On Gettier's Counterexamples

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Reply Thu 6 Mar, 2008 09:22 pm
By illustrating hypothetical cases in which a person has a justified true belief, and yet still does not have knowledge, Edmund Gettier's famous counterexamples (see footnote 1) certainly complicate, if not invalidate altogether, the definition of knowledge as justified true belief.

In Gettier's first counterexample, Smith "has strong evidence" (i.e., justification) for two propositions: "Jones is the man who will get the job," and "Jones has ten coins in his pocket." His evidence is "that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones's pocket ten minutes ago." From the two propositions, Jones reasonably infers a third: "[t]he man who will get the job has ten coins in his pocket." As it turns out, it is actually Smith and not Jones who gets the job. And Smith, by sheer coincidence, also happens to have ten coins in his pocket. Gettier's conclusion is that Smith did not really know that "[t]he man who will get the job has ten coins in his pocket," even though his belief in this proposition was justified and true.

In Gettier's second counterexample, Smith has "strong evidence" for the proposition, "Jones owns a Ford." His evidence is that "Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford." Smith also has a friend named Brown, "of whose whereabouts he is totally ignorant." Choosing three locations "quite at random," Smith "constructs" three disjunctive propositions:

1. Either Jones owns a Ford, or Brown is in Boston.
2. Either Jones owns a Ford, or Brown is in Barcelona.
3. Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Smith is aware that each of these propositions is entailed by the original proposition, "Jones owns a Ford," and he accepts them "on the basis" of his justified belief that the original proposition is true: he is "therefore completely justified in believing each of" them. However, what Smith does not know is that Jones has recently gotten rid of his Ford and is now driving a rental car. What he also does not know is that Brown, by some bizarre coincidence, is actually in Barcelona. Thus, Smith's belief that "either Jones owns a Ford, or Brown is in Barcelona" (proposition #2) is not only justified, but also true. And yet it can hardly be considered knowledge.

After illustrating these two cases, Gettier leaves us with a seemingly inevitable conclusion: the definition of knowledge as merely justified true belief-which he attributes to Plato, among others-does not "state a sufficient condition for someone's knowing a given proposition." In other words, it is not enough simply to have a justified true belief-one must have something more in order to possess knowledge.


[CENTER]***[/CENTER]


Although the logic behind Gettier's counterexamples is as close to being flawless as any logic can be-perhaps even as flawless as Descartes' cogito ergo sum-his overall argument is not without its weaknesses. Two unfounded assumptions tarnish the otherwise brilliant luster of his reasoning, leading us to question his method and doubt his conclusions. Let's have a look at them.


ASSUMPTION #1: Plato defines knowledge simply as "justified true belief."


In making this assumption, Gettier seems to suggest that Plato would consider any kind of evidence or reasoning (including Smith's) to be legitimate justification. This is by no means obvious. In the Meno, Plato's persona, Socrates, speaks of justification as the "tie of the cause" that fastens true beliefs to their rightful origin in the soul (201); and in the Theaetetus, Socrates refers to justification as "an account" or λογοs (98). While it is tempting to read "tie of the cause" to mean any kind of causal connection, or to construe "account" to mean any kind of account, nothing about these descriptions indicates that they should be interpreted so broadly. In fact, in the Theaetetus, Plato (via Socrates) examines no fewer than three different explanations of justification, and every one of them he rejects. This alone should prove that Plato did not regard every kind of "account" or "tie" as a genuine form of justification; for if he did, he would have accepted every explanation.

The truth of the matter is that Plato never did decide exactly what justification is, nor did he ever settle upon a definition of knowledge that he felt was final or perfect. The Theaetetus, which is his last major attempt to tackle the issue of knowledge, ends famously in aporia: neither justification nor knowledge is fully elucidated.

Thus, when Gettier suggests that his counterexamples prove Plato's definition of knowledge to be "false," he betrays an unfamiliarity with Plato's writings. For if Plato never explained justification to his own satisfaction-at least not in any of his extant dialogues-then it is reasonable to assume that he himself must already have been aware that his definition of knowledge was incomplete, tentative, and imperfect. Gettier's counterexamples therefore do not tell us anything new-and they certainly do not refute Plato. At most, they merely remind us that the question of knowledge has not yet been answered.


ASSUMPTION #2: Smith does not have knowledge.


In order to make the judgment that Smith does not have knowledge, Gettier must appeal to some prior standard, or idea, of what knowledge is: he must have before his mind an ideal conception of Knowledge, and then he must compare this conception to his perception of Smith's belief, to see whether the two are identical. If they are not identical, then Smith's belief (or at least Gettier's perception of it) falls short of the ideal conception, thus provoking Gettier to deliver his negative judgment.

Gettier's conception, if expressed in language, would most likely assume the form of a definition-e.g., "Knowledge is X." This definition would be (or rather, would express) Gettier's own theory of knowledge, his own epistemology. One has to wonder, however, what would happen if Gettier were to put forth and defend his theory before the eyes of the world. Would the theory be universally excepted? or would it be contested by other brilliant philosophers with counterexamples similar to his? Seeing that even Plato's putative theory has been called into question, it is hard to imagine that Gettier's theory would be immune to any criticism-or any defects.

Yet even if Gettier's theory were somehow immune, and therefore were the closest human approximation to the one correct conception of knowledge, this would not necessarily mean that Gettier knows it to be such. For Gettier's belief in his conception may be no different than Smith's belief that the man who gets the job will have ten coins in his pocket-it may be justified and true, and yet still not constitute knowledge.

Gettier's judgment that Smith does not have knowledge is an assumption because the conception that provoked it is-in the end-also an assumption. If Gettier's readers did not already have a roughly similar conception in mind-if they did not already share a somewhat related epistemic "worldview"-then they would not so readily assent to his judgment; they would not so easily be persuaded by his argument. A recent study (see footnote 2) published in Philosophical Topics, in which individuals from both Western and non-Western cultures were asked to respond to several Gettier-style counterexamples, shows this to be the case. While Westerners were far more likely to say that the hypothetical subject (i.e., Gettier's "Smith") does not have knowledge, non-Westerners were far more likely to say that he does. This raises a mischievous question: Are non-Westerners epistemically deficient, or are Westerners-and hence Gettier himself-simply wrong about knowledge?

If Gettier knows that he is not wrong, and if he can somehow get me to know that he knows, then I will retract my claim that his judgment is based on an assumption. Very Happy


1 Is Justified True Belief Knowledge?
2 Normativity and Epistemic Intuitions
 
kennethamy
 
Reply Fri 7 Mar, 2008 06:50 am
@saiboimushi,
saiboimushi wrote:
By illustrating hypothetical cases in which a person has a justified true belief, and yet still does not have knowledge, Edmund Gettier's famous counterexamples (see footnote 1) certainly complicate, if not invalidate altogether, the definition of knowledge as justified true belief.

In Gettier's first counterexample, Smith "has strong evidence" (i.e., justification) for two propositions: "Jones is the man who will get the job," and "Jones has ten coins in his pocket." His evidence is "that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones's pocket ten minutes ago." From the two propositions, Jones reasonably infers a third: "[t]he man who will get the job has ten coins in his pocket." As it turns out, it is actually Smith and not Jones who gets the job. And Smith, by sheer coincidence, also happens to have ten coins in his pocket. Gettier's conclusion is that Smith did not really know that "[t]he man who will get the job has ten coins in his pocket," even though his belief in this proposition was justified and true.

In Gettier's second counterexample, Smith has "strong evidence" for the proposition, "Jones owns a Ford." His evidence is that "Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford." Smith also has a friend named Brown, "of whose whereabouts he is totally ignorant." Choosing three locations "quite at random," Smith "constructs" three disjunctive propositions:

1. Either Jones owns a Ford, or Brown is in Boston.
2. Either Jones owns a Ford, or Brown is in Barcelona.
3. Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Smith is aware that each of these propositions is entailed by the original proposition, "Jones owns a Ford," and he accepts them "on the basis" of his justified belief that the original proposition is true: he is "therefore completely justified in believing each of" them. However, what Smith does not know is that Jones has recently gotten rid of his Ford and is now driving a rental car. What he also does not know is that Brown, by some bizarre coincidence, is actually in Barcelona. Thus, Smith's belief that "either Jones owns a Ford, or Brown is in Barcelona" (proposition #2) is not only justified, but also true. And yet it can hardly be considered knowledge.

After illustrating these two cases, Gettier leaves us with a seemingly inevitable conclusion: the definition of knowledge as merely justified true belief-which he attributes to Plato, among others-does not "state a sufficient condition for someone's knowing a given proposition." In other words, it is not enough simply to have a justified true belief-one must have something more in order to possess knowledge.


[CENTER]***[/CENTER]


Although the logic behind Gettier's counterexamples is as close to being flawless as any logic can be-perhaps even as flawless as Descartes' cogito ergo sum-his overall argument is not without its weaknesses. Two unfounded assumptions tarnish the otherwise brilliant luster of his reasoning, leading us to question his method and doubt his conclusions. Let's have a look at them.


ASSUMPTION #1: Plato defines knowledge simply as "justified true belief."


In making this assumption, Gettier seems to suggest that Plato would consider any kind of evidence or reasoning (including Smith's) to be legitimate justification. This is by no means obvious. In the Meno, Plato's persona, Socrates, speaks of justification as the "tie of the cause" that fastens true beliefs to their rightful origin in the soul (201); and in the Theaetetus, Socrates refers to justification as "an account" or λογοs (98). While it is tempting to read "tie of the cause" to mean any kind of causal connection, or to construe "account" to mean any kind of account, nothing about these descriptions indicates that they should be interpreted so broadly. In fact, in the Theaetetus, Plato (via Socrates) examines no fewer than three different explanations of justification, and every one of them he rejects. This alone should prove that Plato did not regard every kind of "account" or "tie" as a genuine form of justification; for if he did, he would have accepted every explanation.

The truth of the matter is that Plato never did decide exactly what justification is, nor did he ever settle upon a definition of knowledge that he felt was final or perfect. The Theaetetus, which is his last major attempt to tackle the issue of knowledge, ends famously in aporia: neither justification nor knowledge is fully elucidated.

Thus, when Gettier suggests that his counterexamples prove Plato's definition of knowledge to be "false," he betrays an unfamiliarity with Plato's writings. For if Plato never explained justification to his own satisfaction-at least not in any of his extant dialogues-then it is reasonable to assume that he himself must already have been aware that his definition of knowledge was incomplete, tentative, and imperfect. Gettier's counterexamples therefore do not tell us anything new-and they certainly do not refute Plato. At most, they merely remind us that the question of knowledge has not yet been answered.


ASSUMPTION #2: Smith does not have knowledge.


In order to make the judgment that Smith does not have knowledge, Gettier must appeal to some prior standard, or idea, of what knowledge is: he must have before his mind an ideal conception of Knowledge, and then he must compare this conception to his perception of Smith's belief, to see whether the two are identical. If they are not identical, then Smith's belief (or at least Gettier's perception of it) falls short of the ideal conception, thus provoking Gettier to deliver his negative judgment.

Gettier's conception, if expressed in language, would most likely assume the form of a definition-e.g., "Knowledge is X." This definition would be (or rather, would express) Gettier's own theory of knowledge, his own epistemology. One has to wonder, however, what would happen if Gettier were to put forth and defend his theory before the eyes of the world. Would the theory be universally excepted? or would it be contested by other brilliant philosophers with counterexamples similar to his? Seeing that even Plato's putative theory has been called into question, it is hard to imagine that Gettier's theory would be immune to any criticism-or any defects.

Yet even if Gettier's theory were somehow immune, and therefore were the closest human approximation to the one correct conception of knowledge, this would not necessarily mean that Gettier knows it to be such. For Gettier's belief in his conception may be no different than Smith's belief that the man who gets the job will have ten coins in his pocket-it may be justified and true, and yet still not constitute knowledge.

Gettier's judgment that Smith does not have knowledge is an assumption because the conception that provoked it is-in the end-also an assumption. If Gettier's readers did not already have a roughly similar conception in mind-if they did not already share a somewhat related epistemic "worldview"-then they would not so readily assent to his judgment; they would not so easily be persuaded by his argument. A recent study (see footnote 2) published in Philosophical Topics, in which individuals from both Western and non-Western cultures were asked to respond to several Gettier-style counterexamples, shows this to be the case. While Westerners were far more likely to say that the hypothetical subject (i.e., Gettier's "Smith") does not have knowledge, non-Westerners were far more likely to say that he does. This raises a mischievous question: Are non-Westerners epistemically deficient, or are Westerners-and hence Gettier himself-simply wrong about knowledge?

If Gettier knows that he is not wrong, and if he can somehow get me to know that he knows, then I will retract my claim that his judgment is based on an assumption. Very Happy


1 Is Justified True Belief Knowledge?
2 Normativity and Epistemic Intuitions



Gettier appeals to our intuition that when someone happens to be right "by accident" he doesn't know. In the past, this intuition has be believed to dealt with the the criterion of justification. A person who claims to know, an is right, is not right "by accident" if he has adequate justification for his claim to know. Gettier's examples purport to show that a person who claims to know may have adequate justification for his claim, and yet be "right by accident". I do not think that Gettier claims to know this is true, as you seem to think. He just puts out his counter-examples, and let's others ask themselves whether Smith really does know when he has true justified belief. Most people would, I think, say, that Smith has true justified belief, but that his belief, nevertheless, is true "by accident" and, therefore, Smith does not know. Notice that Gettier is not arguing that truth, justification, and belief are not necessary conditions for knowing. Gettier is arguing that those are not sufficient conditions for knowing.

There seem to be two possible ways to deal with Gettier.

1. Try to show that, in fact, Smith's beliefs are not really justified. This way tries to retain the conditions as sufficient as well as necessary.

2. Accept Gettier's argument, and then try to find a fourth condition which, when added to the traditional three conditions, would constitute a set of sufficient and necessary conditions for knowledge.

Or, of course, it may be that Gettier is correct, and there is no such sufficient and necessary set of conditions.
 
saiboimushi
 
Reply Fri 7 Mar, 2008 12:44 pm
@kennethamy,
Thanks for responding. My post was actually an attempt to establish a third way of dealing with Gettier. The two ways that you mention are natural responses to Gettier--if you share his assumptions.

As much as I respect Gettier, his paper fails to persuade me that Smith does not have knowledge, or that the JTB account does not state sufficient conditions for one's knowing a proposition. Although Gettier's claims are probably true, how--how--how, I ask, can we know that they are true??

When I first read Gettier years ago, I bought into his assumptions--perhaps too much. I thought, "Oh my God, Plato was wrong!" (This scared me.) And, "There must be a way to fix or augment the JTB account so that it can resist Gettier's logic!"

I have since come to believe that the problem of knowledge is much bigger than what Gettier or his successors/opponents apparently consider it to be. One question encapsulates this problem fairly well: "If humans ever ran into the true definition of knowledge, how would they know that it was true?"

This question terrifies me. :eek:
 
kennethamy
 
Reply Fri 7 Mar, 2008 07:23 pm
@saiboimushi,
saiboimushi wrote:
Thanks for responding. My post was actually an attempt to establish a third way of dealing with Gettier. The two ways that you mention are natural responses to Gettier--if you share his assumptions.

As much as I respect Gettier, his paper fails to persuade me that Smith does not have knowledge, or that the JTB account does not state sufficient conditions for one's knowing a proposition. Although Gettier's claims are probably true, how--how--how, I ask, can we know that they are true??

When I first read Gettier years ago, I bought into his assumptions--perhaps too much. I thought, "Oh my God, Plato was wrong!" (This scared me.) And, "There must be a way to fix or augment the JTB account so that it can resist Gettier's logic!"

I have since come to believe that the problem of knowledge is much bigger than what Gettier or his successors/opponents apparently consider it to be. One question encapsulates this problem fairly well: "If humans ever ran into the true definition of knowledge, how would they know that it was true?"

This question terrifies me. :eek:

I do not know that Gettier is making any claims except that if a person is right by accident, then even if he is right, that person does not know, and, of course, that the cases he gives are those when he believes that Smith is right by accident. These are really cases of "the stopped clock". If a clock happens to stop when it shows 3 o'clock, and someone says the time is 3 o'clock, then even if it is 3 o'clock, the person is right, but only by accident.

Your intuition is that Smith does know. But you should be able to back this intuition up. And that means you have to show that Smith's beliefs are justified. But why do you think that is true? It certainly does not look like it.

To your question, how would anyone know that a particular definition of "knowledge" was correct, I suppose the answer would be whether one could find counter-examples to the proposed definition. If one could not when trying very hard (and that would include other experts) then that would be good reason to suppose that the definition was correct. After all, isn't that the sort of thing we find in the sciences? Someone proposes an hypothesis, and others try to shoot it down. If the others cannot shoot it down then it seems to me rational to accept the hypothesis provisionally.
 
saiboimushi
 
Reply Fri 7 Mar, 2008 07:38 pm
@kennethamy,
Although my intuition is that Smith does not know, I have doubts whether my intuition actually constitutes knowledge. I do not want to "back up" my intuition as much as I want to interrogate it, to break it down, to expose the assumptions that weave through it. I love Gettier's counterexamples and agree with them to an extent, but I have grave doubts about his overall method and conclusions.

*

If no one can disprove a claim, I am not sure that I know that this makes the claim true. For how would I come to know that a true claim is one that cannot be refuted? And if there are no real truths but only "provisional" truths, then how would I come to know that either?
 
kennethamy
 
Reply Fri 7 Mar, 2008 08:01 pm
@saiboimushi,
saiboimushi wrote:


*

If no one can disprove a claim, I am not sure that I know that this makes the claim true. For how would I come to know that a true claim is one that cannot be refuted? And if there are no real truths but only "provisional" truths, then how would I come to know that either?


Of course, if no one can disprove the claim, it does not follow that it is true. Nevertheless, if there is an earnest attempt by experts to disprove a claim, then that constitutes evidence that the claim is true. In philosophy, as in science, we should not expect certainty, but only plausibility and probability. After all, we cannot be absolutely certain that water is H20, for some genius may find evidence that confutes that too. But, I am willing to take bets that water is H20. Aren't you? Knowledge is not the same as certainty. One can believe one knows, and it later on turn out that one is wrong, and one did not know in the first place. But that does not mean that one cannot believe that one knows, and, in fact, know. Perhaps we cannot know we know. But that does not mean that we do not know.
 
saiboimushi
 
Reply Fri 7 Mar, 2008 08:42 pm
@kennethamy,
I like this discussion because we're touching on some real fundamentals.

You mentioned that we should not expect certainty in philosophy or science, which may be true. But what is certainty?

You also said that we can know something without knowing that we know it, but I am not sure that this is true. Perhaps we would need to identify a mind that knew something but did not know that it knew it. This would seem to be a difficult task, however, considering that we may not know what knowledge is. For how do we identify a mind that knows something if we do not know what it looks like to know something? How do we identify an instance of knowledge? And if we do not or cannot identify one, does this mean that knowledge does not exist?
 
kennethamy
 
Reply Sat 8 Mar, 2008 10:34 am
@saiboimushi,
saiboimushi wrote:
I like this discussion because we're touching on some real fundamentals.

You mentioned that we should not expect certainty in philosophy or science, which may be true. But what is certainty?

You also said that we can know something without knowing that we know it, but I am not sure that this is true. Perhaps we would need to identify a mind that knew something but did not know that it knew it. This would seem to be a difficult task, however, considering that we may not know what knowledge is. For how do we identify a mind that knows something if we do not know what it looks like to know something? How do we identify an instance of knowledge? And if we do not or cannot identify one, does this mean that knowledge does not exist?


Certainty is the impossibility of mistake. That is why Descartes's Cogito is often advanced as a paradigm of certainty. It is said that it is impossible to be wrong about whether one exists.

But it must be true that one can know without knowing that one knows, because, after all, one could not know that one knows without knowing in the first place. You could not know you knew unless you knew. (I could not know that I know that 2+2=4 unless I already knew that 2+2=4. Don't you agree?)

The question of what knowledge is, seems to me a separate consideration from question whether one can know without knowing one knows. The answer to that seem clearly to be. yes, however "knowledge" is defined, for the reason I just gave.
 
saiboimushi
 
Reply Sat 8 Mar, 2008 02:42 pm
@kennethamy,
To be certain about a proposition is to believe that it is true without any chance of its being false--perhaps even without any chance of knowing it "by accident"? I would think that if knowledge existed, it would have to be something like this. One would have to find a method by which one could come to know that a definition like this is the true definition of knowledge, and then one would have to articulate the definition in such a way that it is immune to counterexamples. I do not think that this is necessarily an impossible task, though it will be arduous and require much in the way of serious, serious thought. However, I see no reason why humans should not strive for absolute certainty in all cases. That they have failed to attain certainty so far does not prove that such a task is impossible.

Humans are both too modest and too arrogant when it comes to knowledge: while they are quick to say that certainty is impossible, they strive to show that human beings can nevertheless know specific things. Humans want to have knowledge without the certainty: they want to know that they are right, but cannot believe that they could ever be absolutely right. But what if knowledge is somewhere in between, neither all-too-human nor completely superhuman? Perhaps we need to rethink the problem of being, to find out what mind really is, and what humans really are. But now I am rambling. I will try to explain more in future posts.

Now, for all I know, you may be right about knowing if one knows. My suspicion, however, is this: Until we find out what it means to know, and eventually come to know that we know what it means to know, we probably will not know that it is possible to know something without knowing that one knows it. I think we must find out what knowledge is first before we can talk about whether it is possible in this case or that, whether it can do this or that, whether its limits are here or there. But I admit that I could be wrong.
 
kennethamy
 
Reply Sun 9 Mar, 2008 04:32 pm
@saiboimushi,
saiboimushi wrote:
To be certain about a proposition is to believe that it is true without any chance of its being false--perhaps even without any chance of knowing it "by accident"? I would think that if knowledge existed, it would have to be something like this. One would have to find a method by which one could come to know that a definition like this is the true definition of knowledge, and then one would have to articulate the definition in such a way that it is immune to counterexamples. I do not think that this is necessarily an impossible task, though it will be arduous and require much in the way of serious, serious thought. However, I see no reason why humans should not strive for absolute certainty in all cases. That they have failed to attain certainty so far does not prove that such a task is impossible.

Humans are both too modest and too arrogant when it comes to knowledge: while they are quick to say that certainty is impossible, they strive to show that human beings can nevertheless know specific things. Humans want to have knowledge without the certainty: they want to know that they are right, but cannot believe that they could ever be absolutely right. But what if knowledge is somewhere in between, neither all-too-human nor completely superhuman? Perhaps we need to rethink the problem of being, to find out what mind really is, and what humans really are. But now I am rambling. I will try to explain more in future posts.

Now, for all I know, you may be right about knowing if one knows. My suspicion, however, is this: Until we find out what it means to know, and eventually come to know that we know what it means to know, we probably will not know that it is possible to know something without knowing that one knows it. I think we must find out what knowledge is first before we can talk about whether it is possible in this case or that, whether it can do this or that, whether its limits are here or there. But I admit that I could be wrong.


I don't see why it would not be possible to know without knowing that I know. Since, as I pointed out, I would surely have to know first, in order to know that I know. I could not know I know without knowing, could I?
 
saiboimushi
 
Reply Sun 9 Mar, 2008 04:36 pm
@kennethamy,
You may be right, but what does it mean to know?
 
 

 
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