Concept

Validity

The property of an argument whose conclusion is true in every situation in which all of its premises are true, whatever its terms are taken to mean. It depends on the form of the argument alone, and a single situation making the premises true and the conclusion false refutes it.

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

The 256 syllogistic forms, and the 24 that work. A grid with one cell per syllogistic form, marked according to whether it is valid and what it needs to be valid.

Twenty-four out of two hundred and fifty-six

Aristotle's syllogisms are four sentence forms in four arrangements, which makes 256 patterns of argument. Fifteen of them are valid. Nine more become valid if you assume the things being talked about exist, and the gap between those numbers is a two-thousand-year-old disagreement.

logic · Class diagrams

Two majorities of one class must overlap. regions (outside, S, M, SM, P, SP, MP, SMP): 3,2,0,4,2,0,4,2.

Syllogisms that say most

The syllogism knew four words — all, no, some, some not — and two thousand years of logic decided which of its 256 forms were valid. Add 'most', a word everyone uses in arguments, and the 256 become 864. A diagram with marks for 'empty' and 'occupied' can no longer decide them, because 'most' compares sizes; but writing the number of things in each region turns every form into a linear programme, and the programme decides all of them at once. Thirty-one are valid, including one Augustus De Morgan found in 1847: if most M are S and most M are P, then some S are P. And 'most' cannot be passed along a chain: ninety-nine per cent of S can be M, ninety-nine per cent of M can be P, and no S be P at all.

logic · Class diagrams

Named alongside it

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

Counterexample Quantifier Syllogism Venn diagram Categorical statement Decision procedure Existential import Linear programming

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