Law of identity
From: http://www.importanceofphilosophy.com/Metaphysics_Identity.html. Copyright © 2001 by Jeff Landauer and Joseph Rowlands
Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is. “This leaf is red, solid, dry, rough, and flammable.” “This book is white, and has 312 pages.” “This coin is round, dense, smooth, and has a picture on it.” In all three of these cases we are referring to an entity with a specific identity; the particular type of identity, or the trait discussed, is not important. Their identities include all of their features, not just those mentioned.
The law of identity can be expressed as , where x is a variable ranging over the domain of all individuals
Identity is the concept that refers to this aspect of existence; the aspect of existing as something in particular, with specific characteristics. An entity without an identity cannot exist because it would be nothing. To exist is to exist as something, and that means to exist with a particular identity.
To have an identity means to have a single identity; an object cannot have two identities. A tree cannot be a telephone, and a dog cannot be a cat. 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 reality has an identity, it is knowable. Since it exists in a particular way, it has no contradictions.