Logic & Markedness

The purpose of this essay is to establish the validity of the following four propositions. 1. The assumption that symbolic logic is valid a priori is false, as are the corollaries implicit in this assumption, namely, that symbolic logic is the one and only logic; that it is the logic of effective practical reasoning and action; and, that it is the logic that governs natural language. 2. Typological logic, such as that explored by C. S. Peirce, is the necessary and natural logic that governs natural language, and it is the logic that governs effective reasoning, and it is the logic that governs the dynamics of human interaction. 3. Following from the false premise in 1., it has been assumed that there is one and only one type of opposition; Contrary to this assumption, it follows from 2. that there are two logical types of opposition. 4. From typological logic a law can be deduced and stated in terms of the second type of opposition which predicts the phenomena of markedness in language. The central focus of attention in this essay is on natural language and the primary point of view is that of the science of linguistics. What is at issue is the frame of reference in terms of which linguistics attempts to apprehend, analyze, and explain the phenomena of natural language. The first question that is being put is this: What is the position of symbolic logic 1 in the theory of language? And, by implication, what is the position of symbolic logic in the structure and use of language, in the process of thinking and talking in general? 2 This question arises from the following conflict: Symbolic logic is commonly supposed to hold a position of dominant authority, a priori authority, in the thinking of our society, and consequently in linguistic theory as well. But, the authority and validity of symbolic logic, whether a priori or not, is contradicted in practical fact by the compelling force of empirical evidence-ubiquitous, systematic, overwhelming evidence-which has accumulated in the study of language over the past fifty years, proving beyond any shadow of doubt that symbolic logic is not in fact the logic that governs natural language, and that it is not the logic that governs normal, correct, or even reasonable reasoning. In actual behavior, in thinking, in talking, in acting, people do not obey the laws of symbolic logic, except …