Inferentialism and Its Mathematical Precursor
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
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DOI - Digital Object Identifier
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Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Inferentialism and Its Mathematical Precursor
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Inferentialism and Its Mathematical Precursor
Popis výsledku anglicky
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.
Klasifikace
Druh
C - Kapitola v odborné knize
CEP obor
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OECD FORD obor
60301 - Philosophy, History and Philosophy of science and technology
Návaznosti výsledku
Projekt
<a href="/cs/project/GA16-12624S" target="_blank" >GA16-12624S: Pojetí pojmu v kontextu moderního myšlení</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2018
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název knihy nebo sborníku
From Rules to Meanings. New Essays in Inferentialism
ISBN
978-1-138-10261-3
Počet stran výsledku
11
Strana od-do
323-333
Počet stran knihy
357
Název nakladatele
Routledge
Místo vydání
New York
Kód UT WoS kapitoly
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