Concept

Counterexample

A single case satisfying a claim's hypotheses and failing its conclusion, which is enough to refute the claim entirely.

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

Also named here as quantifier — the same set of essays touches all of them, so they are one junction rather than several.

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

Every row, or one column

For every person there is someone who loves them, and there is someone who loves everyone, are the same six words in a different order. Draw the relation as a grid and they become two obviously different questions — one about rows, one about columns.

logic · quantifiers

Named alongside it

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

Quantifier Categorical statement Decision procedure Existential import Negation Predicate logic Quantifier order Relation Syllogism Uniformity Validity Venn diagram

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