Logic and rationality: Difference between revisions

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==Forms of reasoning==

[[Deductive reasoning]] concerns the [[logical consequence]] of given premises. On a narrow conception of logic, logic concerns just deductive reasoning, although such a narrow conception controversially excludes most of what is called informal logic from the discipline. Other forms of reasoning are sometimes also taken to be part of logic, such as [[inductive reasoning]] and [[abductive reasoning|Abduction]], which are forms of reasoning that are not purely deductive, but include [[material inference]]. Similarly, it is important to distinguish deductive validity and inductive validity (called "strength"). An inference is deductively valid [[if and only if]] there is no possible situation in which all the premises are true but the conclusion false. An inference is inductively strong if and only if its premises give some degree of probability to its conclusion.

The notion of deductive validity can be rigorously stated for systems of formal logic in terms of the well-understood notions of [[semantics]]. Inductive validity, on the other hand, requires us to define a reliable generalization of some set of observations. The task of providing this definition may be approached in various ways, some less formal than others; some of these definitions may use logical association [[rule induction]], while others may use [[mathematical model]]s of probability such as [[decision tree]]s. For the most part this discussion of logic deals only with deductive logic.