Denials of Closure?

A question about the literature on closure principles, either for knowledge or justification. The usual story seems to be that denials of closure are first found in Dretske’s “Epistemic Operators” from 1970. Anyone know of earlier denials?


Denials of Closure? — 11 Comments

  1. I can’t recall where or when Kyburg first presented the lottery paradox, but in footnote 10 of his Believing on the Basis of the Evidence (1994, Computational Intelligence vol. 10(1))Kyburg claims that it was originally intended as an argument against deductive closure. I suspect that his presentation of the lottery paradox may have pre-dated the Dretske article and if this is true then Kyburg must have had some idea of rejecting closure in accord with his claim.

  2. Thanks for the pointer; I’ll check to see if there is anything explicit in there about denying closure. “Conjunctivitis” is from 1970, but the book “Probability and the Logic of Rational Belief” is 1961, and I’m pretty sure the lottery paradox is there.

  3. Jon,

    I was thinking of the 1961 book. The paradox is clearly there, and so if Kyburg 1994 is to be believed at least his idea of denying closure pre-dates Dretske by 9 years.

  4. One can read the later Wittgenstein (On Certainty) as implicitly denying some closure principle: He argues that our ordinary knowledge is based on things which we don’t know but just (have to) take for granted (certainties, “Weltbilder”, etc.).

  5. Peter, can you explain here? The closure principle I have in mind claims something like this: if you know p and competently deduce q from p (while acquiring no defeaters in the process), then you know q. I don’t see how the Wittgensteinian view you describe undermines this principle.

  6. With respect to Kyburg, ‘Probability and Randomness’ is the first paper spelling out both epistemological probability (outside of the last chapter of his PhD thesis, that is), and the first statement of the lottery paradox. It was written before Kyburg (1961) and delivered at the 1959 meeting of ASL and the 1960 meeting of the International Congress for the History and Philosophy of Science. However, it did not appear in print until 1963, in Theoria (29): 27-55. This paper is reprinted in Epistemology and Inference (1983).

    It is also correct that Kyburg has consistently viewed the paradox as an argument against (unrestricted) closure principles.

  7. Jon, that’s exactly the kind of closure principle I have in mind (sorry for the briefness of my remark!). Let me try to explain in more detail.

    It seems to me that Wittgenstein says or at least strongly suggests something along the following lines (in ‘On Certainty’, for instance; I don’t have my copy with me at the moment, so I can’t refer to particular paragraphs; the Wittgenstein experts will know where exactly to look for this kind of example):

    Ludwig might know, for instance, that there is a tree over there. He also knows that if there is a tree over there, then he is not merely dreaming that there is a tree over there. However, in the context of this particular language game (doing botany, etc.) he cannot claim to know that he is not dreaming. Ludwig only takes this for granted (and we always have to take some things for granted). It constitutes the “ground” of his knowledge about trees and bushes; but this ground, as Wittgenstein says somewhere, is not itself known (only taken for granted).

    I don’t think Wittgenstein thinks one can identify certain propositions as the basic ones for all language games; what is the indubitable ground in one language game might be up for grabs in another language game. So, there is also some context-sensitivity here (though not quite what is called “contextualism” these days).

    Now, one problem with all this is that the notion of a language-game is a bit elusive. But whatever a language game is, what Wittgenstein is saying in ‘On Certainty’ suggests a denial of epistemic closure. Even if Wittgenstein never actually used terms like “closure”.

    I’m not claiming that this is the only interpretation of Wittgenstein, and I’m not too worried about Wittgenstein-philology. But it seems to me that all one needs for a denial of closure can be found in Wittgenstein. Even if he himself might have never explicitly discussed closure (but who knows, perhaps there is a manuscript somewhere…)

    I hope this clarifies things a bit, cheers

  8. Jon, although there is no doubt that Kyburg articulated the lottery paradox in his writings, as well the main normative reasons to deny certain forms of closure, but there are earlier antecedents to this idea.

    One important example is the beautiful page and a half that Ramsey called `Knowledge’, dated 1929 (pages 110-11 in his Philosphical Papers, edited by Mellor).

    […] we cannot without self contradiction say p and q and r and … and one of p, q, r,… is false. […] But we can be nearly certain that one is false and yet nearly certain of each; but p, q, r, are then infected with doubt.

    This characteristically crisp presentation not only indicates the gist of the paradox but also suggests that the doxastic notion obtained via high probability rules cannot be full belief (in recent papers Kyburg talks about `risky knowledge’).


  9. Yes, Jon you are right. Reliabilism is the main point of the paper. But it contains an addendum that is also very rich (although seldom read) concerning a debate with Moore (and to some extent Russell). It starts in the fourth paragraph. Clearly it is an additional issue that he wants to discuss as well. To mark the separation of the two topics the fourth paragraph starts with `One more thing’. His reaction to Moore’s argument against skepticism is perhaps the least developed part of the addendum, but still it contains various nice insights (as usual).



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