Gottlob Frege

Thesis - A Fregean Response to Moore and Altman

by Sean Martin

Frege on Self-Presentation Draft

by Guy Longworth

Frege, Kant e le Vorstellungen

by Alberto Vanzo

co-authored with Gabriele Tomasi. Rivista di storia della filosofia, n.s., 61 (2006), suppl., 227-38.

Gottlob Frege criticized Kant's use of the term "representation" in a footnote in the Foundations of... more Gottlob Frege criticized Kant's use of the term "representation" in a footnote in the Foundations of Arithmetics. According to Frege, Kant used the term "representation" for mental images, which are private and incommunicable, and also for objects and concepts. Kant thereby gave "a strongly subjectivistic and idealistic coloring" to his thought. The paper argues that Kant avoided the kind of subjectivism and idealism which Frege hints in his remark. For Kant, having Vorstellungen requires the capacity of synthesis, by virtue of which the mind goes beyond its subjective states, and its modifications become presentations of an independent world.

The text of this paper is not freely accessible online. If you would like to receive an offprint, do no hesitate to contact me.

Words Without Objects (BOOK)

by henry laycock

Clarendon Press, Oxford (this is not the complete book, unfortunately)

CLICK ON THE 'DOWNLOAD' - NOT THE 'QUICK VIEW' [ERROR!]

The book seeks to resolve the so-called ‘problem of mass nouns’ — a problem which cannot be resolved on the basis of a... more The book seeks to resolve the so-called ‘problem of mass nouns’ — a problem which cannot be resolved on the basis of a conventional system of logic. It is not, for instance, possible to explicate assertions of the existence of air, oil, or water through the use of quantifiers and variables which take objectual values. The difficulty is attributable to the semantically distinctive status of non-count nouns — nouns which, although not plural, are nonetheless akin to plural nouns in being semantically non-singular. Such are the semantics of a non-singular noun, that there can be no such single thing or object as the thing of which the noun is true. However, standard approaches to understanding non-singular nouns tend to be reductive, construing them as singular expressions — expressions which, in the case of non-count nouns, are true of ‘parcels’ or ‘quantities’ of stuff, and in the case of plural nouns, are true of ‘plural entities’ or ‘sets’. It is argued that both approaches are equally misguided, that there are no distinctive objects in the extensions of non-singular nouns. With plural nouns, their extensions are identical with those of the corresponding singular expressions. With non-count nouns, because they are not plural, there can be no corresponding singular expressions. In consequence, there are no objects in the extensions of non-count nouns at all. In short, there are no such things as instances of stuff: the world of space and time contains not merely large numbers of discrete concrete things or individuals of diverse kinds, but also large amounts of sheer undifferentiated concrete stuff. Metaphysically, non-singular reference in general is an arbitrary modality of reference, ungrounded in the realities to which it is non-ideally or intransparently correlated.

Introduzione

by Andrea Bianchi

Words as Concepts

by Andrea Bianchi

Logic as Social Action

by William Brooke

Why Wander into Fiction? Analytic Philosophy and the Case Study of Henry James

by Kristin Boyce

Dissertation completed at The University of Chicago (August, 2010) under the direction of James Conant and Michael Kremer (co-chairs), Daniel Brudney, and Jonathan Lear.

When reading a great work of literature, it is not unusual to feel that something of philosophical importance is being... more When reading a great work of literature, it is not unusual to feel that something of philosophical importance is being achieved. But it has often proved difficult to do justice to such a feeling from within an analytic philosophical framework. One source of this difficulty is that the analytic tradition has defined itself in part by distinguishing sharply between the “logical” (that which pertains to the expression and justification of truth-evaluable content) and the “psychological” (that which pertains to effects on the psychological faculties of a reader or viewer, especially the feelings and imagination). This has created an obstacle to the possibility of seeing literary works as vehicles of serious philosophical thought because the sort of force that literary works have for their readers has been associated with a “merely psychological” capacity to powerfully engage the feelings and imagination. In seeking to overcome this obstacle, many analytic philosophers have assumed that if a work of literature is philosophically significant, this must be because of what it contributes to the “logical” task of expressing or justifying a philosophical view of some sort. I call this the “natural analytic assumption”. I argue not only that this assumption is not compulsory but also that making it precludes the possibility of doing full justice to some of the very literary works that have struck many as most philosophically powerfully.

I make this argument by drawing on one central case study: the literary project of Henry James. I turn to James’s work in particular because his writings have already attracted the attention of a number of leading philosophers, many of whom make the natural analytic assumption. The first stage of my argument involves examining in some detail the work of four such interpreters: Daniel Brudney, Alice Crary, Martha Nussbaum and Robert Pippin. I bring out how the natural analytic assumption shapes—intentionally or unintentionally—their respective accounts of literature and argue that making this assumption cripples their capacity to do full justice to the philosophical significance of James’s work.

The second stage of the argument involves developing an alternative account of the philosophical significance of James’s work. I do this by building on the work of philosophers such as Stanley Cavell and Cora Diamond who seek to account more adequately for the philosophical significance of the literary form of uncontroversially philosophical texts that are central for the analytic tradition, namely, Wittgenstein’s Tractatus and Philosophical Investigations. These interpreters do not make the natural analytic assumption. Instead, some such interpreters argue that Wittgenstein’s work takes the unusual literary forms it does as part of his effort to inherit and more fully develop methods of elucidating confusion and illusion which had their beginnings in the work of another brilliant philosopher of form, albeit non-aesthetic form: Gottlob Frege. Frege develops a special form of representing thought which he conceives of as, in part, an aid to the philosopher in the task of “liberating the human spirit” from confusions and illusions of thought. The larger argument in the second half of the dissertation is that the literary forms of representation that James develops contribute in a similar way to the elucidations of what I call confusions and illusions of living. James himself suggests the comparison between illusions of thought and illusions of life. In the opening paragraphs of The Wings of the Dove, he compares the disintegration of a meaningful sentence into meaningless sounds or marks to the disintegration of the unity and progression of a meaningful life into a mere succession of disconnected movements. Many of his works are centrally preoccupied with the possibility that our lives can lapse into such meaningless successions. I argue that what is philosophically most powerful and distinctive about his works lies in the ways in which they can serve to exhibit a reader’s life to the reader herself so as to allow her to recognize when her living is breaking down in this way—when her living has, to follow James’s own way of speaking, lapsed into a mere “death-in-life”.

Given that the analytic tradition developed in part out of the possibilities opened by Frege’s brilliant self-consciousness about form, it is surprising that this tradition has underestimated as consistently as it has the philosophical potential of both aesthetic and non-aesthetic forms of representation. The dissertation argues that keeping in view the methodological underpinnings of Frege’s self-consciousness about the usefulness of his Begriffsschrift can help us think more adequately about what philosophical uses various aesthetic forms may have. Furthermore, it demonstrates that doing fuller justice to aesthetic forms of representation in this way affords an important opportunity to more fully to develop some of the analytic tradition’s own best possibilities. Although by Frege’s lights the clarification of confusion plays a merely secondary role in his overall project, such clarification is recognized by central figures of the analytic tradition, such as Carnap and Wittgenstein, as philosophical work of the first importance. One central dimension of the inheritance of Frege's work within the analytic tradition, especially in the hands of the later Wittgenstein, has been a gradual expansion of our appreciation of the diversity of forms of philosophical confusion there can be, along with an exploration of the correlative diversity of methods of clarification best suited to their treatment. The dissertation argues that, in effect, central aspects of the literary project of Henry James can bring into view possibilities for yet further stages in such a development.

LITERATURE, LOGIC AND THE LIBERATING WORD: THE ELUCIDATION OF CONFUSION IN HENRY JAMES

by Kristin Boyce

Published in Journal for Philosophical Research, Volume 35 (2010).

Henry James is an author who has on the one hand attracted the attention of many leading philosophical interpreters of... more Henry James is an author who has on the one hand attracted the attention of many leading philosophical interpreters of literature even while on the other hand he poses a certain kind of difficulty for a tradition which has tended to prioritize what is said while relegating how it is said to the margins: the philosophical gravity of James’s work seems clearly to lie in the manner in which James writes, especially in the difficult style which characterizes his late phase. Many of James’s philosophical interpreters have recognized this but they nevertheless characterize the philosophical interest of how James writes in such a way as to leave the emphasis, in the end, still on a philosophical “what”: what philosophical view his difficult style implies or corroborates. I develop an interpretation of the philosophical significance of James’s late style that does not reduce it in this way to a philosophical “what.” I argue that features of James’s late style—its compression and rigor—invite a comparison between his literary forms of representation and the logically perspicuous modes of representing thought developed by Gottlob Frege. One use to which Frege puts his Begriffsschrift is as a tool in the task of clarifying forms of philosophical confusion. I argue that what is most philosophically important about James’s literary forms of representation is that they can be used to represent a reader’s life, to the reader herself, in such a way as to make it possible for her to recognize her confusion.

Variables, generality and existence

by henry laycock

DRAFT CONFERENCE VERSION - ALMOST IDENTICAL WITH PUBLISHED VERSION

In that semantic tradition of which Frege and Russell are among the most distinguished members, the project of... more In that semantic tradition of which Frege and Russell are among the most distinguished members, the project of formalizing natural-language sentences is not simply a matter of developing smooth and effective techniques for the representation of reasoning. Over and above the representation of valid inference as valid, and invalid inference as invalid, there is a further objective. Logic in this tradition is what Frege himself famously calls a concept-script, the import of the notion being chiefly that in natural languages, as Frege emphasizes, ‘the connection of words corresponds only partially to the structure of concepts’, thereby compelling the logician to ‘conduct an ongoing struggle against language and grammar, insofar as they fail to give clear expression to the logical’. In the more recent past, a kindred overall approach is forcefully expounded in the work of Quine, who writes, albeit with a positivistic slant, that

the simplification and clarification of logical theory to which a canonical logical notation contributes is not only algorithmic, it is also conceptual ... each elimination of obscure constructions or notions that we manage to achieve, by paraphrase into more lucid elements, is a clarification of the conceptual scheme of science.

The approach is one with which I find myself in general sympathy; indeed the contrast between clear and less-than-clear ‘expressions of the logical’ is vital to the thesis of this work. Though it has not always received the understanding and respect which it deserves, the ideal of a logically transparent language represents, in my estimation, no merely interesting episode in the history of ideas. It embodies, rather, a permanently valid insight, an enduringly valuable ideal for any analytical conception of philosophy.

Frege, Russell and Wittgenstein on the Judgment Stroke

by Floor Rombout

MSc Logic Thesis

Frege is highly valued as a logician by Russell and Wittgenstein, the latter nonetheless concludes in his Tractatus... more Frege is highly valued as a logician by Russell and Wittgenstein, the latter nonetheless concludes in his Tractatus that one of Frege's central notions, the judgment stroke, is "logically quite meaningless".
In order to see why Wittgenstein thinks so, we will investigate the 'indirect interpretation thesis', which says that Wittgenstein's interpretation of Frege was strongly influenced by the reading Russell gives of the Begriffsschrift in Principia Mathematica and Principles of Mathematics. This is done by analyzing the different conceptions of logic, focusing on the representations of judgment and assertion in Frege, Russell and the early Wittgenstein.
Stong similarities can be found between the interpretations of Russell and Wittgenstein, this makes the indirect interpretation thesis plausible, although Russell's influence cannot be the only reason why Wittgenstein rejected the judgment stroke as a logical symbol.

Cohering The Parts: the search for a teleological direction in the coherence theory of truth

by Xavier Meulders

draft only

Science is often considered as a set of propositions referring to an objective world existing independently of the... more Science is often considered as a set of propositions referring to an objective world existing independently of the human mind. Due to their very being, propositions are either true or false. This ultimately means that theories in which science is equated with a certain whole of propositions, must rely on a correspondence theory of truth. But when we try to incorporate the role of human knowledge into the scientific process, we discover that the correspondence theory simply breaks down. This leaves us with a coherence theory of truth, in which it are not propositions but judgements that form the most fundamental elements of a scientific theory. When examining the nature of judgement, we come to the conclusion that the notion of truth used in a coherence theory is fundamentally different from the one used in a correspondence theory. It is a primitive notion that cannot be defined or analysed, since the coherence theory has ‘bracketed’ the validity of the world of objective axioms and propositions. But examples of it can be given, such as the law of non-contradiction which brings our whole edifice of judgements into a coherent, non-contradictory whole. Nevertheless, the truth-standards of a coherence theory are not merely formal. They are in fact driven by a certain ‘telos’ toward an ever clearer disclosure of the world as it is in itself. But then it might be interesting to examine the very origin of this ‘telos’ or ‘drive’. Husserlian phenomenology, for instance, has searched for this drive in the notions of ‘transcendental subjectivity’ and ‘the lifeworld’. But even these notions are not self-sufficient in the sense that they can provide an adequate explanation of the directedness of our intentional life. And this ultimately leads us to the inevitable realm of the philosophy of God.

A mechanised environment for Frege's Begriffsschrift notation

by Josh Parsons

Aspekte der Frege-Hilbert-Korrespondenz

by Kai Wehmeier

In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine according to which consistency of an... more In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert's later work in foundations, which we consider to have been greater than previously assumed. This conjecture is based on a hitherto neglected revision of Hilbert's talk "Über den Zahlbegriff".

Auf der Suche nach Freges Nachlaß

by Kai Wehmeier

(with Hans-Christoph Schmidt am Busch)

The Quest for Frege's Nachlass

by Kai Wehmeier

(with Hans-Christoph Schmidt am Busch)

Russell's Paradox in Consistent Fragments of Frege's Grundgesetze der Arithmetik

by Kai Wehmeier

We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by... more We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.

Frege's Permutation Argument Revisited

by Kai Wehmeier

(with Peter Schroeder-Heister)

In Section 10 of Grundgesetze, Volume I, Frege advances a mathematical argument (known as the permutation argument),... more In Section 10 of Grundgesetze, Volume I, Frege advances a mathematical argument (known as the permutation argument), by means of which he intends to show that an arbitrary value-range may be identified with the True, and any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identifiability thesis, following Schroeder-Heister (1987)). As far as we are aware, there is no consensus in the literature as to (i) the proper interpretation of the permutation argument and the identifiability thesis, (ii) the validity of the permutation argument, and (iii) the truth of the identifiability thesis. In this paper, we undertake a detailed technical study of the two main lines of interpretation, and gather some evidence for favoring one interpretation over the other.

Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects

by Kai Wehmeier

In this paper, I consider two curious subsystems of Frege’s Grundgesetze der Arithmetik: Richard Heck’s predicative... more In this paper, I consider two curious subsystems of Frege’s Grundgesetze der Arithmetik: Richard Heck’s predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T_Delta in monadic second-order logic, consisting of axiom V and Delta^1_1- comprehension (in a language containing an abstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both H and T_Delta prove the existence of infinitely many non-logical objects (T_Delta deriving, moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege’s proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T_Delta to Cantor’s theorem which is somewhat surprising.

On the Consistency of the Delta^1_1-CA Fragment of Frege's Grundgesetze

by Kai Wehmeier

(with Fernando Ferreira)

It is well known that Frege’s system in the _Grundgesetze der Arithmetik_ is formally inconsistent. Frege’s... more It is well known that Frege’s system in the _Grundgesetze der Arithmetik_ is formally inconsistent. Frege’s instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege’s basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege’s theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Delta^1_1-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case.