deduction theorem

Let ‘P’ and ‘Q’ stand for (simple or compound) propositions.

The deduction theorem says that: if Q can be logically inferred from P, then ‘If P then Q’ can be proved as a theorem in the logical system in question.

This gives a method for dispensing with rules of inference in favor of axioms and theorems; but it does not hold for all logical systems, and in any case not all rules of inference can be dispensed with, for reasons due to Lewis Carroll.

Source:
L Carrol; What the Tortoise Said to Achilles

Related:

• Craig’s theorem
• deductivism
• Pythagoreanism
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• relevance logics

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