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.
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.
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.
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?
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.
Rather, the blackout is not an absolute prevention of all access to data. They describe the workarounds they provide on their about page and explain the purpose of the inconvenience.
EDIT: Retraction only to prevent further gwernization.
The intent is clearly to nod in the direction of the inconvenience of a world suddenly without Wikipedia, without actually making us suffer such a fate.
And, of course, if Wikipedia actually managed to find a way to successfully prevent people from reading wikipedia content for a day they would be massively undermining their own position. A big part of the argument against SOPA is “it will not work to prevent copyright infringement anyway!” An actual successful block on all wikipedia content would amount to “OK guys, this is how it is really done!”
Retraction to prevent further gwernization. I LIKE this comment.
There exist deductive systems for second order logic.
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.
Good question. I don’t know the answer. If they’re not equivalent, then I see your point.
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.
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?
Wikipedia is accessible if you disable JavaScript (or use a mobile app, or just Google cache).
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.
A policy that anyone who responds to comments from the ‘recent comments’ page can be expected to find contemptible.
Or just wait for the page to load, then click the Cross button before the blackout page loads.
The blackout is a lie.
Edit: Apparently, saying ‘the blackout is a lie’ offends people. I have no idea why that would be.
Rather, the blackout is not an absolute prevention of all access to data. They describe the workarounds they provide on their about page and explain the purpose of the inconvenience.
EDIT: Retraction only to prevent further gwernization.
The thing is… why even call it a ‘blackout’?
The intent is clearly to nod in the direction of the inconvenience of a world suddenly without Wikipedia, without actually making us suffer such a fate.
And, of course, if Wikipedia actually managed to find a way to successfully prevent people from reading wikipedia content for a day they would be massively undermining their own position. A big part of the argument against SOPA is “it will not work to prevent copyright infringement anyway!” An actual successful block on all wikipedia content would amount to “OK guys, this is how it is really done!”
Retraction to prevent further gwernization. I LIKE this comment.