The changes
in logic in the twentieth century were revolutionary. Before, so-called
“classical” logic was the only dominant paradigm and was seen as an explanation
of reasoning when each question had only one correct answer. But in the late
twentieth century a few isolated mathematicians pursued different pluralist
viewpoint on it. Classical logic is
adequate for the needs of mathematics, but it is inappropriate for an
examination of everyday nonmathematical language; it disregards causality,
relevance, and other components of everyday reasoning. The semantics of
classical propositional logic can be described just in terms of true (1) and
false (0); for example, the table for classical implication is shown below[1]. But some non-classical
logics deal with statements whose values need not be absolutely false or
true, but may lie somewhere in between. However, most of today’s introductory
logic textbooks still concentrate on just classical logic, and others can be
found only in more advanced books and in research journals, heavily algebraic
and inaccessible to beginners. So the power of modern logic made anything
before obsolete, or, more correctly, is seen through radically new eyes.
| P | Q | P → Q | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 0 | |
| 1 | 1 | 1 | |
[1] Classical & Nonclassical Logics. An
introduction to the mathematics of propositions
October
2005 - by Eric Schechter (Vanderbilt University) [http://www.math.vanderbilt.edu/~schectex/logics/]
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