I found that a very accomplished essay with a well developed and argued thesis. I also largely agree, but a few questions below, and you avoid the problems of logic. I suspect you'd like the 'Law of the Reducing Middle' I proposed in an earlier essay to replace the problematic 'excluded' middle. The 'reducing middle' is a Bayesian, 'Bell' or quantum mechanical curve. It suggests NO two things in the universe are identical, so 1=1 is never quite true! I think that was 'It from Bit'; 'The Intelligent Bit' 2014, but I think you'd also like last years (scored top).
This year my essay shows how QM's orthogonal Cos2 curves CAN be produced by classical interactions! (Of course few scientist even dare look!). The model is simply founded on extension of Pythogorus theorem to 3D dynamics.
Do we not need a certain degree of discretion in continuity? i.e. must the rotation defining a spherical 'body' not be considered as discrete from any other bodies rotation?
Do you think that without such discrete 'motions' anything could 'exist' at all?
Fundamentally we argue the same of mathematics limitations, but you invoke a new, interesting and well justified rationale. All in all an exceptional essay worth an exceptional score, which I hope help gets you into the finalists. I do hope you get to read min before the deadline and comment. There are other slightly more philosophical elements.
Very best of luck in the contest.