The Alice-Bob story is an everyday scenario where Bob forms his belief that it is raining for a legitimate reason (i.e., he justifiably forms his belief). That's the kind of scenario that a theory of knowledge is intended to describe, whether it's JTB or any other theory.

Now consider a planet orbiting a star. That can be described using Newton's theory of gravity. However it turns out that there are cases (such as with Mercury's orbit) where Newton's theory makes the wrong prediction.

Just as we can observe a planet's orbit, so we can observe how people use knowledge terms in everyday scenarios. In a Gettier scenario, JTB makes the wrong prediction (i.e., it predicts that Smith has knowledge whereas people don't regard Smith's belief as knowledge). — Andrew M

Arguably, to say that Smith lacks knowledge, Gettier needs a theory of knowledge based on which he can make such a claim, no? What's this theory is all I'm asking.

Arguably, to say that Smith lacks knowledge, Gettier needs a theory of knowledge based on which he can make such a claim, no? What's this theory is all I'm asking. — TheMadFool

Gettier didn't need a theory (beyond the JTB theory he was challenging), he just needed to be aware of people's ordinary use of the terms "know", "knowledge", etc. He was able to identify scenarios where people regarded a person's belief as true and justifiably held, but they didn't also regard it as knowledge (also subsequently shown experimentally across different cultures). Note that he wasn't the first to recognize this - see Russell's stopped clock case which is perhaps a more straightforward scenario.

That's the parallel of people observing Mercury's position and noticing that it wasn't where Newton's theory said it should be. Those people didn't have a better theory - that would have to wait until Einstein came along.

As for what a better theory might be, I think the "no false premises" approach is basically right (but note the possible objections at that link).

Gettier didn't need a theory (beyond the JTB theory he was challenging), he just needed to be aware of people's ordinary use of the terms "know", "knowledge", etc. — Andrew M

Are you suggesting that Gettier problems are based on [weak] intuition rather than [strong] rational analysis? Gettier doesn't seem to have shared that sentiment as the title of his article - Is justified true belief knowledge? - suggests an intent to make a strong refutation of JTB theory.

By the way, any ideas on the exact nature of the people's ordinary use of the terms "know", and "knowledge"? That people don't find the JTB theory sufficient to describe knowledge bespeaks a need for something else over and above JTB.

Note that the average person knows nothing about JTB. And most of us, especially when not doing philosophy, normally use language conventionally. So Gettier didn't need to base his analysis on people's stated intuitions (which may well be weak), but on how people conventionally speak in the relevant scenarios. And you may be surprised at how much information you can extract from such an analysis.

Here's a possible scenario for Russell's clock (based on an earlier thread).

(1) Alice: What's the time?
(2) Bob: 3pm.
(3) Alice: How do you know?
(4) Bob: I looked at the clock just now
(5) Alice: Ah, OK.
(6) Carol: That clock is broken.
(7) Alice: Oh. So what time is it?
(8) Carol: I'll check the internet time clock ... It actually is 3pm.
(9) Alice: Really? (laughs) OK.

Note that the word "know" is only used once in that exchange. Yet an analysis shows, for Alice, a Gettiered JTB (at 5) and knowledge (at 9).

There are close parallels with the soundness of an argument here, and the no false premises response, which I agree is a partial solution, is treating the justification as if it were an argument for the belief, which suggests that something like validity should also be a requirement: it is not enough that the premises of the justification are true, they must also be relevant in some sense.

The problem here seems to be that if you apply 'no false premises' recursively to the premises, and also require them make a valid argument for the belief, you end up with the requirement that only proofs are acceptable as justifications.

I agree with you that this would not be very useful, but I am beginning to wonder whether, unless we accept either that view, or the view that knowledge is a matter of believing a fact simpliciter, then we must recognize that knowledge is a conditional thing.

A Bayesean might propose that a justification should increase the likelihood that the belief is of a fact (which is a weakened form of validity and soundness; those two, in combination, raise the probability that the argument is correct to 1), and that the resulting conditional probability is a measure of the strength of that knowledge. In the clock example, the argument behind the justification at step 4 presumably includes the premise that the clock normally runs reliably, a claim that has a certain probability attached to it, which is used to update the prior (which, in some circumstances, might simply be that there is a 1/24 probability that it is 3-something pm.) The new fact introduced by Carol at 6 reverts the probability that it is actually 3pm to whatever the prior was before Bob mentioned looking at the clock (such as the afforementioned 1/24.) When Carol checks on the internet at step 8, they get a different justification to substitute for the original.

A similar observation can be made about Gettier's first case: when it is revealed that Smith, not Jones, got the job, the conditional probability behind Smith's belief crashes to the probability that Smith's unexamined pocket contains ten coins. The discovery that it does constitutes a new justification.

This is just off the top of my head; I would be surprised if there are not paradoxes arising from this view.

Another aspect of Gettier's examples is that there is no causal connection: whether someone has 10 coins in their pocket, and who gets chosen for the job, have no causal relationship, and neither do Jones' car ownership and Brown's location in the second case (note that this causal disconnect is absent in the clock example.)

As these issues lie at the foundations of epistemology, they are not trivial.

:up: Good comments! The conditional approach seems reasonable to me.

Thanks! It occurred to me just now that a simplified definition along these lines might be that a justification has to be a valid argument that is more likely sound than not.

On the other hand, having a quantitative concept of justification seems to fit with the jury instruction to return guilty if the premise that the defendant committed the crime is true 'beyond reasonable doubt', and also with the phrase that 'extraordinary claims require extrordinary evidence'. As probability is constrained between 0 and 1, the odds that the justification is sound might be a better measure, in order to encompass both extraordinary evidence and unreasonable doubt (Update: maybe the log of the odds? The odds itself asymptotically approaches the probability when the latter is small, and they both approach zero, which means that a metric using either probability or odds would not discriminate much between extraordinary claims and claims that are merely improbable.).

In either variant of this view, Gettier's second case still seems problematical, but perhaps we can dispose of it by noting that proposition h (the one that Gettier regards as problematical for JTB) is a disjunction of two beliefs, only one of which (Jones owns a Ford) could be knowledge by either of the definitions I gave above. If the other belief (that Brown is in Barcelona) happens to be true, then this would establish that the proposition h states a fact, but not that Smith has a justification for believing it, as the only justifications he has for h concern only Jones' car, and they turn out to be false. Here we have the disjunction of two propositions, neither of which are part of Smith's knowledge, so it seems reasonable to say that their disjunction is not known by Smith, either.

It occurred to me just now that a simplified definition along these lines might be that a justification has to be a valid argument that is more likely sound than not. — A Raybould

Yes. And if the argument is sound, then the person has knowledge. Obviously there is no guarantee of that since the conclusion or a premise could be false (unbeknownst to them). But that's the trade-off that has to be made for claims to be justifiable at all, and therefore for knowledge to be possible.

On the other hand, having a quantitative concept of justification seems to fit with the jury instruction to return guilty if the premise that the defendant committed the crime is true 'beyond reasonable doubt', and also with the phrase that 'extraordinary claims require extrordinary evidence'. — A Raybould

Yes, in some contexts the standard for justification is higher.

Here we have the disjunction of two propositions, neither of which are part of Smith's knowledge, so it seems reasonable to say that their disjunction is not known by Smith, either. — A Raybould

Works for me.

Interesting point. Gettier's claim is that the JTB definition can be satisfied (e.g. by the example you give), yet still not count as knowledge. But if Gettier knows exactly why the example doesn't count as knowledge, then he should be able to give an alternative definition, or provide an additional clause, which he doesn't. And if he doesn't know why the example doesn't count as knowledge, then what reason does he have for the claim that it doesn't?

My take on this is that Gettier is basing his claim on a presumption made by the JTB definition itself, which is that the truth of a belief is not sufficient for knowledge because a belief can be true purely by accident. So another clause is needed, and that, according to the JTB definition, is justification. Gettier's point is that justification doesn't do the job it's intended for, since, as the relevant examples show, a belief being justified doesn't necessarily prevent it from being true purely by accident.

One may question whether non-accidental truth is necessary for knowledge, but that is already presumed by the JTB definition, which is Gettier's target.