After reading Prof. Fefferman’s stimulating review of Jeremy Gray’s , “Plato’s Ghost,” in the Sept.-Oct. 2009 issue, I obtained a copy of the book, and read the section entitled, “The Rise of Mathematical Platonism,” to see whether there were any applications of mathematical Platonism to cosmology. The only one I could find stems from Gray’s quotation of the mathematician, Alain Connes, who maintains, “There exists independently of the human mind, a raw and immutable reality,” that indeed is, “far more stable than physical reality for not being located in space-time.” An application of this view to cosmology would be that mathematics did not spring into existence with the Big Bang, but existed before it. However if this view is to be scientific, then according to Popper’s criterion, it must be falsifiable empirically. The simplest way this could come about would be if the universe had an earlier state that eventually collapsed into the Big Crunch and then bounced into the Big Bang. But, if Einstein’s cosmological constant were present in that previous universe, it could not have been dominant, otherwise that universe would not have collapsed, but accelerated to infinity. The same would hold true for a form of quintessence (frequently proposed as an alternative to the cosmological term) that did not allow that previous universe to collapse. Thus it would appear that if mathematical Platonism is scientific, in the sense of Popper, it has important implications for cosmology.
posted by Frank Tangherlini
August 28, 2009