I’m glad you’re writing this. It has been a great refresher for me.

]]>Safari. The problem really does seem to be intermittent for me.

]]>What browser/OS do you normally use?

]]>The winning strategy approach is fun, but one needs to get any negation signs within the string of quantifiers out to the front first, otherwise it gets seriously confusing.

I have tried something that is, I think, equivalent to the winning strategy approach. It is outlined on pages 53 and 54 of the document linked below, with some prefatory remarks on pages 50 and 51:

These notes are for budding philosophers who are not necessarily mathematical, so they assume that we have a specific universe in mind, which the students will almost certainly think of as finite, and that each object has been labelled with a constant.

]]>I’ve tried that too. In fact, I have even gone as far as to play the game with a room full of people I’m lecturing to. I very much like the idea in theory but I’m not sure I’ve ever managed to help anyone with that approach. It’s quite easy to get people to see who has a winning strategy (especially if I make sure that I’m the one with the winning strategy, so they get to feel indignant about it), but not so easy to get them to understand the link between that and the original statement with mixed quantifiers — unless they’ve got a pretty good understanding already.

]]>Second: the book that I am using is a bit sloppy. At the beginning it tries to avoid using quantifiers! As a result some confusions arises. For instance it gives the following exercise:

” Is the following statement true or false?

(n^2-n-2=0 implies n=2) or (n^2-n-2=0 implies n=-1)”

As you can see no quantifiers are used. But I think it is a good example on how important it is to write the quantifiers at the right place:

(for any n, n^2-n-2=0 implies n=2) or (for any n, n^2-n-2=0 implies n=-1) is false.

For any n, ((n^2-n-2=0 implies n=2) or (n^2-n-2=0 implies n=-1)) is true.

]]>I think I’ll have to stop putting full stops inside my LaTeX, which is annoying as it means that some of them will no longer go on the same line as the symbol they follow.

Oddly enough, although most of the time I don’t see the problem, there was one time when I saw the AO that resulted from B with a full stop after it in LaTeX. Come to think of it, perhaps that was on a different computer and different browser, in which case it wouldn’t have been so odd after all. I can’t remember whether it was.

]]>You’ve just said you fixed _np_ So can you tell us what prime you’re talking about please?” you would get short shrift. When we say that we have “fixed” _p_ it is a sort of lie: actually we are talking about an arbitrary, general _p_ which is another way of saying that we are talking about all _np_

As before, I think the problem is your latex interpreter is translating a final period to an initial “n”. No idea why.

Note: If you’re not seeing it yourself, try with Chrome. It may be for instance that WordPress is delivering correct Unicode to your browser and falling back to an incorrect image in my Chrome.

]]>I guess you mean “If you have read the post on ‘NOT’, you may remember a general rule that I mentioned…” 🙂

*Oops — thanks. Changed now.*

That’s an interesting comment and it reflects the fact that I have two different hats. One is my philosophical hat: I am not a Platonist and do not, for example, think that there has to be a fact of the matter about the truth or otherwise of CH. The other is my everyday mathematical hat, where I’m perfectly happy to reason using the most classical of classical logic. The second is my main hat for these posts, since classical logic seems entirely appropriate for the kinds of statements that are included in the first year of the Cambridge Mathematical Tripos. The advice I would give to undergraduates is to learn to reason classically and then worry about the philosophical side only later and only if it interests them.

]]>By the way, I also felt that your cautious wording concerning “some people” who might find it conveivable that Goldbachs conjecture could be true without there being any particular reason for it has been phrased exactly as it is so as to avoid any personal commitment to platonism.

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