Definition
A truth table is a grid that lays out every possible combination of truth values for the basic statements in a compound expression and records the truth value of the whole in each case. It is the standard tool for working with truth-functional connectives.
Because a truth-functional connective is fully determined by its inputs, a finite table can capture its meaning completely. For two basic statements there are four rows; for three there are eight; in general, n statements require two-to-the-power-n rows.
Why it matters
How it works
To test an argument with a truth table, list a column for each premise and one for the conclusion, then fill in every row. If you find even one row where all premises are true but the conclusion is false, you have a counter-example and the argument is invalid. If no such row exists, the argument is valid.
Priest uses truth tables to make validity vivid and concrete: instead of imagining possible situations, you simply read them off a grid. The method is decisive for propositional logic, but it scales only with truth-functional connectives — once quantifiers or non-truth-functional conditionals enter, the simple table no longer suffices.