An Epistemic Puzzle About Knowledge and Rational Credence

ABSTRACT

I present some puzzling cases regarding knowledge and its relation to rational credence. They seem to entail a failure of an apparently correct principle: (a) if S knows P, then the epistemic justification S has for believing Not-P is not greater than her epistemic justification for believing P. The cases at issue involve the following two conflicting facts, relative to a given subject S and a proposition P in a determinate context. Firstly, some people have a very strong intuition that: (b) S has perceptual knowledge of P. Secondly, all of us, when reflecting on the relevant data, have a very strong intuition for this other thesis: (c) the epistemic justification S has for believing Not-P is much greater than her epistemic justification for believing P. The cases seem to be instances of the base-rate fallacy, so that—apparently—the subject would be irrational if she believed proposition P. My main aim here is to present the puzzle. But, I also provide a solution for it that preserves thesis (b) without renouncing Bayesian epistemology, which is the basis for thesis (c).

Acknowledgements

The main ideas in this work have been presented at two scientific meetings: EPISOC Seminary (Univ. Autónoma de Madrid, Spain, 14-2-2017) and Third Workshop on Concepts and Perception (Univ. Nacional de Córdoba, Argentina, 17-11-2017). The debate in a Logos Reading Group about knowledge, modality and probabilities that I coordinated during the course 2014–15 has been fruitful too. I am indebted to the respective audiences and to some other people who have discussed these issues with me. Thanks particularly to Juan Comesaña, José A. Díez, Carl Hoefer, Daniel Kalpokas, Manolo Martínez, Fernando Martínez Manrique, Claudia Picazo, Daniel Quesada, Sven Rosenkranz, Ernest Sosa, Ignacio Vicario, Agustín Vicente and two anonymous referees of International Studies in the Philosophy of Science.

Notes

1 We may think of the tag ‘(KJ)’ as standing for ‘knowledge requires appropriate justification’, where having appropriate justification for P would entail—in the context of this discussion—that the total evidence does not support a higher rational credence in Not-P than in P.

2 We may accept these data because they are only approximations (about 80%; about 20%). The equality of the two magnitudes Prob(seems-blue|blue) and Prob(seems-green|green) is innocuous. But if Prob(seems-blue|blue) were exactly 0.8, it would be unrealistic that Prob(seems-green|blue) were exactly 0.2. Even if there is some degree of cognitive penetration (Archibald has the expectation that all cabs are blue or green), it seems unrealistic that in all cases of misperception the perceived car would appear blue or green to Archibald (for instance, we should expect that sometimes it would appear red). On the concept of cognitive penetration, cf. Siegel (2012).

3 On the other hand, I do not see any incompatibility between theses defended or suggested by me in this article and Buchak’s (2014) two main official theses: ‘[full] belief cannot be reduced to credence’ and ‘the notion of [full] belief is ineliminable from our moral practices of holding each other responsible: we cannot construct the norms associated with these practices using credences alone’ (Buchak 2014, 288). I do not propose an identification of the norms she mentions. (KJ) would be, or would entail, just a norm.

4 Interestingly, Williamson’s epistemicism about vagueness—Williamson (1994)—would allow him to postulate a relevant difference between MARBLE and CAB in case he wanted to defend (K).

5 For the sake of clarity, I have made some simplifications. I will mention two of them in this caveat. (1) In the analysis, I have also assumed that Elizabeth accepts the other data, concerning the reliability of her visual system (the data about values r and s). I will hold to these assumptions, as to change them does not significantly affect the main discussion. (2) More importantly, I have assumed Elizabeth’s acceptance of another proposition: she assigns 1 to her credence in ‘this marble seems red’. A more accurate and thorough study of the whole puzzle may well require changing this assumption, which suggests the infallibility of Elizabeth’s beliefs about her sense data. However, the core of the puzzle is perceptible in my simplified version.

6 This is so according to standard orthodox Bayesianism. For Bayesian treatments that depart from this orthodoxy, cf. Williamson (2000, 205–237) and Titelbaum (2013).

7 Lewis (1981, 14) writes: ‘Absolute certainty is tantamount to firm resolve never to change your mind not matter what, and that is objectionable’. Nevertheless, in the sentence preceding that fragment, he contemplates (when discussing about the Newcomb problem) a possible exception: ‘Nothing should ever be held as certain as all that, with the possible exception of the testimony of the senses’.

Additional information

Funding

This work was supported by Ministerio de Economía Competitividad (Government of Spain): [Grant Number FFI2015-63892-P]; Ministerio de Economía Competitividad (Government of Spain) and European Union: [Grant Number FFI2016-81858-REDC]; AGAUR (Catalan Government): [Grant Number 2017SGR63]; European Union: [Grant Number FFI2015-63892-P].