[ExI] Gemini on Mathematical Realism

[Ben Zaiboc]

On 06/10/2026 22:32, Jason Resch wrote:
> Godel used almost the same argument to reach the same conclusion:
>
> "[The existence of] absolutely undecidable mathematical propositions, seems to disprove the view that mathematics is only our own creation; for the creator necessarily knows all properties of his creatures, because they can’t have any others except those he has given to them.


This is not true. A creation often has properties that its creator didn't explicitly give it, and has no prior knowledge of.

John Conway didn't know all the properties of his Game of Life, that has become a famous example of not knowing what a system will do before it does it. Mandelbrot didn't know all the properties of fractals. Those are just two immediately obvious examples. There are many more.

Given this, it would seem that Godel was wrong, and the existence of undecidable propositions does not disprove the view that maths is our creation.

In fact, the Game of Life is a good illustration of the whole thing: Glider guns had to be discovered, they weren't known until someone chanced upon them, but neither did they exist prior to Conway creating the rules of the game. So there was no pre-existing 'platonic' glider gun, until someone set up the rules that brought it into existence.
-- 
Ben