Complete the account of the material conditional.
The conditional is false in exactly ______ of the four assignments, namely when the antecedent is ______ and the consequent is false. It is therefore ______ whenever the antecedent is false, which is why it captures only ______ of what "if" means in ordinary English.
Word bank: one · true · true · part · all
Hints
- There is only one falsifying combination.
- A false antecedent cannot produce that combination.
Show the answer
The conditional is false in exactly one of the four assignments, namely when the antecedent is true and the consequent is false. It is therefore true whenever the antecedent is false, which is why it captures only part of what "if" means in ordinary English.
One falsifying row, and therefore truth in the other three. The material conditional is a deliberate simplification of "if", it drops relevance and causation, keeping only what deduction needs.
Practise The Language of Propositional Logic
The app has 4 more questions on this lesson, and keeps your place in the course. Philosophy I is free to start.
More questions on The Language of Propositional Logic
- A conditional fails only when it promises something and does not deliver. In how many of the four assignments…
- In logic, "P or Q" is true when both P and Q are true.
- Logical connectives are truth-functional, meaning the truth value of a compound depends solely on the truth…
- Arrange these compounds so that each is true in strictly more of the four assignments than the one before it.
- Which translations are correct?
- Sort each sentence by whether the main connective is a conjunction, a disjunction or a conditional.