Identity Law

An Identity Law is a Law of Thought that states "A is A", i.e. [math]\displaystyle{ \forall_A \;,\;A=A }[/math].

• AKA: Law of Identity, Principle of Identity.
  • …
• Example(s):
  • Identity Relation,
  • Mathematical Equality.
  • …
• Counter-Example(s)
  • Logical Fallacy.
  • Law of Double Negation,
  • Law of Contradiction,
  • Law of Excluded Middle.
• See: Boolean Logic, Propositional Calculus, Identity Function, Equivalence Relation.

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References

2018a

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Law_of_identity Retrieved:2018-5-27.
  • In logic, the law of identity states that each thing is identical with itself. By this it is meant that each thing (be it a universal or a particular) is composed of its own unique set of characteristic qualities or features, which the ancient Greeks called its essence. It is the first of the three classical laws of thought.

    In its symbolic representation, "a=a”, "Epp”, or "For all x: x = x".

2018b

• (Encyclopaedia Britannica, 2018) ⇒ https://www.britannica.com/topic/laws-of-thought Retrieved:2018-5-27.
  • QUOTE: Laws of thought, traditionally, the three fundamental laws of logic: (1) the law of contradiction, (2) the law of excluded middle (or third), and (3) the principle of identity. That is, (1) for all propositions p, it is impossible for both p and not p to be true, or symbolically ∼(p · ∼p), in which ∼ means “not” and · means “and”; (2) either p or ∼p must be true, there being no third or middle true proposition between them, or symbolically p ∨ ∼p, in which ∨ means “or”; and (3) if a propositional function F is true of an individual variable x, then F is indeed true of x, or symbolically F(x) ⊃ F(x), in which ⊃ means “formally implies.” Another formulation of the principle of identity asserts that a thing is identical with itself, or (∀x) (x = x), in which ∀ means “for every”; or simply that x is x.

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