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

5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-

[following from a formula in proof-theory]

7 ideas
Deduction is when we suppose one thing, and another necessarily follows [Aristotle]
If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein]
The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock]
A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
Normal deduction presupposes the Cut Law [Rumfitt]