law of non-contradiction (2nd law)


... I've always felt that the 2rd law is a consequence of the 3nd law
... but maybe not?


source: oregon state edu
  1. The Law of Identity - A is A Everything is the same as itself; or a statement cannot not remain the same and change its truth value.
  2. The Law of Non-Contradiction - NOT (A and not A) Nothing can both exist and not exist at the same time and in the same respect; or no statement is both true and false.
  3. The Law of Excluded Middle - Either (A or not A) Something either exists or does not exist; or every statement is either true or false.

source: Wikipedia

In classical logic, the law of non-contradiction (LNC) (or the law of contradiction (PM) or the principle of non-contradiction (PNC), or the principle of contradiction) is the second of the three classic laws of thought. It states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive.

The law of non-contradiction, along with its complement, the law of excluded middle (the third of the three classic laws of thought), are correlates of the law of identity (the first of the three laws). Because the law of identity partitions its logical Universe into exactly two parts, it creates a dichotomy wherein the two parts are "mutually exclusive" and "jointly exhaustive". The law of non-contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle, an expression of its jointly exhaustive aspect.
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Tags

  1. 3 laws
  2. excluded middle
  3. lem
  4. non-contradiction
  5. 2nd law

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