Notre Dame Journal of Formal Logic

Is There a Modal Syllogistic?

Adriane A. Rini


Aristotle's modal syllogistic has been described as "incoherent," "a failure," "a realm of darkness." Even the gentler critics claim that it is inconsistent. I offer an interpretation according to which validity in the modal syllogistic is always obtained by substituting modal terms in the nonmodal syllogistic, and restricting the principles of modal conversion. In this paper I discuss the apodeictic syllogistic, showing that the restrictions I propose are powerful enough to do all the work Aristotle requires and, in fact, are supported by a close analysis of Aristotle's text. The upshot of this is that there is for Aristotle no separate modal syllogistic.

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Notre Dame J. Formal Logic Volume 39, Number 4 (1998), 554-572.

First available: 5 December 2002

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Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 03-03: Historical (must also be assigned at least one classification number from Section 01) 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Rini, Adriane A. Is There a Modal Syllogistic?. Notre Dame Journal of Formal Logic 39 (1998), no. 4, 554--572. doi:10.1305/ndjfl/1039118870.

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