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My question is about quite basic epistemology but I am stumped.

To what extent do Gettier cases challenge the proposal that knowledge is justified true belief? Should we care?

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Welcome letha

First pass

Material is easily available online about the Gettier problem and associated Gettier cases. Such cases describe situations in which someone, S, believes that p, p is true, and S is justified in believing that p - but in which S does not know that p. Justified true belief (JTB) is not sufficient for belief, this is the claim involved.

In a Gettier-style counter-example or Gettier case, someone has justified true belief but not knowledge. Such cases were first proposed by Edmund Gettier to show that the traditional analysis of propositional knowledge as justified true belief is incorrect. Typically, one does not have knowledge in such cases because an element of luck in the way in which the belief is formed prevents it from counting as knowledge. (Corine Besson, 'Logical Knowledge and Gettier Cases', The Philosophical Quarterly (1950-), Vol. 59, No. 234 (Jan., 2009), pp. 1-19: 1; E. Gettier, 'Is Justified True Belief Knowledge?', Analysis, 23, 1963: 121-3.)

An element of luck? Well, consider one of Gettier's examples:

Gettier challenges this [the JTB] analysis by constructing counter-exam- ples with the help of certain entailments. He introduces the first counter-example by telling us that Smith and Jones have applied for the same job, and that Smith has strong evidence for the following:

(P) Jones is the man who will get the job, and Jones has ten coins in his pocket.

The evidence might be, Gettier tells us, that the company president has assured Smith that Jones will get the job and that Smith has counted the coins in Jones's pocket ten minutes earlier. P logically entails the following:

(Q) The man who will get the job has ten coins in his pocket.

That P entails Q is so obvious that S(mith) can be presumed to know it. Since S is justified in believing that P, it follows that S is justified in believing that Q. As it happens, unbeknownst to Smith, he and not Jones will get the job; also unbeknownst to him, he has ten coins in his pocket. So, Q is true. But, S does not know that Q. So, on the reasonable assumption that S can believe what he is justified in believing, i.e., that he can believe that Q, it fol- lows that Q is a counter-example to the analysis of knowledge as justified true belief. (Don S. Levi, 'The Gettier Problem and the Parable of the Ten Coins', Philosophy, Vol. 70, No. 271 (Jan., 1995), pp. 5-25: 6.)

Refinement

To refine matters:

You might think that knowledge is justified true belief, i.e. that S knows that p if and only if it is true that p, and S believes that p, and S is justified in believing that p. This elegant account is known as the tripartite theory of knowledge, and it captures several plausible ideas about knowledge, including that falsehoods cannot be known and that unreasonable or irrational beliefs, even if true, do not amount to knowledge. However, it is subject to a family of counterexamples, known as Gettier cases. We can divide these into three types. First, there are cases in which someone reasonably infers a true conclusion from a false premise that she believes with justification. The cases from Gettier's paper (1963, pp. 122-123) are of this type. Second, there are cases in which someone believes some true proposition, and is justified in so believing, but in which her belief is caused by something other than the truth of that proposition. Roderick Chisholm's (1966) case of the sheep in the field (p. 23n) is of this type. Third, there are cases in which someone believes some true proposition on some basis, and is justified in so believing, but in which an unusual or abnormal environmental condition makes it such that she would easily have believed something false on the same (or a similar) basis. Carl Ginet's (1988) fake barn case (p. 106) is of this type.

In these cases, it seems that the person who believes that p does not know that p, despite its being the case that it is true that p, that she believes that p, and that she is justified in believing that p. Justified true belief is therefore insufficient for knowledge, and the tripartite theory of knowledge is false. The premise that, in Gettier cases, the person who believes that p does not know that p, has been widely endorsed by epistemologists. The basic form of the Gettier problem, therefore, has consisted of a challenge for theorists of knowledge: amend or replace the tripartite theory of knowledge with a theory of knowledge that is immune to (at least this kind of) counterexample. (Allan Hazlett, 'The maturation of the Gettier problem', Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, Vol. 172, No. 1, Special Issue: THE GETTIER PROBLEM AT 50 (January 2015), pp. 1-6: 2; R. Chisholm, Theory of knowledge. London: Prentice-Hall; C. Ginet, 'The fourth condition', D. F. Austin (Ed.), Philosophical analysis (pp. 105-117). New York: Kluwer.

Hazlett probes the development of the Gettier problem and the different responses it has generated. As the problem now stands in the literature it has only a distant association with the light but penetrating sketch that Gettier gave in his 3-page article.

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Geoffrey Thomas has explained it widely and precisely. https://philosophy.stackexchange.com/a/69166/43419

To sum up and to add some info:

It is widely agreed that Gettier cases refute JTB conception of knowledge. Gettier's cases feature lucky guesses, more than what we'd usually call "knowledge".

A Gettier case. Imagine that I take bus line 2, which I believe will take me to the library. I've checked the route and it does stop near the library. However, there has been an unnoticed technical error and the screen shows the incorrect line number in each bus. A bus of line 3 approaches to my stop, but its screen shows line 2 information, so I get in. This bus shouldn't stop near the library, but near the train station instead. However, there is a demonstration I didn't know of and the road is cut, so the bus changes its route and stops near the library, only for that day. Then, even though my belief that "This bus will take me to the library" was true and justified, most people will think that it was mistaken, and that I didn't know at all what bus I was taking.

It is important to note that the extent to which Gettier cases defy the JTB conception of knowledge is dependent of the (epistemic) intuitions on if there was knowledge or not in such lucky cases. You may find that different authors differ in their epistemic intuition on a variety of counterexamples.

Finally, Gettier's challenge has definitely had an impact in contemporary epistemology, and that's a reason to care about it. Since the publication lf his article Is JTB knowledge? in 1963 there has been a flourishment of alternative epistemologies, primarly approaching to ethics: there you have virtue epistemology (Ernest Sosa), the studies on epistemological responsibility (Lorraine Code, James Montmarquet, Linda Zagzebski), and also the epistemology of testimony (Miranda Fricker), which is highly topical today.

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