Mrs Fox's feelings

Basking in the warmth of Heaven, she floats weightless and naked, far far above the factory chimneys and church spires of the world, in the upper reaches of a sultry sky. It's an intoxicatingly fragrant atmosphere, surging and eddying with huge gentle waves of wind and pillowy clouds – nothing like the motionless, transparent oblivion she'd always imagined Paradise would be. It's more like a breathable ocean, and she treads the heavy air, narrowing the distance between her body and that of her man who's flying beside her. When she's close enough, she spreads her thighs, wraps her arms and legs around him, and opens her lips to receive the incarnation of his love.

Michel Faber, The Crimson Petal and the White, 671

Is very high credence belief?

Imagine holding an almost spherical die with thousands of tiny faces. Each of them is highly unlikely to end up on top when you roll the die. For each face, you have a very high credence in the proposition that it will not end up on top. But when one of them does end up on top, you would not be surprised.

When something that we believe turns out not to be the case, we are surprised. So you did not, for any of those faces, believe that it would not end up on top (you believed that it very probably would not). Very high credence is not belief (despite what many philosophers believe).

I see a red car outside my window, and I can see that its red colour is out there, where the car is. If you told me that the red colour that I was seeing was on the surface of the car, where its paint was, I would not believe you: your saying that would remind me that the red that I see is only in my perception, that it is not actually out there where the car is. Still, I would feel some surprise at that thought, for all that it would be a very familiar surprise. Even though I have a very low credence in the proposition that the red that I see is out there, where the car is, I cannot help believing, each time I look at the car, that its colour is out there. Seeing that it is out there is, at least momentarily, believing that it is out there. That is just the way my perception works. And yours? What about when you look out of a window. Consider any particular arrangement of cars, leaves et cetera that might be outside some window that you could easily get to. Presumably the chance of there being that particular arrangement is very low. You would be surprised if that was the view, were you to look out of that window.

It would be like putting a tiny red dot on one of the faces of that almost spherical die, rolling the die and seeing the red dot on top of it when it stops rolling.

Still, it would also be surprising if you had been able to imagine the view from that window in very much detail before you looked. So, suppose that you go to that window and look through it: you would probably have an unsurprising view. And you could then ask yourself whether you believed, before you looked, that that view was not going to be what you saw. Look now. I think that before you looked, if you did look, you did not believe that you would not have that view. Had you had such a belief, would you not have been much more surprised? Perhaps you were surprised (perhaps, for example, there was a red car there, and you were not expecting there to be one); but even then, your surprise would not, I think, have been like the surprise that we feel when something that we believe turns out not to be the case. It would be less, I think, than your surpise at the red of the car not actually being out there where the car is.

If I believed, of each of that die's faces, that it would not end up on top, then I would believe that none of them would end up on top.

That is how my beliefs appear to me (if I believe that an object is a car, and I believe that it is red, then I believe that it is a red car). How do yours appear to you? Beliefs are what they are, and what they are is not a million miles away from us. We can find out for ourselves what our beliefs are, our particular beliefs, and also beliefs in general (beliefs of various kinds) if we are philosophically inclined, and sufficiently logical. I wonder if philosophers who say that belief is very high credence are confusing belief with a mathematical model of belief.

Turri's Maxwell's Car

When Maxwell arrives at work in the morning, he always parks in one of two spots: C8 or D8. Half the time he parks in C8, and half the time he parks in D8. Today Maxwell parked in C8. It’s lunchtime at work. Maxwell and his assistant are up in the archives room searching for a particular document. Maxwell says, “I might have left the document in my car.” The assistant asks, “Mr. Maxwell, is your car parked in space C8? It’s not unheard of for cars to be stolen.” Maxwell thinks carefully for a moment and then responds, “No, my car has not been stolen. It is parked in C8.”

With that example, John Turri's "Epistemic closure and folk epistemology" post at the Certain Doubts blog began, and he went on to add that:

The epistemic closure principle says, roughly, that if one knows that P, and one knows that if P then Q, and one infers Q, then one knows Q.

Maxwell may have been misapplying logic, when he thought carefully: he recalled that he had parked in C8, rather than D8, and so he thought that his car was in C8 (unless it had, as his assistant noted, been stolen), from which he may have concluded that it was not stolen. (But perhaps he took the low chance of his car having been stolen to be reason enough to think that it had not been stolen. And for all we know the archive's windows looked down on C8.)

Most people think that Maxwell knew that his car was parked in C8 (assuming that it had not been stolen, etc.), but not that it had not been stolen, which contradicts Closure: if Maxwell knows that his car is in C8, and he knows that if his car is in C8 then it has not been stolen (he did seem to know that because he did seem to infer, from it being in C8, that it had not been stolen), then Closure says that Maxwell did know that his car had not been stolen.

Logically, if Maxwell's car was in C8, then it had not been stolen; and the whole point of logic is that logical reasoning takes us from knowledge to knowledge. So it seems to be logical, to go from Maxwell knowing that his car was in C8, rather than D8 (which I think he did know), to Maxwell knowing that his car was in C8 (which most people think he did know), to Maxwell knowing that his car had not been taken out of C8 (which most people think he did not know).

But of course, we can see from this example why that is invalid; and so we also have this insight into why skeptical scenarios are not threats to knowledge (and also why they are). If we are BIVs then we do not have real hands, so how can we know that we have real hands but not know that we are not BIVs? If we are BIVs then we think we have real hands (which is good enough for us BIVs).

50 senses of "know"

People say things like "I do not think it, I know it," thereby showing that saying that you know something is saying that you are sure of it. Are you, in effect, promising that what you say is true? Knowledge is like certainty, but some claims to knowledge do seem like gambles:

Consider a boy sitting an exam, a boy who is not sure of an answer but puts it down anyway, and suppose that it turns out to be correct. Would you say that he did not know the answer?

Still, knowledge is important because we want bodies of knowledge that can be relied upon. When cause for doubt about what philosophers take themselves to know is shown by skeptical scenarios, their natural reaction is to doubt that they did have knowledge. So the following definition has some intuitive plausibility:

Proposition P is known by subject S when S's justification for believing P guarantees that P is true.

How much of a guarantee S would need to provide might depend, for example, upon the kind of uses that such knowledge might be put to. But there are certainly a wide range of uses of "know": scientific knowledge, what we personally take ourselves to know, and everything in between. Perhaps philosophers can disagree about the meaning of "know" without any of them being wrong.

Gettier's Smith's Job

Smith applies for a job, as does X. Smith thinks that X will get the job, and knows that X has 10 coins in his pocket, so Smith thinks that the man who gets the job will have 10 coins in his pocket. As it turns out, Smith gets the job, and also has 10 coins in his pocket, and so his italicized belief was true. Since Smith was justified in thinking that X would get the job (his new boss had told him that X would get the job) his italicized belief was also justified; but, it was not knowledge, according to Gettier.

One problem with all of that is that it is a bit obscure what exactly is going on: there was a bit of inferring going on, and as a rule we cannot rely on such things as, for example, epistemic closure: If you know that P, and also that P implies Q, then even if you infer Q, you do not necessarily know Q (there was a good example by John Turri at Certain Doubts). Still, one thing is obvious: Smith's reasons for believing the italicized belief were no part of the reasons why it was true, and so it was not knowledge.

However, because those reasons turned out not to be that good (X did not get the job), there is also a question mark over whether they really were good enough to count as justification in the sense required for knowledge (only a question mark). A statement known to be false was always a statement that could have been false (that really could, not just could theoretically). When we think of knowledge we think of statements that can be relied upon, that are justified in ways that basically guarantee their truth.

Much Knowledge is Epistemic Luck

In a recent post (linked to here) I observed how we simply assume that we can refer directly to the things around us: we cannot know that their substances are not changing in ways that leave their properties the same, because we can only know their properties. Were their substances changing, reference to them would keep failing (assuming that reference is direct).
     And similarly, we cannot really rule out that we are Brains In Vats: all of our evidence is compatible with our brains having been harvested by aliens (in a real world where such aliens are common) and put into high-tech vats that simulate worldly experiences. While we are unlikely to have been harvested recently (as recently noted (although note that we cannot rule out as unlikely a world where are are frequently, but not too frequently, re-vatted)) it is not unlikely (by the standards of the apparent world) that there are such aliens (what is strange is that we see no aliens).
     But of course, we can and do simply assume that there are not such aliens, that we are not currently asleep in our beds and dreaming, that all of our particles are not always being switched with identical particles, and so forth. It is upon such foundations that our knowledge of the external world is built. And of course, we are not BIVs, we are not dreaming, and so on; or at least, I do assume not. And so we do have knowledge of the external world. But, because those are assumptions, such knowledge is epistemic luck.

Something like Fake Barns

What is adequate justification for holding a belief? It depends on one's context. A true belief that was well-justified when it was formed might cease to count as knowledge within a stricter setting, such as a court-room or a laboratory. And the famous Fake Barns involve unusual contexts. And of course, one needs to be sufficiently rational. Suppose that I see a red car, in a normal road (no fake cars), for example, and so form the belief that there is a red car. But, I also have a lot of irrational beliefs that there are various objects. When there is a red car, I believe that there is, and I am unlikely to have the belief that there is a red car if there is not a red car, although I am quite likely to have some belief that there is something when there is nothing. (It is easy to think of other examples of true beliefs that might seem at first glance to be justified but which do not count as knowledge because they are held by someone who is in some way unqualified.)

What Do Philosophers Do?

What do you know, for sure? Being sure that you have hands,
for example, could be justified ( you may be using them now,
to operate a phone or a keyboard), but you can hardly rule out
the following scenario, according to which you have no hands:

Your brain was recently harvested by aliens and you are now in a vat
experiencing a detailed simulation; your memories have been altered,
but for you "hand" still refers to things outside the vat. And out there,
those aliens have turned the real world into one enormous brain-farm.

You cannot rule that out,
but you can know that it is unlikely
that your brain was only recently harvested
and so you can, of course, know that you have hands.