Epistemic Closure, and KK

Epistemic Closure, at the least the single premise variety, is usually formulated like this:

(EC) IF you know that P and you know that (if P, then Q), THEN you know or are at least in a position to know that Q.

There are loads of alleged counterexamples. My favorite is the zebra one. You go to the zoo. You see a zebra in the cage. You believe that there's a zebra in the cage, and intuitively you know that there is a zebra in the cage. You also know that if there is a zebra in the cage, then there is not a cleverly disguised mule in the cage. This because nothing can be both a zebra and a cleverly disguised mule. Suppose that you go on to believe that there is not a cleverly disguised mule in the cage based on this bit of reasoning. It seems to many, including me, that you do not know that there is not a cleverly disguised mule in the cage. It is relatively hard to know that something is not a cleverly disguised mule. It requires thorough investigation. It can't be known simply by looking at a zebra-looking creature.

I find these sorts of counterexamples totally convincing. What can we do to save something like closure if we want to take the zebra intuition seriously? What's gone wrong with closure as it's stated.

In my view, what gone wrong is that there has been level confusion (see Alston). We forget that often when we know something, we don't know that we know it. What we know is that we believe it. When you look at a zebra in a cage and form a corresponding belief, you (i) know that there is a zebra in the cage, at least typically, and (ii) know that you believe as much. But do you know that you know? In my ears, that would require knowing that the creature is not a painted mule. To know that you know, it seems, you have to know that the relevant alternatives do not obtain.

This suggests a strengthening of the antecedent of (EC).

(KK EC) IF you know that you know that P and you know that (if P then Q), then you know or are at least in a position to know that Q.

Quickly, let me tie this together with another famous counterexample to (EC). This one is by way of Kripke. Suppose that you know that P. You know that (if P then any evidence suggesting not-P is misleading). So, you know that any evidence suggesting the contrary of anything you know is misleading.

This sounds like a recipe for dogmatism. Consider an instance. I know that my sister is in Boulder. Suppose that my mom calls and tells me that my sister is not in Boulder (perhaps she believes that my sister is not in Boulder). Certainly, I am not in a position to know that the evidence that my mom is giving me that suggests that my sister is not in Boulder is misleading.

What's gone wrong? Well, intuitively, what's gone wrong is that I don't know that I know my sister is in Boulder. I presume as much, as I believe it and think it's true. But I don't think I am in a position to know that I know that my sister is in Boulder. If I did know that I know my sister was in Boulder, I would know that the evidence my mom is giving me is misleading.

Can Possibilities be Representational?

In metaphysics these days, nearly everyone accepts that there really are these things: possibilities. Nobody is quite sure what a possibility is. But possibilities appear to be absolutely indispensable to philosophical theorizing. Thus, almost all of us accept that there are possibilities.

There is an interesting disagreement, though, among those who think that there are possibilities. The disagreement is this: are possibilities representations or are possibilities the things represented by representations?

For instance, many of my friends think that possibilities are something like sets of sentences, perhaps in some idealized language. This would be a view on which possibilities are representations. That set of sentences represents a way the world could be down to the finest detail.

Lewis thought that possibilities were cosmos-like. For Lewis, possibilities were no more representational than stars or stones are representational. Lewis' view falls in the second category, where possibilities are the things that are represented.

I think the majority of people who believe that possibilities exist think that possibilities are representational somehow. I know that I used to think that possibilities are representational, in part because I was timid about positing strange things like non-representational possibilities. But now, I can't make sense of the idea that possibilities are representions. Here are my thoughts.

Start from the view that possibilities are representations. You can think of possibilities as long conjunction of sentences, or sets of sentences, or some such. Now consider the following questions: what do possibilities represent? It would seem that the representation relation is existence entailing. That is, if X represents Y, then X and Y must both exist. Moreover, if possibilities are representational, then they must represent something. What could it be? What could possibilities represent? Honestly, I don't know. I don't think there are any good answers to this question. Here are bad answers.

1. "Possibilities represent ways the world could be." But, then, what are possibilities? I thought possibilities were ways the world could be. More exigently, what are ways the world could be? Surely they aren't representational also. For what could they be representing? If possibilities represent non-representational ways the world could be, we might as well jettison possibilities for the non-representational ways the world could be that they represent.

2. "Possibilities represent possibilities." Think about how strange this is. We have sets of sentences that represent other sets of sentences, where those other sets of sentences represent still further sets of sentences. That would be totally weird. Worse, it would have catastrophic consequences. It would be a resultant mystery why we care about possibilities, or why they're useful in other philosophical definitions.

3. "Possibilities represent themselves." This is totally strange too. Think of other representations. Think of an arrow on a map, and imagine someone telling you that the arrow on the map represents that very arrow on that very map. My reaction would be: what do you mean, you've confused me. And, again, on this view, it is a mystery why we would care about things are possible.

3. "Nothing. Representational possibilities don't in fact represent anything." This is also really weird. First, it makes us wonder whether the possibilities are really representational. It might seem that in such a case possibilities are failed attempts to represent. But worse, why admit that there are possibilities, if later you are going to retreat to the view that possibilities are representational and then later retreat to the view that possibilities don't represent anything. What theoretically virtuous role could possibilities play if possibilities are representations of nothing? Also, if possibilities are representational, but don't represent anything, what makes them different possibilities? Do the possibilities have different representational properties? It would seem that they don't, since none of the possibilities represent anything.

I think that possibilities must be the things represented by other things. Possibilities can't be representational devices.

Possiblities: Deflation vs. Inflation

Here is a very common philosophical scenario. I'll present it in terms of a dialog.

A: Possibilities are exhausted by BLAH. (Where BLAH could be the spatiotemporal arrangments of the particles, or the distributions of the qualities, or the distributions of the qualities plus the modal properties, or whatever.) Thus, if possibility X and possibility Y do not differ in terms of BLAH, then possibility X and possibility Y are one and the same possibility.

B: Ah, but consider these two possibilities. [Fill in the blank with the two descriptions for the possibilities]. Intuitively, these are two different ways the world could be.

A: Yes. It does seem that way. But what you have shown is that there are at least two ways of describing the same possibility. The difference that we feel in your two descriptions is a linguistic difference, not a metaphysical or modal difference.

B: But it seems to be a real difference. People might care about the difference. [Fill in other enjoining complaints].

A: Well, you agree that the two descriptions pick out possibilities that do not differ in terms of BLAH. In what might the difference consist? Could you design a test to determine whether you were in of the worlds and not the other?

B: No, I couldn't design such a test. And I already told you what the difference of the two possibilities consists in. They are the same in terms of BLAH, but differ in other terms. What more do you want from me,

A: I see only one possiblity and two ways of describing it.

Back to the main thread. I wish we had some rules for when A's move and when B's move are legitimate. Being in B's shoes more often than not, it seems to me that A could forever cling to her view that the difference I am positing is merely a linguistic difference. I can't think of any decisive way of putting the point that would rationally compel her to acknowledge what plainly seems to me two possibilities.

But now I think I might be able to turn that into an argument. Maybe A's position is unstable. Consider the person who think that possibilities are exhausted by the distribution of the qualities. And then consider a more conservative person who thinks that possibilities are exhausted by the spatiotemporal relations among the fundamental particles. The person who thinks that possibilities are exhausted by the distribution of qualities posits more possibilities than the person who thinks that possibilities are exhausted by the spatiotemporal relations among the fundamental particles.

But now we can put the person who thinks that possibilities are exhausted by the distribution of qualities in a tricky situation. Point out to this person that the person who thinks possibilities are exhausted by spatiotemporal relations could make the same moves that she is making right now trying to defend the view that possibilities are exhausted by the distribution of the qualities. Then ask her why the other person is mistaken in making that move. If she can't come up with something--as I think she can't--then either she has to grant you that there are distinct possibilities alike in terms of qualities or move to the more conservative position.

I will try to give an example of exactly this line of argument in a later post.

Distinct Qualtiatively Identical Possibilities

A possibility is a way that the world could be. Some philosophers hold that there cannot be distinct possibilities that are qualitatively identical. "Qualitatively identical" is a technical term. Think of it this way: two things are qualitatively identical if no matter how thoroughly we investigated, and no matter how good the tools we used in such an investigation, we couldn't tell the two objects apart.

I take it as a datum that there are possibilities in which there are qualitative duplicates. For instance, imagine a Max Black world. In the Max Black world there are only two objects, both are perfect spheres made of iron exactly three inches in diameter. No other objects exist in the Max Black world. If the two spheres of iron are just exactly alike, then they are qualitatively identical.

The question that I want to address is whether there are qualitatively identical possibilities. Sure, there can be qualitatively identical iron spheres. But are there different ways the world can be that are qualitatively identical? I think I have an argument that are qualitatively identical but distinct possibilities.

Imagine a Max Black world with two iron spheres. Bow imagine that there is a two-sided red arrow exactly between the balls. The world ends up looking something like this: [ O <--> O ].

Now imagine that the arrow has the following feature. At time T one of the sides of the arrow will randomly turn blue. So, at and after T one of the sides of the arrow is red and the other side of the arrow is blue. Let us agree to call the iron sphere closest to the red arrow the Red Sphere, and the iron sphere closest to the blue arrow the Blue Sphere. So here is one possibility. It could be that the by random the side of the two-sided arrow closest to the Blue Sphere turns blue.

But which side of the arrow turned blue was a random matter. It could just have easily been that the other side of the arrow turned blue. That is, here is another possibility. It could have been that by random the side of the two-sided arrow closest to the Red Sphere turned blue. This is a different possibility. At least it had better be. When considering the world in which the blue side of the arrow is closest to Blue Sphere we need to be able to truly say: it could have been the case, but actually isn't, that the blue side of the arrow was closest to the Red Sphere.

But now notice that we have two possibilities that are qualitatively identical. In both worlds we have two qualitatively identical iron spheres, and a two-sided arrow between them which is half red and half blue. Both worlds look something like this, where 'b' indicates the blue side of the arrow:
[ O <-->b O].

One interesting thing about this argument is that it suggests that there can be non-qualitative differences among possibilities originating from the identities of non-actual things like our non-actual iron sphere.

Desires as Evidence for Normative Belief

Why is it that when you believe that Ф-ing is good, you thereby have a reason to Ф?

Sometimes this question is posed antagonistically to cognitivists/realists about normativity. The thought, I think, is that typically when one stands in the belief relation to a proposition one does not thereby have a motivation to do something. What’s so special about the normative propositions, asks the non-cognitivist/anti-realist. Why is standing in the belief relation to normative propositions motivating for action?

It seems that there is an easy answer. Desires are motivating. Nobody doubts this. And, desires are evidence for the truth of normative propositions, or at least we use desires as evidence for the truth of normative propositions.

Consider. Someone asks you whether it would be good to increase the sales tax to improve the roads. What do you do? That is, as a conscientious epistemic agent yourself, what goes on in your head in trying to determine whether imposing the tax would be good? One thing I do is put myself in a hypothetical situation in which I am confronted with the choice, and then introspect for my consequent hypothetical desires. If I find that I have the strong desire to choose to impose the tax, I take that as evidence that it would be good to impose the tax. If I find I have a strong desire to choose not to impose the tax, I take this as evidence that not imposing the tax would be good.

In general, I take my desire of X to Y to be evidence that X is better than Y. Defeasible evidence, perhaps only a bit of evidence, but evidence nevertheless.

Thus, we expect a correlation. We expect that the normative propositions I believe often will have motivational force. The reason is that for many of the normative propositions I believe I have used my desires as evidence for whether the normative propositions are true. If I didn’t have the desires I have, I wouldn’t have had as much evidence for the normative propositions I believe, so, probably, I wouldn’t have believed as I do.

Using desires as evidence is especially important in the normative sphere where it is harder to get evidence for the truth of propositions. It is harder to get evidence that Ф-ing is good than it is to get evidence that Ф-ing is typically done by women.

On my view, it isn’t constitutive of believing that Ф-ing is good that one thereby has a motivation to Ф. One could believe that Ф-ing is good and yet have no motivation at all to Ф. But that seems to me appropriate, even desirable.

I take it that this puzzle is supposed to be deeper than my dealings with it. Am I missing something?

French Kisses and Butterfly Kisses

I think that the following puzzling case about belief ascriptions is very important to studies of: (i) the nature of belief, (ii) the contents of belief, and (iii) the nature of representation. The case comes from an example that David Barnett communicated to me in person.

Harry and Harriet are both young and sexually unschooled. Last night was a romantic encounter for the two of them. They played footsie at the show, held hands waiting for the taxi and snuggled together during the taxi ride home. The next day, Harry writes in his diary:

Last night, Harriet and I French kissed. It was fabulous. I love French kissing. I didn't know if I would like it. It seemed weird before we tried it. But now I know. French kissing is amazing!!! My friends told me that if Harriet and I French kissed, then we reached second base. So, Harriet and I reached second base. They also said that many diseases, like Strep throat, can be spread through French kissing. For that reason I especially hope that Harriet wasn't sick. I don't want to catch Strep throat!

According to Wikipedia, a French kiss is a passionate, romantic or sexual kiss in which one participant's tongue touches the other's tongue (or lips) and usually enters his/her mouth. Harry and Harriet did no such thing. Neither Harry's lips nor his tongue ever touched Harriet. In fact what happened was that the two put their eyes close to each other and fluttered their eyelashes. Harry and Harriet didn't French kiss, they butterfly kissed.

There is a tension here. On what hand it seems:

(1) Harry believes that he French kissed Harriet.

After all, he says that he believes that he French kissed Harriet. He wrote it in his diary. He uses the belief in his reasoning, as when he uses his belief that he French kissed Harriet to infer that he reached second base with Harriet, or when he uses his belief that he French kissed Harriet to ground his desire that Harriet was not sick. Moreover, he may well have used a modus ponens style argument to form his belief. (a) Harriet and I co-fluttered out eyelashes. (b) If Harriet and I co-fluttered our eyelashes, then we French kissed. So, (c) Harriet and I French kissed.

But on the other hand, it seems:

(2) Harry does not believe that he French kissed Harriet.

After all, he has no illusions about what took place between him and Harriet. He doesn't believe that his lips touched hers, or that he ever put his tongue in her mouth.

(1) and (2) seems to be contradictory.

Clearly, Harry misunderstands the phrase 'French kiss'. He thinks that the co-fluttering of eyelashes is called 'a French kiss' when in fact it is called 'a butterfly kiss'. What is unclear is whether Harry believes that he French kissed Harriet.

One important thing that seems to me to hang in the balance is the following sort of thesis.

No Surprise if You’re Right Thesis: Suppose that S has consistent beliefs, and we number his beliefs B1, …, Bn. Take Bi such that there are possible worlds in which all of B1-Bn including Bi are true and there are possible worlds in which all of B1-Bn except for Bi are true. The No Surprise if You’re Right Thesis has it that because S has the belief, Bi, S will be more surprised if a world in which all of B1-Bn except for Bi is true is actual than if a world in which all of B1-Bn including Bi is actual. In other words, if S had to guess among the the many possible world as to which is actual, S would choose a world in which Bi is true.

Notice that Harry would be shocked if in fact he and Harriet French kissed last night. That would imply that he had forgotten his lips touching hers!

Vagueness and Identity

Many metaphysicians are interested in a question which can be put roughly in the following way: can it be vague whether A and B are identical?

Sometimes sloppy metaphysicians ask whether "identity can be vague." But this sloppiness borders on being a category mistake. Vagueness most naturally, and in the first instance, applies to questions, not objects or relations. It can vague as to whether Harry is bald, or vague as to how many grains of sand are in the Sahara Desert. But the notion of a vague object or a vague relation is confused. The best we can say of a "vague object" is that there are objects such that it is vague as to where their borders are. And the best we can say of "vague relations" is that there are objects and relations such that it is vague as to whether those objects bear the relation in question, or that it is vague how many pairs of objects bear that relation. If we want to investigate vagueness and its relation to identity, we must investigate it via a question, such as: can it be vague as to whether A and B are identical.

Here is an argument that it can be vague as to whether A and B are identical.

N.B., I will use 'clearly' in the following way: it is clearly the case that P iff it is true that P and it is not vague as to whether P.

Consider the Sahara Desert. There are grains of sand such that it is vague as to whether those grains of sand are parts of the Sahara Desert.

Now imagine that we discover a heretofore unknown tribe which uses the name 'Schmahara Desert' in the following two ways. First, the Schmahara Desert, like the Sahara Desert, is a desert. Thus (we may pretend) both the Sahara and the Schmahara are entirely composed of grains of sand. Second, the following bi-conditional holds: a grain of sand G is clearly part of the Schmahara Desert iff G is clearly part of the Sahara Desert.

There are three options:

(i) It is clearly the case that the Sahara Desert and the Schmahara Desert are identical.
(ii) It is vague as to whether the Sahara Desert and the Schmahara Desert are identical.
(iii) It is clearly not the case that the Sahara Desert and the Schmahara Desert are identical.

We can rule out (iii) straight away. For it to be clearly not the case that the Sahara Desert and the Schmahara Desert are identical, there would have to be some grain of sand such that it is clearly a part of one but clearly not a part of the other.

Here is a way to rule out (i). It might be that for every grain of sand G except for G*, it is vague as to whether G is part of the Sahara Desert iff it is vague as to whether G is part of the Schmahara Desert. But, we may imagine, G* is such that it is vague as to whether G* is part of the Sahara Desert but it is clearly not the case that G* is part of the Schmahara Desert. In other words there are more grains of sand by one for which it is vague whether they are part of the Sahara Desert than there are grains of sand for which it is vague whether they are part of the Schmahara Desert.

Because it is vague as to whether G* is part of the Sahara Desert, it is vague whether the Sahara Desert is bigger than the Schmahara Desert.

If it were clearly the case that the Sahara Desert and the Schmahara Desert were identical, then it could not be vague as to whether the Sahara Desert is bigger than the Schmahara Desert.

So not (i).

So, (ii), it is vague whether the Sahara Desert is identical to the Schmahara Desert.

So, in general, it can be vague as to whether A and B are identical.