Which findings of Kurt Godel? Care to explain? Because for example this seems like it has nothing to do with the incompleteness theorems unless one doesn't understand the incompleteness theorems at all and is just hand-waving.
"Yet space, time, and causality cannot be proven to be empirically real themselves". This is akin to mathematical axioms that escape proof within a formal system. Of course one can debate whether the analogy applies for space and time as it does in arithmetic, but this is beside the point. My point was that Schopenhauer's quote was not even remotely close to being naive, especially considering when it was said (i.e. years before Godel and others proved similar conclusions).
>This is akin to mathematical axioms that escape proof within a formal system.
No it isn't. Unless you understand quantum gravity better than anyone else does, there is absolutely no connection whatsoever between the possible empirical reality of spacetime and causality, and Godel's description of mathematical incompleteness.
Spacetime is observable, not axiomatic. The whole point of theories like loop quantum gravity - and one of the main reasons that the string theories are poor relations - is that LQG theories take an explicit interest in possible mechanisms that explain the observed properties of spacetime and causality.
In the jargon, they are 'background independent.'
For example, take a look at Causal Dynamical Triangulation:
Its a relatively naive statement. What is 'before' and 'after' time is defining time in terms of time. While it does seem ridiculous to say something is 'before' time, it doesnt seem anywhere as ridiculous to say something is unrelated to time, beyond time, or independent from time.
The naivete is that a sophisticated philosopher would understand this, and at the very least not push forward a philosophical argument that really hinges on connotations of words instead of logical/philosophical pillars.
Anyways if the statement didnt have a famous philosophers name attached to it i doubt it would have gotten any response, its a pretty baseline/naive reaction to a complex scientific idea.
You can use Godel's proof to show that a physics model based on space, time and causality can not exmplain those. And that if there is one that explains those, it must be based on some other set of concepts, that it can not explain.
Yet, realism is in a completely different level. You can not reason about it using mathematical constructs. (Too bad that's the only tool we have.)
Can you really? Incompleteness doesn't necessarily say this. It makes certain statements about certain types of contradictions in certain types of systems. There is still a lot of work left to be done before you can apply it here.
You may be saying this has already been done elsewhere but without references u can't just throw this out there as a given.
