) the psychological version of the law of non-contradiction--that one cannot think a thought and its negation simultaneously. Irad Kimhi's Thinking and Being marks a radical break with Frege's legacy in analytic philosophy, exposing the flaws of his approach and outlining a novel conception of judgment as a two-way capacity. In closing the gap that Frege opened, Kimhi shows that the two principles of non-contradiction--the ontological principle and the psychological principle--are in fact aspects of the very same capacity, differently manifested in thinking and being. As his argument progresses, Kimhi draws on the insights of historical figures such as Aristotle, Kant, and Wittgenstein to develop highly original accounts of topics that are of central importance to logic and philosophy more generally. Self-consciousness, language, and logic are revealed to be but different sides of the same reality. Ultimately, Kimhi's work elucidates the essential sameness of thinking and being that has exercised Western philosophy since its inception.--. (shrink)

"By looking at Frege's lectures on logic through the eyes of the young Carnap, this book casts new light on the history of logic and analytic philosophy. As two introductory essays by Gottfried Gabriel and by Erich H. Reck and Steve Awodey explain, Carnap's notes allow us to better understand Frege's deep influence on Carnap and analytic philosophy, as well as the broader philosophical matrix from which both continental and analytic styles of thought emerged in the 20th century."--BOOK (...) JACKET. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:82 Reviews c:\users\arlene\documents\rj issues\type3501\rj 3501 061 red.docx 2015-07-10 4:07 PM LOGICISM BEYOND PRINCIPIA MATHEMATICA Chris Pincock Philosophy / Ohio State U. Columbus, oh 43210–1365, usa [email protected] William Demopoulos. Logicism and Its Philosophical Legacy. Cambridge: Cambridge U. P., 2013. Pp. xii, 272. isbn: 9781107029804.£60.00; us$104.99 (hb). his book brings together eight previously published essays along with three new essays and a brief introduction. In one way or another, each (...) essay pursues either logicism or some broader implication of logicism that a major figure like Russell or Carnap explored. In a narrow sense, logicism is just the position that grounds the concepts and claims of arithmetic (or all of mathematics) in logic. However, in Demopoulos’ hands, logicism becomes a project of much greater significance. A note added to Chapter 5, the classic 1985 article “Bertrand Russell’s The Analysis of Matter” (co-authored with Michael Friedman), indicates this broader scope and Demopoulos’ own take on logicism. Originally Demopoulos and Friedman had concluded their article with both the observation that there are serious “intellectual tensions produced by logicism’s attempt to account for both pure mathematics and applied mathematics (mathematical physics)” and the pessimistic conclusion that “it appears that we can account for the distinctive character of the one only at the expense of the other” (p. 107). Now Demopoulos indicates that even though “something close to [this] is true of Carnap’s Ramsey-sentence q= Reviews 83 c:\users\arlene\documents\rj issues\type3501\rj 3501 061 red.docx 2015-07-10 4:07 PM reconstruction of the language of science”, “the four previous chapters are an extended argument against” the earlier conjecture. For Demopoulos, the main problem is to make sense of both pure and applied mathematics in something like the original logicist form found in Frege, Russell and Carnap.The solution to this problem arises only when we have pinpointed exactly where these logicist projects failed and how their failures can be overcome. Chapter 1 focuses on Frege and his logicism for arithmetic. Demopoulos’ main contention is that Frege aims to reduce arithmetic to logic in order to demonstrate the autonomy of arithmetic from geometric intuition and empirical experience. Frege’s worry about intuition is not motivated by scepticism or by a concern about the cogency of our knowledge of arithmetic (p. 11).The point of logicism is to free arithmetic from the obscurity associated with intuition and to get a clearer grasp of the generality that is characteristic of arithmetic. (Chapters 8 and 9 develop this point in more detail and use it to motivate a brand of logicism for arithmetic that is taken to improve on current neo-Fregean approaches.) For this reason Hume’s Principle takes a central role in Frege’s reconstruction of arithmetic for it not only establishes the autonomy of arithmetic, but also secures the core use of arithmetic in application, i.e. in counting (p. 19). Unlike Dummett and other commentators Demopoulos does not think that this aspect of Frege’s logicism is flawed. Instead, flaws arise only with the accounts of applied mathematics offered by later figures like Russell and Carnap.The root of these problems is that they extend a particular logicist strategy to other areas of mathematics, such as geometry, and to our scientific knowledge more generally. Chapter 2 considers “Carnap’sThesis”, which Demopoulos summarizes as “the assertion that certain applied mathematical theories are not factual” (p. 28). Although the thesis is clearly central to Carnap throughout his career, Demopoulos ultimately argues for a non-Carnapian basis for the factual/nonfactual distinction.The root of the difference is the kind of criteria of identity that are appropriate for the objects at the heart of the theory: … the factuality of an applied mathematical theory will be shown to turn on the recognition that the criteria of identity appropriate to its objects are empirically constrained in a way that the criteria of identity appropriate to the objects of a nonfactual theory are not. (P. 28) For arithmetic, the natural numbers associated with two sortal concepts are identical just in case the objects that... (shrink)

Keith Donnellan wrote his paper on definite descriptions in 1966 at Cornell University, an environment where nearly everybody was discussing Wittgenstein’s ideas of meaning as use. However, his idea of different uses of definite descriptions became one of the fundamental tenets against descriptivism, which was considered one of the main legacies of the Frege–Russell– Wittgenstein view; and I wonder whether a more Wittgensteinian interpretation of Donnellan’s work is possible.

In this article, we will revisit a motivation to consider the advantages of a theory about structured contents over a semantics of possible worlds. We will argue that a structure represents the strategic organization of the content of “p” under conditions in which asserting it does not imply contradictory consequences. These are the winning conditions for the assertion of ‘p’. When ‘p’ is modally sensitive – it can change its winning parameters – knowledge of the structure thus represents the rational (...) point for assertions (about non-actualized realities) that are organized to maximize what can be deduced from ‘p’. In these cases, the known relevant structure is intensional. We will argue that actualist Possible World Semantics, seeking the conversion of intensional knowledge into a de re representation of possible states, pays the price of being blind to structural divergences; it can only poorly explain these structural divergences between non-actual states of information and correlate it with divergence between winning strategies of assertion. Our argument will begin exposing Frege’s legacy; resort to Dummett’s concept of ingredient sense as an alternative to Kripke’s grade two knowledge; and briefly go through a semantic strategy of Stalnaker and Thomason to represent modal statements. In addition to these authors, we will explore the contribution of Russell, Kaplan and Ecthemendy to our argument. (shrink)

Theories of meaning developed within the analytic tradition, starting with Gottlob Frege, and within continental philosophy, starting with Husserl, can be distinguished by their disagreement about the phenomenon of collapse or failure of meaning. Our text focuses on Frege’s legacy, taken up by Rudolph Carnap, which culminated in a view of the collapse of meaning defined first by a purely syntactic conception of categorial error and second, when Tarski entered the scene, by the paradoxes created by the conflict between (...) the use of the predicate truth and the concept of proof. As positivism’s conventionalism and late model-theoretic semantics became the paradigms derived from this position, the result, in our view, was a conception of meaning success and meaning failure dominated by dependence on a technological conception. We will argue that this dependence leads to the inability to evaluate the breaks in rational parameters and crises of meaning addressed by the phenomenological and transcendental perspectives. Husserl’s critique of logic as technology is the basis for the reflexive standpoint on the phenomena of meaning failure that leads to a theoretical and eidetic ideal approach to that phenomenon. It is then suggested that this phenomenological reflective standpoint on the problem of meaning failure is the origin of the doors that lead to the divergent paths between the analytic and continental traditions. Thus, this is an article with three argumentative phases connected into a larger unity. The first phase presents Husserl’s critique of a purely extensional, syntactic, and recursive conception of logical consequence and the concept of truth; the second presents Hussel’s larger conception of meaning-failure; the third—presented in an appendix— presents a lesson on the division between continental and analytic philosophy. (shrink)

The division of the problems about Meaning in an extensional and an intensional theory was accused of unnecessarily duplicating the theoretical problems involved in the knowledge of Meaning. The result was either 1. an aggressive rejection of the intensional part of the problem or 2. the adoption of non-classical semantics to account for intensions. This paper suggests a reading of Frege's theory of Meaning that preserves the contribution of the intensional aspect of the question without sacrificing the benefits of (...) the classical insights. For this, however, we need to expand his theory to cases of semantic values which are not directly assertive, that is, what Micheal Dummett called ingredient value. This solution preserves the direct and intuitive insights of classical semantics, expanding it to cases where the designation of truth or falsehood does not have a unified interpretation: speculative, modal, ambiguous, relative cases or cases in which theories disputing Meaning is not straightforwardly mapped to the truth or the not-truth. The paper is a contribution to support the pragmatic interpretation of Frege's legacy by Micheal Dummett. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviews 85 RUSSELL’S CONTRIBUTION TO PHILOSOPHY OF LANGUAGE James Connelly Philosophy, Trent U. Peterborough, on k9l 1z6, Canada [email protected] Graham Stevens. The Theory of Descriptions: Russell and the Philosophy of Language. Basingstoke, uk: Palgrave Macmillan, 2011. Pp. xiii, 197. isbn: 978-0230 -20116-3. £50; us$85. ver the past decade, Graham Stevens has built his reputation as a lucid, durable, and oftentimes ground-breaking historian of analytic philosophy. His latest book, entitled (...) TheTheory of Descriptions: Russell and the Philosophy of Language, will only add to that burgeoning scholarly legacy. If it has not been established already, this book will doubtless cement Stevens’ place amongst the leading Russell scholars in the world today. It may very well herald Stevens ’ arrival on the scene as a noteworthy contributor to contemporary philosophy of language as well. The central goal of the book is “to bring the historical and purely philosophical analyses of [Russell’s] work into closer alignment” (p. 3). Stevens hopes to overcome a “striking disparity” (p. 2) in the ways that Russell’s contributions to the philosophy of language have been conceived by expositors of his philosophy, on the one hand, versus philosophers of language, on the other. In particular, though contemporary philosophers of language would tend to view Russell’s enormous contribution to that subject as being “undeniable” (p. 1), and to be “bewildered” (p. 94) by any suggestion to the contrary, expositors of Russell’s philosophy have nevertheless been at pains to emphasize that Russell “was not engaged in the philosophical study of language” (p. 2). As Stevens notes, this situation is especially puzzling since “these two groups [of scholars] overlap to a considerable extent” (p. 2). Stevens’ strategy for overcoming this disparity is two-pronged. First he aims to tackle, head on, the fallacious arguments of Monk,1 Dummett,2 and others, to the effect that Russell was not engaged in the philosophy of language. According to Stevens, such arguments have principally appealed to either (1) ______ 1 Ray Monk, “What Is Analytical Philosophy?”. 2 Michael Dummett, Frege: Philosophy of Language. l= 86 Reviews Russell’s dismissal of ordinary language philosophy, (2) his early, non-linguistic, conception of the nature of propositions, or (3) his view that natural language was inherently defective for philosophical purposes, and so called for replacement by a “logically perfect language”. In regards to (1), Stevens argues in a word that “[o]rdinary language philosophy has had its day” (p. 176). Over the past several decades, in other words, leading philosophers of language have come to agree with Russell in viewing ordinary language philosophy as “an outdated, and rather eccentric, relic of mid-twentieth century British philosophy” (ibid.).The classic Russell– Strawson debate over the question whether ordinary language lacks an exact logic3 has been settled decisively in Russell’s favour, as philosophers of language have transformed “the attempt to systematically specify the semantics of large regions of natural language” (ibid.) into a “central project” (ibid.). In regards to (2), moreover, Stevens notes that by this line of reasoning, absurdly, David Kaplan would not qualify as a philosopher of language since he “explicitly invokes the Russellian non-linguistic conception of a proposition as the conception appropriate for providing the content of properly context-situated indexical sentences” (p. 170). And, of course, Kaplan is not at all unique amongst contemporary philosophers of language in appealing to a Russellian conception of propositional content, as the examples of Nathan Salmon,4 Scott Soames,5 and many others show. In regards to (3), finally, Stevens argues that Russell’s dim view of natural language was grounded in his conception of logical form as non-linguistic, and that that conception, in turn, derives simply from the poverty of syntactic theory available to Russell, prior to the Chomskyian revolution in linguistics during the second half of the twentieth century. In light of the conceptual and analytic resources made available by this revolution, however, there exists “no insurmountable obstacle to assimilating Russell ’s notion of logical form to something akin to the modern notion of lf” (p. 172), where lf is conceived as one of four levels of syntactic representation within Chomsky’s Government and Binding Theory... (shrink)

In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic.

This is the 1991 (2nd) edition of the 1986 book (MIT Press), considered to be the classic defense of Millianism. The nature of the information content of declarative sentences is a central topic in the philosophy of language. The natural view that a sentence like "John loves Mary" contains information in which two individuals occur as constituents is termed the naive theory, and is one that has been abandoned by most contemporary scholars. This theory was refuted originally by philosopher Gottlob (...) Frege. His argument that the naive theory did not work is termed Frege's puzzle, and his rival account of information content is termed the orthodox theory. In this detailed study, Nathan Salmon defends a version of the naive theory and presents a proposal for its extension that provides a better picture of information content than the orthodox theory gives. He argues that a great deal of what has generally been taken for granted in the philosophy of language over the past few decades is either mistaken or unsupported, and consequently, much current research is focused on the wrong set of questions. Salmon dissolves Frege's puzzle as it is usually formulated and demonstrates how it can be reconstructed and strengthened to yield a more powerful objection to the naive theory. He then defends the naive theory against the new Frege puzzle by presenting an idea that yields both a surprisingly rich and powerful extension of the naive theory and a better picture of information content than that of the original orthodox theory. Nathan Salmon is Professor of Philosophy, University of California at Santa Barbara. (shrink)

One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.

It is Frege's third contribution that makes the point of departure for the present paper. Not merely did Frege show how to manipulate symbols more exactly; he also gave a searching account of what these symbols mean. Consider a philosophical problem that arises out of the simplest arithmetic. When we say that 5 = 2 + 3, what do we mean? Do we mean that 5 is identical with 2 + 3? But in some ways 5 and 2 + (...) 3 are obviously different. Or do we mean that 5 and 2 + 3 are equal but not identical, equality being a relation that falls short of complete identity? But in that case, some ordinary ways of speaking in mathematics must be false. Suppose a pupil is asked for the positive square root of 25. The phrasing of the question implies that there is one and only one. No doubt he may answer, '5'. But then it follows that the answer '2 + 3' is not allowable, since ex hypothesi 5 and 2 + 3, though equal, are not identical. Yet ordinarily the answer '2 + 3' would be regarded as strange but not as wrong. (shrink)

This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

[Considerations on the interpretation of Frege's. logico-philosophical legacy].

I shall make two main claims. My first main claim is that Frege started out with a view of logic that is closer to Kant’s than is generally recognized, but that he gradually came to reject this Kantian view, or at least totally to transform it. My second main claim concerns Frege’s reasons for distancing himself from the Kantian conception of logic. It is natural to speculate that this change in Frege’s view of logic may have been spurred by a (...) desire to establish the logicality of the axiom system he needed for his logicist reduction, including the infamous Basic Law V. I admit this may have been one of Frege’s motives. But I shall argue that Frege also had a deeper and more interesting reason to reject his early Kantian view of logic, having to do with his increasingly vehement anti-psychologism. (shrink)

I shall discuss some of the issues concerning a notorious doctrine of Frege that sentences are names of truth-values. I am interested in a problem raised by Kripke that the doctrine obscures the distinction between judgeable and unjudgeable contents. I shall present what I take to be Frege’s account of judgeable content: a proper expression of a judgeable content is susceptible to an analysis into a predicate and an argument-word, where a predicate is understood as a concept-word used to attribute (...) a certain property to the referent of the argument-word. In the light of this analysis, I shall argue that the doctrine does not obscure the distinction. The problem will also be discussed within the formal context of Grundgesetze. A new light will be shed on his rather peculiar conception of the symbol ‘ ${\boldsymbol \vdash}$’. (shrink)

(Translation of Frege's Grundgesetze II, §§ 86-137).

Down through the ages, logic has adopted many strange and awkward technical terms: assertoric, prove, proof, model, constant, variable, particular, major, minor, and so on. But truth-value is a not a typical example. Every proposition, even if false, no matter how worthless, has a truth-value:even “one plus two equals four” and “one is not one”. In fact, every two false propositions have the same truth-value—no matter how different they might be, even if one is self-contradictory and one is consistent. It (...) is not such a big surprise that every true proposition, no matter how worthless, has a truth-value. Every proposition, whether valuable or worthless, has a truth-value.But it is a little strange that every two true propositions, no matter how different they might be, have the same truth-value. The Pythagorean Theorem has the same truth-value as the proposition that one is one. It is a stretch to think of truth-values as values in any of the normal senses of the word ‘value’. (shrink)