George Bowles and Thomas Gilbert claim that illatives such as so, therefore, and hence convey the meaning that the premise confers upon the conclusion a probability greater than 1/2. This claim is false, for there are straightforward uses of these illatives that do not convey the meaning that the probability is greater than 1/2. In addition, because Bowles' and Gilbert's claim is false, a revision of their definition of argument is required.

It is not only overtly probabilistic illatives like ‘makes it certain that’ but also apparently non-probabilistic ones like ‘therefore’ that have probabilistic import. Illatives like ‘therefore’ convey the meaning that the premise confers on the conclusion a probability not only greater than 0 but also greater than 1/2. But because they do not say whether that probability is equal to or less than 1, these illatives are appropriately called ‘neutral’.

In this paper I examine five distinctions between deductive and inductive arguments, concluding that the best of the five defines a deductive argument as one in which conclusive favorable relevance to its conclusion is attributed to its premises, and an inductive argument as any argument that is not deductive. This distinction, unlike its rivals, is both exclusive and exhaustive; permits both good and bad arguments of each kind; and is both useful and needed in evaluating at least some arguments.

I criticize a case made by George Bowles for a certain theory pertaining to the evaluation of arguments on which the (degree of) attributed favourable relevance of an argument's premises to its conclusion is relevant to its evaluation, but nevertheless argue that such favourable relevance is indeed relevant to an argument's evaluation.

My project is a systematic inquiry into the problem of relevance, which has been identified as an enduring difficulty in, for example, informal logic and information science where it plays a fundamental role in argument and information searches, respectively. My first task involves determining exactly what the problem of relevance is. To achieve that, I collected problem statements from the literature but I also analysed literature on relevance to discover further problems. The key problem that I investigate concerns the question, (...) 'What is relevance?', which I take to concern the meaning and occurrence of relevance. Concerning the semantic question, I suggest that it demarcates a point of time prior to asking it. Subsequently, I identified and evaluated approaches to elucidating the notion of relevance, rejected intuitionism and stipulation as suitable approaches, and selected philosopher/physicist Mario Bunge's approach to scientific philosophy and his conceptual system to frame my study. I also assess potential information sources; rejected constructed examples that prove to be contrived or are used to illustrate a stipulated definition; and selected dictionary definitions, actual statements, and carefully constructed examples as information sources to complement my review of the literature on relevance. To elucidate relevance, I traced the concept back to its Greek roots, analysed statements, and concluded that the term 'relevance' since its inception in Scottish law in the early 1500's has been limited largely to relations of significance. Understanding relevance in terms of both connection and significance is crucial to construct, identify, or evaluate relevance statements and thereby develop a representative theory of relevance. It also provides a solution to many controversies such as degree of relevance and it helps elucidate notions such as strength and sufficiency of an argument. I suggest that as significance can vary in degree, so too can relevance but a connection between objects is presupposed in both cases. Strength is a measure of significance and sufficiency is the strength required to establish a conclusion. Finally, I offer a provisional and partial theory of relevance where I summarize my prior analyses and integrate/comment on published positions on relevance. (shrink)