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Definition:
An anitlogism is a set of inconsistent propositions where two of them entail the contradictory
of a third. Usually, though, the term is limited to the combination of two premises from a valid
syllogism combined with the contradictory of the syllogism's conclusion.
There is also the "principle of antilogism," which stipulates that when two propositions logically entail a third, then a combination of one of the premises and the contradictory of the conclusion logically entails the contradiction of the other premise.
For example, consider this valid syllogism:
1a. Premise: All men are mortal.
2a. Premise: Socrates is a man.
3a. Conclusion: Therefore, Socrates is mortal.
The principle of antilogism allows us to also argue:
1b. Premise: All men are mortal. (same as 1a)
2b. Premise: Socrates is not mortal. (contradictory of 3a)
3b. Conclusion: Therefore, Socrates is not a man. (contradictory of 2a)
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Related Resources:
What is the Logic and the Philosophy of Language?
The two fields Logic and the Philosophy of Language are often treated separately, but they are nevertheless close enough that they are presented together here. Logic is the study of methods of reasoning and argumentation, both proper and improper. The Philosophy of Language, on the other hand, involves the study of how our language interacts with our thinking.What is Philosophy?
What is philosophy? Is there any point in studying philosophy, or is it a useless subject? What are the different branches of philosophy - what's the difference between aestheitcs and ethics? What's the difference between metaphysics and epistemology?
