So the question is how do we know if an argument without premises is valid.
First of all, how would that go? I mean, what would an argument without premises look like (in terms of propositional logic)? Would there just be a conclusion? I also read that in case of a tautology, that would be a valid argument and I simply don't understand how there even can be a truth table created if there are no premises.
Also, why is $p$ or not $p$ an argument without premises? Isn't $p$ itself a premise?
Excuse my probably very simple questions, I'm very new to propositional logic or rather discrete math as a whole.
Best Answer
An argument without premises is a single sentence : the conclusion.
A sentence is valid
Regarding truth table, there is no issue with a truth table for a single formula.
Tautologies are exactly those formulas whose rightmost column in the truth table shows only the value TRUE.