Modern symbolic logic was developed beginning in the latter part of the nineteenth century for the purpose of formalizing mathematical reasoning, in particular that process by which mathematicians arrive at conclusions on the basis of a small number of distinct basic principles. This kind of reasoning is characterized by a particular type of cogency: The conclusions are not merely probable or plausible on the basis of whatever evidential support the basic principles might provide, but certain and indubitable. In particular mathematical reasoning enjoys a property referred to as monotonicity by modern logicians: if a conclusion follows from given premises A, B, C, … then it also follows from any larger set of premises, as long as the original premises A, B, C, …are included.

By contrast in many instances of ordinary or everyday reasoning, people arrive at conclusions only tentatively, based on partial or incomplete information, reserving...