February 20, 2008

Must and Can

In “Modals and Conditionals Again” Angelica Kratzer treats natural language ‘must’ as the expression of a two-place relation between a premise set and a proposition. The trick is getting the relation straight. Consider the following 'must' claims:

Deontic: “One must not microwave kittens!”

Doxastic: “In light of what Jack mistakenly believes, Jill must be in love with him.

Epistemic: “Oh…, the gun must have been loaded.”

Dispositional: “If you must smoke, then please use an ashtray (and not my rhododendra)”

Bouletic: “You must wear that fabulous dress”

For Kratzer the two-place relation is 'must in view of', giving
Deontic: “In view of our duties, one must not incinerate kittens”

Doxastic: In view of what Jack mistakenly believes, Jill must be in love with him.

Epistemic: “In view of what we now know, the gun must have been loaded.”

Dispositional: “If, in view of what you are disposed to do, you must smoke, then use an ashtray”

Bouletic: “In view of what my preferences state, you must wear that fab dress”

The natural way to read these claims is as follows:

'In view of premise set A it must be that p' is true iff
p follows from A.

And the corresponding dual operator 'can' is read:

In view of A it can/might/may be that p iff
p is compatible with A.

Two well-known problems emerge for this sort of semantics. First it forces a vacuous reading of 'must' claims that relate a proposition to an inconsistent premise set. And second, it gives rise to all sorts of unwelcome modal collapses, and relatedly, forces a vacuous reading of 'must' claims that relate non-contingent propositions to premise sets. In my talk at Kioloa, I criticized a proposal by Kratzer for dealing with the first problem. I then argued that the two problems are related and sketched a unified solution.

Kratzer's proposal tells us that ‘musts’ and ‘cans’ follow from the appropriate consistent subsets of the given premise set. More specifically, let A be an inconsistent premise set of, say, legal judgments.
A = {p, ~p, q}
And let X be the set of all A’s consistent subsets.
X = {ΓΈ, {p}, {~p}, {q}, {p, q}, {~p, q}}
Kratzer’s proposal says:

"In view of A, it must be that p" is true iff
each set in X has a superset in X from which p follows.

The problem with inconsistent premise sets, of course, is that they entail everything. However, it is false that each set in X has a superset in X from which an arbitrary proposition follows. So, unlike the natural proposal with which we began, Kratzer's proposal doesn't predict the absurd claim that, in view of the law, we must commit murder.

However, the restriction not only blocks the application of 'must' to arbitrary propositions, but it blocks the application of 'must' to any contradicted premise. So claims like the following are predicted to be false:
"In view of what Graham believes, the Liar sentence must be true"
"In view of what Graham believes, the Liar sentence must not be true".
Moreover, Kratzer's proposal always blocks the application of 'must' to premises responsible for the inconsistency and it sometimes blocks the application of 'must' to important consequences that (at least partially) depend on at least one of the contradicted premises.

Here's an example of the latter type of case. White House chief of staff “Scooter” Libby was convicted of obstruction of justice and making false claims to federal investigators during the CIA leak investigation. Bush commuted his prison sentence from 33 months to 0 on the grounds that any term of imprisonment for such nonviolent first offenses by experienced government service employees is too harsh. This contradicts US federal sentencing guidelines and practice, which prescribe hard time for such offenders. In view of federal sentencing guidelines, what now must be prescribed for the sentencing of a like criminal c for like crimes? It would be irresponsible to let Bush’s incompetence and nepotism overly influence the federal justice system. Hence, in view of federal sentencing guidelines, c must do hard time.

But Kratzer’s view doesn’t predict this. For it depends on at least one contradicted legal judgment---viz., criminals of this sort are to do hard time. And when that is the case, it will be false that, for each consistent subset of the sentencing guidelines, there will be a superset among them from which it follows that c is to do hard time.

A second problem with the Kratzer proposal is that it says nothing about what to do when the proposition p fails to be a contingent matter. When p is necessarily true, then it follows from every set. Therefore, in every context, p must be the case. For instance, the view predicts that, in view of what Michael (the intuitionist) believes, excluded middle is correct. But Michael the intuitionist denies the unrestricted truth of excluded middle. To pick another example of this kind, we want to say that Obama might actually win in November. But suppose in fact Hillary wins. Then in view of what we know it must be that Hillary actually wins. That's because 'Hillary actually wins' is necessarily true (if true). So, in view of what we know, it must be that actually Hillary will win. But then, by the duality of the operators, it is false that in view of what we know Obama might actually win.

The problem of inconsistent premise sets and the problem of collapsed modals are at root the same problem. In each case we assume that the deontic/doxastic/epistemic/legal/bouletic "possibilities" are a subset of the logical possibilities. And that is not how it should be. After all, in view of what we know, it may be that Goldbach’s conjecture is false. Ex hypothesi, it’s true. And, for all we knew before the telescope, Hesperus might not have been Phosphorus. And, for all we know right now, Obama might actually be the next US president. Ex hypothesi, Clinton wins.

The view I proposed in Kioloa was this:

'In view of A, it must be that p' is true
all the relevantly similar (possible or impossible) A-worlds are p-worlds.

'In view of A, it can be that p' is true
some relevantly similar (possible or impossible)
A-worlds are p-worlds.

I treat 'musts' as counterfactuals because the corresponding strict conditional, which would quantify over all possible and impossible worlds, would be too strong and rarely (if ever) come out true. The corresponding 'can' claims would be too weak and would usually (if not always) come out true. The important insight is that, with the introduction of impossible worlds, we drop the assumption that the relevant accessibility relation is a subset of S4/S5 accessibility. In so doing, we block the familiar modal collapses and the special problems of inconsistent premise sets, and we get that much closer to the correct understanding of 'must and 'can'.

February 19, 2008

Epistemology Beach Update

Epistemology at the Beach
Below is an update on what the workshop participants were going on about. Pics are here, and here.

Patrick Greenough argued that Stanley's certainty account of assertion doesn't work. Among the counterexamples were warranted assertions of future contingents, for which the relevant brand of certainty is virtually impossible to achieve.

I responded to some of Angelica Kratzer's recent work on 'must' and 'can'. Kratzer thinks about 'must' claims as 'must in view of claims'. (Will post on some of this soon.) The view I defended was this: 'In view of premise set A, it must be that p' is true iff 'p' is true at all the relevantly similar (possible or impossible) A-worlds. This gives us the right predictions for cases of inconsistent premise sets and awkward cases where p is not a contingent matter (e.g., "in view of what Dummett believes it must be that excluded middle is false").

Yuri Cath argued against the view that knowledge-how is a species of knowledge-that. The strategy was to construct cases of knowledge-how (e.g., knowledge how to juggle) for which the relevant corresponding beliefs (e.g., that w is a way to juggle) are Gettiered or corresponding justification for such beliefs is defeated.

Brent Madison discussed the question of whether causation is necessary for epistemic basing. He argued that contrary to what is presupposed in much of the literature on basing relations, Lehrer's case of the gypsy lawyer doesn't undermine the requirement.

Stephen Hetherington disagreed with the orthodox belief that all Gettier cases are cases of knowledge failure. The discussion was driven by a pretheoretic intuition about the kind of luck that generates Gettier's original cases.

Declan Smithies defended a JJ-principle---viz., one is justified in believing p only if one is justified in believing that one is justified in believing that p. He argued that it explains various Moorean paradoxes and the role of justification in critical reflection.

Dave Chalmers sought an epistemic constraint on truth that avoids the Church-Fitch paradox of knowability. Dave takes it that each basic truth is knowable by somebody. Let 'b' express the conjunction of all the basic truths. All non-basic truths are knowable in the sense that someone is in a position to know that p is materially implied by b.

Daniel Star defended his view that a fact X is a reason for an agent N to F just when X is evidence that N ought to F.

Berit discussed the knowledge argument (construed as an argument against a priori physicalism). She defended it against a number of objections, including the old fact reply and the missing concepts reply.

Wolfgang Schwartz took issue with the standard interpretation of Frank Arntzenius' example of the traveler who in fact passed the mountains on her way to Shangri-La. It is usually treated as a case where the traveler must eventually update to .5 her credence that she came by way of the mountains, lest she violate the principle of Indifference. Wo, by contrast, defended the view that she should retain the credence she had when passing the mountains (viz. 1), lest she violate Conditionalization and Reflection.

Jonathan Schaffer closed the workshop with a paper about a brand of skepticism which threatens the broadest range of knowledge. Knowledge entails basing. Hence, any knowledge (even a priori knowledge and the cogito) is threatened by the debasing demon who, at the final stage of the basing process, intervenes to make it the case that the otherwise properly based belief is based on a guess or wishful thinking. The demon covers his tracks by leaving the victim with no indication that the normal process has been tampered with.

February 15, 2008

Epistemology at the Beach

Epistemology at the Beach is a workshop this weekend hosted by Dave Chalmers' Centre for Consciousness and Daniel Stoljar's Basic Knowledge grant and organized by Declan Smithies. The location is the ANU Coastal Campus. I'll try to blog the event.

Participants: Jonathan Schaffer, Patrick Greenough, Berit Brogaard, Joe Salerno, Brent Madison, Yuri Cath, Wolfgang Schwartz, Declan Smithies, Daniel Star, David Chalmers, Stephen Hetherington, Daniel Stoljar, Susanna Schellenberg, David Bourget, Aisling Crean, JC Bjerring, John Cusbert, Holly Lawford-Smith, Masafumi Matsumoto, Doug Edwards, Federico Luzzi, Paul Dimmock, Grant Reaber, Fiona MacPherson and Stuart X.


Patrick Greenough: Assertion, Knowledge and Certainty
Joe Salerno: Must and Can


Yuri Cath: Knowing How Without Knowing That
Brent Madison: Causation and the Epistemic Basing Relation
Stephen Hetherington: Gettiered Knowledge
Declan Smithies: Critical Reflection and Epistemic Responsibility
David Chalmers: Knowability and Scrutability


Daniel Star: Reasons: Explanations or Evidence?
Berit Brogaard: On the Knowledge Argument
Wolfgang Schwartz: I’m Certain That I Went By The Mountains
Jonathan Schaffer: The Debasing Demon

February 05, 2008

John Hawthorne: Wade Memorial Lecturer

For more info contact John Greco
jgreco2 AT slu DOT edu