The Law of Identity

From Logic

Aristotle's Law of Identity

For propositions: "If a proposition is true, then it is true."

We can state this simply as A equals A

Or, in logical form., as:

A ≡ A

('≡' refers to "If and only if', meaning that if "A" is true, then "A" must be true)

And the law of Identity is necessarily true. It is a tautology.

Aristotle wrote on the necessity of the law being true, thusly:

"Now 'why a thing is itself' is a meaningless inquiry (for -- to give meaning to the question 'why' -- the fact or the existence of the thing must already be evident'-e.g. that the moon is eclipsed-but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical', unless one were to answer 'because each thing is inseparable from itself, and its being one just meant this' this, however, is common to all things and is a short and easy way with the question)." - Metaphysics Book VII, Part 17

Metaphysically, we can say that everything that exists has a specific nature. Each entity exists as something in particular and not it's own negation or antithesis.

Furthermore, we can say that existence necessitates identity: an 'entity without an identity' is a contradiction, an oxymoron. To lack identity is to not exist. To exist is to exist as something, and that means to exist with a particular identity.

Each entity exists as something specific, its identity is particular, and it cannot exist as something else. An entity can have more than one characteristic, but any characteristic it has is a part of its identity. A car can be both blue and red, but not at the same time or not in the same respect. Whatever portion is blue cannot be red at the same time, in the same way. Half the car can be red, and the other half blue. But the whole car can't be both red and blue. These two traits, blue and red, each have single, particular identities.

The concept of identity is important because it makes explicit that reality has a definite nature. Since it exists in a particular way, it has characteristics. Since reality has an identity, it is knowable.

Finally, it is important to separate the logical law of identity from the metaphysical law: the universe exists and has an identity, but this in itself is not the 'law of identity', for the logical law to exist, a mind must glean it, a priori.

References

• Copi, I. M, Cohen, C., (2001), "Introduction to Logic", 11th Edition.
• Landauer, J. & Rowlands J., (2001)