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lecture14

# lecture14 - Inference rules We are now going to turn to a...

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Inference rules We are now going to turn to a new method for determining the validity of arguments: proofs (or derivations ). A proof is a series of steps proceeding from the premises of an argument to its conclusion via principles of correct reasoning: inference rules . Thus proofs stay closer to ordinary ways of reasoning than do truth-tables. Inference rules are rules of permission: they give us permission to proceed from one step of the proof to another.

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Inference rules We can think of inference rules as little valid arguments that we can employ in the course of a derivation. The rules of inference are truth-preserving – if the premises of the rule are true, the conclusion must also be true. Thus if we can construct a legitimate derivation from the premises of an argument to its conclusion, we know that it is valid . However failure to construct a legitimate derivation does not show that an argument is invalid . It might be that although a derivation is possible, we’re simply not able to think of it. Thus truth-tables are still required to test for invalidity .
Modus Ponens (MP) If you have a conditional on a line, and the antecedent of that conditional on another line, you may infer the consequent: p → q p q Since p is sufficient for q, if p is true, q must be too.

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