## Tuesday, January 19, 2021

### Sheep in sheep's clothing

Suppose you know the following facts. In County X, about 40% of sheep wear sheep costumes. There is also the occasional trickster who puts a sheep costume on a dog, but that’s really rare: so rare that 99.9% of animals that look like sheep are sheep, most of them being ordinary sheep but a large minority being sheep dressed up as sheep.

You know you’re in County X, and you come across a field with an animal that looks like a sheep. There are three possibilities:

1. It’s an ordinary sheep. Probability: 59.94%

2. It’s a sheep in sheep costume. Probability: 40.06%

3. It’s some other animal in sheep costume. Probability: 0.10%.

You’re justified in believing that (1) or (2) is the case, i.e., that the animal is a sheep. And if it turns out that you’re right, then I take it you know that it’s a sheep. You know this regardless of whether it’s an ordinary sheep or a sheep in sheep costume.

But now consider County Y which is much more like the real world. You know that in County Y, only about 0.1% of sheep wear sheep costumes. And there is the occasional trickster who puts a sheep costume on a dog. In County Y, once again, 99.9% of animals that look like sheep are sheep, and 99.9% of those are ordinary sheep without sheep’s costumes.

Now you know you’re in County Y and you come across an animal that looks like a sheep. You have three possibilities again, but with different probabilities:

1. It’s an ordinary sheep. Probability: 99.80%

2. It’s a sheep in sheep costume. Probability: 0.10%.

3. It’s some other animal in sheep costume. Probability: 0.10%.

In any case, the probability that it’s a sheep of some sort is 99.9%. It seems to me that just as in County X, in County Y you know that what you’re facing is a sheep regardless of whether it’s an ordinary sheep or a sheep in sheep costume.

But if what you’re facing is a sheep dressed up as a sheep, then you are in something very much like a standard Gettier case. So in some standard Gettier cases, if you reason probabilistically, it is possible to know.

Bill Seager said...

Couldn't you use an analogous argument to show that if I hold
a losing lottery ticket (prior to the lottery) I can *know*
I will lose. We have a losing lottery ticket with genuine
losing number, a losing lottery ticket with a tag over
the number with another losing number, and a winning
lottery ticket with a tag over it with a losing number.
(Once the lottery happens the tags can be removed say).

Dan said...

You say 'In any case, the probability that it’s a sheep of some sort is 99.9%. It seems to me that just as in County X, in County Y you know that what you’re facing is a sheep regardless of whether it’s an ordinary sheep or a sheep in sheep costume.'

Are you claiming that if 'X is the case' is 99.9% probable then you know 'X is the case'?

So everyone who ever bought a national lottery tickets knows they have lost. Even though obviously, some dont loose.

I would have thought it is only if I cannot see how it can be other than that I am 100% confident that X is the case, that I can say I have knowledge.

It may turn out I am mistaken - that there was some way X is not the case. But I dont realise that when I declare that I have knowledge. In this example I may test the fur of the sheep and find sheep DNA and declare 'I now know its a sheep' because I dont realise it may be a dog wrapped in the skin of a sheep. But if I know that there are dogs wrapped in sheep skin around, then I wont declare knowledge without checking whether this creature is a dog wrapped in fur or not. The DNA test on the fur will not be sufficient for me.

Leon Leontyev said...

I think we can resist the conclusion by pointing out a subtle difference between the two scenarios. In the scenario where 40% of sheep wear sheep's clothing, a very large percentage of animals that wear sheep's clothing are sheep. Not so in the second scenario: only 50% of animals that wear sheep's clothing are sheep. On this basis I think we can say that if you encounter a sheep in sheep's clothing in the first case you (still) know it's a sheep, but if you encounter a sheep in sheep's clothing in the second case you don't know it's a sheep. In both cases you're justifiably highly confident it's a sheep, but only in the first case are you justifiably highly confident it's a sheep conditional on it being in sheep's clothing.

Alexander R Pruss said...

I do think that if you in fact have a losing ticket, then you know it. And if you have winning ticket then you can justifiably, but incorrectly, think you know you have a losing ticket.
I think the only good way to deny knowledge in lottery cases is to demand infallibility from knowledge, which than loses us pretty much all ordinary knowledge.

Alexander R Pruss said...

Mr Leontyev:

I agree that there is such a difference, but I do not know that it makes a difference to knowledge. Here is, perhaps, a reason for thinking this difference makes a difference with respect to knowledge. In X, finding out that the animal facing you is wearing a sheep's costume would leave you still with a high probability that it's a sheep, while in Y, finding that out would leave you with only 0.5 probability that it's a sheep.

So, in Y there is some feature F--namely, wearing a sheep's costume--such that of the things that look like sheep and have F, equal numbers are dogs and equal numbers are sheep. So if you found out that the animal in front of you has F (say, by asking an honest and well-informed person: "Does this animal have F?"), you would lose your rational belief that it's a sheep.

Does the existence of such a feature F make any difference? I don't think so. In X, there is presumably such a feature, too. For instance, suppose your sheep is Dolly and one of the dogs dressed as a sheep is Rex. Then let F* be the disjunctive feature: is Dolly or Rex. Equal numbers of the things that look like sheep and have F* are sheep and are dogs. So if you found out that the animal in front of you has F* (say, by asking an honest and well-informed person: "Does this animal have F*?"), you would lose your rational belief that it's a sheep.

You might say that the fact that F* is a disjunctive feature makes X not be parallel to Y. But there is probably some non-disjunctive feature that would work as well as F*. For any two ordinary objects A and B in a finite set S, if we search long and hard enough we will very likely find something non-disjunctive that A and B have in common with each other but not with anything else in S. Maybe both Dolly and Rex have owners with initials "LL" and none of the other animals do; or maybe Dolly and Rex have the same length of tail up to some precision and none of the other animals do; or maybe they are both born on January 14; or maybe.... There are so many non-disjunctive properties that it is very likely that eventually we will find one that both Dolly and Rex have, and that none of the other animals do. Then call that property F* and run my argument with it.

Leon Leontyev said...

Mr Pruss:

My response is this. The dialectical relevance of the difference between X and Y that I pointed out is not that in Y there is some feature F such that of the things that look like sheep and have F, equal numbers are dogs and sheep, whereas in X there is no feature with such proportions. I take it that this is what you took me to mean since otherwise, pointing out that there is such a feature in X, namely F*, is of no relevance. Rather, the dialectical relevance of the difference between X and Y is that in X the feature F is such that of the things that look like sheep and have F, the vast majority are sheep, but in Y, F is not such (only half are sheep). Put another way, that a creature has F is strong evidence in X, but not in Y, that the creature is a sheep. (It seemed to me like you initially correctly identify the dialectical effect of my objection, but then your response committed you to a different interpretation of my objection).

Still one might wonder, why is it relevant that in X, but not in Y, the proposition that the creature has F is strong evidence that the creature is a sheep? After all, there is another property G, namely looking like a sheep, such that having G is strong evidence of being a sheep in both X and Y, and your belief in both scenarios is based on G. Here is a plausible test for knowledge:

Step 1. Consider the most psychologically proximal explanation for the agent's belief in a particular case. Typically this will be some phenomenal property or state, such as a thing visually appearing to be a sheep, or another belief. Step 2. Find the external property (if there is one) that best explains being in this psychological state from step 1 (if there is no such property go to step 3). In *normal* cases of knowledge (so neither of your cases X and Y), this will typically be the property that one has come to know. For example, in normal cases of knowing that this is a sheep, it being a sheep is what best explains it visually appearing to be a sheep. In case X, it wearing a sheep's costume is what best explains it looking like one. Step 3. Ask, in what proportion of relevant cases is the explanatory state compatible with the agent's belief? If that number is high enough then the agent knows. That number is high enough in X, but not in Y. Importantly, the property of being Dolly or Rex, while it does explain why the thing looks like a sheep, doesn't explain it best. Indeed, being Dolly or Rex explains why the thing looks like a sheep only because Dolly and Rex are wearing a sheep costume.

This method may need some refining (don't think it works in the fake barn case, for instance), but I think it's on the right track.

Alexander R Pruss said...

I don't see why Step 2 is relevant. Our probabilistic reasoner is not employing inference to best explanation: they aren't reasoning: "It looks like a sheep, so probably it's a normal sheep looking like a sheep." They are, instead, reasoning purely probabilistically: "It looks like a sheep, and 99.9% of the things that look like sheep are sheep." That's why they assign credence .999 to its being a sheep in Case Y. If they went through the "normal sheep looking like a sheep" inference, they would have only assigned credence .998 to its being a sheep. Their .999 credence already takes into account the fact that some of the sheep that look like sheep are dressed-up sheep.

Consider also Case Z. In Z, in the morning things are like in Y and in the evening things are like in X. Thus, in the morning, 0.1% of the sheep wear sheep costumes. In the evening, 40% of the sheep wear sheep costumes. Moreover, let's suppose that if a sheep wears a sheep costume in the morning, it does so in the evening, too. Alice comes by in the morning and sees Dolly looking like a sheep, but alas Dolly is a sheep in sheep's costume. On your view, Alice doesn't know that Dolly is a sheep. Bob comes by in the evening and sees Dolly looking like a sheep, and Dolly is still a sheep in sheep's costume. On your view, it seems that Bob knows that Dolly is a sheep. Now imagine that Alice comes back in the evening and sees Dolly. Surely when Alice comes back in the evening, she knows whatever Bob knows. So if Alice comes back in the evening, she learns that it's a sheep. But how can that be? After all, already in the morning she knows exactly what she will see in the evening: she will see Dolly looking like a sheep.

Alexander R Pruss said...

(I'm assuming Alice knows it's the same sheep. Maybe she knows this farmer owns only one sheep.)

Leon Leontyev said...

The reason step 2 matters is because we're assessing for knowledge, not just justification. Moreover, none of the steps are intended from the agent's point of view; the agent isn't expected to reason from best explanation. Gettier cases show us that not all evidential states that confer justification confer knowledge. The test is intended to separate those that do confer knowledge from those that merely confer justification.

Z is of course a very tricky case, but if there are Gettier cases then it is possible to learn things that one previously only justifiably believed. Let's examine why you take issue with that.

"So if Alice comes back in the evening, she learns that it's a sheep. But how can that be? After all, already in the morning she knows exactly what she will see in the evening: she will see Dolly looking like a sheep."

Compare: I set my alarm for 6am and go to sleep. In the morning the alarm wakes me up and I learn that it's 6am. But how can that be? After all, last night I knew exactly what I will hear in the morning: I will hear the alarm.

You might reply "that's a temporal fact! In case Z all the relevant facts that Alice knows in the evening are eternal."

That's not quite so. That Dolly is a sheep is eternal. That Dolly looks like a sheep is (relative to the duration of the case) eternal. There is, however, something that Alice comes to know in the evening, that she didn't know in the morning, and that she knew she would come to know. She learns that if Dolly is in a sheep's costume then Dolly is a sheep. She didn't know this in the morning because, in the morning, her confidence that Dolly is a sheep conditional on being in a sheep's costume was only a half. She knows it in the evening because her confidence that Dolly is a sheep conditional on being in sheep's costume is now very high. And she knew in the morning that her confidence in the evening that Dolly is a sheep, conditional on being in sheep's clothing would be high. (There are, of course, tricky issues surrounding probabilities of conditionals and conditional probability, but I hope whatever your view on that there is a way to massage the point that you will assent to). Since some sheep go in and out of their sheep's costume, Alice would treat "being in a sheep's costume" to be a temporal predicate, even though Dolly is always in a sheep's costume.

Of course you may not think that learning this fact is relevant, but at least I've identified something that Alice learns, and that she knew she would, contrary to what you thought.

Alexander R Pruss said...

It seems that if you know that you will know p, then you are already in a position to know p (assuming p is a tenseless proposition).

Imagine it's evening. Alice walks blindfolded to the field. She is about to take off her blindfold in order to learn whether Dolly is a sheep. But she already knows what things will look like when she takes off her blindfold. What's the epistemic point of taking off the blindfold, then?

Moreover, if we time index, as I think we should, your conditional "if Dolly is in a sheep's costume, then Dolly is a sheep" becomes two conditionals:
1. If Dolly is in a sheep's costume in the morning, then Dolly is a sheep.
2. If Dolly is in a sheep's costume in the evening, then Dolly is a sheep.
Alice already knows (2) in the morning. So I don't see anything for her to learn.

Here's another plausible principle: One does not gain any knowledge by gaining evidence one already knew with certainty. But in my setup, Alice in the morning knew with certainty that Dolly would look like a sheep in the evening.

It seems to me that the best way to get out of my argument is to deny purely statistical knowledge. This denies knowledge in lottery cases and in X. But once one accepts that there is knowledge in lottery cases, I think one should accept what I say.