Monday, January 30, 2012

Buridan on logical form

I posted four extensive works by Jean Buridan at the weekend, and just noticed this interesting argument in Book I question 6 of his Questions on the Prior Analytics, which is connected with my earlier discussion on context and indexicals.  He asks whether an expository syllogism - a syllogism in which the middle term is an expression that demonstratively identifies a subject - is valid in virtue of its form.

Sexta quaestio est utrum syllogismus expositorius sit bonus gratia formae.The sixth question is whether the expository syllogism is good [i.e. valid] in virtue of its form
Et arguitur quod non: quia iste syllogismus videtur esse expositorius 'hic homo est albus, hic homo est niger; ergo nigrum est album', et tamen consequentia non est bona, quia conclusio est manifeste falsa et tamen possibile est quod ambae praemissae sint simul verae, scilicet si in maiori demonstratur Socrates et in minori Plato.And it is argued that it is not, for the syllogism “this man is white, this man is black, therefore a black thing is a white thing, and yet the consequence is not good, because the conclusion is manifestly false and yet it is possible that both premisses are true at the same time, namely if Socrates is pointed to in the major, and Plato is pointed to in the minor

He replies that if one suppositum is signified in the major and another in the minor, the middle term is varied, and if the middle term is varied, it is not a good syllogism, nor is it a good expository syllogism. I don’t quite understand how this shows that the syllogism is valid in virtue of its form, however.

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