Currently we have Mathematical logic→Symbolic logic and First-order logic→First-order predicate calculus. I want to make the arrows point in opposite directions. From where I stand, "symbolic logic" and "predicate calculus", while certainly valid terms, are old-fashioned and more likely to be used by philosophers rather than mathematicians.
I think logic is every bit a branch of philosophy as of mathematics...but I don't really care where the articles live, as long as the titles are precise and accurate. --LMS
- It certainly is, Larry, and I wish there were more articles about philosophical logic in Wikipedia (I'm gonna act on that wish too ;)), currently the balance is in favor of mathematical logic. But "symbolic logic" is really just an alias for "mathematical logic" and "first-order logic" is of primary technical importance in mathematical logic as well, so using the modern mathematical names as defaults seems justified to me, for these two concepts. --AV
The article states that we want the set of axioms to be recursively enumerable. Is that enough, or do we want the set to be recursive? --AxelBoldt
I don't mind changing 'symbolic logic' to 'mathematical logic', but personally I wouldn't replace 'first order predicate calculus' with 'first order logic'.
As to AxelBoldt's question, you'd have to remind me of what the difference is. The basic idea is that for any wff, a turing machine should be able to determine whether or not that wff is an axiom, the turing machine being guaranteed to halt. -- SJK
That would make the set of axioms a recursive set. A recursively enumerable set is one where the accepting turing machine is not required to stop, or equivalently a set whose elements can be produced one after the other on the tape of a turing machine. --AxelBoldt
The point is that for many purposes recursively enumerable is enough. However the article is wrong as it is now, i.e. its "explanation" of what r.e. is is actually about recursive sets. So maybe we should change the requirements to recursive and add in parentheses that sometimes even r.e. is enough, or something. --AV