<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1982-596x</journal-id>
<journal-title><![CDATA[Educação e Filosofia]]></journal-title>
<abbrev-journal-title><![CDATA[Educ. Filos.]]></abbrev-journal-title>
<issn>1982-596x</issn>
<publisher>
<publisher-name><![CDATA[Universidade Federal de Uberlândia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1982-596x2015000100343</article-id>
<article-id pub-id-type="doi">10.14393/REVEDFIL29n57p343</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[David Hilbert e o Axioma de Arquimedes: entre a geometria e a física]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González]]></surname>
<given-names><![CDATA[Carlos Gustavo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade Federal de Uberlândia Instituto de Filosofia ]]></institution>
<addr-line><![CDATA[Uberlândia MG]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2015</year>
</pub-date>
<volume>29</volume>
<numero>57</numero>
<fpage>343</fpage>
<lpage>379</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S1982-596x2015000100343&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S1982-596x2015000100343&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S1982-596x2015000100343&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[A rela&#231;&#227;o entre geometria e f&#237;sica na obra de Hilbert &#233; analisada atrav&#233;s do caso do Axioma de Arquimedes. Come&#231;ando com as quest&#245;es geom&#233;tricas e as formais, em particular a defini&#231;&#227;o de modelos n&#227;o arquimedeanos para provar a independ&#234;ncia, passa-se logo &#224; concep&#231;&#227;o de Hilbert da geometria como uma ci&#234;ncia emp&#237;rica, para depois estudar a afirma&#231;&#227;o de Hilbert de que o Axioma de Arquimedes deve ser testado empiricamente. Nesse sentido, esse autor enuncia uma formula&#231;&#227;o emp&#237;rica do axioma, a qual, segundo afirma, deveria ser submetida &#224; experimenta&#231;&#227;o. Tal enunciado coloca tr&#234;s tipos de quest&#245;es. Primeiro, se &#233; realmente um enunciado emp&#237;rico ou se &#233; um princ&#237;pio metodol&#243;gico que n&#227;o pode ser testado. Segundo, se &#233; uma interpreta&#231;&#227;o adequada desse axioma. Por &#250;ltimo, como poderiam ser idealizados testes a partir desse enunciado. Sendo as primeiras quest&#245;es problem&#225;ticas, pior &#233; o caso da terceira, pois resulta dif&#237;cil conceber experimentos bem definidos nos quais a formula&#231;&#227;o emp&#237;rica possa ser testada, diferente, por exemplo, do caso da medi&#231;&#227;o dos &#226;ngulos de um tri&#226;ngulo entre tr&#234;s picos encomendada por Gauss.Na estudo da formula&#231;&#227;o emp&#237;rica tamb&#233;m s&#227;o analisados os coment&#225;rios de Leo Corry e de Michael St&#246;ltzer sobre o assunto, resultando em questionamentos sobre sua adequa&#231;&#227;o e verificabilidade. Al&#233;m disso, &#233; salientada a import&#226;ncia de diferenciar os conceitos de mensura&#231;&#227;o, pr&#243;prio do Axioma de Arquimedes, e de continuidade no sentido definido por Dedekind, baseado fundamentalmente na cr&#237;tica que Sommer faz a Hilbert.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[The relationship between geometry and physics in the work of Hilbert is analyzed through the case of the axiom of Archimedes. Starting with geometrical and formal issues (in particular, the definition of non-Archimedean models used for proving its independence), following with Hilbert conception that the physics is an empirical science, finally it is studied the Hilbertian statement that the axiom must be empirically confirmed. In this sense, he conceives an empirical statement of the axiom which must be confirmed by experiment. This statement arises three kind of questions. First, whether it actually is an empirical statement or a methodological rule which is not able to test. Second, whether it is a suitable interpretation of the axiom. Third, how can be created tests in relation to the empirical statement. Besides the fact that the two initial questions are difficult, the case of the third is worst, because, as far as I know, nobody proposed such a test, i.e. how can be designed well defined experiments to confirm the empirical statement (different, for example, of the case of the measurement of the sum of the angles of a triangle, performed by Gauss). The criticisms of Leo Corry and Michael St&#246;ltzer are analyzed too, in particular the questions about adequacy and verification of the empirical statement. Furthermore, it is emphasized the relevance of the distinction between the concepts of measurement, inherent to the Archimedean axiom, and the one of the continuity (in Dedekind's sense), based upon the criticism of Sommer on the Foundations of Geometry of Hilbert.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Hilbert]]></kwd>
<kwd lng="pt"><![CDATA[Axioma de Arquimedes]]></kwd>
<kwd lng="pt"><![CDATA[Geometria]]></kwd>
<kwd lng="pt"><![CDATA[Física]]></kwd>
<kwd lng="en"><![CDATA[Hilbert]]></kwd>
<kwd lng="en"><![CDATA[Axiom of Archimedes]]></kwd>
<kwd lng="en"><![CDATA[Geometry]]></kwd>
<kwd lng="en"><![CDATA[Physics]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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</article>
