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Journal articles on the topic 'Logicism'

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Published: 4 June 2021
Last updated: 11 February 2022

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1

Feferman, Solomon. "Logic, Logics, and Logicism." Notre Dame Journal of Formal Logic 40, no. 1 (January 1999): 31–54. http://dx.doi.org/10.1305/ndjfl/1039096304.

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2

Boccuni, Francesca. "Minimal Logicism." Philosophia Scientae, no. 18-3 (October 1, 2014): 81–94. http://dx.doi.org/10.4000/philosophiascientiae.974.

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3

Jeffrey, Richard. "Logicism Lite*." Philosophy of Science 69, no. 3 (September 2002): 474–96. http://dx.doi.org/10.1086/342453.

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4

Boccuni, Francesca. "Plural Logicism." Erkenntnis 78, no. 5 (March 23, 2013): 1051–67. http://dx.doi.org/10.1007/s10670-013-9482-z.

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5

Linsky, Bernard, and Edward N. Zalta. "What is Neologicism?" Bulletin of Symbolic Logic 12, no. 1 (March 2006): 60–99. http://dx.doi.org/10.2178/bsl/1140640944.

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Logicism is a thesis about the foundations of mathematics, roughly, that mathematics is derivable from logic alone. It is now widely accepted that the thesis is false and that the logicist program of the early 20th century was unsuccessful. Frege's [1893/1903] system was inconsistent and the Whitehead and Russell [1910–1913] system was not thought to be logic, given its axioms of infinity, reducibility, and choice. Moreover, both forms of logicism are in some sense non-starters, since each asserts the existence of objects (courses of values, propositional functions, etc.), something which many philosophers think logic is not supposed to do. Indeed, the tension in the idea underlying logicism, that the axioms and theorems of mathematics can be derived as theorems of logic, is obvious: on the one hand, there are numerous existence claims among the theorems of mathematics, while on the other, it is thought to be impossible to prove the existence of anything from logic alone. According to one well-received view, logicism was replaced by a very different account of the foundations of mathematics, in which mathematics was seen as the study of axioms and their consequences in models consisting of the sets described by Zermelo-Fraenkel set theory (ZF). Mathematics, on this view, is just applied set theory.
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6

Rodríguez Consuegra, Francisco. "El logicismo russelliano: su significado filosófico." Crítica (México D. F. En línea) 23, no. 67 (December 13, 1991): 15–39. http://dx.doi.org/10.22201/iifs.18704905e.1991.792.

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After a brief presentation of Russell' s logicism, I attempt a global explanation of its philosophical significance. I reject the existence of two different kinds of logicism (Putnam) with the argument that Russell was trying to justify the existing mathematics and, at the same time, to escape from a mere formal calculus. For the same reason, the logicist definitions cannot be regarded as new axioms to be added to Peano's postulates (Reichenbach): according to Russell it is necessary to show that there is a constant meaning satisfying those postulates. The lack of a clear definition of logic in Russell (and Frege) is a consequence of his whole philosophy, therefore we must not look for it in the concept of necessity (Griffin), nor must we interpret this lack as a gap in the system (Grattan-Guinness). Russell's starting point was Moore's notion of truth as something indefinable and intuitive according to which we immediately recognize the true propositions. The problem of logicism is rather the deep tension between the ontological preeminence of relations (structures) and their terms (fields). [F.R.C.]
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7

BRUNGS, Alexander, and Frédéric GOUBIER. "On Biblical Logicism." Recherches de Théologie et Philosophie Médiévales 76, no. 1 (June 30, 2009): 199–244. http://dx.doi.org/10.2143/rtpm.76.1.2037163.

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8

FREY, Adrian. "LOGICISM AND CARNAP’S." Grazer Philosophische Studien 83, no. 1 (2011): 143–69. http://dx.doi.org/10.1163/9789401200721_009.

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9

Gandon, S., and B. Halimi. "Introduction: Logicism Today." Philosophia Mathematica 21, no. 2 (May 14, 2013): 129–32. http://dx.doi.org/10.1093/philmat/nkt018.

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10

Rayo, A. "Nominalism, Trivialism, Logicism." Philosophia Mathematica 23, no. 1 (June 16, 2014): 65–86. http://dx.doi.org/10.1093/philmat/nku013.

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11

Schiemer, Georg. "Logicism and ramsification." Metascience 23, no. 2 (March 22, 2014): 255–61. http://dx.doi.org/10.1007/s11016-014-9884-9.

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12

Bird, Alexander. "The Logic in Logicism." Dialogue 36, no. 2 (1997): 341–60. http://dx.doi.org/10.1017/s0012217300009549.

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RésuméLe logicisme de Frege engage à deux thèses: (1) les vérités de l'arithmétique sont ipso facto vérités de logique; (2) les nombres naturels sont des objets. Dans cet article je pose la question: quelle conception de la logique est-elle requise pour étayer ces thèses? Je soutiens qu'il existe une conception appropriée et naturelle de la logique, en vertu de laquelle leprincipe de Hume est une vérité logique. Leprincipe de Hume, qui dit que le nombre de Fs est le nombre de Gs ssi les concepts F et G sont équinumériques, est la pièce maîtresse de l'argumentation néologiciste en faveur de (1) et (2). Je défends cette position contre deux objections: a) le principe de Hume ne peut pas à la fois être d'ordre logique, comme le requiert (1), et avoir la portée ontologique requise par (2); et b) l'usage logiciste du principe de Hume à l'appui de (2) se ramène à une preuve ontologique d'un genre plus large, qui est non valide.
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13

Bays, Timothy. "The Fruits of Logicism." Notre Dame Journal of Formal Logic 41, no. 4 (October 2000): 415–21. http://dx.doi.org/10.1305/ndjfl/1038336884.

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14

Park Jeong-Il. "Wittgenstein’s Criticism of Logicism." CHUL HAK SA SANG - Journal of Philosophical Ideas ll, no. 43 (February 2012): 257–85. http://dx.doi.org/10.15750/chss..43.201202.008.

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15

Proops, Ian. "Russell's Reasons for Logicism." Journal of the History of Philosophy 44, no. 2 (2006): 267–92. http://dx.doi.org/10.1353/hph.2006.0029.

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16

Roeper, Peter. "A Vindication of Logicism." Philosophia Mathematica 24, no. 3 (September 7, 2015): 360–78. http://dx.doi.org/10.1093/philmat/nkv026.

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17

Tourinho, Carlos Diógenes C. "O PROBLEMA DOS FUNDAMENTOS NA FENOMENOLOGIA DE HUSSERL: O SURGIMENTO DE UM NOVO IDEALISMO TRANSCENDENTAL NO SÉC. XX." Síntese: Revista de Filosofia 40, no. 126 (August 20, 2012): 73. http://dx.doi.org/10.20911/21769389v40n126p73-84/2013.

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Resumo: Concentrando-se nos “Prolegômenos” de Husserl, o presente artigo aborda os argumentos do psicologismo e do anti-psicologismo no que se refere ao tema controverso das relações entre a Psicologia e a Lógica. Mostra-nos que o caminho trilhado pelo psicologismo conduz a um ceticismo nocivo à filosofia, enquanto o anti-psicologismo incorre em uma espécie de “logicismo dogmático”, para o qual estariam cortadas as relações com a experiência. O artigo destaca, então, o desafio de Husserl: encontrar um terceiro caminho em relação ao lugar da experiência no legítimo conhecimento, sem que tal caminho incorresse no ceticismo resultante do psicologismo, nem tampouco na tautologia do logicismo dogmático.Abstract: Focusing on Husserl’s Prolegomena, the present paper approaches the arguments of psychologism and anti-psychologism with regard to the controversial topic of the relationship between psychology and logic. It shows us that the path taken by psychologists leads to a skepticism harmful to philosophy, while anti-psychologism incurs a kind of “dogmatic logicism” that would cut off the relations with experience. Therefore, this article highlights Husserl’s challenge to find a third way regarding the role of experience in true knowledge, without falling into either the skepticism of psychologism, or the tautology of dogmatic logicism.
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18

Fernández, Ángel Nepomuceno. "Sistemas de cálculo como formas de Logicismo." Crítica (México D. F. En línea) 25, no. 73 (January 7, 1993): 15–35. http://dx.doi.org/10.22201/iifs.18704905e.1993.876.

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The logicism may be regarded like a fossil stone that has not utility nowadays. In this sense, logicism took care of the research about the foundations of mathematics but apparently its task arrived at its end many years ago because of sorne results that were eetablished during the century. However it is not wholly right. Understanding logicism as an attempt to reduce classical mathematics to logic means we can distinguish: 1) the idea according to which mathematic is logic in sorne way, and 2) a metaphysical program of research to: a) define mathematical notions as logical notions, and b) show that the mathematical theorems are logical theorems. The failure (if so) concerned to 2), since 1) was assumed by many logicians. Recovering logicism is not easy and there may be several ways. One of them is the one followed by N.B. Cocchiarella whose systems (there are more than one) represent a form of logicism (Frege's or Russell's form). From those systems -though a bit changed from my own point of view- we can define a modal calcule that may have application in computer science, what would not be a stale work. From a common language we take in account two systems in order to show that Cocchiarella's modified system is as powerful deductively as that of Church modified functional second order calcule. We can obtain new systems that represent form of logicism and are more powerful than that of Church enlarging Cochiarella's modified system. These new systems, that becomes modal systems provided that one adds appropiate modal tools (then they may be used in computer science), may be useful to study logicism itself (as historical philosophy of logic and mathematics).
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19

Thomas-Bolduc, Aaron. "New Directions for Neo-logicism." Bulletin of Symbolic Logic 25, no. 2 (June 2019): 219–20. http://dx.doi.org/10.1017/bsl.2019.10.

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20

Govier, Trudy. "Issues of Logicism and Objectivity." Informal Logic 37, no. 3 (September 11, 2017): 211–22. http://dx.doi.org/10.22329/il.v37i3.4832.

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Concerning Harald Wohlrapp’s theories, many fascinating issues arise. I shall concentrate here on aspects especially relevant to the treatment of pro and con argumentation, a type of what has been called conductive argument. Though initially intrigued by my efforts to describe and explore conductive argument, Harald Wohlrapp later concluded that my treatments were seriously flawed and that an alternative approach can serve to replace that problematic and much contested conception. Much of the difference between our approaches concerns what he deems to be a logicistic approach (referred to here as logicism) on my part.
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21

Rumfitt, Ian. "SINGULAR TERMS AND ARITHMETICAL LOGICISM." Philosophical Books 44, no. 3 (July 2003): 193–219. http://dx.doi.org/10.1111/1468-0149.00300_1.

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22

Rumfitt, Ian. "I–Ian Rumfitt: Frege's Logicism." Aristotelian Society Supplementary Volume 73, no. 1 (June 1, 1999): 151–80. http://dx.doi.org/10.1111/1467-8349.00053.

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23

Long, Steven A. "Aquinas on Being and Logicism." New Blackfriars 86, no. 1003 (May 2005): 323–47. http://dx.doi.org/10.1111/j.0028-4289.2005.00088.x.

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24

Allen, James F., and Henry A. Kautz. "Logicism is alive and well." Computational Intelligence 3, no. 1 (February 1987): 161–62. http://dx.doi.org/10.1111/j.1467-8640.1987.tb00184.x.

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25

HANSON, WILLIAM H. "Second-Order Logic and Logicism." Mind XCIX, no. 393 (1990): 91–99. http://dx.doi.org/10.1093/mind/xcix.393.91.

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26

MILNE, PETER. "Frege, Informative Identities, and Logicism." British Journal for the Philosophy of Science 40, no. 2 (June 1, 1989): 155–66. http://dx.doi.org/10.1093/bjps/40.2.155.

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27

Raatikainen, Panu. "Neo-Logicism and Its Logic." History and Philosophy of Logic 41, no. 1 (November 11, 2019): 82–95. http://dx.doi.org/10.1080/01445340.2019.1680517.

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28

Cook, Roy T. "Frege's Cardinals and Neo-Logicism." Philosophia Mathematica 24, no. 1 (September 29, 2015): 60–90. http://dx.doi.org/10.1093/philmat/nkv029.

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29

Ferreirós, José. "Hilbert, logicism, and mathematical existence." Synthese 170, no. 1 (June 7, 2008): 33–70. http://dx.doi.org/10.1007/s11229-008-9347-1.

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30

Kolman, Vojtěch. "Logicism as Making Arithmetic Explicit." Erkenntnis 80, no. 3 (December 23, 2014): 487–503. http://dx.doi.org/10.1007/s10670-014-9712-z.

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31

Tabata, Hirotoshi. "Frege's theorem and his logicism." History and Philosophy of Logic 21, no. 4 (December 2000): 265–95. http://dx.doi.org/10.1080/01445340010013707.

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32

Perrine, Timothy. "Arithmetic, Logicism, and Frege’s Definitions." International Philosophical Quarterly 61, no. 1 (2021): 5–25. http://dx.doi.org/10.5840/ipq202124162.

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This paper describes an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions. It also reviews two interpretations that try to resolve this puzzle: the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation and critiques the careful and sophisticated defenses of the analysis interpretation given by Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s texts either are inconsistent with the analysis interpretation or do not support it. I also defend the explicative interpretation from the recent charge that it cannot make sense of Frege’s logicism. While I do not provide the explicative interpretation’s full solution to the puzzle, I show that its main competitor is seriously problematic.
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33

한대석. "A Critical Examination of Logicism II." Studies in Philosophy East-West ll, no. 83 (March 2017): 463–516. http://dx.doi.org/10.15841/kspew..83.201703.463.

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34

Park, Jun-yong. "Dedekind on Axiomatics and His Logicism." Journal of the New Korean Philosophical Association 96 (April 30, 2019): 1–36. http://dx.doi.org/10.20433/jnkpa.2019.04.96.01.

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35

Oleinik, P. I. "SCOTTISH NEO-LOGICISM: "BAD COMPANY" OBJECTION." Historical and social-educational ideas 7, no. 7/2 (January 19, 2016): 147–50. http://dx.doi.org/10.17748/2075-9908-2015-7-7/2-147-150.

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36

WALSH, SEAN. "LOGICISM, INTERPRETABILITY, AND KNOWLEDGE OF ARITHMETIC." Review of Symbolic Logic 7, no. 1 (February 14, 2014): 84–119. http://dx.doi.org/10.1017/s1755020313000397.

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AbstractA crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here, an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of representation from contemporary mathematical logic. It is argued that the theory-based versions of such logicism are either too liberal (the plethora problem) or are committed to intuitively incorrect closure conditions (the consistency problem). Structure-based versions must on the other hand respond to a charge of begging the question (the circularity problem) or explain how one may have a knowledge of structure in advance of a knowledge of axioms (the signature problem). This discussion is significant because it gives us a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the philosophy of mathematics.
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37

Clark, P. "Logicism, the Continuum and Anti-Realism." Analysis 53, no. 3 (July 1, 1993): 129–40. http://dx.doi.org/10.1093/analys/53.3.129.

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38

Irvine, A. D. "Epistemic logicism & Russell's regressive method." Philosophical Studies 55, no. 3 (March 1989): 303–27. http://dx.doi.org/10.1007/bf00355328.

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39

MacFarlane, John. "Frege, Kant, and the Logic in Logicism." Philosophical Review 111, no. 1 (January 2002): 25. http://dx.doi.org/10.2307/3182569.

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40

Oleinik, Polina I. "«The measure» of neo-logicism: mathematical aspect." Vestnik Tomskogo gosudarstvennogo universiteta. Filosofiya. Sotsiologiya. Politologiya, no. 2(34) (June 1, 2016): 164–70. http://dx.doi.org/10.17223/1998863x/34/19.

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41

Park, Junyong. "Logicism and the Meanings of Logical Constants." Journal of the New Korean Philosophical Association 84 (April 30, 2016): 177–207. http://dx.doi.org/10.20433/jnkpa.2016.04.84.177.

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42

Henry, Paget. "African Philosophy in the Mirror of Logicism." CLR James Journal 4, no. 1 (1993): 70–78. http://dx.doi.org/10.5840/clrjames1993414.

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43

Hale, Bob. "WILLIAM DEMOPOULOS Logicism and Its Philosophical Legacy." British Journal for the Philosophy of Science 66, no. 2 (June 1, 2015): 459–63. http://dx.doi.org/10.1093/bjps/axu008.

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44

Cline, Gene. "Historicism, Logicism and Moralism in the Classroom." Teaching Philosophy 15, no. 1 (1992): 5–15. http://dx.doi.org/10.5840/teachphil19921514.

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45

Forbus, Kenneth D. "Logic versus logicism: a reply to McDermott." Computational Intelligence 3, no. 1 (February 1987): 176–78. http://dx.doi.org/10.1111/j.1467-8640.1987.tb00191.x.

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46

Reck, Erich H. "Frege, Dedekind, and the Origins of Logicism." History and Philosophy of Logic 34, no. 3 (August 2013): 242–65. http://dx.doi.org/10.1080/01445340.2013.806397.

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47

MacFarlane, J. "Frege, Kant, and the Logic in Logicism." Philosophical Review 111, no. 1 (January 1, 2002): 25–65. http://dx.doi.org/10.1215/00318108-111-1-25.

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48

Schirn, Matthias. "Frege’s Logicism and the Neo-Fregean Project." Axiomathes 24, no. 2 (October 6, 2013): 207–43. http://dx.doi.org/10.1007/s10516-013-9222-7.

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49

MacBride, Fraser. "Speaking with Shadows: A Study of Neo‐Logicism." British Journal for the Philosophy of Science 54, no. 1 (March 1, 2003): 103–63. http://dx.doi.org/10.1093/bjps/54.1.103.

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50

Galavotti, Maria Carla. "Harold Jeffreys' Probabilistic Epistemology: Between Logicism And Subjectivism." British Journal for the Philosophy of Science 54, no. 1 (March 1, 2003): 43–57. http://dx.doi.org/10.1093/bjps/54.1.43.

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