Traces the development of British philosopher Russell's (1872-1970) ideas on mathematics from the 1890s to the publication of his Principles of mathematics in 1903. Draws from Russell's unpublished manuscripts, correspondence, and published works to point out the influence of Hegel, Cantor, Whitehead, Peano, and others. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

Nudges involve designing social “choice contexts” to promote what “experts” regard as beneficial for individuals and the society, by making the “right” choices easier. The most common form of nudge...

According to the received view, Russell rediscovered about 1900 the logical definition of cardinal number given by Frege in 1884. In the same way, we are told, he stated and developed independently the idea of logicism, using the principle of abstraction as the philosophical ground. Furthermore, the role commonly ascribed in this to Peano was only to invent an appropriate notation to be used as mere instrument. In this paper I hold that the study of Russell's unpublished manuscripts and Peano's (...) (and disciples) writings (as part of a larger investigation only pointed out here) shows, on the contrary, that Russell obtained the method to transform definitions by abstraction into nominal definitions and the general logicist idea from Peano (and his school). The only original insight from Russell, the principle of abstraction, partially derived from Moore's early philosophy, was finally abandoned because it was not of practical use. (shrink)

B. Russell, Foundations of logic 1903-05, The Collected Papers of Bertrand Russell, Volume 4, Edited by Urquhart, A. with the assistance of Lewis, A. C. London and New York:Routledge, 1994, Hi+ 743 pp. £100.

Two unpublished contributions to meetings can be found in the Alfred Tarski Papers, at the University of California, Berkeley. The meetings took place in 1965, in Chicago and London, respectively....

In this article I try to show the philosophical continuity of Russell's ideas from his paradox of classes to Principia mathematica. With this purpose, I display the main results (descriptions, substitutions and types) as moments of the same development, whose principal goal was (as in his The principles) to look for a set of primitive ideas and propositions giving an account of all mathematics in logical terms, but now avoiding paradoxes. The sole way to reconstruct this central period in Russell (...) is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg. Thus the logical problems (doubts about propositions, matrices and functions) are parallel to the ontological (the searching for genuine logical subjects) and methodological ones (the status of eliminative reduction). Paradoxes were the cause that the kind of (constructive) definition already applied by Russell, as an inheritance of Moorean analysis, obtained a new trait: ontological elimination, which, beginning with a ?no classes theory? and the theory of descriptions, led to a new theory of judgment (already present in manuscripts from 1906), ?incomplete symbols, and logical constructions. (shrink)

I expose and discuss here the different arguments Bradley used against the tenability of relations as genuine entities, as well as the corresponding arguments against predicates, both in metaphysical and logical terms, and this always in the framework of his semantic general ideas on judgment and truth. Also, I have found useful to try to find similar arguments in Frege, in order to show that, no matter how different their respective goals and methods may have been, both philosophers tried to (...) solve very similar problems regarding the nature of judgment and the role of relations in explaining its deep unity. Then I shall point out the multiple nature of the general problem involved, and finish with some reflections about its importance for analytical philosophers, especially for Russell. (shrink)

In this article I propose a new explanation of the relationship between Russell and ther first Wittgenstein. There are five main novelties in my interpretation; the use of all relevant unpublished manuscripts of Russell; the discovery of the first apparition of the “multiple theory of judgment” in a purely logical and unpublished context; the role of the Bradleian objection against relations in the evolution of the nation of form in both Russell and Wittgenstein; a general point of view to obtain (...) a common explanation of all the criticisms of Wittgenstein against Russell and of the abandonment to Theory of Knowledge; and the first account of the contribution of Whitehead to the progressive Russellian evolution from atomism to holism. (shrink)

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of definition, as (...) they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence. (shrink)

I expose and discuss here the different arguments Bradley used against the tenability of relations as genuine entities, as well as the corresponding arguments against predicates, both in metaphysical and logical terms, and this always in the framework of his semantic general ideas on judgment and truth. Also, I have found useful to try to find similar arguments in Frege, in order to show that, no matter how different their respective goals and methods may have been, both philosophers tried to (...) solve very similar problems regarding the nature of judgment and the role of relations in explaining its deep unity. Then I shall point out the multiple nature of the general problem involved, and finish with some reflections about its importance for analytical philosophers, especially for Russell. (shrink)

This is an essay-review of C. Wade Savage and C. Anthony Anderson (editors), Rereading Russell: Essays in Bertrand Russell's Metaphysics and Epistemology, Volume XII of Minnesota Studies in the Philosophy of Science, Minneapolis, University of Minnesota Press, 1989. The book is devoted to studying Russell's later philosophy, although the actual content concerns also Russell's early logical and epistemological writings. Here I study and criticize a group of contributions (mainly those by Hylton, Goldfarb, Cocchiarella, Pears and Demopoulos/Friedman) from a global and (...) methodological approach to Russell's whole philosophy I have developed in other publications. (shrink)

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of definition, as (...) they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence. (shrink)

The main thesis of this paper is that some of the most important ideas and symbolic devices that made Russell's theory of descriptions possible were already present in writings by Frege and especially Peano that Russell knew well. The paper contains a detailed comparison between the relevant parts of Russell's theory--including manuscripts recently published--and some of Frege and Peano's insights, as well as a discussion of numerous possible objections that could be posed to the main claim. Even if Russell was (...) not actually influenced by those insights, the parallelism is close enough to be worth analyzing, especially in the case of Peano, whose writings are not very well known. (shrink)

Shaughan La Vine, Understanding the Infinite.Cambridge, Massachussets :Harvard University Press, 1994, ix + 372 pp.£31.95/$47.95 B.Russell, Foundations of logic 1903‐05, The Collected Papers of Bertrand Russell, Volume 4, Edited by Urquhart, A.with the assistance of Lewis, A.C.London and New York:Routledge, 1994, Hi+ 743 pp.£100 Ray Monk and Anthony Palmer, Bertrand Russell and the Origins of Analytical Philosophy.Introduction by Ray Monk and Anthony Palmer.Bristol, U.K.:Thoemmes Press, 1996. xvi + 383 pp.£48.00/$78.00 ; £16.95/$29.95 T.J.Holopainen, Dialectic & Theology in the Eleventh Century.Leiden:E.J.Brill, 1996. (...) vii+171pp.$78. (shrink)