Kane, I've been enjoying your series. I started out as an standard set theory guy and propositional logic believer. It was Brouwer that converted me to liking ML. I had a mild argument w/another math friend the other day that alleged that Brouwer's rejection of double negation is not really addressed in ML, since nec(nec) is nec is the same thing in form. or not nec(not nec) is nec. He forgets I responded that T-F logic doesn't consider the idea of worlds. That Brouwer extended T-F. We dissent.
The website I use to the screencapture is on the bottom of the video - screencast-o-matic. The sound is recorded with my BOSS Micro BR and I use Audacity to edit it. Then I put the sound and video together using Windows Movie Maker. So nothing fantastic.
Thanks so much for this video series. I have a question about the interpretation of the possibility operator though: Should we find that P is true in some possible world, does that mean that possibly P (diamond P) is true in every world, or just the real world?
Mr Kane, I am very interested to find your excellent videos. Would it be impertainent to enquire about your work in philosophy? If not, are you a tenured academic or a PHd?
I wonder if you could fix the fluke in the symbolism by giving "impossible that P (or whatever variable)" its own symbol so that it reads "necessarily impossible p" instead of "necessarily not p".
Joe Watson Media even though this comment is quite old. One would have to specify the base in which something is written in order to make it necessarily true then. Because 1+1=1 in boolean 1+1=10 in base 2 1+1=2 in anything higher Just like 2+2=4 could be 2+2=11 in base 3 or 2+2=10 in base 4 Apparently we simply chose to calculate our every day stuff in base 10 because we used our hands and fingers back in the day. In a possible world (or even simply on a different planet with a higher developed species) with 3 fingers on each hand we might even calculate in base 6. I think these kind of examples aren't good examples as they're not world-independent
If we assume logics etc formal stuff are just kinds of models, parts of our thought, then why ought the actual world be logically possible? Physicists are stuck with "objective" probability distributions, could that be interpreteted as formal models being unable to precisely describe microlevel, whose contradictions however filter statistically out at macrolevel? I don't see how you could rule that out, and I feel it kind of waters down the talk about possible worlds, though it would still be meaningful to think it as an evaluation of models our thinking process can come up with.
