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For example, his theory of topical "middles" and their role in his theory of consequence.
He also contributed to general metamathematics (the theory of consequence operation) and intuitionistic logic.
Burley's mature theory of consequence, as presented in the longer version of De Puritate, is best discussed against the background of the theory of consequence presented in Ockham's Summa Logicae, so let us now turn to Ockham first.
This research arose from the need for an even more abstract way of developing the theory of consequence relations.
Part III.3 is in effect Ockham's theory of consequence, although it also includes discussions of semantic paradoxes like the Liar (the so called insolubilia) and of the still little-understood disputation form known as "obligation".
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Finally, one of the fields in which Albert is considered a major contributor is the theory of consequences.
Autrecourt's theory about the evidentness of inferences was contested by his contemporaries and should be understood in the light of the late-medieval theory of consequences.
But whereas Buridan maintained the central role of Aristotelian syllogistic, Albert, like Burley, integrated syllogistic and the study of conversions into the theory of consequences.
In any case, Burley seems to have been on Albert's mind when he wrote his commentary on the Nicomachean Ethics as well as when we was developing his theory of consequences.
As a logician, he was at the forefront of the movement that expanded the analysis of language based on the properties of terms, especially their reference (in Latin: suppositio), but also in the exploration of new fields of logic, especially the theory of consequences.
The precise historical origins of 14th century theories of consequence are still debated among scholars.
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