Closure, Counter-Closure, and Inferential Knowledge

The first thing to note about these principles is that (as I will be understanding them), they are not merely classificatory principles for demarcating/separating cases of knowledge from non-knowledge. As I will be understanding (and using) them, (C) and (CC) are intended to be featured in epistemological explanations of why some agent S knows that Q (as opposed, e.g., to merely truly believing that Q). This is why I have added the locutions “thereby” and “via deductive inference,” which are not typically included in the statements of (C) and (CC). The explanatory (and dialectical) role(s) of these locutions will become clearer in due course. The second thing to note about these two principles is that, although there is an obvious sense in which they are epistemologically symmetrical, there are also (perhaps less obvious) senses in which they are epistemologically asymmetrical. Specifically, consider the following central epistemological explanandum. 1Much of the dialectic in this paper has recently been covered in a similar way by Federico Luzzi [12]. I was unaware of Luzzi’s work when I (independently, and often in very different ways) arrived at many of the same general conclusions he does [8]. However, my present emphasis on epistemological vs. psychological explanation (as well as my emphasis on the relationship between closure and counter-closure, and my discussions regarding generalized counter-closure and ampliative inference) is rather different than his. Having said that, I have learned a great deal from Luzzi’s work (and from many fruitful conversations with him about these issues). My thinking about these issues has been informed by useful discussions with many people (in addition to Federico Luzzi) over the past several years. I cannot list them all here, but I am especially indebted to the following people (in alphabetical order): Brian Ball, Michael Blome-Tillmann, Tim Button, Cian Dorr, Jane Friedman, John Hawthorne, Allen Hazlett, Peter Klein, Matthew McGrath, Martin Montminy, Susanna Rinard, Miriam Schoenfield, Ian Schnee, Jonathan Vogel and Fritz Warfield. 2For instance, in his excellent survey of analytic epistemology, Audi [2, Ch. 8] emphasizes the traditional importance of both of these principles. Interestingly, though, he does voice some worries about CounterClosure. The name “Counter-Closure” seems to have been coined by Federico Luzzi [13].