I've talked about Gettier before and much of what I say here will overlap with what I've already said. It turns out I'm much more comfortable lecturing on something if I write about it the night before. Hopefully this won't always be the case 'cuz it takes up a lot of time...
Why Should You Care About Gettier?
You should care about Gettier because he showed that (so far) there is no coherent definition of knowledge. Why should we care about defining knowledge anyway? Well, because conceivably, there's a difference between simply believing something and knowing something. What might the difference be? What does it mean to "know"? Since the ancient Greeks all the way up until 50 years ago to know something meant 3 conditions were met:
(1) The subject believes p.
(2) The subject is justified in believing p.
(3) P is true.
These 3 conditions for knowledge are collectively known as the justified true belief theory of knowledge (JTB). Sounds pretty plausible right?
Lets look at counter example to the JTB theory or, as they are now called, Gettier cases:
Gettier Case 1
Suppose Smith and Jones apply for the same job. When he goes to the bathroom, Smith overhears the boss say that Jones is going to get the job. Also, while in the waiting room Jones emptied his pockets and put all the contents on the table, counted them (there were ten coins) then put them back in his pocket. From this information Smith infers the proposition: "the man who will get the job has 10 coins in his pocket." From the available evidence, the proposition seems like a valid inference.
What actually happens is that Smith ends up getting the job. Now here's the crazy part: it turns out that, unbeknownst to himself, Smith also has exactly 10 coins in his pocket! Given what's happened, can we say that Smith knew that "the man who will get the job has 10 coins in his pocket?"
Lets see what the JTB theory says:
(1) Did he believe that the man who will get the job has 10 coins in his pocket? Yup.
(2) Was he justified in believing the man who will get the job has 10 coins in his pocket? Yup.
(3) Is it true that the man who will get the job has 10 coins in his pocket? Yup.
So it seems that according to the JTB theory Smith knew that the man who will get the job has 10 coins in his pocket but something isn't quite right! Lets look at one more example before we figure out what's gone wrong:
Gettier Case 2
Bob has a friend, Jill, who has driven a Buick for years. Bob therefore thinks that Jill drives an American car. He is not aware, however, that her Buick has recently been stolen, and he is also not aware that Jill has replaced it with a Pontiac. Does Bob really know that Jill drives an American car or does he only believe it?
Lets see how the JTB theory handles this:
(1) Does Bob believe that Jill drives an American car? Yup.
(2) Is Bob justified in believing that Jill drives an American car? Yup.
(3) Is it true that Jill drives an American car? Yup.
According to the JTB theory Bob knows that Jill drives an American car. But something doesn't seem right about that. It looks like he just happened to have gotten lucky.
Lets figure out what's going wrong in these cases.
Why Gettier Cases Happen:
Gettier cases happen because of our acceptance of two assumptions about justification.
Assumption 1: It's possible to have a justified belief that turns out to be false. For example, when I'm at work I can assume that my car is where I left it because I remember parking it and I saw it in its spot as I walked to my building. Of course it could happen that someone steals my car or that it gets towed. The fact that my belief about my car's location turns out to be false doesn't undermine the fact that I was justified in believing it was where I parked it.
Assumption 2: It's possible to make valid inferences from one justified belief to another. For example, if I'm justified in believing it's raining then I can make the inference that there are clouds. Since the initial belief (it's raining) is justified the inferred belief (there are clouds) is also justified. In fancy talk: If I know that P entails Q and P is justified then I'm also justified in believing Q.
Rejecting (2) would make life really difficult and if logic is to have any value, we need to keep (2).
To see how the interaction of these 2 principles causes Gettier cases lets take a look at an example from Dretske.
Example 3:
Suppose you see a stack of your friend's (John) mail. The address is in San Francisco. You reasonably apply assumption 1 and form the belief that John lives in San Francisco. It turns out however that he lives in LA. The fact that your belief about where he lives is false doesn't mean you aren't justified in believing he lives in SF. Based on your false belief that he lives in SF you make a valid inference and form a new belief: John lives in California. This is a perfectly valid inference. Now, you have a justified (via assumption 2) true belief about where John lives. However, you reached your belief that he lives in California through the false belief that he lives in SF so you don't really know he lives in California. The inference from the false belief is what undercuts our ability to call the belief "knowledge". The JTB fails to capture what we mean by "knowledge".
Attempted Rescue of the JTB Theory:
In example 3 what prevents us from calling the belief that John lives in California knowledge is the inference from a false belief (John lives in SF). In example 1, the belief that "the man who has ten coins in his pocket will get the job" isn't knowledge because it is inferred from the false belief "Jones is going to get the job." In example 2, the belief "Jill owns an American car" isn't knowledge because because it's inferred from the false belief that Jill owns a Buick.
Do you see the solution? All we need to do is add a 4th condition to the JTB model. Now, a person knows p when she:
(a) has the belief that p;
(b) is justified in believing p;
(c) p is true; and
(d) p isn't inferred from a false belief.
Ta da! So long as all four conditions are met, we can say that a person knows p.
Ut oh! Party Time!
In my other life I'm a party planner. Every month I plan a wonderful party. The thing is I need to know which room to rent for the party. My decision is based on how many attended the previous month's party. If there are fewer than 40 people at this month's party I rent the standard room. If there are 40 or more then I rent the large room.
I ask my assistant: how many people attended this month? He says 78. I then make the inference from the belief that 78 people attended to the belief that I will need to rent the large room. This seems like a legitimate inference, right? 78 is definitely greater than 40. But hold on a tick. It turns out my assistant miscounted. There were only 77 guests. I've just made an inference from a false belief (i.e., violated condition (d)) yet it seems as though we can say that I know I will need to rent the large room.
Not So Fast!
Hold on to your horses. There's something fishy going on here. Yeah, OK, strictly speaking you made an inference from a false belief but there was an implied probability judgement. You know that the margin of error of your assistant's counting is large enough not to matter for the inference; that is, the likelihood of him miscounting by a margin of 35% is very small. In other words, if the counting is off by a bit it's not going to affect the truth of the inferred belief (in this case that I'll need a large room). Lets add our 5th condition to the JTB theory:
(e) p has to have a sufficiently high probability of truth in order to count as knowledge.
Who's a Loser Now?
So it looks like we've got our theory of knowledge all figured out. As long as p meets all 5 conditions then we can count it as knowledge. Lets take a closer look at the 5th condition and see if it stands up to scrutiny:
The fifth condition is that in order for p to count as knowledge, in addition to the previous 4 conditions it also must have a sufficiently high probability of truth. Might there be a counter-example?
Suppose there is a lottery with 1 billion tickets. There's a 1/1 000 000 000 chance that ticket 0 000 000 000 will win. There's the same chance that ticket 0 000 000 001 will win. Of each ticket it's reasonable to say that you believe they won't win. There is a very high probability that ticket 0 000 000 000 won't win but could you say that you know that it won't win? It seems that no matter how great the odds that it won't win, you can't say that you know it won't win. It appears as though we have constructed a counter-example to (e): Even though there is a very high probability that "I won't win" is true I can't say that I know I won't win.
Ok, Lets Try A Different Approach
As I mentioned at the beginning of the article, the cause of the problem for the JTB theory is not that we need additional conditions rather that we have accepted assumptions 1 and 2. So why don't we reject one or both of them?
Lets Reject the Idea that It's Possible to Have a Justified Belief that Turns out False
Well, first of all, we already saw what happens if we do this: We end up like Descartes rejecting everything except for the fact that we exist (without a body). Basically, what happens is that the only types of justifications that count are one's where the p couldn't possibly turn out false. That's not going to work too well or at least make knowledge very difficult to come by.
Consider the John in California example. If we reject assumption 1 then based on the fact that all John's mail is addressed to SF we can no longer say that we are justified in believing he lives in SF. This seems a bit counter-intuitive. How much evidence would we need before it would be impossible for the belief to turn out false? Aside from the practicality issue, this course seems implausible.
Showing posts with label Gettier. Show all posts
Showing posts with label Gettier. Show all posts
Thursday, September 11, 2014
Thursday, September 12, 2013
Gettier: The Challenge to the Traditional Conception of Knowledge
Introduction and Context
Gettier's "Is Justified True Belief Knowledge?" is considered to be one of--if not the most--important articles of 20th Century philosophy. Pre-Gettier, the standard definition of knowledge (since at least Aristotle) was "justified true belief". Pretty much everyone we've studied so far held this account of knowledge to be correct (with the exception of Goldman who wrote post-Gettier and was focused only on justification). In his groundbreaking article, G-money provides several counter-examples to the long-standing traditional account. Let check it aus...
The Traditional (JTB) Account of Knowledge
At its core the traditional account of knowledge has 3 necessary and sufficient conditions:
S knows that p if and only if
(a) p is true,
(b) S believes that p, and
(c) S is justified in believing that p.
(Recall from the previous post that 'S' stands for 'any subject/person' and 'p' stands for 'any proposition/assertion that can be true or false, but not both.)
Gettier's Objective
Gettier's main objective is to show that the traditional conditions for knowledge in the JTB model aren't sufficient (aren't enough). In other words, in some cases, meeting the 3 conditions isn't enough for something to count as knowledge--there need to be additional conditions.
The Set Up: Why Gettier Cases Happen
Before looking at Gettier's actual examples, lets take a look at the general structure that will underpin his attack: Gettier cases (i.e. counter-examples to the JTB model) work against the traditional account of knowledge because of the interaction between 2 widely accepted epistemological principles. So long as we accept both principles, we'll end up with Gettier counter-examples to the JTB model.
The first principle is that (A) it's possible to have a justified belief that is false. Most people accept this. Often we have very good reasons for believing things that at some later point we learn to be false. The only way to reject this is to say that the only justified beliefs you can have are ones that, under no possible circumstances, will ever turn out to be false. Since all sorts of unexpected things can happen in life, this bar is too high for all but Descartes and his followers.
The second part of the set up involves an assent to logical inference. That is, most of us believe that (B) some beliefs can be justified by prior beliefs. A classic example would be
If I have good evidence for the belief that (p) it's raining, then I can infer that (q) there are clouds.
Or If if have good evidence for the belief that (p) Jill drives a Ford, then I can infer (q) that Jill drives an American car.
In cases where I know p, I can also be justified in knowing q. In other words, every time I have good reason to think p is true, I can legitimately infer that q will also be true. So, if I'm justified in believing p, and q obviously follows from p, then it seems I am also justified in believing q.
Let me repeat that cuz it's super important: If q clearly follows from p, and I'm justified in believing p, then it follows that I'm also justified in believing q.
The traditional account along with just about everyone, professional philosopher or not accepts that we can make legitimate inferences. What the Gettier cases show is that accepting both (A) and (B) gets us into trouble if we also want to hold on to the tradition definition of knowledge.
Case 1: The Oasis
Suppose we're walking in the desert. Up in the distance I see an oasis (this is the 'p'). I turn to you and say "there's an oasis over there." Now, since (p) I see an oasis, I make the inference from believing that I see an oasis to (q) there is an oasis "over there."
(If I see something, then I reasonably infer that it exists).
As it turns out, I'm actually seeing a mirage not an oasis. Now, here's the crazy part: just behind the dune I'm pointing at there is an actual oasis. So our situation is that I've met all the criteria for the traditional definition but I don't seem to have knowledge! Most people would say that I don't know there is an oasis over there. Consider
(i) I have a true belief (there really is an oasis "over there"--it's just not the one I think I'm seeing);
(ii) I believe that there is an oasis "over there" (I inferred it from the fact that I see an oasis which is actually a mirage);
(iii) I'm justified in believing there is an oasis "over there" (I don't know that I'm seeing a mirage rather than an actual oasis)
In this case, it looks like I have a bonafide justified true belief but we probably don't want to say that I know that there is an oasis over there. Oh! Snap!
Case 2: The Job and the Coins
Suppose Smith and Jones have applied for a certain job. Suppose also that Smith has strong evidence for the following proposition:
(d) Jones is the man who will get the job and Jones has 10 coins in his pocket. (This is the p)
Maybe Smith's evidence is that the owner of the company (who is also in charge of hiring) told him Jones would get the job. Also, Smith, himself, counted the coins in Jones' pocket while they were in the waiting room.
The next assertion (e) follows logically from (d) (in philosophy we say "it is logically entailed by d")
(e) The man who will get the job has 10 coins in his pocket. (This is the q. We can say that e obviously follows from d)
I don't think anyone would disagree that if we have strong justification for believing that d is true then we can also be justified in believing that e is true. Smith believes (e) and is justified in believing (e).
Now here's where it gets crazy again. Suppose that contrary to all the evidence that Smith had for Jones getting the job, Smith himself ends up getting the job. And, to top it off, Smith, unbeknownst to himself, (because he never bothered to count) also has ten coins in his pocket. This means that (e) is true (the man who got the job--Smith--has 10 coins in his pocket) even though (d) (from which (e) was inferred) is false!
How does this affect the traditional theory of knowledge? Well, it looks like
(i) Smith has a true belief (e)
(ii) Smith believes (e)
(iii) Smith is justified in believing (e) is true.
Even though all the conditions are met for the traditional definition of knowledge, we probably don't want to say that Smith knows. Why? Are intuitions tell us that well, the belief is only true by accident and so it shouldn't count Smith was justified in believing (e) because it obviously follows from (d), but that's not why (e) turns out to be true! But the traditional theory only stipulate that the 3 conditions be met--it doesn't say anything about how. So, this example seems to show that the traditional theory fails because we don't want to say that Smith really knew that the successful job applicant would have ten coins in his pocket.
Case 3: The Ford and Mr. Brown
Suppose that for the last 5 years, every workday, Jones has picked up Smith in a Ford to go to work. Most of us would agree that Smith is justified is believing that
(f) Jones owes a Ford.
Now suppose Smith has another friend named Mr. Brown. At random Smith selects 3 place names and constructs the following propositions:
(g) Either Jones owns a Ford, or Brown is in Boston;
(h) Either Jones owns a Ford, or Brown is in Barcelona;
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.
All of these (g, h, i) are entailed by (i.e., follow from) (f).
Wut? Hold the phone...how do (g, h, i) follow from (f)?...
Aside: Formal Logic
This particular examples requires a little bit of knowledge about formal logic. Don't be scurd. It's not as bad as you think. At first it seems weird to say that g, h, i are all follow from (f), but they do, and I'll explain.
Consider the following example:
I have 2 legs. It's true right? Now consider this next proposition:
I have 2 legs or I have 2 horns. Also true, right? Why?
In an "or"-statement (called a "disjunction" in fancy philosophy-talk), so long as one part is true, the whole statement is true. So, in this case, so long as it's true that I have 2 legs, it doesn't matter what I put on the other side of the "or" because the entire disjunction will still be true. For example, I can say "either the earth is a sphere or unicorns that fart rainbows exist". Because the first part of the disjunction is true, it doesn't matter if the second half is false (or true), the net result is the same; the entire disjunct is true. In a disjunction, only one side needs to be true for the entire disjunction to be true.
Ok, that should be enough to get us through the rest of this Gettier case...
Case 3 Continued
Now where were we? Oh, yes. We were saying that the disjunctions (g, h, and i) all obviously follow from (f). That is, if (f) is true, we can also infer that (g, h, and i) are also true because we know that one side of the disjunct is true (and that's all that's needed for the whole disjunction to be true). So long as we know that "Jones owns a Ford," it doesn't matter one hoot what we add to it in an "or" statement.
Smith could have said "Jones owns a Ford or sharktopus will eat every UNLV student." Since the "Jones owns a Ford" part is true, it doesn't matter about the truth of the sharktopus part--the entire disjunctive clause is still true as a whole.
The bottom line so far is that since Smith has strong evidence for (f), he can infer (g, h, i) and be justified in believing (g, h, i). Finally, we should note that Smith has no idea where Brown is. He just randomly picked places for (g, h, i).
Here comes the tricky part. Who needs the quickee-mart? Imagine two further conditions for our little situation. First, it turns out that Jones doesn't own a Ford! Unbeknownst to Smith, Jones sold his Ford yesterday and now drives a Prius. Second, it turns out that Brown is actually in Barcelona (the place in h)! It follows that (h) is true! (But not for the reasons that Jones thinks it is).
If these two new conditions are true then
(i) (h) is true (because Brown is in Barcelona not because Jones owns a Ford),
(ii) Smith believes (h) is true (but for the wrong reason--because he believes Jones owns a Ford),
(iii) Smith is justified in believing that (h) is true (because he had good evidence to believe that (f) Jones owns a Ford and (h) follows from (f)).
Again we have an example where someone has met the 3 traditional criteria for knowledge, yet we would not want to say that Jones knows that (h) either Jones owns a Ford or Brown is in Barcelona.
Possible Objections
One attempt to rescue the traditional model is to add a fourth stipulation. Notice that in Gettier's examples the problem seemed to be that an inference was being made from a false belief. So, in Case 1, we inferred "there's an oasis over there" from the false belief "I see an oasis." In case 2, we inferred that the man who got the job would have 10 coins in his pocket from the false belief that Jones, who has ten coins in his pocket, would get the job. In case 3, we inferred that either Jones owns a Ford or Brown is in Barcelona from the false belief that Jones owned a ford. In order to correct that problem, it seems we should add a fourth condition to the traditional model of knowledge:
(iv) S does not infer a truth from a falsehood.
Problem solved right? HA! This is philosophy!
Gettier Reply
Suppose I run an annual event and for planning purposes I need to know how many people attended this year so I can rent a room for next year. I really only care if there were more or less than 40 people. If it's more than 40 then I need to rent a big room, if it's less, then the standard room will do. I ask one of my co-organizers how many people attended the event. He says there were 78 people.
At this point it seems that I can legitimately make the inference from "there were 78 people" to "there were more than 40 people at the event"; i.e., I know there were more that 40 people. As it turns out, my co-organizer got it wrong, in fact, there were only 77 people. It still seems, however, that I am able to legitimately say that I know there were more than 40 people.
So? Well, this example shows that, contra (iv), you can make an inference from a falsehood and still have that inferred belief count as knowledge. Doh!
Counter-reply
But not so fast. When you inferred that there were over 40 people based on the co-organizer's assertion about 78 people, there's an implied probability judgment. You know that the probability of someone miscounting by about 35% is virtually impossible. You know that even if they're off by a few, there will still be more than 40 people and so the number the co-organizer cites doesn't have to be exact for you to make the inference. A proposition just has to have a high probability of being true. So, we add a fifth condition:
(v) p has to have a sufficiently high probability of truth.
Now we've got it! Right?
Getter Reply 2: Lottery Paradox
Suppose a billion ticket lottery. Of ticket number 0000000000 there's a 1 in a billion chance that it will win. So, you say (reasonably) that you believe it won't win. You can say the same of ticket 0000000001 that you believe it won't win either. In fact, you can say of every ticket that you believe it won't win. But if you bought a ticket and said I know this ticket won't win, people would say, no, you don't know that. One of the tickets will win. You have a very high probability belief that the ticket won't win, but you don't know that it won't win. This proves that, contra (v), you don't need to have a sufficiently high probability of truth for knowledge.
Anyhow, this back and forth can go on for a while, but in the end, philosophers have given up on trying to rescue the traditional model from Gettier by using extra conditions.
Conclusion: Why the Gettier Problem Can't be Overcome
As I said near the beginning (in the set up section), the production of Gettier cases relies on the acceptance of two principles: (A) You can be justified in believing something that turns out to be false, and (B) the justification of some beliefs can be other justified beliefs (i.e., we can make logical inferences).
Lets Try (A)
Any solution to the Gettier problem will involve rejecting one of these principles. Suppose, for example, to get out of the "oasis" problem, we reject (A). But now, if we actually see a real oasis, we can't say we know there's an oasis because there's always a chance (no matter how small) that it is a mirage or that we are hallucinating.
As the lottery paradox shows, it doesn't matter how small the chance is, we still can't say we know it's an oasis so long as there's an infinitesimal chance that we could be wrong. Well, rejecting (A) isn't going to work...how about (B)?
Lets Try (B)
Suppose, in order to escape the Gettier problems we reject (B). Recall, the problem arose because we made the inference from a false believe. Well, now we're just going to ban inferences. But if we do this, then if I actually do see a mirage I'm not allowed to make the inference that "there's a mirage over there"! And if Jones actually does get the job, Smith can't make the inference that "the man who gets the job will have 10 coins in his pocket." Well, that's gonna suck!
Because no one (except very extreme skeptics a la Descartes) wants to abandon either (A) or (B) philosophers have given up trying to rescue the traditional model of knowledge.
Holy crap! Progress in philosophy! (If you count discarding a theory as progress).
Gettier's "Is Justified True Belief Knowledge?" is considered to be one of--if not the most--important articles of 20th Century philosophy. Pre-Gettier, the standard definition of knowledge (since at least Aristotle) was "justified true belief". Pretty much everyone we've studied so far held this account of knowledge to be correct (with the exception of Goldman who wrote post-Gettier and was focused only on justification). In his groundbreaking article, G-money provides several counter-examples to the long-standing traditional account. Let check it aus...
The Traditional (JTB) Account of Knowledge
At its core the traditional account of knowledge has 3 necessary and sufficient conditions:
S knows that p if and only if
(a) p is true,
(b) S believes that p, and
(c) S is justified in believing that p.
(Recall from the previous post that 'S' stands for 'any subject/person' and 'p' stands for 'any proposition/assertion that can be true or false, but not both.)
Gettier's Objective
Gettier's main objective is to show that the traditional conditions for knowledge in the JTB model aren't sufficient (aren't enough). In other words, in some cases, meeting the 3 conditions isn't enough for something to count as knowledge--there need to be additional conditions.
The Set Up: Why Gettier Cases Happen
Before looking at Gettier's actual examples, lets take a look at the general structure that will underpin his attack: Gettier cases (i.e. counter-examples to the JTB model) work against the traditional account of knowledge because of the interaction between 2 widely accepted epistemological principles. So long as we accept both principles, we'll end up with Gettier counter-examples to the JTB model.
The first principle is that (A) it's possible to have a justified belief that is false. Most people accept this. Often we have very good reasons for believing things that at some later point we learn to be false. The only way to reject this is to say that the only justified beliefs you can have are ones that, under no possible circumstances, will ever turn out to be false. Since all sorts of unexpected things can happen in life, this bar is too high for all but Descartes and his followers.
The second part of the set up involves an assent to logical inference. That is, most of us believe that (B) some beliefs can be justified by prior beliefs. A classic example would be
If I have good evidence for the belief that (p) it's raining, then I can infer that (q) there are clouds.
Or If if have good evidence for the belief that (p) Jill drives a Ford, then I can infer (q) that Jill drives an American car.
In cases where I know p, I can also be justified in knowing q. In other words, every time I have good reason to think p is true, I can legitimately infer that q will also be true. So, if I'm justified in believing p, and q obviously follows from p, then it seems I am also justified in believing q.
Let me repeat that cuz it's super important: If q clearly follows from p, and I'm justified in believing p, then it follows that I'm also justified in believing q.
The traditional account along with just about everyone, professional philosopher or not accepts that we can make legitimate inferences. What the Gettier cases show is that accepting both (A) and (B) gets us into trouble if we also want to hold on to the tradition definition of knowledge.
Case 1: The Oasis
Suppose we're walking in the desert. Up in the distance I see an oasis (this is the 'p'). I turn to you and say "there's an oasis over there." Now, since (p) I see an oasis, I make the inference from believing that I see an oasis to (q) there is an oasis "over there."
(If I see something, then I reasonably infer that it exists).
As it turns out, I'm actually seeing a mirage not an oasis. Now, here's the crazy part: just behind the dune I'm pointing at there is an actual oasis. So our situation is that I've met all the criteria for the traditional definition but I don't seem to have knowledge! Most people would say that I don't know there is an oasis over there. Consider
(i) I have a true belief (there really is an oasis "over there"--it's just not the one I think I'm seeing);
(ii) I believe that there is an oasis "over there" (I inferred it from the fact that I see an oasis which is actually a mirage);
(iii) I'm justified in believing there is an oasis "over there" (I don't know that I'm seeing a mirage rather than an actual oasis)
In this case, it looks like I have a bonafide justified true belief but we probably don't want to say that I know that there is an oasis over there. Oh! Snap!
Case 2: The Job and the Coins
Suppose Smith and Jones have applied for a certain job. Suppose also that Smith has strong evidence for the following proposition:
(d) Jones is the man who will get the job and Jones has 10 coins in his pocket. (This is the p)
Maybe Smith's evidence is that the owner of the company (who is also in charge of hiring) told him Jones would get the job. Also, Smith, himself, counted the coins in Jones' pocket while they were in the waiting room.
The next assertion (e) follows logically from (d) (in philosophy we say "it is logically entailed by d")
(e) The man who will get the job has 10 coins in his pocket. (This is the q. We can say that e obviously follows from d)
I don't think anyone would disagree that if we have strong justification for believing that d is true then we can also be justified in believing that e is true. Smith believes (e) and is justified in believing (e).
Now here's where it gets crazy again. Suppose that contrary to all the evidence that Smith had for Jones getting the job, Smith himself ends up getting the job. And, to top it off, Smith, unbeknownst to himself, (because he never bothered to count) also has ten coins in his pocket. This means that (e) is true (the man who got the job--Smith--has 10 coins in his pocket) even though (d) (from which (e) was inferred) is false!
How does this affect the traditional theory of knowledge? Well, it looks like
(i) Smith has a true belief (e)
(ii) Smith believes (e)
(iii) Smith is justified in believing (e) is true.
Even though all the conditions are met for the traditional definition of knowledge, we probably don't want to say that Smith knows. Why? Are intuitions tell us that well, the belief is only true by accident and so it shouldn't count Smith was justified in believing (e) because it obviously follows from (d), but that's not why (e) turns out to be true! But the traditional theory only stipulate that the 3 conditions be met--it doesn't say anything about how. So, this example seems to show that the traditional theory fails because we don't want to say that Smith really knew that the successful job applicant would have ten coins in his pocket.
Case 3: The Ford and Mr. Brown
Suppose that for the last 5 years, every workday, Jones has picked up Smith in a Ford to go to work. Most of us would agree that Smith is justified is believing that
(f) Jones owes a Ford.
Now suppose Smith has another friend named Mr. Brown. At random Smith selects 3 place names and constructs the following propositions:
(g) Either Jones owns a Ford, or Brown is in Boston;
(h) Either Jones owns a Ford, or Brown is in Barcelona;
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.
All of these (g, h, i) are entailed by (i.e., follow from) (f).
Wut? Hold the phone...how do (g, h, i) follow from (f)?...
Aside: Formal Logic
This particular examples requires a little bit of knowledge about formal logic. Don't be scurd. It's not as bad as you think. At first it seems weird to say that g, h, i are all follow from (f), but they do, and I'll explain.
Consider the following example:
I have 2 legs. It's true right? Now consider this next proposition:
I have 2 legs or I have 2 horns. Also true, right? Why?
In an "or"-statement (called a "disjunction" in fancy philosophy-talk), so long as one part is true, the whole statement is true. So, in this case, so long as it's true that I have 2 legs, it doesn't matter what I put on the other side of the "or" because the entire disjunction will still be true. For example, I can say "either the earth is a sphere or unicorns that fart rainbows exist". Because the first part of the disjunction is true, it doesn't matter if the second half is false (or true), the net result is the same; the entire disjunct is true. In a disjunction, only one side needs to be true for the entire disjunction to be true.
Ok, that should be enough to get us through the rest of this Gettier case...
Case 3 Continued
Now where were we? Oh, yes. We were saying that the disjunctions (g, h, and i) all obviously follow from (f). That is, if (f) is true, we can also infer that (g, h, and i) are also true because we know that one side of the disjunct is true (and that's all that's needed for the whole disjunction to be true). So long as we know that "Jones owns a Ford," it doesn't matter one hoot what we add to it in an "or" statement.
Smith could have said "Jones owns a Ford or sharktopus will eat every UNLV student." Since the "Jones owns a Ford" part is true, it doesn't matter about the truth of the sharktopus part--the entire disjunctive clause is still true as a whole.
The bottom line so far is that since Smith has strong evidence for (f), he can infer (g, h, i) and be justified in believing (g, h, i). Finally, we should note that Smith has no idea where Brown is. He just randomly picked places for (g, h, i).
Here comes the tricky part. Who needs the quickee-mart? Imagine two further conditions for our little situation. First, it turns out that Jones doesn't own a Ford! Unbeknownst to Smith, Jones sold his Ford yesterday and now drives a Prius. Second, it turns out that Brown is actually in Barcelona (the place in h)! It follows that (h) is true! (But not for the reasons that Jones thinks it is).
If these two new conditions are true then
(i) (h) is true (because Brown is in Barcelona not because Jones owns a Ford),
(ii) Smith believes (h) is true (but for the wrong reason--because he believes Jones owns a Ford),
(iii) Smith is justified in believing that (h) is true (because he had good evidence to believe that (f) Jones owns a Ford and (h) follows from (f)).
Again we have an example where someone has met the 3 traditional criteria for knowledge, yet we would not want to say that Jones knows that (h) either Jones owns a Ford or Brown is in Barcelona.
Possible Objections
One attempt to rescue the traditional model is to add a fourth stipulation. Notice that in Gettier's examples the problem seemed to be that an inference was being made from a false belief. So, in Case 1, we inferred "there's an oasis over there" from the false belief "I see an oasis." In case 2, we inferred that the man who got the job would have 10 coins in his pocket from the false belief that Jones, who has ten coins in his pocket, would get the job. In case 3, we inferred that either Jones owns a Ford or Brown is in Barcelona from the false belief that Jones owned a ford. In order to correct that problem, it seems we should add a fourth condition to the traditional model of knowledge:
(iv) S does not infer a truth from a falsehood.
Problem solved right? HA! This is philosophy!
Gettier Reply
Suppose I run an annual event and for planning purposes I need to know how many people attended this year so I can rent a room for next year. I really only care if there were more or less than 40 people. If it's more than 40 then I need to rent a big room, if it's less, then the standard room will do. I ask one of my co-organizers how many people attended the event. He says there were 78 people.
At this point it seems that I can legitimately make the inference from "there were 78 people" to "there were more than 40 people at the event"; i.e., I know there were more that 40 people. As it turns out, my co-organizer got it wrong, in fact, there were only 77 people. It still seems, however, that I am able to legitimately say that I know there were more than 40 people.
So? Well, this example shows that, contra (iv), you can make an inference from a falsehood and still have that inferred belief count as knowledge. Doh!
Counter-reply
But not so fast. When you inferred that there were over 40 people based on the co-organizer's assertion about 78 people, there's an implied probability judgment. You know that the probability of someone miscounting by about 35% is virtually impossible. You know that even if they're off by a few, there will still be more than 40 people and so the number the co-organizer cites doesn't have to be exact for you to make the inference. A proposition just has to have a high probability of being true. So, we add a fifth condition:
(v) p has to have a sufficiently high probability of truth.
Now we've got it! Right?
Getter Reply 2: Lottery Paradox
Suppose a billion ticket lottery. Of ticket number 0000000000 there's a 1 in a billion chance that it will win. So, you say (reasonably) that you believe it won't win. You can say the same of ticket 0000000001 that you believe it won't win either. In fact, you can say of every ticket that you believe it won't win. But if you bought a ticket and said I know this ticket won't win, people would say, no, you don't know that. One of the tickets will win. You have a very high probability belief that the ticket won't win, but you don't know that it won't win. This proves that, contra (v), you don't need to have a sufficiently high probability of truth for knowledge.
Anyhow, this back and forth can go on for a while, but in the end, philosophers have given up on trying to rescue the traditional model from Gettier by using extra conditions.
Conclusion: Why the Gettier Problem Can't be Overcome
As I said near the beginning (in the set up section), the production of Gettier cases relies on the acceptance of two principles: (A) You can be justified in believing something that turns out to be false, and (B) the justification of some beliefs can be other justified beliefs (i.e., we can make logical inferences).
Lets Try (A)
Any solution to the Gettier problem will involve rejecting one of these principles. Suppose, for example, to get out of the "oasis" problem, we reject (A). But now, if we actually see a real oasis, we can't say we know there's an oasis because there's always a chance (no matter how small) that it is a mirage or that we are hallucinating.
As the lottery paradox shows, it doesn't matter how small the chance is, we still can't say we know it's an oasis so long as there's an infinitesimal chance that we could be wrong. Well, rejecting (A) isn't going to work...how about (B)?
Lets Try (B)
Suppose, in order to escape the Gettier problems we reject (B). Recall, the problem arose because we made the inference from a false believe. Well, now we're just going to ban inferences. But if we do this, then if I actually do see a mirage I'm not allowed to make the inference that "there's a mirage over there"! And if Jones actually does get the job, Smith can't make the inference that "the man who gets the job will have 10 coins in his pocket." Well, that's gonna suck!
Because no one (except very extreme skeptics a la Descartes) wants to abandon either (A) or (B) philosophers have given up trying to rescue the traditional model of knowledge.
Holy crap! Progress in philosophy! (If you count discarding a theory as progress).
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