The Laws of Thought?: An Hypothesis
Historically, the three laws of thought have always been taken to be the laws of contradiction, identity, and excluded middle. However, in contradistinction to this, the present discussion is offered as an hypothesis for supposing that three different laws of logic, namely, Modus Ponens (MP), Modus Tollens (MT) , and Syllogism (Syll) may be the only "laws of thought" in practice, and that the laws of contradiction, identity, and excluded middle actually stand as governing principles to logical thinking instead of "laws of thought" per se. The fundamental unit of any reasoning process is the implication sign with its two arguments. Thus, in thinking activity concerned with logical reasoning, as distinct from other types of thinking, namely, judgment and conception, always there is present some implicative proposition. Always there appears to .be one unit-thought implying some other unit-thought. Thus, P 3 Q, where P and Q are general or particular, unique, or complex. Moreover, there appear to be only certain things which can happen to this sequence of unit-thoughts from the standpoint of valid inferential activity, uiz., ( a ) its antecedent can be affirmed (Modus Ponens), ( b ) its consequence can be denied (Modus Tollens), or ( c ) its consequence implies some third unit-thought (Syll). Thus, these would, in actual practice, constitute the fundamental forms of valid inference. And where complex arguments are entertained by the mind, any or all of these forms may be employed to arrive at a given conclusion. This hypothesis was brought out when I tried to produce quantitative evidence for other laws of logic in the research connected with my doctoral dissertation. Because the argument would hold for any law selected, the point will be illustrated by using the transposition law. This law is expressed in logical symbolism as