= 27d567bc2d48d9f40e9ccc20ea370b15)
abramdemski comments on The Pascal's Wager Fallacy Fallacy - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (121)
We could similarly argue that the definable objects should be thought of as "meta-countable" rather than countable, right? The reals-implied-by-a-theory would always be uncountable-in-the-theory. (I'm tempted to imagine a world in which this ended the argument between constructivists and classicists, but realistically, one side or the other would end up feeling uneasy about such a compromise... more likely, both.)
I think you're confusing levels here. When I spoke of "the surrounding theory" above, I didn't mean the, uh, actual ambient theory. (Sorry about that -- I may have gotten a little mixed up myself) And indeed, like I said, definability only depends on the language, not the theory. Well -- of course it still depends on the actual ambient theory. But working internal to that (which I was doing), it only depends on the language. And then one can talk about the metalanguage, staying internal to the same ambient theory, etc... (mind you, all this is assuming that the ambient theory is powerful enough to talk about this sort of thing).
So at no point was I intending to vary the actual ambient theory, like you seem to be talking about.
Warning: I don't quite understand just how logicians think of these things and so may be confused myself.