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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

Table of Contents

    • 0.1 Related:
  • 1 Videos
  • 2 Related Products
    • 2.1 Advances in Natural Deduction: A Celebration of Dag Prawitz's Work (Trends in Logic)
    • 2.2 The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
    • 2.3 Logic and Discrete Mathematics: A Concise Introduction
    • 2.4 Logic and Structure (Universitext)
    • 2.5 First Course in Mathematical Logic (Dover Books on Mathematics)
    • 2.6 Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science)
    • 2.7 What Is Mathematical Logic? (Dover Books on Mathematics)
    • 2.8 Interpreting Biomedical Science: Experiment, Evidence, and Belief
    • 2.9 Metalogic: An Introduction to the Metatheory of Standard First Order Logic
    • 2.10 Upside-Down Meta-Interpretation of the Model Elimination Theorem-Proving Procedure for Deduction and Abduction

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