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Full Idea
The style of proof called 'induction on formula construction' (or 'on the number of connectives', or 'on the length of the formula') rest on the fact that all formulas are built up from atomic formulas according to strict rules.
Gist of Idea
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms
Source
Theodore Sider (Logic for Philosophy [2010], 2.7)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.52
A Reaction
Hence the proof deconstructs the formula, and takes it back to a set of atomic formulas have already been established.
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] |