Frege/Russell/early Wittgenstein

INTUITION IN MATHEMATICS?

by Carlo Penco

Frege on Self-Presentation Draft

by Guy Longworth

Wittgenstein on the Substance of the World

by Ian Proops

Published in The European Journal of Philosophy, 12: 1, 106–126.

The *Tractatus* contains an argument that there are simple, necessarily existent objects, which, being simple, are... more The *Tractatus* contains an argument that there are simple, necessarily existent objects, which, being simple, are suited to be the referents of the names occuring in the final analysis of propositions. The argument is perplexing in its own right, but also for its invocation of the notion of "substance". I argue that if one locates Wittgenstein's conception of substance in the Kantian tradition to which his talk of "substance" alludes, what emerges is an argument that is very nearly--but not quite--cogent.

Wittgenstein's Logical Atomism

by Ian Proops

Published in the Stanford Encyclopedia of Philosophy.

An article explicating Wittgenstein's logical atomism and surveying the relevant secondary literature. An article explicating Wittgenstein's logical atomism and surveying the relevant secondary literature.

The new Wittgenstein: A critique

by Ian Proops

An essay challenging Cora Diamond's influential approach to reading Wittgenstein's Tractatus. According to Diamond,... more An essay challenging Cora Diamond's influential approach to reading Wittgenstein's Tractatus. According to Diamond, the Tractatus contains no substantive philosophical theses, but is purely an exercise in the debunking of nonsense. I argue that a convincing case for this claim has not yet been made--either by Diamond herself, or by the numerous defenders of this so-called "resolute" reading. Having critically examined the arguments that have been offered in favor of the resolute reading, I go on to marshal textual evidence--using both published and unpublished sources--supporting the view that Wittgenstein advanced, and indeed took himself to have advanced, a host of substantive philosophical theses even in the (so-called) "body" of the Tractatus. I argue that resolute readers of the Tractatus have not begun to offer a satisfactory explanation of these problematic texts; and I argue that the "frame/body" distinction alleged by resolute readers does not stand up to critical scrutiny.

Russell and the Universalist Conception of Logic

by Ian Proops

Published in Noûs, 2007, 41: 1, 1–32

The paper examines the widespread idea that Russell subscribes to a "Universalist Conception of Logic".... more The paper examines the widespread idea that Russell subscribes to a "Universalist Conception of Logic". Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results are, by an large, unfavorable to the Universalist interpretation.

Logical Syntax in the Tractatus

by Ian Proops

An essay on Wittgenstein's conception of nonsense and its relation to his idea that "logic must take care of... more An essay on Wittgenstein's conception of nonsense and its relation to his idea that "logic must take care of itself". I explain how Wittgenstein's theory of symbolism is supposed to resolve Russell's paradox, and I offer an alternative to Cora Diamond's influential account of Wittgenstein's diagnosis of the error in the so-called "natural view" of nonsense.


This is a pre-publication copy. The published version appears in: Richard Gaskin, ed.,*Grammar in Early Twentieth-Century Philosophy* (Routledge, 2001).

Soames on the metaphysics and epistemology of Moore and Russell

by Ian Proops

Draft only. Published in Philosophical Studies (2006): 129 (3):627–635.

A critical discussion of selected chapters of the first volume of Scott Soames’s Philosophical Analysis in the... more A critical discussion of selected chapters of the first volume of Scott Soames’s Philosophical Analysis in the Twentieth Century. It is argued that this volume falls short of the minimal standards of scholarship appropriate to a work that advertises itself as a history, and, further, that Soames’s frequent heuristic simplifications and distortions, since they are only sporadically identified as such, are more likely confuse than to enlighten the student. These points are illustrated by reference to Soames’s discussions of Russell’s logical system and the place of the theory of descriptions in his ontological development. It is then argued that Soames’s interpretation of the point of G.E. Moore’s famous “proof” of an external world, while not straightforwardly undermined by the textual evidence, is nonetheless questionable, and plausibly overlooks what is novel in Moore’s discussion. This, it is argued, in his attempt to offer a common sense “refutation of idealism”, rather than (as is more commonly supposed) an anti-skeptical argument “from differential certainty”.

The Tractatus on Inference and Entailment

by Ian Proops

Draft only. Published in Erich Reck, ed., *From Frege to Wittgenstein: Essays on Early Analytic Philosophy* (O.U.P.), 283–307

In the Tractatus Wittgenstein criticizes Frege and Russell's view that laws of inference (Schlussgesetze)... more In the Tractatus Wittgenstein criticizes Frege and Russell's view that laws of inference (Schlussgesetze) "justify" logical inferences. What lies behind this criticism, I argue, is an attack on Frege and Russell's conceptions of logical entailment. In passing, I examine Russell's dispute with Bradley on the question whether all relations are "internal"

Russell on Substitutivity and the Abandonment of Propositions

by Ian Proops

Published in The Philosophical Review, 2011, 120: 2, 151–205

The paper argues that philosophers commonly misidentify the substitutivity principle involved in Russell’s puzzle... more The paper argues that philosophers commonly misidentify the substitutivity principle involved in Russell’s puzzle about substitutivity in “On Denoting” (the so-called "George IV puzzle"). This matters because when that principle is properly identified the puzzle becomes considerably sharper and more interesting than it is often taken to be. This article describes both the puzzle itself and Russell's solution to it, which involves resources beyond the theory of descriptions. It then explores the epistemological and metaphysical consequences of that solution. One such consequence, it argues, is that Russell must abandon his commitment to propositions.

Kant's Conception of Analytic Judgment

by Ian Proops

Published in Philosophy and Phenomenological Research, 2005, vol. 70, no. 3, 588–612.

In the Critique of Pure Reason Kant appears to characterize analytic judgments in four distinct ways: once in terms of... more In the Critique of Pure Reason Kant appears to characterize analytic judgments in four distinct ways: once in terms of “containment,” a second time in terms of “identity,” a third time in terms of the explicative–ampliative contrast, and a fourth time in terms of the notion of “cognizability in accordance with the principle of contradiction.” The paper asks: Which of these characterizations—or apparent characterizations—best captures Kant’s conception of analyticity in the first Critique? It suggests: “the second.” It argues, further, that Kant’s distinction is intended to apply only to judgments of subject–predicate form, and that the fourth alleged characterization is not properly speaking a characterization at all. These theses are defended in the course of a more general investigation of the distinction’s meaning, its epistemology, and its tenability.

La ética y los límites de la argumentación moral. El desafío del emotivismo

by Nicolas Zavadivker

Publicado por la Facultad de Filosofía y Letras de la Universidad Nacional de Tucumán (Argentina), San Miguel de Tucumán, 2011.

Este trabajo se ocupa del desarrollo histórico-filosófico de las posiciones subjetivistas sobre los valores... more
Este trabajo se ocupa del desarrollo histórico-filosófico de las posiciones subjetivistas sobre los valores surgidas a partir del siglo XVIII con David Hume, en el seno de la tradición del empirismo analítico. Partiendo de esta posición, se centra en la transformación del subjetivismo axiológico de raigambre analítica en el siglo XX hacia el emotivismo, en el marco del giro lingüístico de la filosofía contemporánea. Los filósofos cuyas posiciones se examinan son David Hume, Ludwig Wittgenstein, Alfred Ayer, Bertrand Russell y John Leslie Mackie.
A partir de la dicha indagación, se examinan las posibilidades actuales del emotivismo como propuesta de análisis del lenguaje moral. En las Conclusiones se toma posición frente a dos importantes objeciones que surgieron contra el emotivismo: su incapacidad para dar cuenta de las pretensiones de verdad o de validez que estarían presentes en todo juicio de valor, y su imposibilidad de ofrecer una explicación suficiente del sentido de la discusión moral, al restringir la misma a mera retórica y negar que existan razones para apoyar un juicio de valor.
Mediante un examen crítico de esas dificultades, se vislumbra en qué medida el emotivismo (y más en general el no-cognitivismo) puede aún hoy ser reivindicado como una posición metaética posible, o bien si debe considerarse definitivamente superado. En ese sentido, se analiza también qué aspectos del emotivismo pueden reformularse de modo de mantener alguna vigencia, incorporando elementos del estudio de los juicios de valor provenientes de otras tradiciones metaéticas.
El capítulo I contextualiza la corriente del ‘empirismo analítico’, a la vez que se ocupa del tipo de tratamiento con que esta tradición filosófica abordó la problemática de la ética en general y del estatus de los valores en particular. Desde el capítulo II al VI, se presentan las posiciones de Hume, el 1º Wittgenstein, Ayer, Russell y Mackie. El capítulo VII ofrece un intento de clasificación de las distintas posturas que reciben el nombre genérico de ‘subjetivismo axiológico’. El capítulo VIII versa acerca de las relaciones del empirismo analítico con diversos temas relevantes para la ética (argumentos contra el objetivismo axiológico, posibilidad de fundamentar la ética, papel de la razón en la práctica moral, emotivismo y empirismo, etc.). Finalmente las Conclusiones recapitulan las diferentes posiciones metaéticas y de la argumentación moral expuestas, a los fines de reexaminarlas a la luz de algunas de las críticas que pretendieron impugnar el emotivismo. Se intenta así demarcar el papel que juegan las pretensiones de verdad o de validez en los juicios de valor, no tenidas en cuenta por dicha doctrina. También se examina y se defiende la posibilidad de dar cuenta de un genuino razonamiento moral en el marco de una posición emotivista.

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.

Object

by henry laycock

I have converted my own copy of this 2010 piece, which appears in the Stanford Encyclopedia of Philosophy, from WP into PDF for this document.
A LIVE-LINKS COMPLETE BIBLIOGRAPHY FOLLOWS
http://philpapers.org/sep/object/

ABSTRACT. The Frege / Russell account of the object-concept is here called into question. The most general category or... more ABSTRACT. The Frege / Russell account of the object-concept is here called into question. The most general category or concept of an object is a formal one -- a logico-semantic category which is not (as is commonly supposed) exhaustive of what may be thought or said to be. Bona fide objects, whether abstract or concrete, must be countable - 'no entity without identity' (and hence without distinctness). But stuff or matter is not countable and cannot be understood in terms of objects. The issue is significant, if only because the predicate calculus rests upon the object-concept: non-count nouns have no place within the notation

Freges Sinne trotz Zwillingserde?

by Fabian Hundertmark

Not published

Tractarian First-Order Logic: Identity and the N-Operator

by Kai Wehmeier

joint with Brian Rogers

On Ramsey's 'Silly Delusion' regarding Tractatus 5.53ff

by Kai Wehmeier

I supply a semantics and a tableaux calculus for a first-order logic based on Hintikka’s strongly exclusive... more I supply a semantics and a tableaux calculus for a first-order logic based on Hintikka’s strongly exclusive interpretation of the variables, and prove that the calculus is sound and complete with respect to the semantics.

Wittgensteinian Tableaux, Identity, and Co-Denotation

by Kai Wehmeier

Wittgensteinian predicate logic (W-logic) is characterized by the requirement that the objects mentioned within the... more Wittgensteinian predicate logic (W-logic) is characterized by the requirement that the objects mentioned within the scope of a quantifier be excluded from the range of the associated bound variable. I present a sound and complete tableaux calculus for this logic and discuss issues of translatability between Wittgensteinian and standard predicate logic in languages with and without individual constants. A metalinguistic co-denotation predicate, akin to Frege’s triple bar of the Begriffsschrift, is introduced and used to bestow the full expressive power of first-order logic with identity on W-logic in the presence of constants.

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.

Wittgensteinian Predicate Logic

by Kai Wehmeier

We investigate a first-order predicate logic based on Wittgenstein’s suggestion to express identity of object by... more We investigate a first-order predicate logic based on Wittgenstein’s suggestion to express identity of object by identity of sign and difference of objects by difference of signs. Hintikka has shown that predicate logic can indeed be set up in such a way; we show that it can be done nicely. More specifically, we provide a perspicuous cut-free sequent calculus, as well as a Hilbert-type calculus, for Wittgensteinian predicate logic and prove soundness and completeness theorems.