[gerdesj]

"According to Pythagoras everything is number, and God is a mathematician. This point of view has worked pretty well throughout the development of modern science. However now a neo-Pythagorian doctrine is emerging, according to which everything is 0/1 bits, ... , God is a computer programmer, not a mathematician, and the world is a ... a giant computer" [p13 of the pdf]

If you only have one finger then zero and one are just as real (ahem) as numbers that arise naturally when you have 10 fingers. The 10 toes are a bonus. I doubt that we can really know what Pythagoras really thought but given some of the results attributed to him I think Chaitin does him a disservice.

Getting wound up over whether French is a sophisticated enough language to describe numbers and some of the odder consequences of allowing construction to equate existence will probably only lead to a headache.

As a civilian wandering on the outskirts of all this philosophical foot stamping, I believe there are a fair few pretty rigorous arguments out there that can't be denied by resorting to "it looks wrong, cos reasons" style illustrations in a 13 page pdf.