Aristotle on Circular Proof

in Phronesis
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Abstract

In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that Aristotle’s third argument in 1.3 is successful. I argue that both chapters are concerned with the same conception of circular proof, namely the propositional one. Contrary to what is often thought, the syllogistic conception provides an adequate analysis of the internal deductive structure of the propositional one. Aristotle achieves this by employing a kind of multiple-conclusion logic.

Phronesis

A Journal for Ancient Philosophy

Sections

References

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1)

Barnes 1994, 106.

3)

See Barnes 1976, 280; 1994, 104-8; Lear 1980, 80.

4)

Philoponus, in Post. An. xiii.3, 50.23-51.4 Wallies; Ross 1949, 515.

5)

For example, Pr. An. 1.15, 34a5-33; 1.25, 41b36-42a31; 2.2, 53b11-20, 53b23-4.

7)

Irwin 1988, 127-8; Detel 1993, ii. 96-7.

9)

See Irwin 1988, 125-6.

20)

Pacius 1597, 325-6; Lear 1980, 80; Smith 1989, 193-4. Pace Barnes (1981, 38; 1994, 106), who takes a circular proof to consist of three syllogisms such as those in [iii]-[v].

27)

See Barnes 2007, 498-500.

36)

See Malink 2009, 132-5.

47)

See Shoesmith and Smiley 1978, p. ix and 129-32; cf. also Schröter 1955, 60-1.

48)

See Siebel 1996, 150-2.

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