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Peirce's theory of deductive reasoning

Charles Sanders Peirce held that the most important division of kinds of deductive reasoning is that between corollarial and theorematic. He argued that while all deduction ultimately depends in one way or another on mental experimentation on schemata or diagrams, in corollarial deduction:

"It is only necessary to imagine any case in which the premises are true in order to perceive immediately that the conclusion holds in that case"

while in theorematic deduction:

"It is necessary to experiment in the imagination upon the image of the premise in order from the result of such experiment to make corollarial deductions to the truth of the conclusion."

Peirce also held that corollarial deduction matches Aristotle's conception of direct demonstration, which Aristotle regarded as the only thoroughly satisfactory demonstration, while theorematic deduction is: