@north,
Define Identity:
The first paragraph of chapter one: Conservation of Continuous Qualtities, From Piaget's The Child's Conception of Number...
Every notion, whether it be scientific or mearly a matter of common sense, presupposes a set of principals of conservation, either explicit, or implicit... It is a matter of common knowledge that in the field of emperical sciences, the principal of inertia (conservation of rectilinear and uniform motion) made possible the development of modern physics, and that the principal of conservation of matter made possible the devolpment of modern chemistry... It is unnecessary to stress the importance in every-day life of the principal of identity; any attempt by thought to build up a system of notions requires a certain permanence in their definitions... In the field of perception, the schema of the permanent object presupposes the elaboration of what is no doubt the most primitive of all these principals of conservation, which is a necessary condition of all rational activity, and we are not concerned with whether it is sufficient to account for this activity, or explain the nature of reality...
Can you make sense of that if you cannot make sense of me??? Unless all concepts represent a shared identity they have no rational value, or perhaps, rather: Value to Reason... Identity is a principal of logic, and of philosophy, and I had no more than figured it out on my own on one of these forums without the value of an explaination that I discovered the above paragraph... I must have missed that day in class, and it sort of hurt to see that what i figured out everyone else took for granted, as we all do... Well, it is true that in every essential detail Dogs are identical, along with Hydrogen Atoms... Knowledge demands system, and identity is system in its most basic form... Don't confuse identity with equality across the board...
He goes on to say: This being so, arithmetical thought is no exception to the rule... A set or collection is only conceivable if it remains unchanged irrespective of the changes occurring in the relationship between the elements... For instance, the permutations of the elements in a given set do not change its value... A number is only intelligeable if it remains identitcal to itself, whatever the distribution of the units of which it is composed... A continuous quantity such as length or volume can only be used in reasoning if it is a permanent whole, irrespective of the arragement of its parts...
Are you getting the sense yet, with words like number, length, or volume, all identities, and all conserved???...
