# Semantic consequence and Sound Argument

Is that correct to say that semantic consequence is equivalent to the concept of sound argument in classical propositional logic? If it is the case, arguments or theories with contradictory premises are of no interest of study. If it is not the case, what is the rationale to lead with arguments and theories with contradictory premises if everything can be proved either true or false?

• A valid argument corresponds to semantical cons. A sound arg is a valid one with true premises. Commented Apr 7, 2022 at 15:32
• Thus, an argument with inconsistent premises and a conclusion whatever is classically valid. See Ex Falso. Commented Apr 7, 2022 at 15:43
• Any argument with a contradiction included will turn out to be valid under Mathematical Logic. Propositional logic falls under Mathematical logic. Sound arguments are not the concern in Mathematical logic---Validity is. Soundness means that all premises must be true in the real world & if so then the conclusion must necessarily follow to be true also. That is, the conclusion is impossible to be false while the premises are true. In this way all SOUND arguments must be valid. There is no such thing as a sound but invalid argument. Semantics indicates that is how a certain language works. Commented Apr 7, 2022 at 16:03
• Everything cannot be proven true or false. You have some concepts wrong. If you are thinking PROOF must be available for something to be true you are mistaken. Many things are true without human beings being aware of them. For example there are other galaxies many light years away from us and likely have existed before our galaxy. There is no proof though because we haven't found all galaxies. Because we have no proof doesn't mean much of anything. We would be committing a fallacy to say "x must be true because we have no proof otherwise." Don't get too caught up with requiring PROOF. Commented Apr 7, 2022 at 16:10
• Thanks for your comments. When I say proof, I'm referring to some deductive method for propositional classical logic. But, of course, I don’t take it as being the single method of reasoning. Commented Apr 11, 2022 at 11:15