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About

I'm Greg Restall, and this is my website. I work in Philosophy at the University of Melbourne. [Email: greg at consequently.org; Skype: greg_restall; Post: Department of Philosophy, University of Melbourne, Parkville 3010, Australia.]

Writing

These are the three last modified entries on my writing page.

“Truthmakers, Entailment and Necessity 2008,” an addendum to “Truthmakers, Entailment and Necessity,” to appear in Truth and Truth-making, edited by E. J. Lowe and A. Rami, Acumen, 2008. →
[with Rebecca Kukla and Mark Lance] Appendix to Rebecca Kukla and Mark Lance ‘Yo!’ and ‘Lo!’: the pragmatic topography of the space of reasons, Harvard University Press, to appear. →
“Curry’s Revenge: the costs of non-classical solutions to the paradoxes of self-reference,” in The Revenge of the Liar, ed. JC Beall, Oxford University Press, pages 262–271, 2008. →
“Anti-Realist Classical Logic and Realist Mathematics,” under revision. →
“Proof Theory and Meaning: on second order logic,” to appear in the Logica 2007 Yearbook, Filosofia. →

Classes

In Semester 2, which starts on July 31, I’ll be teaching an honours seminar 161-438 Logic and Philosophy, in which we cover proof theory and its applications to semantics.

Events

AAL2007: the annual conference of the Australasian Association for Logic, University of Melbourne November 9 to 11, 2007.

Recent Past

University of Melbourne Philosophy Undergraduate Workshop, University of Melbourne September 21 to 23, 2007.

Logic Colloquium 2007, Wrocław, Poland, July 14-19, 2007.

1st GPMR Workshop on Logic & Semantics on Medieval Logic and Modern Applied Logic, Rheinische Friedrich-Wilhelms-Universität Bonn, Germany, on June 28-30, 2007.

Logica 2007, Hejnice Monastery, Czech Republic, 18-22 June 2007.

Heart of Philosophy Café talk and discussion on “What Marx, Freud and Nietzsche have taught me about belief in God”. Tuesday May 8, 7--9pm in the Merrick's General Store.

On Regret and Slingshots

Here’s a silly puzzle for you.

Regret seems like a factive emotion. You can’t truly regret that you forgot to feed the cat today if, indeed, you did feed the cat. If you did feed the cat and you forgot that you did, then it seems to you like you’re regretting not feeding the cat, but you’re as mistaken about your regret as you are about feeding the cat. You think you didn’t feed the cat and you’re sorry that you didn’t, but that’s not regret. Or so some people think, anyway.

Now, suppose that regret is factive like that. Then it’s plausible to think that the circumstance you’re regretting is in some way a ‘component’ of that regretting. (On this view, that’s why it’s factive: if the circumstance of my not-feeding-the-cat isn’t there, then I can’t be related to that circumstance in “regretful” manner.)

If this is the case, then it’s plausible to think that disjunctive regrets are a strange sort of thing. Regretting that p or q might be a relationship to a situation in which p is true (when it’s the truth of p that makes the disjunction true) or one in which q is true (the other case). A regret that p or q might be the same kind of thing as a regret that p (if p is the case) or a regret that q.

So, let’s suppose that in general, a disjunctive regret that p or q — since it is a regretting relationship to a circumstance in which p or q is true — brings with it a regret that p or a regret that q, since either the p-or-q circumstance is one in which p is true, or it’s one in which q is true. Call this the disjunction principle.

Now, it seems that regretting that (p and q) and regretting that (q and p) are no different to one another. Similarly, regretting that (it’s not the case that (p and q)) is no different to regretting that (either it’s not the case that p or it’s not the case that q) and so on. It seems a little bit plausible that if A and B are two statements that are logically equivalent then regret that A and regret that B don’t differ. Call this the equivalence prinicple.

Oh, suppose that the classical story of logical equivalence, that you were taught when you were taught truth tables, is correct. This is enough to get the puzzle going.

These things can’t all be right. Unless you have a lot on your mind. Here’s why.

Suppose you regret that p. Then, p is logically equivalent to (either (p and q) or (p and not q)). So, your regret that p means that you also regret that (either (p and q) or (p and not q)), by the equivalence prinicple. By the disjunction principle, you either regret (p and q) or you regret (p and not q). Suppose, without loss of generality, that it’s (p and q). Now (p and q) is equivalent to ((p and q and r) or (p and q and not r). So by the eqiuvalence principle … You see how it goes.

This is a version of the slingshot argument for regrets. Clearly, you shouldn’t believe the equivalence thesis (in its classical guise, at least) and the disjunction thesis for regrets. I’ve argued before in favour of the disjunction thesis and against classical equivalence for truthmakers.

What should we think in this case? Are either of the equivalence or the disjunction theses plausible? I’ve got my own ideas but I’ve written enough for one night.

(Thanks to Robert Anderson for getting me thinking about regrets and disjunctions and proposing something like the disjunction thesis. He thought of it when worrying about bets and regrets and Lloyd Humberstone’s puzzle mentioned in the previous post.)

Posted 11:18 PM on May 2, 2006

Comments

This puzzle leads to some really interesting ways of thinking how regret might behave. Can we argue that, as it is stated, the equivalence principle is incorrect? Regret that is intensional: Lois Lane regrets that she did not propose to Superman; but she does not regret that she did not propose to Clark Kent.

What are the implications of having a knowledge of equivalence principle instead of a plain equivalence principle?

Knowledge of equivalence principle (KEP): if A and B are two statements that are logically equivalent and I know that they are logically equivalent then regret that A and regret that B do not differ.

This would deal with the Superman situation as if Lois Lane knew that Clark Kent and Superman are logically equivalent then she must have the same regret or lack of about marriage to Clark Kent as to Superman.

It seems that if we use KEP then the slingshot argument will not lead to us regretting one big disjunctive fact. For we now need to know that p is logically equivalent to [either (p & q) or (p & not q)], and to know this we at least have to think about it. So if we keep producing bigger and bigger disjunctions that are logically equivalent to p that we know are logically equivalent to p we should not be too surprised that we also have a really big disjunction that we regret. Crucially though this regret will only ever be as big as the disjunction that we know is logically equivalent to p, and we do not shoot off into an infinite regress.

This maybe marries up with thoughts on the cable-guy paradox about whether we could plausibly both regret and not regret the same action under different descriptions of that action.

As an aside, another question that arises from the way that the disjunction principle is worded, is whether:

(1) I regret that (p or q)

means:

(2) I either regret that p or regret that q

Might the disjunction not be inclusive? I take it that even if it is you can still generate a similarly ever increasing disjunction (it will just increase in size even more rapidly). Did you phrase it this way because you think (2) must be the interpretation of (1)? Any examples that I have run through are such that it would not make sense to have an inclusive interpretation of the disjunction principle. E.g. I regret that (I did not eat breakfast or pick up my wallet before I left the house)because I am hungry and cannot afford lunch. It looks like I do not regret the conjunction of these facts as if merely one of them was different I would not be hungry and so would no longer regret the other. I cannot seem to make sense of an inclusive disjunction that is regretted, but this may just be a failure of imagination on my part.

Duncan Watson , May 3, 2006 02:39 AM

My quick thought is just that the disjunction principle might just seem plausible because we only regret “simple” states of affairs, in some relevant sense. Most of the disjunctions that immediately come to mind are disjunctions of simple states, so they are not themselves simple, so we regret one disjunct or the other. But a disjunction of two conjunctions might be simpler in the relevant sense than either disjunct, so we might be able to block the particular argument here.

Kenny Easwaran , May 3, 2006 07:27 AM

I think that I don’t buy the disjunction principle for regrets, either, as it seems to be pretty hyperintensional. I don’t buy the equivalence principle either. However, it seems that there’s something a bit like regret which might satisfy the disjunction principle. I’m thinking of regret in the same way that Barwise and Perry analyse the factive see in Situations and Attitudes. If you read “regrets” in that kind of way — so, if I regret dropping that vase and making you unhappy, I regret dropping the Ming Dynasty vase and making you unhappy, even if I don’t know it’s a Ming Dynasty vase — then the disjunction thesis might be plausible. (If I see the vase, I see a Ming Dynasty vase, even though I don’t see that it’s a Ming Dynasty vase.)

Greg Restall , May 3, 2006 04:37 PM

For me, regret corresponds to a negated bulomaic operator plus a (probably past) time operator, so it is bi-modal. So part of your intuitions have to do with the syntax. But, from the side of the possible worlds semantics, what theorems are involved when you have a modal logic with bulomaic operators? Can we have a theorem like

[T] Not-bulomaic A implies not A?

Tony Marmo , May 13, 2006 12:31 PM

I’m somehow reminded of the problems with the AGM postulates for belief revision, particularly around semantically unrelated disjunctions (why should I believe that Montreal is in Quebec or that the generalized continuum hypothesis is green and stinky just because I believe the former?). I suspect the problem there and here has to do with the fact that the problem (belief revision and whatever this falls under) is characterized purely syntactically. I guess this makes me sympathetic to those that are making use of intensional contexts, etc.

Keith Douglas , May 14, 2006 03:07 AM

What would the other persons think of the following statement: [1] Your boss regrets that there is no job for your friend. [2] Your friend regrets that you have such a boss. What are your intuitions about the acceptability or the meaning of these statements?

PS.: Greg I’ve sent you an e-mail to talk about another issue if you can, please.

Tony Marmo , May 14, 2006 07:44 AM

What if you construed I regret that A or B as non(A or B) (which is the same as non-A and non-B)? If you maintain that, for the cases you are interested, x regrets that P entails that non-P, then the denied disjunction is the same as the conjunction of the negated parts.

PS2.: I have somehow already managed to find that demonstration involving Sequent Calculus and Analytic Tableaux, without resorting to the known theorems.

Tony Marmo , May 15, 2006 08:46 AM

About Tony’s “…[1] Your boss regrets that there is no job for your friend. “[2] Your friend regrets that you have such a boss.”

Statement 2 doesn’t quite sound right to me. I don’t think the emotion the person is having would either be factive or, more specifically, “regret”. I have to think more why but it seems to have something to do with the person not being or feeling responsible (however vicarious or unrelated the responsibility is) for the fact to obtain that produces their emotion. Perphaps they would more rightly have an epistemic emotion… “is unhappy”, “is sad”.

Robert Anderson , May 16, 2006 03:04 PM