Acknowledges his indebtedness to both Stanley Kubrick.
Philosophers dislike inconsistency, seeing it as worse than an mere embarrassment. Woods wants us to lighten up, buts sees that inconsistency damages theories.
Negation-inconsistent systems have at least one statement and its negation.
In absolutely inconsistent systems, all statements and their negations are are contained. But if we assume
1. A ^ ~A assumption
2. A ^elim
3. A v B v-intro for arbitrary B
4.~A ^ elim
5. B Disjunctive Syllogism
From the proof of ex falso (from a falsehood, every and all propositions follow) above, any proposition can be proven (including both B and ~B) from any set containing any inconsistent propositions. Hence, environmental wreckage (wrecks system) and economic/utility wreckage (does not offer any new knowledge) both ensue, it seems.
Woods: Environmental wreckage does not imply economic wreckage. We can do damage control, including
CONCEDING THE INCONSISTENCY: preclusion
( pereventing inconsistencies from entering), or expulsion (driving inconsistenies out).
DENYING THE INCONSISTENCY: self-cancellation (A and ~A say nothing, so no harm) or ambiguation (redefining what terms mean).
None of these strategies is completely successful. Some other attempts:
1. Falsify ex falso: Show that the derivation above is invalid
2. Suppress ex falso and admit and contain inconsistencies, either with with hostility (inconsistency-robust logics & Gabbay-Hunter logics) or somewhat welcomingly (via dialethism).
Some background considerations: Realism (logical facts about the world), quasi-realism (logical facts are facts about logical systems), anti-realism (no logical fact is a world fact).
Woods: we needn’t worry about ex falso, even if it’s true. The doctrine is true and demonstrable. Ex falso can be proven in natural language without the use of connective truth values (the L-L proof).
If this L-L proof works then all damage control measures will fail (including paraconsistency and dialethism).
Some empirical evidence: Both Newton and Leibniz admitted that the calculation of infinitesimals generated inconsistencies. Then calculus is an environmental wreck, but it wasn’t economic wreckage, since calculus was useful for two hundred years.
Ditto Halmos’ book on set theory, which was formally inconsistent, with no damage to its pedagogical value.