# Tyrrell_McAllister comments on Completeness, incompleteness, and what it all means: first versus second order logic - Less Wrong

43 16 January 2012 05:38PM

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Comment author: 17 January 2012 05:28:07PM 2 points [-]

I was under the impression that second-order logic was purely descriptive (i.e. a language to write precise statements which then may judged true or false) and did not allow for deduction.

There exist deductive systems for second order logic.

Comment author: 17 January 2012 11:18:28PM 5 points [-]

Right. There exist deductive systems, plural. Are they equivalent, like the ones for first-order logic are? As I understand it, If you want to do deduction in second-order logic, you need to specify a deductive system; you can't just do deduction in second-order logic alone. Whereas in first-order logic there's no need to specify the deductive system because they're all equivalent.

Comment author: 18 January 2012 02:51:40PM 1 point [-]

Right. There exist deductive systems, plural. Are they equivalent, like the ones for first-order logic are?

Good question. I don't know the answer. If they're not equivalent, then I see your point.

Comment author: 18 January 2012 08:59:14AM 0 points [-]

The different deductive systems described there (can't access the link, wikiped closed) all seem the same - they differ only in the axioms they use, which isn't really a difference in deductive systems.

Comment author: 18 January 2012 07:57:12PM 2 points [-]

But the question is, starting from the same axioms -- not logical axioms, not axioms of the deductive systems, but the axioms of whatever it is you're trying to reason about -- would they produce the same theorems?

Comment author: 18 January 2012 11:24:28AM 0 points [-]

Wikipedia is accessible if you disable JavaScript (or use a mobile app, or just Google cache).

Comment author: 19 January 2012 01:37:59AM 2 points [-]

If anyone is curious, I'm downvoting everyone in this thread - not only is this a terrible place to discuss SOPA and blackout circumventions (seriously, we can't wait a day and get on with our lives?), there's already a SOPA post in Discussion.