Contrast and Comparison paragraph. Alisa Demina

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

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[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/]