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Full Idea
Use of the Deduction Theorem greatly simplifies the search for proof (or more strictly, the task of showing that there is a proof).
Gist of Idea
The Deduction Theorem greatly simplifies the search for proof
Source
David Bostock (Intermediate Logic [1997], 5.3)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.206
A Reaction
See 13615 for details of the Deduction Theorem. Bostock is referring to axiomatic proof, where it can be quite hard to decide which axioms are relevant. The Deduction Theorem enables the making of assumptions.
Related Idea
Idea 13615 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock]
13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |