Premises and conclusions

PREMISES AND CONCLUSIONS

Premises and conclusions The key relationship in formal logic is implication, what we have in mind when we say that one or more statements (our premises) leads to another statement (our conclusion), or that this other statement is what follows what we start with. As a single string we express this with the signal C, but typically we find it easier to use a notation in which we separate the premises and the conclusion.
If PQC and P together imply Q, we write this as PQC,P |- Q
(The symbol before the conclusion is called the assertibility sign or, less formally, a turnstile.)

One thing to avoid is confusing the validity of a conclusion with its actual truth. A conclusion is valid if it must be true when in fact all its premises are true. This leads to the rather unexpected point that, given inconsistent premises, an argument is automatically valid. Similarly, any conclusion that is a tautology gives us a valid argument regardless of the premises.

Return to deductive reasoning.

Go on to testing for validity.

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