more on this theme | more from this thinker
Full Idea
If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'.
Gist of Idea
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
Source
JC Beall / G Restall (Logical Consequence [2005], 4)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.8
A Reaction
These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules.
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |