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You need to use the branching rule from the middle of page 88. On the left branch you put "~(A v B), 0", which will close in another step. On the right branch put "A v B, 0" and "0r_(A v B)0", and then you can continue with the conditional rule.


Frank Hubeny's answer is quite good, but let me add to it re: Herbrand semantics. In particular, I'm going to push back against the argument pro Herbrand logic cited in that answer. It is true that Herbrand semantics permits only countable structures*, but that's not the full story: since first-order logic has the downwards Lowenheim-Skolem property, if ...


I don't think everything exists. It only exists if it can exist. But since dragons never existed just before we imagined them doesn't mean they can or ever will exist.


If I'm understanding correctly, I could use your logic to make the argument that unicorns exist as follows: unicorn = unicorn there exists some x = unicorn therefore, unicorns exist I agree that (1) holds. I also agree that (2) implies the conclusion. Step (2) strikes me as more problematic. Why is there some x = unicorn? If I assume that you are using (1)...


I'd like to add an addition to A.K.'s otherwise very good answer to address the topic of progressing to the "state of the art." A.K.'s reading list will get you the basics. That will be very doable on your own. By contrast, it's very difficult to progress to the state of the art without a mentor or PhD advisor, simply because you won't have any orientation ...

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