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It seems to me Gettier problems challenge the Justified, True Belief account of knowledge.

As I see it, they can be solved by assuming that knowledge requires something else: a set of propositions Q which are held by the subject and which represent his background of implicit beliefs.

I will make this definition clear:

Q contains all propositions q such that:

  1. q is not a tautology
  2. q is not p
  3. The justification of S's belief that p depends on "S believes that q"

Equipped with this set we can formulate a slightly different JTB* account for knowledge:

"S knows that p" if and only if:

  1. p and each one of q is true
  2. S believes p and each one of q in Q
  3. S is justified in believing that p

Note: We do not require each q to be justified. We merely assume that those beliefs are held by S. In this sense, Q represents some belief which are held and which grant a justification for p.

Let's have a look at a Gettier problem:

"Let it be assumed that Plato is next to you and you know him to be running, but you mistakenly believe that he is Socrates, so that you firmly believe that Socrates is running. However, let it be so that Socrates is in fact running in Rome; however, you do not know this."

The key here is that "S believes that q" where q is the proposition "Socrates is next to me". Intuitively this belief justifies p ("Socrates is Running"); for if q was not believed by S, he wouldn't have a justification for p. But q is false, so this doesn't qualify as knowledge, even though p is true.

Is this a possible solution for Gettier problems? Why not?

  • 4
    This seems similar to the No False Lemma’s proposal: S knows p iff p is true, S believes p, and S didn’t infer p from a false statement. This blocks Gettier’s original case, and perhaps also your running example. It’s normally thought though that Fake Barn Land (where you happen to look at the only real barn among countless barn facades) disproves this proposal: when you come to believe ‘There’s a barn there’, your belief isn’t inferred from any false lemma. (In your terminology, Q is empty.) – MarkOxford Jun 13 '18 at 12:16
  • I made some grammar and spelling edits. You may roll them back or further edit. Welcome to the SE! – Frank Hubeny Jun 13 '18 at 13:01
  • It seems to me that if we only know p where 'p and each one of q is true' then to say we know p is to say we know that this condition has been met. To say 'I know x' would be to say 'I know x is true'. False knowledge would be impossible while false beliefs would be common. I find it confusing the way 'knowledge' is elided with 'belief' when we usually mean different things by these words. . – PeterJ Jun 13 '18 at 13:32
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    To add to Mark's excellent comment, for every Gettier "fix" offered so far there was promptly constructed a counterexample, SEP has a nice survey, some even proposed "algorithms" for doing so. It is generally believed that the Gettier problem can not be "solved" for a good reason, in the end nothing gets done without "cooperation of environment", in one way or another to have knowledge we must get lucky. – Conifold Jun 13 '18 at 17:41
  • @MarkOxford i do have some doubts wheter Q is empty in the Fake Barn Land case. Implicit beliefs about the reliability of our experience are ubiquitous. We do assume we aren't deceived by our senses. In this case S is assuming, or at least i think so, that his visual experience doesn't deceive him under such conditions. It's a reasonable assumption we make everyday in our life, but which may turn to be false , and in fact is false in this context. Does that sound reasonable to you? – Nikolaj Di Rondò Jun 13 '18 at 17:41
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Gettier examples tug at the notion of justified. They need to allow for a notion of justification where the assertion at issue is in fact wrong. If justification can lead to incorrect beliefs are we justified in calling it justification? People will allow for this. They will say that, in the face of overwhelming evidence, that a belief is justified, meaning that they wouldn't blame the person for making decisions based on their believing the assertion even if the assertion proved to be false. But this criterion for justification ought not to be equated to the justification required for a true belief to be counted as knowledge. If the level of justification only establishes that an assertion is probably true that is generally considered to be insufficient for knowledge even if it turns out that the assertion is true. I may believe that 5 (fair) coin tosses were not all heads and I would probably be correct but that shouldn't count as actually knowing that they were. The same is true for 20, 100,or 1000 coin tosses. If the level of justification doesn't guarantee the truth of the assertion then it is only luck that the justified belief is true. A lucky guess isn't knowledge. Gettier problems confuse the first notion of justification with the second. "Knowledge" is an idealised concept like circles. You will never find an object in the real world that satisfies the math definition of a circle. That doesn't stop it from being an extremely useful concept however both in math and practical applications, (extremely useful ) but no one is at all concerned that "circles don't exist".

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Yes, but only by making the justification condition extremely stringent, so that one is justified in believing that p if and only if p is a self-evident truth which is immune from error. This is the Cartesian approach - Descartes' 'clear and distinct ideas' are just such truths.

Two questions are whether there are such truths (hard to maintain post-Quine's 'Two Dogmas of Empiricism' but possible) and whether a concept of knowledge as stringent as this would be of practical value. On the Cartesianly-tightened justification condition, it will turn out that we know virtually nothing - or at the very least that the concept of knowledge will apply only within limits much narrower than those within which it currently operates. Its social role would be drastically diminished. This is not a decisive objection but may be an inconvenient consequence. Or not - depending on what you want from epistemology.

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