jpulgarin

I don't think there's a flaw in this argument. I'm pretty sure that is a theorem of PA for any sentence . However, even if we consider to be a sentence like , that does not mean that we can conclude that is a theorem of PA, since proving that there doesn't exist a proof for a given sentence in PA is equivalent to proving that PA is consistent, which is not possible if we assume that PA is consistent.

Sorry :/, it was my fault for posting it at such short notice. No one else came.

There's a chance I'll be back in Bogota during the first week of March. If so, I'll make sure to post it with a bit more notice.

Do you go to Medellin every once in a while? I'm thinking of starting a regular meetup here.

Largely a result of Salsa dancing.

Do casual sex partners count under the "Number of Current Partners" question?

The instructions tell me that higher numbers are for "polyamorous relationships" which makes it seem like a monogamous person who has multiple casual sex partners should answer 0 for that question.

I genuinely do not understand how you were insulted by my comment. Could you please explain it to me so I can avoid in the future.

Note, I am not purposely insulting you in this comment.

find tickets for free for strange trips around the world (there are loads)

Can you please elaborate?

There's no disagreement here, you're just confused about semantics.

I see in a reply of yours that you're interested in salsa dancing. By far the most important factor in getting better is to quickly achieve a level of competency that makes salsa socials really fun. I don't think I've gone more than 7 days in the last 2.5 years without attending a salsa social, and this has been the biggest factor in my improvement.

You may already be at this stage since you said you enjoy dancing, but if not I suggest you learn the basics from a friend or a class (I would spend no more than 10 hours on this stage), and then force yourself to attend a bunch of salsa socials, until you start *really* enjoying the experience.

Once you've reached this stage, you've solved the motivation problem, and now you can optimize towards becoming a really good dancer (if you even want to at this point - it's not necessary to reap the majority of the benefits).

Thanks Sam. I thought about this some more and realized where I went wrong - I was applying the deduction theorem incorrectly (as other comments in this thread have pointed out).

By the way, when you say that PA proves its own inconsistency, do you mean that PA⊢□(¬Con(PA)) or that PA⊢¬Con(PA)? From your reasoning I agree that if we assume ¬□C→C then we can arrive at PA⊢□C and PA⊢□(¬C), from which we can conclude that PA⊢□(¬Con(PA)). If you meant that PA⊢¬Con(PA) though, could you explain how you arrived at that?