Difference between premise and antecedent, and difference between proposition and statement?

Question

Given the conditional statement if P then Q, is P the antecedent and Q the consequent? Can I also say P is the premise and Q is the conclusion? Is the conditional statement a proposition? Are propositions and statements the same thing? I would like to learn the rigorous definitions of logic so I appreciate any and all help/direction

Answer 1

"Is P the antecedent and Q the consequent?" Yes. Grammarians also sometimes use the terms protasis and apodosis respectively. It is not correct to say premise and conclusion. A conditional is a single sentence, and the antecedent and consequent are component clauses within it. Premises and conclusions are sentences in their own right that appear in an argument. An argument consists of a set of premises and a conclusion with the express or implied claim that the conclusion follows from the premises.

The term 'proposition' is used in several different ways by philosophers. Minimally, it means a declarative statement that is capable of being true or false. I listed some of the other uses in my answer to this question.

Some writers use 'statement' interchangeably with 'proposition' while others use statement to indicate an utterance of a proposition, and reserve proposition itself for the semantic content or meaning of what is uttered.