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Three Worlds

Bill Vacellia's exchange with Kevin, on the mertis of dualism vs. materialism when talking about the mind, continues to be of interest. In fact, I think Bill is begining to get in stride because this is terrific:
Suppose we consider an analogy. Distinguished philosophers have proposed that there are three categories of entity. Following Karl Popper, who builds on the work of Gottlob Frege, we can call them World 1, World 2 and World 3 entities. World 1 includes physical items; World 2 mental items; World 3 'abstract' or 'ideal' items. 'Abstract' is not the best term since it suggests something unintended, namely, mental acts of abstraction; but the term is in use, and I'll use it. An abstract entity is one that is not located in space or time and is not causally active or passive. Take a humble arithmetical truth such as 7 + 5 = 12. The truth expressed (which is not to be confused with the sentences used to express it or the thoughts used to think it) can exist and be true whether any World 2 entities exist and whether any World 1 entities exist. I won't trot out all the arguments for this; I'll simply refer the reader to Frege, Popper, et al. Now suppose some benighted soul came along who got it into his head to build a "gradualist bridge" (to use a phrase of Dennett) from World 1 (the physical world) to World 3. He thinks that by a sufficiently deep and protracted investigation of the physical world we can come to explain abstracta as ultimately physical in nature. He thinks that if we only knew enough physics we would be able to understand that there is no independent realm of abstracta. One ought to be able to see that there is something utterly absurd about building a "gradualist bridge" from World 1 to World 3. Why, exactly? Well, physics presupposes mathematics; hence the truths of the latter cannot be reduced to truths of the former. For example, from pure mathematics we know that if d = vt, then v = d/t. That is a necessary truth, true in all possible worlds, including those in which there is no space, time, or moving particles. As such, it cannot be verified or refuted by any empirical test.
Kevin is in good company, however. An awful lot of modern philosophy (~ 1800 to the present) would lead one to the same conclusions. Too bad for modern philosophy.

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