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Outline for Metaphysics: Go over reading and give mini-essay for next class. Go over the problem of change from Dialogue 5. 1. How can a single thing have incompatible properties, which it must if it is to change? Distinguish numerical identity and diversity from qualitative identity and diversity. A=A This piece of chalk is numerically identical with this piece of chalk. Here “this” and “this” refer to numerically identical things, individuals or substances. A is F is qualitatively identical with B is F. This piece of chalk is qualitatively identical with that piece of chalk. Here “this” and “that” refer to numerically different individual things, but they are qualitatively identical. There are two principles concerning the connection between numerical and qualitative identity. One is controversial and the other is not. The controversial principle is called the identity of indiscernibles and it asserts that if “two” numerically different things have all there properties in common, i.e., are qualitatively identical, then they are really one thing. Alternatively, no two things can have all of there properties in common.
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If every property possessed by A is also possessed by B, then A = B. The indiscernibility of identicals is less controversial and for that reason it gives rise to a conflict of intuitions. If A = B, then for any property F, if A is F, then B is F. If two things are really numerically identical, then every property of one is also a property of the other, and everything that is true of one is also true of the other. Problem is that if there is change then there is a single thing that has incompatible properties, the apple is green and then it is red. So we have a problem. If the green apple is identical with the red apple, then every property of the green apple is also a property of the red apple and vice versa, and therefore, the green apple is red and the red apple is green. But since read and green are incompatible properties we have a contradiction. The apple is green and not green and red and not red. On the other hand, if avoid the contradiction by claiming that the apple that is green is not identical with the apple that is red, then you eliminate change, since you then have two apples with different qualities and not one apple that changes.
If you have the same thinking substance can you have two persons? If you have different thinking substances can you have the same person?