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What are syllogisms?

What are syllogisms? Here are some definitions.

Noun
  1. plural of syllogism
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Aristotle was charged with preferring flimsy theories and sterile syllogisms to the solid, fertile facts.
Moreover, modern usage distinguishes between valid syllogisms and invalid syllogisms.
In Hegel's syllogisms of the idea, objectivity attained rational form, while the concept acquired an explicit, material existence.
In the latter, the syllogisms involved must have middle terms that are causes of the state of affairs which is to be demonstrated.
No sophistry and no syllogisms can conjure away this inevitable consequence of inflation.
They give reasons, they use syllogisms, they argue by suggesting counterexamples, they engage in all the hallmarks of reasoned argument.

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