Inferentialism and Its Mathematical Precursor
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F18%3A10384741" target="_blank" >RIV/00216208:11210/18:10384741 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Inferentialism and Its Mathematical Precursor
Original language description
In the chapter, it is argued that a transparent precedent to the inferentialist doctrine of Robert Brandom can be traced back to so-called axiomatism, particularly in the form advocated by Hilbert and, implicitly, by Frege. The dialectical role that axiomatism has played in the history of mathematics provides an important exegetical tool to demonstrate the validity of the grounding principles of inferentialist philosophy including, surprisingly, the social perspective on knowledge. Accordingly, the chhapter interprets the occurrence of the phenomenon of Gödel incompleteness theorems within Hilbert's symbolic program as a split of mathematical self-consciousness into two consciousnesses-known in mathematical logic under the names of "truth" and "proof"-to be interpreted as players in the game of giving and asking for reasons. In this, Lorenzen's transformation of Hilbert's purely symbolic project of operative mathematics and logic into Lorenzen's and Lorenz's dialogical logic is of particular interest, as are Lorenzen's metamathematical concepts of semi- and full-formalism.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
<a href="/en/project/GA16-12624S" target="_blank" >GA16-12624S: The Notion of Concept in the Context of Modern Thought</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
From Rules to Meanings. New Essays in Inferentialism
ISBN
978-1-138-10261-3
Number of pages of the result
11
Pages from-to
323-333
Number of pages of the book
357
Publisher name
Routledge
Place of publication
New York
UT code for WoS chapter
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