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Well, the great mathematician Kurt Godel did that. With great success. Granted, approximately ten people alive on Earth know what he was talking about, but still.
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You mean, rewriting math from scratch, using purely symbolic logic?
I thought that was B. Russel who did that. Godel was the guy who figured out that sufficiently powerful consistent formal systems are incomplete.
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Philosophy is just the categorization of different beliefs & ideas,
this allows us to grasp or model these abstracts a little better.
However, even within this...there is much leyway & crossover.
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This is the tarpit of "turing equivilence" or "moral relativity".
As far as computer scientists can tell, all computers and programming languages are essentially equivilent. Any problem one language or computer can solve, another can solve given enough time.
In practice, however, this isn't true. Because the defininition of "equivilent" here is very loose, and "enough time" can be an extremely huge amount of time.
The "Turing Tarpit" is what happens when people take the equivilence of languages and computers, and claim that it proves that languages are all the same.
They aren't.
While different cultures have different moral/ethical systems, it doesn't mean they are all interchangeable.
While Philosophy catagorizes beliefs and ideas, it doesn't mean the ideas and beliefs are interchangeable.
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Could a logically-correct, ambiguity-free language even be devised? Much like the universality of languages such as Esperanto.
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It is called symbolic math. And the problem is, while people think a particular symbol means true, how can we really know? =)