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
- 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
Last update 2020-06-17. Price and product availability may change.