dc.contributor.author
Eichhoff, Matthias
dc.contributor.author
Weber, Gerald
dc.date.accessioned
2018-06-08T08:08:44Z
dc.date.available
2009-10-22T11:48:17.601Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/19445
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-23098
dc.description.abstract
Roger Penrose has received broad attention for his arguments with the
conclusion “the human mind is nonalgorithmic”. From this position he concludes
that a Quantum Gravitational Theory must be nonalgorithmic. In his writings
Penrose discusses Gödel's famous incompleteness sentence and his
epistemological position he calls Mathematical Platonism. In our article we
reconstruct the implicit logical structure of Penrose's argumentation with the
following results: First, we show that his conclusion “the human mind is
nonalgorithmic” can be obtained if both Gödel's sentence and Mathematical
Platonism are taken as premises. Second, we show that Penrose originally
derives his conclusion solely from Gödel's sentence, using a certain
interpretation that differs from Gödel's own. Third, it is shown that in both
cases the practice of mathematics would prescribe a certain epistemology,
namely Mathematical Platonism. We argue that Penrose did not recognize the
constitutional, indispensable function of Mathematical Platonism for his
considerations and the ensuing consequences for the epistemological state of
his whole argument.
de
dc.relation.ispartofseries
urn:nbn:de:kobv:188-fudocsseries000000000021-2
dc.rights.uri
http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen
dc.subject.ddc
100 Philosophie und Psychologie::100 Philosophie
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Must all mathematicians be platonists?
dc.title.subtitle
a case on Penrose's use of Gödel
refubium.affiliation
Mathematik und Informatik
de
refubium.affiliation.other
Institut für Informatik
refubium.mycore.fudocsId
FUDOCS_document_000000004017
refubium.resourceType.isindependentpub
no
refubium.series.name
Freie Universität Berlin, Fachbereich Mathematik und Informatik
refubium.series.reportNumber
98-3
refubium.mycore.derivateId
FUDOCS_derivate_000000000763
dcterms.accessRights.openaire
open access