| My mistake, I was remembering it incorrectly. Edited my previous reply to include a link to this: http://arxiv.org/abs/1506.03733 Lee Smolin discusses a class of facts that are evoked: "I would like to propose that there is a class of facts about the world, which concerns
structures and objects which come to exist at specific moments, which, nevertheless, have
rigid properties once they exist.
Let us call this possibility evoked." ==== He provides a table of how a fact and it's existence can be described: Has rigid properties and existed prior? The fact was discovered Has rigid properties and did not exist prior? The fact was evoked Has no rigid properties but did exist prior? The fact was fantasized (Smolin does not elaborate on this in the paper) Has no rigid properties and did not exist prior? The fact was invented ==== Roberto Mangabeira Unger and Smolin hypothesize two principles to describe Smolin's view, temporal naturalism: The singlular universe, all that exists is part of one singular universe The reality of time, as in reality is not timeless ==== With all this in mind, yes circles always did have a ratio of circumference to radius of pi. This is a property of the singular universe, and is a fact that was thus discovered. The universe of mathematical possibilities that does not describe the universe was not discovered, it was evoked. P.S. Please forgive the formatting of this response! |
1.In the real universe it is always some present moment, which is one of a succession of moments. Properties of mathematical objects, once evoked, are true independent of time.
2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.