From what I understand, and please correct me if I'm wrong: An "Argument" in sentential logic is a set of propositions, or premises, which logically lead to a conclusion. I took this definition from http://en.wikipedia.org/wiki/Propositional_calculus However, in my text that I am currently studying, How to Prove It A Structured Approach by Velleman, he defines arguments as the following: "We will say an argument is valid if the premises cannot all be true without the conclusion being true as well." -pg.9 These definitions aren't quite the same thing, for example in the following argument: It will either rain tomorrow or not rain tomorrow (premise) Jason (a human being) is either alive, or dead. (conclusion) It is clear that the if the premise is true, then the conclusion is also true in the case where the conclusion is a tautology, my example above being that a human being is either alive or dead. Is this Argument considered valid? It should be, according to Velleman's definition, but I'm not so sure it fulfills the wikipedia definition since the premise does not 'logically' lead to the conclusion. In that case, how do you even show formally that the premises don't 'logically' lead to the conclusion(s)? Also, the problem with the 2nd definition is also apparent because it introduces the possibility of redundancies in the premises, since I could simply make all of the premises tautologies and make any true conclusion. So I guess my first major question is which of these definitions should I follow? Or am I missing something here? Please correct me if I'm mistaken about something.