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Message: <blockquote data-quote="Harzel" data-source="post: 7221970" data-attributes="member: 6857506">Oh, it was a little "technical".  Well that would explain why all of the poorly educated, unsophisticated folks who inhabit these forums could not make heads nor tails of it.Oh, look!  Despite my paltry education, you managed to stumble into my area of expertise.  What an unexpected treat.The syntax of first order logic can be described with a formal language, but there's more to first order logic than that.  Mathematics is a rather broad set of endeavors, some of which study formal languages, and some of which use formal languages as part of their expression; but mathematics is not a formal language.  Programming languages - ok, sure, close enough.True.  Obvious, I would have thought, but true.Not the most lucid description I have ever seen.I don't think you said what you meant here.  I think what you meant was that for every assertion (formally, a sentence in the language) you could prove (from the axioms) whether it was true or false; that is, you could prove either the assertion or its negation.  And this demonstrates your naivete about the subjects you are discussing.  It is possible that that would be the case, but your axioms would have to be limited in ways that would probably make the game pretty limited, for instance not encompassing all the rules of natural number arithmetic.  It would likely be very difficult, under such constraints, to express the rules for a game in which you can attempt anything.  For further info, Google "incompleteness theorem".Nonsense.  Despite the fact we can formalize the axioms in many mathematical domains, numerous unsolved problems remain.  Even things that are provable may not be easy to prove.  Furthermore, purported proofs are sometimes controversial as to their validity, and sometimes are shown to be invalid even after some people have accepted them.Patience, perhaps.  I'm not sure about the degree.</blockquote>

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