The article of Timothy Williamson begins with the following definition:
The Relation criteria:
"Anything whatsoever has the relation of identity to itself, and to nothing else."But what is the case of nonexistence?
Very impressive, isn't it? So we know that identity is a relation. But what is the case whit non-existence? If identity is a relation than it stands between two existing things. But if this is true, what can we answer the following question: Am I identical with a pegasus? The answer, I hope, will be not, but according to professor Williamson this question does not make sense at all, because identity is a relation and if there is a relation it needs at leest two things (or at least one thing about we do not know if they are identical or not).
So nothing can be identical with a non-existing thing? But is Sherlock Holmes identical with Hercul Poirot? Does this question make sense? Can I ask from you that: "Don't you know whether the A Scandal in Bohemia belongs to the adventures of Sherlock Holmes or of Hercul Poirot?
The "oneness" criteria:
The following sentence is the second of the article:
"Things are identical if they are one thing, not two."
It is so evident what is one thing and what is not one thing?
This is a questionable point again. Whether the battle of Stirling is one thing or not? Does this means that if something is identical, than it cannot have any parts? If two things are identical, they are the same thing. This is true. But can it be, that I am an other thing than the person who started to write this post? Am I identical with this person? I'm sure I can be identical with that guy. But am I the same thing as that guy at the beginning of this period of time? I'm not sure. (If you just see the problem of the changing of my properties over time). And I'm not sure about the fact whether do I exist as a past and as a present too, in the present now.
We can go on with the
100% overlap of assessed properties criteria:
"We can refute the claim that they are identical if we can find a property of one that is not simultaneously a property of the other."Does this criteria aims to commit the identity of properties?
If yes, we can say we beg the question or bend it for we didn't really said anything about the identity of things. Identity of things are the 100% overlap of the properties owned by the things but how can two property be distinct? Or do we have to accept the claim that properties are instantiated by substances? Don't we really understand identity from other metaphysical poisition? Does it really matters what metaphysical position do we support for the sake of our question about the identity of two things?
If you don't mind we can go on with this question later. Now let see what can Professor Williamson say to us about the classical notion of identity.
The identity is a logical relation governed by two logical laws: Reflexivity and Leibniz's law.
About reflexivity we shouldn't have any problems as follows by Williamson:
"To say that the identity relation is reflexive is to say that for each thing x, x = x".
Leibniz's law or the indiscernibility of identicals by the Antiquity is the following very simple rule:
"Leibniz’s Law says that if x = y then whatever is true of x is also true of y".
(Just to note, this is not the same law as Leibniz's principle of the identity of indiscernibles which is a less consistent one).
In additionally:
"The two principles also entail that identity is symmetric (if x = y then y
= x) and transitive (if x = y and y = z then x = z)."
Now we know the logical rules to say for something that it is identical with something "else". Take the following exapmle: I see a strawberry tree then I close my eyes. When I open my eyes again I can see (thanks to God) the same strawberry tree. When I go around the house and come back I can see the same strawberry tree. Isn't it suspicious?
Williamson sais it is even more: we cannot say that these strawberry trees are the same ones because we do not specify an entity with this expression. (Simple isn't it?)
Take a stronger example: I see the strawberry tree in the garden and I am arguing about reality with one of my friend then we leave the garden and years later I am selling magical water and leave philosophy debates to others but one day I see the old dead strawberry tree in the garden and I think about my youth and about my theory of idealism. Is this tree the same one?
Williamson doesn't let us without answer:
The problem is hiding in our descriptions. What is the problem?
If x=y then x could not have been distinct from itself and nor from y.
Now here comes the harder statement:
"Thus x and y cannot be contingently identical: they must be identical in
all circumstances. A more complex argument concludes that they cannot be contingently distinct. They are either necessarily identical or necessarily distinct.
Consequently, they are either always identical or always distinct."
It seems very simple for the first instance, but just think about such theories as anomalous monism or bound theory or the problem of the Ship of Socrates. Is it more complicated now?
It seems doesn't it?
Meanwhile we are trying to solve these problems, it is coming clearer that ... I found the first book by Timothy Williamson titled: Identity and discrimination. So I will study it now, than perhaps write something about the topic :). Hopefully.
Cheers
... As a second instance let see what can we find in the Stanford Encyclopedia of Philosophy
Usually the more basic distinction between the types of identity is the qualitative and numerical distinction.
Qualitative identity entails the sameness of properties (two entity are identical iff they have the same properties). The degree of qualitative identity depends on the number of the shared properties.
