<?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>0011-1503</journal-id>
<journal-title><![CDATA[Crítica (México, D.F.)]]></journal-title>
<abbrev-journal-title><![CDATA[Crítica (Méx., D.F.)]]></abbrev-journal-title>
<issn>0011-1503</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Investigaciones Filosóficas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0011-15032025000200033</article-id>
<article-id pub-id-type="doi">10.22201/iifs.18704905e.2025.1695</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Lagunas expresivas en la demostración euclidiana]]></article-title>
<article-title xml:lang="en"><![CDATA[Expressive Gaps in Euclidian Proof]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Seoane]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de la República Facultad de Humanidades y Ciencias de la Educación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Uruguay</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<volume>57</volume>
<numero>170</numero>
<fpage>33</fpage>
<lpage>63</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0011-15032025000200033&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0011-15032025000200033&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0011-15032025000200033&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Algunas demostraciones que Euclides presenta en sus Elementos pueden denominarse polimodales (Seoane 2022). Esta caracterización se basa en un rasgo expresivo: tales demostraciones combinan dos formatos comunicacionales, un formato detallado y otro sumario. Don Fallis llama la atención sobre distintas clases de &#8220;lagunas&#8221; en la demostración matemática; una de esas clases la conforman las &#8220;lagunas entimemáticas&#8221; (Fallis 2003). Su definición parece apuntar al mismo fenómeno que capta (en el caso particular) la idea de formato sumario de la demostración polimodal euclidiana. Sin embargo, diferencias metodológicas con Fallis me llevan a proponer, para captar este caso, una noción alternativa, a la que denomino &#8220;laguna expresiva sumaria (sin costo estructural)&#8221;.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Summary: Some proofs presented by Euclid in his Elements can be called polymodal (Seoane 2022). This characterization is based on an expressive feature: such proofs combine two communication formats, a detailed format and a summary format. Don Fallis draws attention to different classes of &#8220;gaps&#8221; in mathematical proof; one of them consists of &#8220;enthymematic gaps&#8221; (Fallis 2003). Its definition seems to point to the same phenomenon captured (in the case in question) by the idea of a summary format of the Euclidean polymodal proof. However, basic methodological differences with Fallis lead me to propose, in order to capture this case, an alternative notion, which I call &#8220;summary expressive gap (without structural cost)&#8221;.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[demostración informal]]></kwd>
<kwd lng="es"><![CDATA[estilos matemáticos]]></kwd>
<kwd lng="es"><![CDATA[expresión]]></kwd>
<kwd lng="es"><![CDATA[estructura]]></kwd>
<kwd lng="es"><![CDATA[filosofía de la práctica matemática]]></kwd>
<kwd lng="en"><![CDATA[informal demonstration]]></kwd>
<kwd lng="en"><![CDATA[mathematical styles]]></kwd>
<kwd lng="en"><![CDATA[expression]]></kwd>
<kwd lng="en"><![CDATA[structure]]></kwd>
<kwd lng="en"><![CDATA[philosophy of mathematical practice]]></kwd>
</kwd-group>
</article-meta>
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