Identity - a key philosophical concept. Some people would claim that identity is a relation, having the following logical characteristics:

• Reflexivity - "A is identical to A". An example of a non-reflexive relation would be taller than ("A is taller than A" doesn't work)
• Symmetry - if "A is identical to B" then "B is identical to A"
• Transitivity - if "A is identical to B" and "B is identical to C" then "A is identical to C"

"=" sign is used to denote identity, i.e. "x = by" means "x is identical with y".

Leibniz's Law (which can be stated in two versions) says that

1. x = y iff whatever is true of x is also true of y, and vice versa
2. if whatever is true of x is also true of y, and vice versa, then x = y

• The current president of the United States has brown hair
and
• George Bush = current president of the United States
We can reasonably conclude that
• George Bush has brown hair

LLa is can be challenged in cases where it appears that substituting x for y when x=y changes a proposition's truth value. E.g. if

1. Jello = Jam
and
2. Fred thinks jam is his favourite toast topping
according to the idea of substitutivity of identicals we should be able to say that
3. Fred thinks that Jello is his favourite toast topping

Some would claim that in cases where psychological aspects influence things and say the reason for this apparent problem is that we are confusing intensional and extensional references. Intensional relates to the sense of an expression; extensional to its reference. Terms which represent the same thing but cannot be swapped without changing the truth of a proposition are sometimes called referentially opaque.

Not all instances of referential opacity concern psychological states, e.g.

1. Paris is popular because the Eiffel Tower is there
and
2. The Eiffel Tower=my favourite tourist attraction
3. Paris is popular because my favourite tourist attraction is there

Or

1. Nine is necessarily greater than seven
and
2. The number of planets = nine
3. The number of planets is necessarily greater than seven

Frege distinguishes between sense (the ideas that we have about a thing) and reference (the thing itself). He argues that we may understand the same thing in many different senses (e.g. "the morning star" and "the evening star" are different senses, but have the same reference "Venus") (they mean the same thing).

Kripke says that Frege's "sense" is just a description of a thing, e.g. "the morning star" is "the astrological phenomenon which is observed if you.....", in which case names for things are just shorthand for those (perhaps very long) descriptions. But he argues that a name can't mean anything if the meaning includes contingent facts.

E.g. "London" can't mean the capital of England, because it's possible that the capital city could have been Birmingham. Kripke says that some names are just rigid designators - labels that are attached to things which have no "meaning" in themselves. [There are also flaccid designators, such as "the Prime Minister", or "the Queen", which do not always attach to the exact same entity.] For rigid designators though, Kripke agrees with Leibniz's Law of identity, and argues that if any two names refer to the same thing, then they are identical, and necessarily so (reflexivity, x=x).

This leads to the conclusion that there are some empirical discoveries that can be made of non-contingent facts. I.e. we can gain a posteriori knowledge of necessary truths. For example, Jello and Jam are names for the same thing, so they are necessarily identical, although we can't know that a priori.