The Method constraint 157

Primo.

Rigid Variant(α): I ask Primo whether (p_α) that number is prime.

Non-rigid Variant(β): I ask Primo whether (pβ) I have written a prime number.

In both cases Primo answers (rightly) “yes”.²

Safety is satisfied in the rigid case but not in the non-rigid one. pα is the proposition that 47 is a prime number. There is no possible case in which 47 is not prime. Thus there is no possible case in which Primo believes that 47 is prime while it is not. So simple safety holds in α, no matter how closeness is fixed. By contrast, given the setup, I could easily have written another number on the paper, say 49. If I had shown that number to Primo, he would have mistakenly judged it prime. So there is a close case in which Primo believes thatpβbutpβis false. So simple safety does not hold inβ.

Primo clearly does not know that the number is prime, even though he has a true belief that it is. Simple safety explains why he fails to know in β. The truth of Primo’s belief is too accidental in that case, and the safety requirement brings the accidentality out. But it fails to explain why he fails to know inα.

Do the cases pose a problem? Simple safety was only put forward as a necessary requirement on knowledge. Primo’s case β shows that it is not sufficient, but it was not never claimed to be so. That is true, but it does not get simple safety offthe hook, for two reasons. First, simple safety creates an unexpected asymmetry between the two cases (McGinn 1984/2002, 15). The difference between the two propositions appears irrelevant to Primo’s knowledge of them. His epistemic position with respect to one is just the same as his epistemic position with respect to the other. Yet simple safety entails that the first case satisfies a requirement on knowledge that the second does not. Second, since Primo fails to know in the first case, there must be some other requirement Con knowledge

2. The labels come from the fact that α, but not β, involves rigid designation of a number. See McGinn (1984/2002, 14) for a similar case. (I add the rigid/non-rigid variants and remove the deduction step.)

that he fails to satisfy. But ifC explains why Primo fails to know in α, it is to be expected that C also explains why Primo fails to know in β, given the similarity between the cases. So simple safety will either be an under-generalisation ofCor made redundant by it.

(Two caveats to the argument. First, it may be that the only natural requirement Cwe can find to explainα is that ofknowingitself. Simple safety would remain the best non-tautologous requirement we can put forward. To this I will reply by showing that we can do better. Second, a requirementCmay replace simple safety without making it explanatorily redundant. C may be, for instance, the requirement that a case be not relevantly like a case of non-safety.³ Since α is relevantly like β, and β is a case of non-safety, both α and β fail to satisfy this requirement. But since the requirement is formulated in terms of simple safety, the latter still has an explanatory role to play. In reply, I cannot a priori rule out the possibility of such a requirement. But I doubt that one can be put forward which is both satisfactory and which cannot be replaced by a requirement that doesnotappeal to simple safety. For instance, the one just envisaged has no advantage over the simpler requirement that a case benot relevantly like a case of error.)⁴

Are necessary truths a special case? One lesson ofKripke(1980) is that necessary truths are not confined to special domains like mathematics, metaphysics or fundamental sciences. Accordingly, the problem raised by

3. Thanks to John Hawthorne for the suggestion.

4. Revision note. Igor Douven made a further objection to the argument. While the argument indicates thatin cases involving proper names, rigid designators, or natural kinds predicates, simple safety will be made redundant by a condition that covers both cases in the symmetric pair, it is still possible that the condition fails to deal withothercases that simple safety would account for.

Now, a condition that would cover both cases of the pair (and of others like it, see below) does not merely cover cases involving a rigid designator: for it also covers the non-rigid variant of the case. So if anything, it may be that the condition will only apply to casesfor which a rigid variant exist. But using an actuality operator, we show below that forany case, a rigid variant exists. So any condition that meets the challenge of such pairs should cover any cases that simple safety covers. Note that, since a condition cannot covers all the cases covered by simple safety without entailing simple safety, that means that the putative condition will entail simple safety. The method requirement we put forward is a case in point.

4.1. The Method constraint 159 the Prime Number case generalises (McGinn 1984/2002, 14–5). Consider

first a pair of cases based on Ginet-Goldman’s fake barns case (Goldman, 1976, 772–3):⁵

Fake barns Bernard drives by the countryside with his son, pointing at various objects in the field. He sees a barn, points it to his son, and says:

Rigid Variantα: “That building is a barn!” (p_α)

Non-rigid Variantβ: “The building I am pointing at is a barn!” (p_β) The building is a barn. However, fields in the area are full of papier-mâché barn facades that Bernard would have mistaken for barns.

Letbbe the building Bernard is pointing at. pαis the proposition thatbis a barn. Arguably, there is no possibility in whichbis not a barn. If a barn facade made out of papier-mâché had been built at the time and place b was built, it would not have been b, but another building. So there is no possibility in whichp_α is false; hence no possibility in which Bernard believes that that building is a barn while it is not.⁶ By contrast, if details are filled in properly, there is a close possibility in which Bernard would be pointing to a barn facade, and in which he would nevertheless believe that it is a barn. So here as well, simple safety holds forpαand not forpβ. But again, the variants appear perfectly symmetric.

The argument relies on two assumptions. First, I am assuming a measure of essentialism such that a barn could not have been a barn facade. For instance, given essentiality of origins, a building made out of different materials thanbwould not be identical to it. But whatever one thinks about the essence of barns, analogous cases can be formulated for anybody who accepts some measure of essentialism.⁷ Thus if one thinks that animals belong to their species essentially, we can build an analogous

5. The case was suggested to Goldman by Carl Ginet.

6. This is a bit quick. Perhaps there are possibilities in whichbstill exists and is not a barn. For instance,bmay later be converted into a house, etc. But we may assume that any of these possibilities is either distant or such that Bernard would not then mistakenly believe thatbis a barn.

7. Except perhaps somebody who thinks that things only have theirappearance es-sentially.

case involving fake sheep. Second, I assume that the demonstrative “that building” is a rigid designator (Kaplan, 1989; Récanati, 1993). Again, if that is contested, the argument can be recast as long as one accepts that some expressions rigidly designate ordinary objects.⁸ For instance, the case can be recast with proper names. To illustrate both points:

FakeSheep Bertha sees a sheep, baptises it “Ajax”, points it to her son and says:

Rigid Variantα: “Ajax is a sheep!” (p_α)

Non-rigid Variantβ: “The animal I am pointing at is a sheep!” (p_β) Ajax is a sheep. But unknown to Bertha, many other animals in the field are Greek soldiers disguised as sheep in fear of a Cyclops.

Thus it cannot be said that simple safety solves the fake barn case. It only solves variants of the case involving non-essential properties and non-rigid designators.⁹

The problem is further generalised to cases involving predicates. First, there is the predicate analogue of rigidly referring individual terms:

Fool’sGold A small tribe discovers a metal unknown to them in the ground, and baptises it “gold”. However, the area also contains much of an indistinguishable (to them) substance that is not a metal

— call it fool’s gold — which they might have just as well hit upon.

Rigid variant: they believe that gold is a metal.

Non-rigid variant: they believe that the substance they found is a metal.

Again, there is a close possibility in which the second belief is false, but none in which the first is. Second, there are analogous cases involving

8. Perhaps fake-barn style of cases involving rigid designation of places, times or abstract entities can also be constructed. I leave such constructions to others.

9. Seee.g.Pritchard(2005, 162): “We can explain this intuition in terms of our account of veritic epistemic luck by noting that there are going to be a great many nearby possible worlds where Henry forms the same belief on the same basis (by simply looking at the

’barns’) and yet his belief is false.” Whether Henry/Bernard forms the samebelief at nearby worlds depends on whether beliefs have their content essentially. If they do, Bernard forms the same belief only in the non-rigid variants. SeeWeatherson(2004)for a notion of “belief safety” that allows beliefs to have different contents at close worlds.

However, as I argue below, this narrow content approach is insufficiently general.