GotSteel -> RE: OK, if the soul begins from conception, then what about identical twins? (3/8/2012 6:12:34 AM)
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ORIGINAL: tweakabelle That logic and reason alone will not deliver a complete answer. This is not a personal insight, but an application of the absolute limits that apply all knowledges generated by using those marvellous analytical tools - if in doubt, ponder the implications of Godel’s Theorem. quote:
ORIGINAL: http://cscs.umich.edu/~crshalizi/notabene/godels-theorem.html There are two very common but fallacious conclusions people make from this, and an immense number of uncommon but equally fallacious errors I shan't bother with. The first is that Gödel's theorem imposes some some of profound limitation on knowledge, science, mathematics. Now, as to science, this ignores in the first place that Gödel's theorem applies to deduction from axioms, a useful and important sort of reasoning, but one so far from being our only source of knowledge it's not even funny. It's not even a very common mode of reasoning in the sciences, though there are axiomatic formulations of some parts of physics. Even within this comparatively small circle, we have at most established that there are some propositions about numbers which we can't prove formally. As Hintikka says, "Gödel's incompleteness result does not touch directly on the most important sense of completeness and incompleteness, namely, descriptive completeness and incompleteness," the sense in which an axiom systems describes a given field. In particular, the result "casts absolutely no shadow on the notion of truth. All that it says is that the whole set of arithmetical truths cannot be listed, one by one, by a Turing machine." Equivalently, there is no algorithm which can decide the truth of all arithmetical propositions. And that is all. This brings us to the other, and possibly even more common fallacy, that Gödel's theorem says artificial intelligence is impossible, or that machines cannot think. The argument, so far as there is one, usually runs as follows. Axiomatic systems are equivalent to abstract computers, to Turing machines, of which our computers are (approximate) realizations. (True.) Since there are true propositions which cannot be deduced by interesting axiomatic systems, there are results which cannot be obtained by computers, either. (True.) But we can obtain those results, so our thinking cannot be adequately represented by a computer, or an axiomatic system. Therefore, we are not computational machines, and none of them could be as intelligent as we are; quod erat demonstrandum. This would actually be a valid demonstration, were only the pentultimate sentence true; but no one has ever presented any evidence that it is true, only vigorous hand-waving and the occasional heartfelt assertion. Gödel's result is of course quite interesting, if you're doing mathematical logic, and it even has some importance for that odd little specialization of logic, the theory of computation. (It is intimately related to the halting problem, for instance.) It also makes a fine piece of general mathematical culture; but it doesn't shake the foundations of the house of intellect, or exalt us above all else that greps.
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