Yes, it does seem to be a consistent construct. However, one of the results of this construct is that no construct in itself can ever be used to prove the consistency of a given construct. This is what Gödel's theorem proved for just regular arithmetic. As such, there really is no way to truly know whether the construct of computer science - or anything with mathematics for that matter - is really consistent.
Which is similar in essence, I believe, to certain considerations in neurology regarding the ability of the brain to study the brain. These are the paths of reasoning that lead some people to start drinking heavily. :)
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