Posted by: Justin | November 8, 2009

E=K: What am I missing?

I haven’t read very much of Williamson’s Knowledge and Its Limits; this is probably answered somewhere in there. But why isn’t this a good argument against E=K?

(1) I know that the sun will rise tomorrow.

(2) It’s not part of my body of evidence that the sun will rise tomorrow.

(3) Therefore, I know a proposition which is not part of my body of evidence.

I think that (1) is true. Maybe some people don’t. In fact, the little bit of the book I did read suggested that Williamson may think something like this. I don’t have a copy of the book in front of me, but somewhere (I think in chapter 9), he talks about a case where I watch someone draw n marbles from a bag, and they’re all red. Intuitively, the proposition that the n+1 marble drawn is red is not part of my evidence. One reason to think this is that it seems compatible with my evidence that the n+1 marble drawn is not red. But if it was part of my evidence that the n+1 marble drawn is red, then this would not be compatible. Williamson’s explanation for why this proposition is not part of my evidence is that I do not know it. For a small n, I can buy this. But what if n is large? Can’t I come to know, by induction, that the next draw is red? This is essentially the worry I’m pressing in (1)-(3) above. It seems that it’s compatible with my evidence that the sun doesn’t rise tomorrow (this could probably be challenged). So the proposition that it will is not part of my body of evidence. But I do know it (given that it’s true). So E=K is false.

Where am I going wrong?



  1. Well, I don’t know much about the book either, I’m sort of ashamed to say. Furthermore, I’m not really sympathetic to this view. So I’m no help.

    By the way, why can’t I tell who posted this? It doesn’t have a place to display the author of the post, I guess.

  2. Hi Josh. It turns out that whether or not the author is displayed is theme specific. So I’ve chosen a different theme that does display the author. I don’t know if I’m crazy about it, but it’ll do for now (read: feel free to change it if you want).

  3. Wow, there are a lot of themes that don’t display the author’s name. Weird. What do you think about this one? It’s not perfect by any means, but it’s kind of appropriate seeing as it’s a SoCal blog and this is the “Ocean Mist” theme. Not that we’re trying to flaunt our beautiful weather and proximity to the ocean or anything… 🙂

  4. This one seems good; let’s go with it.

  5. Hey Justin,

    There’s very little in Knowledge and its Limits about induction. This is weird. It seems the objection is pretty much right. (I offer essentially the same objection in something that I have under review, so I’m biased.) Assuming that inductive inference can generate knowledge, it seems weird to think that once you know that all the F’s are G’s your evidence entails that no unobserved F is a G. Someone could deny that inductive inference generates knowledge, but I think the thing for W to say is that this is right but it doesn’t threaten:
    (IKSE) If we know p non-inferentially, p is part of our evidence.
    (IKNE) If p is part of our evidence, we know p non-inferentially.

    I think Gettier cases cause trouble for (IKNE) and (E–>K), but modifying the account for those, I think we’re close to the right view of evidence. In the new volume on W and his critics, it seems lots of people are dropping the truth requirement. I think that’s unfortunate.

  6. “no unobserved F is a G”

    of course I intended or should have intended:
    “no unobserved F is not a G”

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