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 is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg.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)

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.

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)

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)

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)

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)

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)

In this paper we briefly expose a project which could be summed up as ‘doing justice to Mario Pieri’. The main result of the project will be the publication of a book on him, in which we will mainl...

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....

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)

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)

I. WINCHESTER and K. BLACKWELL (eds.), Antinomies and paradoxes. Studies in Russell's early philosophy. Hamilton, Ontario: McMaster University Library Press, 1989. 248 pp. No price stated.

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.

En 1501, Mario Equicola concluye el _Perigynaecon_, la única obra filógina que el humanista de Alvito compondría en toda su vida. Este tratado se idea con una clara finalidad instrumental, pues el autor deseaba entrar al servicio de Isabella d’Este, marquesa consorte de Mantua. Precisamente por ello, tras cada uno de los argumentos que Equicola presenta y detrás de cada una de las mujeres ejemplares que menciona para ensalzar el valor femenino a lo largo de la historia se pueden establecer (...) paralelismos más o menos claros con los problemas que Isabella tuvo que afrontar en su primera década en la corte mantuana. En este artículo analizamos la función que Veturia desempeña en el seno del elenco de mujeres ejemplares del _Perigynaecon_ y profundizamos en algunos de los motivos que podrían haber empujado a Equicola a decantarse por incluir a la madre de Coriolano entre las mujeres a las que alude en su tratado. (shrink)

According to Ramsey (Representation reconsidered, Cambridge University Press, New York, 2007 ), only classical cognitive science, with the related notions of input–output and structural representations, meets the job description challenge (the challenge to show that a certain structure or process serves a representational role at the subpersonal level). By contrast, connectionism and other nonclassical models, insofar as they exploit receptor and tacit notions of representation, are not genuinely representational. As a result, Ramsey submits, cognitive science is taking a U-turn from (...) representationalism back to behaviourism, thus presupposing that (1) the emergence of cognitivism capitalized on the concept of representation, and that (2) the materialization of nonclassical cognitive science involves a return to some form of pre-cognitivist behaviourism. We argue against both (1) and (2), by questioning Ramsey’s divide between classical and representational, versus nonclassical and nonrepresentational, cognitive models. For, firstly, connectionist and other nonclassical accounts have the resources to exploit the notion of a structural isomorphism, like classical accounts (the beefing-up strategy); and, secondly, insofar as input–output and structural representations refer to a cognitive agent, classical explanations fail to meet the job description challenge (the deflationary strategy). Both strategies work independently of each other: if the deflationary strategy succeeds, contra (1), cognitivism has failed to capitalize on the relevant concept of representation; if the beefing-up strategy is sound, contra (2), the return to a pre-cognitivist era cancels out. (shrink)

In this paper a definition of n-valued system in the context of the algebraizable logics is proposed. We define and study the variety V3, showing that it is definitionally equivalent to the equivalent quasivariety semantics for the “Three-valued BCK-logic”. As a consequence we find an axiomatic definition of the above system.

In this paper we consider twelve classical laws of negation and study their relations in the context of BCK-algebras. A classification of the laws of negation is established and some characterizations are obtained. For example, using the concept of translation we obtain some characterizations of Hilbert algebras and commutative BCK-algebras with minimum. As a consequence we obtain a theorem relating those algebras to Boolean algebras.

We hypothesize that under the predicted scenario of climate change epigenetically mediated environmental sex determination could become an epigenetic trap. Epigenetically regulated environmental sex determination is a mechanism by which species can modulate their breeding strategies to accommodate environmental change. Growing evidence suggests that epigenetic mechanisms may play a key role in phenotypic plasticity and in the rapid adaptation of species to environmental change, through the capacity of organisms to maintain a non‐genetic plastic memory of the environmental and ecological conditions (...) experienced by their parents. However, inherited epigenetic variation could also be maladaptive, becoming an epigenetic trap. This is because environmental sex determination can alter sex ratios by increasing the survival of one of the sexes at the expense of negative fitness consequences for the other, which could lead not only to the collapse of natural populations, but also have an impact in farmed animal and plant species. (shrink)

This article explores the philosophy of Alain Badiou from the vantage point of the concepts of the localization, delocalization, and relocalization of the void as thematized through literary arts, religion, emancipatory politics, and the subject of psychoanalysis. In short, these moments around the void characterize the processes through which truth is processed and seen through their full realization by a philosophical engagement across the various conditions in which these truths occur. The localization of a void is the naming of an (...) indiscernible element that is incommensurable to the rubric of constructible knowledge, sense and meaning which could saturate the space of truth. Thus, the naming that localizes the void acts as a subtraction of the invariant in the variance of situation such that across various points in space and time, we are still able to subtract the universal as the invariant not just as the fidelity to the localized truth but also as the resurrection of truth upon its relocalization at a different place and a different time. At its core, this article is concerned with truth, why truth is persistent, and why we have to struggle to articulate the truth that we are trying to be faithful to again and again with each instance that truth risks being covered-over and obscured. (shrink)

The COVID-19 global health emergency has greatly impacted the educational field. Faced with unprecedented stress situations, professors, students, and families have employed various coping and resilience strategies throughout the confinement period. High and persistent stress levels are associated with other pathologies; hence, their detection and prevention are needed. Consequently, this study aimed to design a predictive model of stress in the educational field based on artificial intelligence that included certain sociodemographic variables, coping strategies, and resilience capacity, and to study the (...) relationship between them. The non-probabilistic snowball sampling method was used, involving 337 people from the university education community in south-eastern Spain. The Perceived Stress Scale, Stress Management Questionnaire, and Brief Resilience Scale were administered. The Statistical Package for the Social Sciences was used to design the architecture of artificial neural networks. The results found that stress levels could be predicted by the synaptic weights of coping strategies and timing of the epidemic, with a predictive capacity of over 80% found in the neural network model. Additionally, direct and significant associations were identified between the use of certain coping strategies, stress levels, and resilience. The conclusions of this research are essential for effective stress detection, and therefore, early intervention in the field of educational psychology, by discussing the influence of resilience or lack thereof on the prediction of stress levels. Identifying the variables that maintain a greater predictive power in stress levels is an effective strategy to design more adjusted prevention programs and to anticipate the needs of the community. (shrink)