Modal Logic and Classical Logic

by Johan van Bentham

Hardcover

First published January 1, 1988

Reviews

[Manny · Rating 3 out of 5]

As someone who works with logic and language, I've always been interested in modal logic. In case you don't know what it is, it's the study of logics that try to qualify truth, as opposed to considering it as an absolute. One of the most thoroughly explored types of modal logic is the logic of knowledge. You have an operator K to represent "know", so K(P) means "I know P", K(~K(P)) means "I know that I do not know P", and so on. As Donald Rumsfeld famously remarked, we know that there are known unknowns. This is just the kind of thing modal logicians spend their time thinking about, so I was a little surprised when everyone complained that what Rumsfeld had said made no sense.

The other day, I suddenly wondered how much work people had done on logics of desire. Just as it makes sense to talk about knowing that you know (or don't know), it also ought to make sense to talk about wanting to want (or not want). It seems that this field is still relatively undeveloped. I found the following interesting passage in The Knowledgerush article on second-order desire:

Given some state of affairs x, there are 12 different possible combinations of first and second order desire in respect of x:

1. I have no desires concerning x, nor do I have any desires concerning having desires concerning x.
2. I desire x, but I have no desires concerning having desires concerning x.
3. I desire ~x, but I have no desires concerning having desires concerning x.
4. I have no desires concerning x, and I desire to have no desires concerning x.
5. I desire x, but I desire to have no desires concerning x.
6. I desire ~x, but I desire to have no desires concerning x.
7. I have no desires concerning x, but I desire to desire x.
8. I desire x, and I desire to desire x.
9. I desire ~x, but I desire to desire x.
10. I have no desires concerning x, but I desire to desire ~x.
11. I desire x, but I desire to desire ~x.
12. I desire ~x, but I desire to desire ~x.

Real-world examples can probably be found for all of these, although for some the examples may be more contrived than for others.
Since such desires must be described symbolically in some sharable form for a comprehensible debate, and since sexual desire is basic to animals, it may be helpful to think of x as being a match with a sexually desirable person who is particularly troublesome or boring, as explained or excused to a third party in language - it is easy to imagine states where it may be desirable or undesirable to (admit to) desire them or not.

(...)

Bring third-order desire into the equation, there are exponentially more possible combinations. It is conjectured, but seemingly unproven, that real-world examples cannot be found for any of these, except for those which are repetitions of the 12 above.

So the authors think that, while it makes sense to talk about desiring to desire, you can't go any deeper than that; it doesn't make sense to talk about desiring to desire to desire.

It seems to me that this is seriously open to doubt, and that there are perfectly natural examples which occur all the time both in literature and in real life. Let's follow their advice, and take "x" as something sexual. So I start by saying "I desire her" - that's a first-order case. Then I can say "I wish I didn't desire her" - that's a second-order case. But surely "I wish I didn't feel so guilty about desiring her" is more or less equivalent to "I desire that it is not the case that I desire that I do not desire her", hence a third-order desire sentence? And there's nothing odd about it when it's written in the normal way, only when it's unpacked into logician-English.

I must look around some more!

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On further consideration, my example may not be as clear-cut as I would have liked. You can reasonably argue that in "I wish I didn't feel so guilty about desiring her", "feel guilty about X" doesn't mean "want ~X" but rather "ought ~X", i.e. a deontic operator. The assumption here, which to me seems intuitively plausible, is that even if you feel that X ought to be true, you may not want X.

A natural question: is there in fact a difference between "I want to not want X" and "I ought to not want X"? To me, these things are indeed distinct, but I can see people disagreeing.