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    I’d definitely recommend reading the original paper, which is linked in the article. IMO Case 2 is a more interesting and persuasive example than Case 1 (which the article uses).

    I’m also a little obsessed with Gettier Problems. Here’s a one I really like:

    • Bob makes empirical claim X, and cites papers A, B, and C.
    • A, B, and C each cite another two papers as empirical evidence for the claim.
    • All six of the second tier papers cite a single originating source, Q, which was written by a giant in the field.
    • In the forward of Q, the author says the claim X is from a thought experiment and not empirical at all.
    • Unrelatedly, there’s an obscure paper R nobody read which does a controlled study and finds evidence supporting X.

    Does Bob know X is true? He has nine papers supporting him, so he’s certainly justified! And there’s a tenth paper he doesn’t about which actually confirms X, so it’s definitely true. But is it knowledge?

    This kind of problem comes up a lot when doing software history or empirical engineering.

    And here’s one from formal methods: you prove your code will sort a list and use a correct theorem prover to verify the proof. Unkown to you, your production environment has a wonky CPU bug that makes the sort function give incorrect outputs for certain classes of inputs. In your problem domain there’s never a case where you will ever need to input something that would trigger the bug. Is your sort function always correct? Do you know this?

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      Nice. I did not anticipate where this was going, or that it was going to be relevant to engineering. Thank you for posting it.

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        Studying epistemology is mind-expanding, because if you think about it long enough, nothing is certain. Any “common-sense” view “I know it when I see it” statement can be trivially questioned by assuming that you are a brain in a jar and your every experience is actually generated by an external source.

        Descartes’ famous “I think, therefore I am” is actually just part of a train of argument that basically ends with poor René appealing that a just and benevolent God would never let an evil demon mediate his every perception. Later philosophers had no such easy get-out and had to dig deeper.

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          One point of clarification: Gettier cases still arise in a common-sense or anti-sceptical framework where one takes it as given that there are a great many empirical facts that we know. They’re not really tied to scepticism in any direct sense.

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            I prefer the Zhuangzi formulation. It’s a lot more interesting than Descartes, IMHO:

            Once, Zhuang Zhou dreamed he was a butterfly, a butterfly flitting and fluttering about, happy with himself and doing as he pleased. He didn’t know that he was Zhuang Zhou. Suddenly he woke up and there he was, solid and unmistakable Zhuang Zhou. But he didn’t know if he was Zhuang Zhou who had dreamt he was a butterfly, or a butterfly dreaming that he was Zhuang Zhou. Between Zhuang Zhou and the butterfly there must be some distinction! This is called the Transformation of Things.

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              That’s a fascinating example. I think what really drives Western epistemology is that “everyone” agrees that the world we live in is the “real” one, and that we can trust our perceptions. But how to prove it?

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                I really like how phenomenology tables this problem.

                If there appears to be a teapot in front of me, I don’t know for certain whether a teapot is “really there”. But I do know for certain that the teapot appears to be there. You can proceed to analyze phenomena as they appear to you.

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            I’ve always called these Red Herrings:


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              These are red herrings which, in addition to being wrong and a distraction, happen to lead you to the correct conclusion.

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              Seeing this on Hackernews, it reinforced my feeling that ordinary philosophy is kind of weird.

              I would look at a model-theoretic equivalent. Suppose you have a model and an axiom systems. You might incorrectly prove a given theory that is actually independent. But it might actually be the case that you working with a model within which that theory happens to be true. This seems like the analogue of the “justified belief that isn’t knowledge” examples. The thing here, is that you easily fill in the “hole” by specifying that one’s justifications have to be correct.

              And altogether, it is surprising that philosophy didn’t put the constraint on “justified” to meaning “a fact that makes another statement true” rather than it being a fact that merely convinces some people.

              I suppose the problem is philosophy is dealing with less certain situations and the philosopher is trying to come up with a compact piece of rhetoric that would convince another human rather than engaging automatable process.

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                That raises questions about what a “justification” is, and what it means for a justification to be “correct”. Epistemology deals with messy questions of understanding and knowledge. I know I’m going to drink water tomorrow. My justification is that every day for my entire life, I drank some water. But inductions make terrible justifications: I could die in my sleep. So the justification is not correct, and yet I still know I’m going to drink water tomorrow.

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                  It’s a very difficult book, but John Hawthorne’s Knowledge and Lotteries discusses this kind of case. There’s some kind of equivalence between “I will drink water tomorrow” (which we tend to think you can know, despite the small probability that you’ll die), and “I know this lottery ticket will lose” (which we tend to think you can’t know, because of the small probability that it will win).

                  I’d disagree that induction doesn’t provide justification in this case. It just provides fallibilist justification–justification that cannot rule out the possibility that the proposition justified is false, though it makes it very unlikely.

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                The Gettier problem is a lot of fun, but one important thing to know is that there has been a massive literature attempting to “upgrade” the JTB condition to something that works (https://plato.stanford.edu/entries/knowledge-analysis/). Arguably, you might summarize the literature as “all attempts fail”, though you’ll find true believers who think that their particular attempt works.