<p>This paper examines the early modern history of Eulerian diagrams and argues that their development was shaped by confessional contexts. While logic is often viewed as a neutral and purely rational discipline, we show that logic diagrams in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(16^{\textrm{th}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>16</mn> <mrow> <mi mathvariant="italic">th</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(17^{\textrm{th}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>17</mn> <mrow> <mi mathvariant="italic">th</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> centuries were embedded in broader religious, philosophical, and institutional traditions. After clarifying the concept of logic diagrams and the specific characteristics of Eulerian representations, we identify methodological challenges in reconstructing their history and outline several external factors that influenced their use. Using two case studies—Nicolaus Reimers Ursus in the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(16^{\textrm{th}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>16</mn> <mrow> <mi mathvariant="italic">th</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> century and Erhard Weigel in the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(17^{\textrm{th}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>17</mn> <mrow> <mi mathvariant="italic">th</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> century—we demonstrate that Eulerian diagrams were predominantly cultivated in Protestant circles, in contrast to Byzantine and Roman Catholic diagrammatic traditions such as crescent diagrams, the square of opposition, and phoebifer axis diagrams. These competing traditions differed not only in form but also in their underlying representations of proof, particularly regarding direct versus indirect methods. The paper argues that confessional affiliation, together with philosophical convictions such as empiricism and rationalism, contributed to the selection and evaluation of diagrammatic techniques. By situating early modern logic within its cultural context, the study highlights the role of external factors in shaping representational practices in logic.</p>

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The Protestant Tradition of Eulerian Diagrams

  • Jens Lemanski,
  • Amirouche Moktefi

摘要

This paper examines the early modern history of Eulerian diagrams and argues that their development was shaped by confessional contexts. While logic is often viewed as a neutral and purely rational discipline, we show that logic diagrams in the \(16^{\textrm{th}}\) 16 th and \(17^{\textrm{th}}\) 17 th centuries were embedded in broader religious, philosophical, and institutional traditions. After clarifying the concept of logic diagrams and the specific characteristics of Eulerian representations, we identify methodological challenges in reconstructing their history and outline several external factors that influenced their use. Using two case studies—Nicolaus Reimers Ursus in the \(16^{\textrm{th}}\) 16 th century and Erhard Weigel in the \(17^{\textrm{th}}\) 17 th century—we demonstrate that Eulerian diagrams were predominantly cultivated in Protestant circles, in contrast to Byzantine and Roman Catholic diagrammatic traditions such as crescent diagrams, the square of opposition, and phoebifer axis diagrams. These competing traditions differed not only in form but also in their underlying representations of proof, particularly regarding direct versus indirect methods. The paper argues that confessional affiliation, together with philosophical convictions such as empiricism and rationalism, contributed to the selection and evaluation of diagrammatic techniques. By situating early modern logic within its cultural context, the study highlights the role of external factors in shaping representational practices in logic.