Monday, 29 October 2018

The Beginnings of Formal Logic

The Topics was written before the Prior Analytics, and in both works, deductions (syllogismoi) have an important role to play. But it is generally believed that the Prior Analytics marks the beginning of formal logic. So what are the grounds on which Aristotle’s discussion of deductions qualify as formal in the one treatise but not in the other?

Marko Malink, in his essay, “The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics,” (Phronesis; Volume 60; Issue 3; 2015), offers four reasons to establish that the Prior Analytics, and not the Topics, qualifies as a treatise of formal logic. The four reasons are:
First, the Prior Analytics abstracts from speaker meaning and only takes into account the literal meaning of the sentences involved in a deduction. Nothing of relevance is left to tacit understanding between speaker and hearer. Every aspect of the meaning that is relevant to an argument’s counting as a deduction is made explicit by some linguistic expression, even if Aristotle is not formalistic and does not prescribe which expressions to use. 
Secondly, Aristotle is concerned to make explicit all premises that are necessary to deduce the conclusion in a given argument. 
Thirdly, Aristotle provides a criterion for determining when all the necessary premises have been made explicit. The criterion is (largely) sound with respect to modern conceptions of valid deductive inference. 
Fourthly, deductions are formulated in a language that is supposed to be free from homonymy and ambiguity.
These four features are present in the Prior Analytics but are absent in the Topics. If they had been present in the Topics then the Topics would have marked the beginning of formal logic. However, Aristotle himself does not use the terminology of ‘form’ and ‘formal’ in his logical works, and Malink points out in his essay that the Aristotelian syllogistic is not formalistic or formalized, even though the logic in the Prior Analytics is accepted as formal.

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