Laws of Logic

 Laws of Logic


Logic relies on fundamental principles known as the three classical laws of thought: the law of identity, the law of excluded middle, and the law of non-contradiction. Together, these laws lay the groundwork for reasoning and logical analysis such that philosophy, mathematics, and everyday conversation could not stand without them. In this blog post, we will delve into these three rules that govern rational discourse.

 

1. Law of Identity: The law of identity states that every object is necessarily identical to itself. For example, if we have a statement A, then A is true if and only if A is true. It can be represented as "A = A".

 

2. Law of Excluded Middle: The law of excluded middle states that for any proposition A, either A is true, or its negation is true as there is necessarily no middle ground or third option. In simpler terms, a proposition is either true or false, and there is no other possibility. This principle can be expressed as "A ∨ ¬A" (A or not A).

 

3. Law of Non-Contradiction: The law of non-contradiction states that any proposition necessarily cannot be both true and false at the same time. For example, if A is true, then not A is false, and vice versa. This principle can be represented as "¬(A ∧ ¬A)" (not (A and not-A)).

 

BONUS: Leibnitz Laws of Identity:

Identity is transitive, if A and B are identical and B is identical to C then A is also identical to C. Identity is symmetrical, if A is identical to B then B is identical to A. Identity is reflexive meaning that the relation can only be applied to the thing and itself. Identity is indiscernible meaning if two things are identical then finding a distinction between them is an impossibility. Those things cannot be identical if they ever differ from each other both timeless or at a time. X and Y are identical if and only if any predicate or property P possessed by X is also possessed by Y and vice versa.

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