I've believed for many years that Plato got something incredibly fundamentally wrong: he believed that logic, math, and the language of thought was primary and preceded existence.

This error underlies all kinds of things all the way up to and including the present-day philosophical fad of "rationalism." (the Yudkowski variety)

It's a popular idea because it's a "truthy" idea. When we introspect, thought feels primary, and there are certain patterns that exist in the universe that are so fundamental that they seem to precede any concrete.

Logic and mathematics are chief among these. It is impossible to imagine a universe where 2+2=15 or not-true=true. The apparent transcendental fixity of these things leads us to think there exists some category of truths that precede existence.

I do believe these things are fixed and axiomatic, but I do not believe this implies that they precede existence. It implies that they are deep fundamental laws of the universe, and nothing more. Being something that exists within and is embodied in this universe means that we have inductively learned (both through evolution and neural learning) these laws. We can't imagine a universe where they are different because such a universe would be fundamentally alien to a degree that would invalidate our very cognitive processes. Something that evolved in such a universe -- if such a universe were even able to support life -- would have an utterly alien form and function.

Ultimately it all reduces to the anthropic principle. We are here and exist in this universe because we are having this conversation. If we didn't exist, we would not be, and if the universe were fundamentally different we might be having a similar conversation in which we assume those laws are axiomatic and immutable, and would be incapable of imagining any different.

I think this is a very bad error, and one with a body count. It leads to beliefs like "only one form of human being is consistent with the eternal order of nature," which implies that anything else is an abomination and should be marginalized or killed.

I leads to insane forms of magical thinking like New Thought / "The Secret" / prosperity gospel / etc. where people believe that our thoughts determine reality. It leads to nonsense like the AI hard takeoff "foom" idea, which only makes sense if you think that a sufficiently intelligent being can deduce all that it needs to know from the laws of logic and mathematics without embodiment. (The Yudkowski super-AI is just a philosopher king.)

I don't think it's a coincidence that Plato is the father of many forms of authoritarianism either. Authoritarianism naturally precedes from the idea of transcendent laws that can be grasped by sufficiently intelligent philosopher kings without feedback from reality.

Edit:

I'm not 100% certain it's impossible to imagine mathematically and logically alien universes. I wonder if one could simulate such a universe by encoding an alien system of logic/math behind the scenes in the form of a kind of translation table. There's been some work in artificial life and cellular automata like this.