structure for 'Theory of Logic'    |     alphabetical list of themes    |     expand these ideas

5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions

[proofs which add assumptions to axioms and rules]

7 ideas
The Deduction Theorem greatly simplifies the search for proof [Bostock]
'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock]
Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock]
The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock]
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]