Notes on the Nature of Reasoning Skills

Whatever the nature of reasoning skills, such skills are rare [4], [2]. Thus, it would be desirable to develop support for them and to cultivate and strengthen them through proper education in reasoning. The background for my discussion is the development of support for reasoning skills that our research team has been conducting for some time (www.athenasoft.org). Design of support or education for reasoning depends on concepts of reasoning skills. The essence of reasoning is to construct or evaluate relations of dependence. If D can be proved from A, B and C, there is a logical dependence between these items. A person has reasoning skills if s/he is capable of recognizing or constructing relations of dependence between possible items of knowledge. A dominating view is that reasoning skills are exhausted by forms of inferences described by deductive or inductive logic. Such ideas of reasoning skills are influenced by formal logic. Aristotle's Organon formed the basis of teaching reasoning skills in university education up to the early 20th century. The success of propositional and quantificational logic under Frege and Russell provided a new model for reasoning. Text books in " baby logic " typically discuss translations into and out from these formalisms together with the logical properties, sometimes including the metalogical properties of reasoning. A parallel success for inductive methods has cast off statistics as a separate science of reasoning. Methods for testing, accepting and rejecting hypotheses are key elements of statistical inference, independent of domain. The success of formalizations of deductive and inductive inference supports the unitary view of reasoning skills (URS). This standpoint claims that reasoning relies on one or possibly two (deduction and induction) type(s) of skills that are independent of what we are reasoning about. It draws support from several (once) central philosophical theories: 1. Logicism, according to which all mathematical necessity is at bottom logical necessity. The only deductively necessary connections we need to accept are those of logic. 2. The regularity view of causation. All (seemingly) causally necessary connections whereby A produces B are really instances of a universally quantified schema " All instances of the A-type are followed by some instance of the B-type ". 3. Explanation and prediction as inferences. To explain (or predict) the fact that C is to provide a set of universal laws A1…Ak and initial conditions B1…Bn such that we can deduce C (or sufficiently increase the probability of …