The Uses of Argument in Mathematics

Abstract

ABSTRACT. Stephen Toulmin once observed that 'it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate ' (Toulmin & al., 1979, p. 89). Might the application of Toulmin's layout of arguments to mathematics remedy this oversight?Toulmin's critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying disagreement about the nature of the proof in question.

Mathematics and Argumentation

“…There have been several substantially independent applications of the Toulmin layout to mathematical reasoning (Alcolea Banegas, 1998;Aberdein, 2005;Inglis et al, 2007;Pedemonte, 2007) as well as attempts to extend the layout better to fit complex mathematical arguments (Knipping, 2001;Aberdein, 2006). Other studies deploy a variety of different methodologies including pragma-dialectics (Krabbe, 1997(Krabbe, , 2008Aberdein, 2007b) and other systems (Douek, 1999;Dove, 2007).…”

STRUKTUR ARGUMENTASI PENALARAN KOVARIASIONAL SISWA KELAS VIIIB MTsN 1 KEDIRI

“…Beberapa penelitian sebelumnya, yaitu Aberdein (2005), Yackel (2002), dan Brinkerhoff (2007) menunjukkan bahwa model argumen Toulmin dapat diperinci sehingga suatu argumen dapat menjadi komponen bagi argumen selanjutnya. Aksi-aksi mental kovariasi muncul secara berurutan sehingga aksi mental yang lebih tinggi tidak dapat muncul jika aksi mental sebelumnya tidak muncul.…”

“…Model argumen Toulmin menawarkan suatu pendekatan untuk menganalisis argumen yang berbeda dari logika formal. Yackel (2002), Aberdein (2005), Aberdein (2006a), Aberdein (2008b), dan Brinkerhoff (2007) juga menunjukkan bahwa Model argumen Toulmin dapat digunakan untuk menangkap struktur argumen formal maupun informal. Hal ini memberikan keleluasaan bagi Model Argumen Toulmin untuk menganalisis berbagai bentuk argumen.…”

Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

“…2 However, he later applied the layout to Theaetetus's proof that there are exactly five platonic solids (Toulmin et al, 1979). Aberdein has shown that Toulmin's argumentation structure can represent more complex mathematical proofs; such as the proof that there are irrational numbers α and β such that α β is rational (Aberdein, 2005), and the classical proof of the Intermediate Value Theorem (Aberdein, 2006). Alcolea (1998) has shown that Toulmin's argumentation structure can also be used to represent meta-level mathematical argument, modelling Zermelo's argument for adopting the axiom of choice in set theory (described in Aberdein, 2005).…”