Tim,
***it does seem ironic that Dick's paper relys on mathematics a product of our experience of what is possible and what is not possible. the point however is that we may be incorrect in our belief of what is possibe or we might be correct. the target data we're looking for is the implicitly imbeded data ie. the noncontradictable data. it would have to be pretty much a given that mathematics be accepted as part of the implicit data.***
There are many other assumptions beyond just accepting the truthfulness of mathematics. Here's a small list:
1) We have to define 'known' and 'unknown' in ontological terms (i.e., absolute terms). However, we have no idea what that means exactly or the many nuances to that assumption.
2) Dick uses symmetry arguments as part of his assumptions in his paper. We have to assume symmetries, however assumption such as these have already been shown by Emmy Noether et al. to produce many of the laws of physics. If I remember right, Dick leaves out the internal symmetries from his assumptions, so is it any surprise that he doesn't produce the standard model? Note: Dick doesn't see symmetry arguments as an assumption because he has framed the introduction of the 'problem' (as he calls it) in terms of a symmetric situation. He uses this symmetric situation to set-up his equations which is, in effect, using symmetry assumptions. Surprise, surprise, he elicits physics equations as a result. Noether isn't even credited in his paper (if I remember right).
3) The way the paper is constructed is based on a deep fallacy that is understandbly misleading. It is the 'bible code' fallacy if you will. We already know in advance what it is we must 'match' our outcome in order to say we have succeeded in the endeavor (e.g., match the codes in the bible with historical dates and events). The fallacy is that whatever doesn't work is discarded and whatever works is kept. Of course, no new predictions are made. In the case of the bible code predictions are always made after the fact. Dick has chosen an even higher ground, he simply refuses to make them! This is why science was superior to all the astrology 'sciences' of the 15th-16th centuries. In fact, astrologers, if I remember right, were the ones using mathematics for better astrology. It wasn't until later that natural philosophers began to use mathematics. If you are interested in this history I can find more about it.
So, the mathematics 'is true' is only the tip of the iceberg. I use it since it is the first and most fundamental fallacy/assumption in his paper (other than the fact that he says he makes no asssumptions!).
Harv |