Significance and decidability

Abstract

According to the empiricist criterion of meaning, a sentence makes a meaningful assertion, and thus can be said to be true or false, only if either it is analytic or it is capable, at least in principle, of experiential test. Sentences of this kind are significant sentences. Although many philosophers disagree that these sentences are all the ones which can be used to convey meaning, the class of sentences identified by the empiricist criterion is nevertheless an interesting one, for these sentences are the ones which are used to make the assertions of empirical science. In this thesis, we are concerned with matters pertaining to the structure of a criterion for significant sentences, the formulation of such a criterion, and application of it as a test to effectively distinguish significant sentences from other linguistic units; we are not concerned with judgment of the worth of such a criterion as one for meaning. One condition of adequacy for a criterion of significance is that it must be in terms of deductive relationships between the sentence in question and other sentences which are observation-sentences. This condition is the empiricist condition, establishing a semantic link for significant sentences, requiring a dependence upon more than merely syntactic relations for significance. There have been a number of attempts to formulate criteria for significance which satisfy the empiricist condition and which are in the form of tests which can be applied to sentences in order to come to a decision about whether or not those sentences are significant. There have been difficulties with these formulations, especially where they apply to sentences of natural languages, i.e., sentences produced using the structures and units of language systems which are historically given. A number of these significance criteria are reviewed in this thesis, and the inadequacies are apparent as faults of being either too inclusive or too exclusive, i.e., either they ascribe significance to some sentences which are neither true nor false, or else they fail to ascribe significance to some sentences which are indeed true or false. On the other hand, criteria for significance which do not have these inadequacies either give up the empiricist condition of adequacy, or else they do not provide a truly independent test for significance of sentences. We propose another formulation of a criterion for significance, which is not shown to be inadequate by any of the arguments or instances which show the other versions to be inadequate; this new formulation is called Criterion M. If we define a logical subsentence of a sentence to be a visible part of a sentence which is itself a sentence, and which is separated from the rest of the main sentence by explicitly or implicitly expressed words which function as logical connectives, then Criterion M can be expressed as follows. [TRUNCATED]