Concept

Paradox

An argument from acceptable premises by acceptable steps to a conclusion that seems unacceptable. Resolving one means finding which premise or step fails, and several famous paradoxes turned out to mark the boundary of a theory rather than an error in it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Three truth values, two of which count as holding. Truth tables of negation, conjunction and disjunction in the logic of paradox, with the values that count as holding — both and true — shaded.

A contradiction that stays where it is

In classical logic one contradiction proves everything: from p and not-p, any q at all. Add a third truth value — both true and false — and count it as holding, and the explosion stops. The classical laws all survive as laws; what goes is exactly the reasoning that carries a contradiction somewhere it was not. Run the other way, the same three tables make a logic of gaps instead of gluts.

logic · Non classical logic

Two losing games that win together

Game A is a coin that wins 49.5% of the time. Game B tosses a bad coin when the capital is a multiple of three and a good one otherwise, and it loses too, because the capital spends more than a third of its time on multiples of three. Choose between the two games at random and the walk drifts upwards by 0.0157 a round; play A, B, B over and over and it gains 0.0574. Nothing is wrong with the arithmetic. The losing coin A wins by knocking the capital off the bad remainder.

probability · Random walk

Named alongside it

The objects these essays reach for when they reach for this one.

Consistency Counterexample Drift Duality Excluded middle Exhaustive search Expected value Many valued logic Markov chain Periodicity Random walk Soundness

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