Why Do We Prove Theorems?
Identifieur interne : 000229 ( Main/Exploration ); précédent : 000228; suivant : 000230Why Do We Prove Theorems?
Auteurs : Yehuda Rav [France]Source :
- Philosophia Mathematica [ 0031-8019 ] ; 1999-02.
Abstract
Ordinary mathematical proofs—to be distinguished from formal derivations—are the locus of mathematical knowledge. Their epistemic content goes way beyond what is summarised in the form of theorems. Objections are raised against the formalist thesis that every mainstream informal proof can be formalised in some first-order formal system. Foundationalism is at the heart of Hilbert's program and calls for methods of formal logic to prove consistency. On the other hand, ‘systemic cohesiveness’, as proposed here, seeks to explicate why mathematical knowledge is coherent (in an informal sense) and places the problem of reliability within the province of the philosophy of mathematics.
Url:
DOI: 10.1093/philmat/7.1.5
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000388
- to stream Istex, to step Curation: 000363
- to stream Istex, to step Checkpoint: 000218
- to stream Main, to step Merge: 000230
- to stream Main, to step Curation: 000229
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Why Do We Prove Theorems?</title><author wicri:is="90%"><name sortKey="Rav, Yehuda" sort="Rav, Yehuda" uniqKey="Rav Y" first="Yehuda" last="Rav">Yehuda Rav</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:51695C330BE038C0B433324B3CA0DB360FE7615E</idno><date when="1999" year="1999">1999</date><idno type="doi">10.1093/philmat/7.1.5</idno><idno type="url">https://api.istex.fr/document/51695C330BE038C0B433324B3CA0DB360FE7615E/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000388</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000388</idno><idno type="wicri:Area/Istex/Curation">000363</idno><idno type="wicri:Area/Istex/Checkpoint">000218</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000218</idno><idno type="wicri:doubleKey">0031-8019:1999:Rav Y:why:do:we</idno><idno type="wicri:Area/Main/Merge">000230</idno><idno type="wicri:Area/Main/Curation">000229</idno><idno type="wicri:Area/Main/Exploration">000229</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Why Do We Prove Theorems?</title><author wicri:is="90%"><name sortKey="Rav, Yehuda" sort="Rav, Yehuda" uniqKey="Rav Y" first="Yehuda" last="Rav">Yehuda Rav</name><affiliation wicri:level="3"><country wicri:rule="url">France</country><wicri:regionArea>Department of Mathematics, University of Paris-Sud, F-91405 Orsay</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Orsay</settlement></placeName></affiliation></author></analytic><monogr></monogr><series><title level="j">Philosophia Mathematica</title><idno type="ISSN">0031-8019</idno><idno type="eISSN">1744-6406</idno><imprint><publisher>Oxford University Press</publisher><date type="published" when="1999-02">1999-02</date><biblScope unit="volume">7</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="5">5</biblScope><biblScope unit="page" to="41">41</biblScope></imprint><idno type="ISSN">0031-8019</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0031-8019</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract">Ordinary mathematical proofs—to be distinguished from formal derivations—are the locus of mathematical knowledge. Their epistemic content goes way beyond what is summarised in the form of theorems. Objections are raised against the formalist thesis that every mainstream informal proof can be formalised in some first-order formal system. Foundationalism is at the heart of Hilbert's program and calls for methods of formal logic to prove consistency. On the other hand, ‘systemic cohesiveness’, as proposed here, seeks to explicate why mathematical knowledge is coherent (in an informal sense) and places the problem of reliability within the province of the philosophy of mathematics.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Orsay</li></settlement></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Rav, Yehuda" sort="Rav, Yehuda" uniqKey="Rav Y" first="Yehuda" last="Rav">Yehuda Rav</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/SophieGermainV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000229 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000229 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= SophieGermainV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:51695C330BE038C0B433324B3CA0DB360FE7615E
|texte= Why Do We Prove Theorems?
}}
| This area was generated with Dilib version V0.6.33. |  |