argumentation

Formal Logic and Argumentation
The name, "formal logic," derives from the word "form." Formal logic is so named because the test of the logic is in the structural form of the argument. An argument in the proper form is said to be valid whereas an argument in improper form is said to be invalid. In this sense, formal logic has "a character like that of pure mathematics."(2)
Using formal logic, a person begins with statements assumed to be true then infers a conclusion based on those statements. Formal, deductive logic is a method of testing inferences but not the premises from which the inferences were made. Another way to make the same point is to say that logic is rational, not empirical; that logic deals with how we make inferences, not with the facts we observe.
Formal, deductive logic is a method of testing inferences. For instance, consider the claim, "If P then Q." Formal logic is a means of testing the "then" part of this equation; in other words, it tests the inference from P to Q. We assume that P is true and test the relationship between the truth of P and the truth of Q.
Formal, deductive logic does not test the truth of a beginning premise; it does not test the "if" part of the proposition "If P then Q." We assume--for the sake of the argument--the truth of the premises and test the relationships among or between premises. Logicians sometimes claim that formal, deductive logic establishes the truth of premises by constructing further arguments which have the original premises as their claims. Philosopher Stephen F. Barker explains this process in the following manner:
My opponent, even if [s]he grants that my conclusion follows from my premise, may question whether my premise is true; [s]he may say that [s]he will not accept my conclusion until I prove my premise. If [s]he challenges my premise in this way, it becomes my duty to try to construct a new argument to establish that premise, that is, a new argument that will have a new premise (or premises) that will have as its conclusion the premise of the first argument. I would hope to be able to choose for my new argument a new premise that my opponent will not challenge; but if [s]he challenges this new premise also, then I must try to prove it too.(3)
Accordingly, if an arguer asserts, "If P then Q" and someone responds, "Yes, but I don't believe P," the arguer might then construct a further argument such as, "If R then P." When the respondent says "But I also don't accept R," the infinite regression possible in this process becomes rather obvious. If our premise is challenged, we must find another premise which will have our original premise as its conclusion. And if the second premise is challenged, we must find a third premise from which we can infer the second. And so on ad infinitum. Ultimately, if we are to make any progress, we must find a situation where the truth of our premises are assumed. Logic can test inferences, but it cannot test the truth of the premises on which the inferences are based.
To further illustrate this concept, consider the concepts of truth, validity, and soundness. A formal, deductive argument is said to be sound if it makes valid inferences from true premises. In other words, an argument which begins with true premises then makes valid inferences is said to be a sound argument. Soundness is the criteria that separates a good argument from a bad one and truth and validity are the necessary and sufficient conditions of soundness. However, since formal, deductive logic only tests the validity of an inference, it is only relevant to one of the two necessary conditions of a sound argument. Thus, determining "truth" of premises is beyond the reach of formal, deductive logic.
Formal logic is not the only tool needed to address practical, human concerns. In the realm of human affairs, we cannot assume the truth of premises. An arguer's initial premise frequently is the most problematic aspect of the argument. A complete system of argumentation must include a substantive dimension to account for, among other things, the acceptability of these initial premises. Such a substantive element is absent from logic.