as my old fried Witty used to say, the limits of my language are the limits of my world.
It's one of Sw Sarvapriyananda's favourite quotes. Wittgenstein was quite Vedantic it seems.
Yes.
Language is itself compression of thoughts. Thoughts themselves are compression of something larger (observations, experiences, combinations of other thoughts, etc). It seems that there is more than one very famous mathematical proof that dictates that systems such as these cannot be complete, or even consistent.
> It seems that there is more than one very famous mathematical proof that dictates that systems such as these cannot be complete, or even consistent.
At least three approaches to similar results arising from questions posed by Hilbert - but do these results impose "a (undefined) limit"?
Axiomatic systems that can never be complete or consistent can still be used to reason about objects without limit; both the countable and uncountable numbers spring to mind.
Is an axiomatic system that can never be complete "limited"? Surely there's always something more to add on that asymptotic(?) approach to 'completeness'?
Is it possible that being complete or consistent is a limit, bounded by completeness , unable to discuss the paradoxical?
I believe that is what "languages determine perceptions of the world" in Sapir-Whorf hypothesis means. Not "not all languages are Sapir-Whorf complete, only some are", which is obviously wrong, and also what is probably catching you. All languages on Earth are probably complete, just except that says nothing about modeling paradigms and syntaxes and all sorts of mannerisms shared and not shared among those equal and complete languages.
It depends on how you define things, but in a very reasonable definition it does actually mean that. If we consider a computational model to be a way using a finite string in countable alphabet to represent every single computable function, then yes, there is an algorithm that can take a program in any computational model 1 and find another program in computational model 2 that also implements the same computable function. Implements here means that both programs will for the same input return the same output if they both halt, or both will not halt.
Now the running time, or algorithmic complexity of both algorithms, is not under consideration here. The x86_64 program running in native hardware might finish the computation in milliseconds, where a browser that does the same computation using purely HTML and css that our universal transpiler generated might run in trillions of years.