The ability to 'detect existence' gives one access to objectivity. The mathematical relationships derive their objectivity from the relationship of existence.
Alexander shows us dramatically the internal self-referent and self coherent nature of objects as mathematical relationships. I claim that these math relationships are reducible to 'the relationship of Existence'.
Here is how free will and determinism might be reconciled: Consider John Cramer's idea of an 'offer wave' going forward in time; and a 'confirmation wave' going backward in time; with a 'transaction' or quantum occuring when the two waves cancel out everywhere except on one path between them.
Suppose antecedent events do determine future events. But suppose you get to choose WHICH TRANSACTION takes place. That is, you choose the whole transaction: which antecedent events shall be selected, which future event shall be selected, to complete a transaction where the future logically follows the past (but with several options as to which past-future combination will occur).
The past gives you a wide menu of events, the future gives you a wide menu of possible events, you get to choose the match-up of these two event-menus, thus a new transaction, a new 'equation' a free choice. The future was determined by the past; but you chose which future would occur using an appropriate matching selection from potential antecedent events.
Julian Barbour may be on the right track by calling time an illusion. The system I described can be generalised. "Future" and "Past" can be translated into "dimensions of transaction freedom". You are free to choose which determinism applies! So free will appears also explained by the idea that the relationship of Existence is Existence; a three-is-one relationship where two patterns create a third new pattern; the whole phenomenon requiring three to be one. God gives us the ingredients, we bake the cake through the freedom He gives us.
Is there a flaw in this argument?