Rocks are hardly immortal. But I see your point.

You lost me at a lizard having a 50% chance of being immortal.

Your Bayesian logic:

Justification-Socrates is probably a man (90%)
Justification-A man is probably mortal (90%)
Belief-Socrates is probably mortal (81%)

My Bayesian logic:

Justification-Socrates is probably a man (90%)
Justification-A man is probably mortal (90%)
Belief-Socrates is probably a mortal man (81%)

Justification-Socrates is probably not a non-man (10%)
Justification-A non-man might be mortal (50%)
Belief-Socrates is probably not a mortal non-man (5%)

Justification-Socrates is probably a mortal man (81%)
Justification-Socrates is probably not a mortal non-man (5%)
Belief-Socrates is probably mortal (86%)

Suppose I buy a lottery ticket and the next day I form the belief that the lottery ticket is a loser (even though I haven’t heard the news about whether it was a winner or loser yet). Now, I form this belief based on the probability that it will be a loser (And what a high probability it is!). If your thesis is correct and knowledge claims are simply reducible to claims about probabilities, then I should know that my lottery ticket is a loser.

The irony here is that you just did what you claimed I was wrong to say philosophers do: you just conflated “probably” with “certainly.” It is plainly false that a lottery ticket “is” a loser when it has a non-trivial probability of winning. It doesn’t matter how low that probability is–unless it’s so low the probability of there ever being any winning ticket in the lifetime of anyone holding any ticket for that draw is very small (as would be the case for a lottery ticket that is media-reported to have lost…I am not aware of that ever occurring in the history of contemporary lotteries). But of course we design lotteries specifically to have winners. So they actually have a very high probability of generating a winner.

Thus you do not “know” a ticket “is” a loser in this scenario. You only know it has a low probability of winning. If you play poker (and philosophers who screw up gambling analogies like you just did usually don’t) then you know the decision you have to make when you have a low probability of having a winning hand is not (A) “I’m going to lose, so I fold,” but (B) “can I afford to lose and still remain a reckonable player in this game, and if no, can I afford to go all in anyway,” because there is a chance you’ll win (otherwise the only rational choice would be (A) not (B)). So you calculate risk. That’s complicated. But it’s partly a function of the probability of losing and the amount you will lose (relative to what you have to lose). Thus, poker players holding “lottery tickets” don’t assume they have already lost. They assume they might yet win, and the only question is, is it worth the risk to find out. Which is entirely compatible with the belief “it is very improbable I will win.”

Case in point: I once was near the end of a poker game and faced very long odds against winning. Several players were showing extraordinary cards and I didn’t have much (just a low pair, not even enough to beat what was showing). But I could afford to lose and buy back in, so I went all in. I won. The other players had been bluffing, and my last draw gave me three of a kind. Obviously I did not do that believing I would lose. Why would I just surrender all my money knowing I was going to lose it? Obviously, though I knew I was almost certainly going to lose, I also knew there was a non-trivial chance I’d win, and I could afford to find out.

Now that we know how gambling knowledge actually functions in the real world, let’s see what happens to your argument…

After all, high probability is sufficient for an epistemic agent to know some proposition.

Which should teach you to stop being certain about things, not to treat probabilities as certainties.

You thus learned exactly the opposite lesson from this fact than you should have.

Everything is a question of risk management. Propositions you can afford to be false you don’t need to have sterling-high probabilities for; probabilities you can’t afford to be false you do need sterling-high probabilities for; and so on in between. Thus, I am comfortable saying I “know” things about ancient history when the probability is 95% or up. But I would never say I “know” my car is safe to drive when it had a 5% chance of exploding.

See the difference?

Our assertions of certainty are really declarations of risk (the probability is high enough to make the risk low enough for us to operate as though x is true). They are not actual assertions of certainty (that x will happen 100% of the time). It is philosophers (and ordinary people, too) who confuse the one for the other. As you keep doing, notably.

But if I can’t know that my lottery ticket is a loser, then knowledge cannot be reduced to claims about probability.

Notice how this conclusion only follows when you confuse probability assertions with certainty assertions–you thus just proved my point, in the very attempt to refute it.

Your example actually proves knowledge is an assertion of probability. The philosopher who claims to “know” he will lose the lottery is simply making a false statement. He has no such knowledge. Only a philosopher who claims to know he will probably lose the lottery is making a true statement.

Therefore, knowledge is reduced to claims about probability. By your own example!

But if your proposal is correct, then I’m asserting the exact same thing. That’s a little bizarre.

Only because you haven’t learned how to think like a gambler or a risk assessor. Gamblers and risk assessors don’t think this is bizarre at all. In fact, they understand that’s how everyone should be thinking–and how in actual practice they do think (by observing their behavior, the true tell–what people claim to be thinking or even think they’re thinking, psychologists long ago discovered, is often not true).

It’s everyone else whose intuitions are wrong. And as a philosopher, you should know never to trust your intuitions when there are experts in the matter to consult first. Talk to real world gamblers and risk assessors about your silly lottery cases and you’ll learn an important lesson: philosophy from the armchair is useless. You need to go talk to people who actually have the knowledge you lack before forming opinions about how things work.

S knows that p if and only if S believes that p, S is justified to believe that p, and p (is true?).

The problem with this is that such knowledge predominantly can never exist. S can never be justified in believing that p when p has any nonzero probability of being false, as almost all propositions about anything substantive do. Therefore, you just defined knowledge out of existence. The only things you can ever know by this definition are things that have no chance of being false, and that’s limited to present uninterpreted experience (“I see colors” vs. “I see a tree ten feet from me”).

So what’s the use of defining knowledge as something no one pretty much ever has or can have? That’s simply useless. Better to define it as something we do commonly have, and more importantly, as what people really mean when they go about their lives (by, again, observing them: hence you need to pay attention to the science of human behavior and decision making before making pronouncements about what they mean when they use words like “know”).

The reason this is so is simply because one can have a justified true belief, but still not have knowledge, since one’s justified true belief has an element of luck to it.

Why do you think that matters?

Imagine a world where the only way you ever acquire knowledge about anything is complete accident. Maybe you drank Harry Potter’s Felix Felicis potion and all lucky accidents go your way. You would quickly learn that what you know is nevertheless typically true. So you would call that knowledge and rely on it in every decision you make.

It simply does not matter how you come by knowledge, so long as it’s usually true. Thus, knowledge by accident is still knowledge.

The worry you may have is that we don’t live in a Felix Felicis world, so beliefs gained by accident will usually not be true, so you operate on the assumption that it won’t be, but that’s just another probability: it may have a low probability of being true, but that is still not zero. So it may yet be true. Why is it such a bad thing to simply admit that sometimes it’s true, and any decision we make based on a mistaken belief that it is true will be correct? You can’t say “because probably it won’t be true” because in Gettier cases it actually has a high probability of being true, because we followed a procedure that reduces the rate of error to something very low. We are therefore not trusting all accidental beliefs to be true. We are only trusting accidental beliefs to be true when they are very unlikely to be false–as when we follow a method that makes the probability of being wrong very low. As has to be the case in Gettier examples (e.g. we have to have a very low probability of being wrong about any false belief used as a premise in a Gettier case, otherwise we would not be justified in believing those premises, and thus neither the conclusion).

So I don’t see any problem here. It’s really just a matter of arbitrary taste or convenience whether you include Gettier knowledge as knowledge.

Now, your other suggestion was to simply change the definition, or add an additional condition that one can’t be epistemically lucky, or the condition that the belief is “not generated by random chance.” But this seems trivial and circular.

All definitions are circular. By definition.

It’s non-informative, and doesn’t really tell us anything interesting.

Definitions never inform you of anything other than what a term will refer to when you use it. My definition does that. And being the only information a definition can ever convey, it cannot be accused of being non-informative.

And yet it does tell you something interesting: that when I use that definition, I am including accidental true beliefs as knowledge, and more generally, that an accidental true belief can exist, and English speaking people can sometimes call it knowledge. That’s three very interesting things.

I think most philosophers agree that there is a condition like that, but they aren’t sure…what sort of factors would eliminate a belief being generated by random chance.

You don’t ever eliminate a belief being generated by random chance. What you do is reduce its probability. As long as you follow any reliable method, which by definition is a method that makes your chances of being wrong very low (as low as you need to accept the consequent risk of being wrong), you accept the product as knowledge (“x is very probably true”). That sometimes the method will fail and x will be true anyway is irrelevant to that conclusion. Indeed, it actually entails that a proposition is slightly more likely to be true than what any reliable method tells you it is, because some of the probability space occupied by failures is actually taken up by successes (accidentally true cases), so that when the probability that x is true is determined to be 99% on method z because z fails only 1% of the time, the probability that x is true is actually slightly greater than 99%, when we account for adding the very small number of cases when x will be true even when z fails. But when we exclude accidental true beliefs from knowledge, we simply stick with the 99% determined by z, and don’t add the very small number of cases when x will be true even when z fails. Even though, on a straightforward utility equation, we should. Because true is true, and the consequences of x being true will be the same regardless of how we came by believing it.

And that is very interesting indeed.

I also have some small quibbles with the cognitive thesis that we have entire lexicons in our brains, but I will leave that for now.

Of course, you should not take that as saying we have alphabetized codices in our brains. Our brains are organized differently than book technology. But if we know what any word means, that means there is a brain circuit tying a sound (the heard word) to a network of other circuits that code for what the word can refer to, which is the meaning of the word (everyone’s codebook will be a little different, e.g. what I imagine a generic tree to be will be different than you, what kinds of things I can recollect or creatively construct as a tree will differ, etc., but overlapping enough to make communication possible: see my discussion of semantics in Sense and Goodness without God, esp. II.2, pp. 27-48). If there are no reference circuits tied into a heard sound circuit, we don’t know what the word means–it’s not in our “lexicon.” If the heard sound is only tied into completely different circuits (e.g. the Chinese word that sounds like “lee” means nothing at all like what the English word “lee” means), then we do not have the same lexicons in our brains. And so forth. Learning a language involves trying to tune our lexical reference circuits to be as similar to our peers’ lexical circuits as possible, and the more dissimilar they are, the less able we will be to communicate with them (we will often say things they misunderstand as something else, and they will often say things we misunderstand as something else; the goal is to reduce those communication errors, and the only way to do that is to try and get the reference circuits as close as possible, which of course our brains evolved to do autonomically, although there are actions we can consciously take to help–hence that technological invention called a language immersion course).

Interesting read. You suggest two possible ways to reply to Gettier cases. I have worries for both, so the following will be the reasons I think your proposals don’t work (or are at least unsatisfying to this philosophy student).

Your first suggestion is to simply argue that justified true belief is knowledge, full stop. You suggest that when one has a belief, one forms a belief about probabilities. You appear to imply, if I understand you, that knowledge claims are reducible to claims about probabilities. As you state:

“By similar logic, if I use a belief-forming method that is highly reliable, let’s say it produces conclusions with 99.99% certainty, I can say I know that any x produced by that method has a 99.99% chance of being true, yet if that method had a flaw–a flaw that rarely affects its conclusions (hence the method’s high reliability)–which resulted in my mistakenly believing my car was in my garage when in fact indeed it was in my garage, I can still legitimately say I know there is a 99.99% probability that my car is in my garage. Because that is entailed by the method’s reliability, which measure of reliability already includes a full accounting of any such flaws (like being accidentally correct). This is less disturbing.”

You also say that philosophers tend to confuse “I know that x is probably true” with “I know that x is true.” And then state, “even though the latter, in all practical respects, is either saying the same thing as the former, or else can never actually be true–because it then would translate as “I know the probability of x is 100%,” which is knowledge no one ever has about anything (other than immediate uninterpreted experiences, but that’s not what we usually need to know).”

Okay, I have two problems with this suggestion. Firstly, I think philosophers do not generally confuse the two. There are reasons some philosophers don’t like to reduce knowledge claims to claims about probabilities, but these reasons are separate from worries about Gettier cases. What are their reasons? Because of well known (perhaps notorious) lottery cases. Suppose I buy a lottery ticket and the next day I form the belief that the lottery ticket is a loser (even though I haven’t heard the news about whether it was a winner or loser yet). Now, I form this belief based on the probability that it will be a loser (And what a high probability it is!). If your thesis is correct and knowledge claims are simply reducible to claims about probabilities, then I should know that my lottery ticket is a loser. After all, high probability is sufficient for an epistemic agent to know some proposition. But, as many philosophers agree, nobody knows their lottery ticket is a loser, even if there is a high probability that it is a loser and the lottery ticket actually ends up a loser. But if I can’t know that my lottery ticket is a loser, then knowledge cannot be reduced to claims about probability. Therefore, knowledge cannot be reduced to claims about probability.

Timothy Williamson also has a brilliant analysis regarding assertion and knowledge and makes this same point. He argues that when we assert something, we are claiming to know something, but knowledge is not reducible to reasoning based on high probabilities (because of lottery cases).

So, according to Williamson, when I properly assert, “your car is in the garage,” I am expressing an epistemic state: that I know that your car is in the garage. Given proposal of knowledge, and if we assume Williamson is right, then when I assert, “your car is in the garage,” I am expressing a belief about probabilities. But, intuitively I’m not expressing a belief about probabilities. There is a world of difference between what I am expressing when I assert “your car is in the garage,” and what I am expressing when I assert “the probability that your car is in the garage is x.” But if your proposal is correct, then I’m asserting the exact same thing. That’s a little bizarre. So, if we accept Williamson’s analysis of assertion and knowledge, I suspect there will arise some difficulties for your proposal.

Secondly, the Gettier cases are generally understood as good counter examples to any analysis of knowledge that argues that knowledge is justified true belief. Or, to present the jtb theory of knowledge more formally,

S knows that p if and only if S believes that p, S is justified to believe that p, and p (is true?).

The reason this is so is simply because one can have a justified true belief, but still not have knowledge, since one’s justified true belief has an element of luck to it. So, justified true belief is not sufficient for knowledge. Hence, the analysis fails. Now, Gettier himself seems to imply that one should just come up with some other non-trivial condition or definition for knowledge, but most have failed.

Now, your other suggestion was to simply change the definition, or add an additional condition that one can’t be epistemically lucky, or the condition that the belief is “not generated by random chance.” But this seems trivial and circular. It’s non-informative, and doesn’t really tell us anything interesting. I think most philosophers agree that there is a condition like that, but they aren’t sure what exactly that means, and what sort of factors would eliminate a belief being generated by random chance.

So, the worry is this: your first proposal seems false or at least has some pretty significant arguments and problems against it, and your second proposal seems trivial.

I also have some small quibbles with the cognitive thesis that we have entire lexicons in our brains, but I will leave that for now.

Cheers,

Ray

I didn’t think I was disagreeing with you – just giving another example of a natural-seeming redefinition whose “consequences might be problematic”. But I will actually agree with sawells (tongue in cheek?) suggestion if I am allowed to assert that one is never justified in believing a falsehood.

In fact, I do think that the definition of “justified” is the crux of the problem of knowledge and agree with Ayer’s claim that it “is to be decided, if at all, on grounds of practical convenience”. The right to be sure “may be earned in various ways; but even if one could give a complete description of them it would be a mistake to try to build it into the definition of knowledge”. (And it was seven years before Gettier that Ayer also wrote “If a witness is unreliable, his unsupported evidence may not enable us to know that what he says is true, even in a case where we completely trust him and he is not in fact deceiving us.”)

ok That’s good. Indeed you are right that, since p=>p, “true belief based on sound reasoning” includes just “true belief” itself as a special case (though I don’t think they are exactly equivalent). So I guess I will have to think harder about what you mean by “not arrived at accidentally”.

Not really. Because “based on sound reasoning” is simply synonymous with “valid and true” reasoning (since “sound” simply means “validly based on true premises”) and thus you are just replacing “justified true belief” with “true belief.” Which fails to work because you can’t tell which beliefs are true or not without justification, and as soon as you add back in “justification” as a separate thing from truth, you reintroduce the possibility of accidental knowledge. This is what Zagzebski demonstrates. Thus, we have to specify that accidental knowledge won’t be counted as knowledge. This does mean that what we accidentally know will still be true, but when we discover that we “knew” it only accidentally, we will say we never really knew it, that we only knew it accidentally. The alternative is to simply admit that we did know it. That it was accidentally justified and true then can be said to make no difference. And the choice between them is largely arbitrary, a matter of either taste, or what you want to pragmatically do with the words “know” and “knowledge.”

Semantic tricks can’t escape propositional logic. Redefining “flat” would simply avoid answering the question, by pretending I asked a different question (one using “flat” in your new way, instead of the way I was using it) and then answering that one, instead of answering the question I actually asked.