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Full Idea
If all truths are implied by a falsehood, then 'if there are no trees in the park then there is no shade' and 'if there are no trees in the park there is plenty of shade' both come out as true. Intuitively, though, the second one is false.
Gist of Idea
If all truths are implied by a falsehood, then not-p might imply both q and not-q
Source
Jennifer Fisher (On the Philosophy of Logic [2008], 08.I)
Book Ref
Fisher,Jennifer: 'On the Philosophy of Logic' [Thomson Wadsworth 2008], p.107
A Reaction
The rule that a falsehood implies all truths must be the weakest idea in classical logic, if it actually implies a contradiction. This means we must take an interest in relevance logics.
| 8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |
| 8941 | We can't explain 'possibility' in terms of 'possible' worlds [Fisher] |
| 8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
| 8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
| 8944 | Vagueness can involve components (like baldness), or not (like boredom) [Fisher] |
| 8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher] |
| 8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |
| 8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher] |
| 8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher] |
| 8952 | We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher] |