Propositional logic game: truth tables, connectives and arguments
A logic game for sixth-form philosophy. A formula appears and you complete its truth table by tapping T or F on each row; in other rounds you formalise a sentence by building the formula from tiles (p, q, ¬, ∧, ∨, →, ↔ and brackets), sort formulas into tautologies, contradictions and contingencies, and decide whether an argument is valid. Everything is worked out row by row, so any equivalent formalisation counts, just as a textbook would accept ¬q → ¬p for “if p, then q”.
Philosophy · Sixth Form
p → q is only false when p is true and q is false: it is the row students get wrong most often. The game brings it back again and again, with negations and brackets, until the table comes without thinking.
“But” is a conjunction, and “p only if q” is p → q while “p if q” is q → p. The sentences are written so that these traps genuinely come up.
Modus ponens, modus tollens and the disjunctive and hypothetical syllogisms are valid; affirming the consequent and denying the antecedent look reasonable but are not. Sorting them, and naming them on hard, is exactly what argument exercises ask for.
"The sentence is “It rains only if it is cold”, with p = it rains and q = it is cold. The student builds q → p, checks it and sees it is wrong: “only if” introduces the consequent, so the formula is p → q. In the next round they fill in the table for ¬p ∨ q and find that its column matches the conditional’s."
Prefer to learn without screens? Try this analogue version:
Write the rows in textbook order: TT, TF, FT and FF (eight rows with three variables).
For a long formula, add a column for each part before the final one.
Formalise five sentences from a newspaper that use “if”, “but” or “only if”.
Write an argument of your own for each rule and another for each fallacy.
If you like Truth Table, these activities work similar skills:
Ten questions with the same mechanics, untimed and marked, on three levels.
The other philosophy game: each idea with its author, period and school.
If you enjoy step-by-step reasoning, solve equations with the balance method.
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