Logic
Logic is the systematic process of valid reasoning through inference - deriving conclusions from information that is known to be true. It is the area of philosophy that is concerned with the laws of valid reasoning.
Logical Conclusions and the Truth
Logic does not necessarily dictate the truth. For example, it is possible to derive a logically valid conclusion, "C" from known facts "A" and "B". However, in some instances, "C" is not certain to be true. There are possibly unknown truths outside of A and B that also influence "C", creating a different conclusion. Logical validity is merely the derivative of the process of inference - it is a valid hypothesis, but further investigation may lead it to be logically false. (Logical conclusions can be described as "the truth, as far as we know.")
Aristotelian Logic
Aristotle was one of the first Western philosophers to describe systematic logic in detail. In his works, Aristotle generalized many of his examples, introducing the use of variables in logic. He illustrated the process of inference by stating the logical process: All x are y; all y are z; therefore, all x are z.
Aristotle described three laws as the basis of all valid logic:
- Law of identity, A is A;
- Law of contradiction, A cannot be both A and not A;
- Law of the excluded middle, A must be either A or not A.
Aristotle also elaborated on syllogistic logic, which sets a standard format for all logical arguments. These sequences have remained virtually unchanged in the Western world, forming the basis of many mathematic principles. These logical patterns also form the basis for computer programming techniques.
Realism vs. Nominalism
During the middle ages, two schools of thought were formed concerning logic. Realism followed Aristotle's idea that reality, the mind and our language and logic were linked: that logic is universal. Nominalism, which relates to materialist and empirical philosophies, says that the structure of our logic is defined by our minds, and does not necessarily correspond with reality. Nominalism describes a definite difference between the nature of the "real" and our conception and interpretation of it.
Practical Logic
The logical systems created by many of these philosophers exist today, almost unchanged—which asserts their validity, at least in terms of the human mind. Mathematics are used constantly in science. In physics, these logical formulas were used to predict—a logical conclusion—the existence of black holes and to create definitions of space-time, Einstein's relativity. The symbolic logic of George Boole has formed the basis for much of computer technology.