(August 5, 2011 at 10:14 pm)Ant Wrote: *Why* do you believe that logic and mathematics transcend time and nature? Why can we not regard each as an internally consistent human construct based on formalising rational argument or reifying counting? Why invoke some kind of Platonic ideal?
It strikes me that several posters are throwing around “logical proof” a lot re science. In fact science does not *prove* anything, but continually seeks to falsify or validate hypotheses, hypotheses which are based on empirical evidence and have empirically testable predictions, to build theories and models that provide the best explanation of reality in light of our current state of empirical knowledge. All theories and models — and scientific “laws” — are in principle tentative and may be revised or discarded in light of new empirical evidence. Hence, science only appraches “the Truth” asymptotically. However, some theories (e.g. evolution, quantum theory, gravity) are so comprehensively validated, that to regard them as untrue, to expect that they might be wholly discarded, is irrational. Note also that some old models are still valid within certain bounds. Newtonian gravitation is still an applicable model for most quotidian purposes.
Those were Statler's words, not mine, but I agree with them for the most part. I believe logic like "A = B and B = C therefore A = C" transcends time and nature because it doesn't really exist, it's a concept which incidentally often applies to reality. I don't believe that logic is embedded in the fabric of the universe or some such. I don't believe either that a logical proof on its own is worth the paper it's written on; evidence is required as a basis for it. For example, if I know empirically that the theory of relativity is correct, I can logically extend that to saying it is impossible to reach the speed of light.
(August 5, 2011 at 10:14 pm)Ant Wrote: Empirical evidence is not restricted to our own (imperfect) senses. We can use instruments to extend the kinds of evidence that is available to us. Thus, it is no harder for a blind person to empirically demonstrate the existence of light than it is for a sighted person to empirically demonstrate the existence of ultrasound. (However, they could never experience the *quality* of light as a sighted person can, but that is quite another matter.)
I tried to make this point several pages back (using electricity and ultraviolet as examples). Hopefully you put it better than me.
(August 5, 2011 at 10:14 pm)Ant Wrote: Philosophical naturalism grounds the scientific method. While Statler and others might argue that it is not logically proven, we can take it as a hypothesis; and because we are having this conversation (that is, because science works!), it is a hypothesis that has been consistently validated. Yes, it might be falsified if some supernatural hypothesis is validated, but, well, that hasn’t happened yet.
The question is, is any supernatural hypothesis coherent? The very word suggests that it is outside the purview of science, but really, that’s the point. It was coined to provide a refuge for the things supposed to be “beyond” science.
Nevertheless, if a “supernatural” entity exists and intercedes in the natural world — such intercession including any kind of communication with us — then it must have natural effects that are amenable to scientific inquiry. The fact that we see no evidence for such effects anywhere in the world or cosmos, at any time, does not falsify the hypothesis, but makes holding the hypothesis valid irrational. This applies equally to ghosts, fairies, Thor, Zeus, the Abrahamic God, Santa Claus, and so on.
Of course, if a “supernatural” entity exists but doesn’t intercede in the natural world (as in deism), that is beyond scientific inquiry, but, then, why should we care?
And if its existence or lack thereof does not affect us in any way, they are equivalent as far as science is concerned.
