Article ID: CBB604456688

Shaping the Enemy: Foundational Labelling by L.E.J. Brouwer and A. Heyting (2019)

unapi

The use of the three labels (logicism, formalism, intuitionism) to denote the three foundational schools of the early twentieth century are now part of literature. Yet, neither their number nor their adoption has been stable over the twentieth century. They were not introduced by the founding fathers of each school: namely, neither Frege nor Russell spoke of ‘logicism’; and even Hilbert did not use the word ‘formalism’ to introduce his foundational programs. At a certain point, only Brouwer used the label ‘intuitionism’ in his scientific production to personify his philosophy of mathematics and he used the label ‘formalism’ for Hilbert’s foundational viewpoint. Starting with Brouwer, the origin of the use of the three labels to represent a foundational meaning, will be analysed in this paper. Thereafter, the role that Brouwer’s pupil Arend Heyting had in the production and use of foundational labels will be considered. On the basis of the comparison of the attitudes of these two scholars I will finally advance the thesis that not only the creation but also the use of labels, far from being a mere gesture of academic reference to literature, can be a sign of the cultural operation each scholar wanted to do.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB604456688/

Similar Citations

Book John A. Goldsmith; Bernard Laks; (2019)
Battle in the Mind Fields (/isis/citation/CBB777839551/)

Article Bobenrieth, Andrés M.; (2010)
The Origins of the Use of the Argument of Trivialization in the Twentieth Century (/isis/citation/CBB001210972/)

Book Patterson, Douglas; (2008)
New Essays on Tarski and Philosophy (/isis/citation/CBB001232382/)

Book Tieszen, Richard L.; (2011)
After Gödel: Platonism and Rationalism in Mathematics and Logic (/isis/citation/CBB001210605/)

Article Godden, David M.; Griffin, Nicholas; (2009)
Psychologism and the Development of Russell's Account of Propositions (/isis/citation/CBB001211038/)

Article Atten, Mark van; Sundholm, Göran; Bourdeau, Michel; Atten, Vanessa Van; (2014)
“Que les principes de la logique ne sont pas fiables” : Nouvelle traduction française annotée et commentée de l'article de 1908 de L. E. J. Brouwer (/isis/citation/CBB001551989/)

Article Humberstone, Lloyd; (2003)
A Strange Remark Attributed to Gödel (/isis/citation/CBB000300864/)

Book Baaz, Matthias; (2011)
Kurt Gödel and the Foundations of Mathematics: Horizons of Truth (/isis/citation/CBB001210590/)

Article Campos, Daniel G.; (2011)
On the Distinction between Peirce's Abduction and Lipton's Inference to the Best Explanation (/isis/citation/CBB001211461/)

Article de Rouilhan, Philippe; (2012)
In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort (/isis/citation/CBB001214124/)

Chapter Lara Piersanti; (2000)
Vailati e Russell (/isis/citation/CBB615477680/)

Chapter Christian Thiel; (2013)
Dubislav and Classical Monadic Quantificational Logic (/isis/citation/CBB499589599/)

Book Schumann, Andrew; (2013)
Logic in Central and Eastern Europe: History, Science, and Discourse (/isis/citation/CBB001213928/)

Book Nedo, Michael; (2013)
Wittgenstein: una biografia per immagini (/isis/citation/CBB001213930/)

Chapter Mancosu, Paolo; (2006)
Tarski on Models and Logical Consequence (/isis/citation/CBB000800123/)

Article Feferman, Solomon; (2012)
On Rereading van Heijenoort's Selected Essays (/isis/citation/CBB001214123/)

Book Giovanni Vailati; Claudia Arrighi; Paola Cantù; Mauro De Zan; Patrick Suppes; (2010)
Logic and Pragmatism: Selected Essays by Giovanni Vailati (/isis/citation/CBB877530276/)

Article Isaac, Joel; (2013)
Donald Davidson and the Analytic Revolution in American Philosophy, 1940--1970 (/isis/citation/CBB001201202/)

Authors & Contributors
Lara Piersanti
Loner, David
Laks, Bernard
Arrighi, Claudia
Goldsmith, John A.
Atten, Vanessa Van
Concepts
Logic
Philosophy
Mathematics
Philosophy of science
Philosophy of mathematics
Biographies
Time Periods
20th century
19th century
20th century, early
21st century
20th century, late
Places
United States
Italy
Eastern Europe
Poland
Germany
France
Institutions
Berlin Group (Philosophy)
Vienna Circle
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment