Monday 7 June 2021

Closure vs underdetermination versions of scepticism

One of the things that confused me while reading Duncan Pritchard’s book Epistemic Angst is the distinction between closure-based and underdetermination-based versions of scepticism. I could see the overall architecture of the ‘output’ of this distinction but not the distinction itself. An instance of the former is given in a footnote of Pritchard’s paper ‘In defence of closure’.

I think the real anti-sceptical import of epistemological disjunctivism lies in responding to what I call underdetermination-based radical scepticism, which turns on a difference epistemic principle to closure, and generates what I claim is a logically distinct radical sceptical argument. See Pritchard (2015, parts 1 & 3) for the details. (Pritchard forthcoming fn 18)

In the book, the need for distinct approaches to the distinct sources of scepticism is summarised in passages such as this.

Although the ultimate skeptical import of the universality of rational evaluation thesis and the insularity of reasons thesis is the same, it is important to note that they pose distinct epistemological challenges. Suppose, for example, that one rejected the universality of rational evaluation thesis and therefore argued that there are in principle limitations on the scope of rational evaluation. In this way, one could argue that closureRK-based inferences need to be restricted in some way to prevent them from taking the subject from local to global rational evaluations. One could thus undermine the closureRK-based radical skeptical paradox. In particular, one could hold that one’s rationally grounded knowledge of everyday propositions—as far as this formulation of the skeptical paradox goes at any rate—is entirely compatible with a lack of rationally grounded knowledge of the denials of radical skeptical hypotheses (on account of the fact that one cannot employ a closureRK-based inference in order to claim that one’s rationally grounded knowledge of everyday propositions, if genuine, would entail the contested rationally grounded anti-skeptical knowledge).

It is far from obvious how that would help one resolve the problem posed by the insularity of reasons thesis, however. That one can have rationally grounded knowledge of mundane external world propositions while lacking rationally grounded knowledge of the denials of radical skeptical hypotheses is one thing; that one can have adequately rationally grounded knowledge of mundane external world propositions when that rational basis (one is aware) does not favor one’s everyday beliefs over skeptical alternatives quite another. As one might put the point, if one’s everyday beliefs do not satisfy the underdeterminationRK principle, then in virtue of what, exactly, do they amount to rationally grounded knowledge? Thus, even with the closureRK principle out of (skeptical) action, one can still employ the underdeterminationRK principle—and, thereby, the insularity of reasons thesis—to motivate a radical skeptical conclusion.

So the general picture is this. Part of the originality of Pritchard’s view is that there are two sources of scepticism, which thus need two distinct treatments. For closure based scepticism, the treatment is an account of hinge epistemology (blocking the effects of closure). For underdetermination, he appeals to disjunctivism. That seems plausible enough, but I’m still not sure what the different sources are. These are each outlined in the first two chapters, one on each. In each case, a principle – closure or underdetermination – is used to generate an argument for scepticism and then an incompatible triad of prima facie plausible claims. And in each chapter, there’s a version of the principle and the argument that stresses an internalist, rationalist approach. For speed, I’ll simply give the quotes hoping that this outline is enough to explain what they are doing.

The Closure Principle
If S knows that p, and S competently deduces from p that q, thereby forming a belief that q on this basis while retaining her knowledge that p, then S knows that q.

The Radical Skeptical Paradox (I)
(S11) One cannot know that one is not a BIV.
(S12) If one cannot know that one is not a BIV, then one cannot know that E.
(S13) One knows that E.…

[T]he epistemic externalist is keen to break the logical link between knowledge and rational support, such that one can have the former without the latter, they surely do not wish to disengage our everyday knowledge from rational support altogether. Or, at least, the skeptic can force a dilemma here. On the first horn of the dilemma is the charge that the epistemic externalist is ultimately offering no response at all to the skeptical problem. On the second horn is the charge that the epistemic externalist is presenting us with an epistemological proposal that is so revisionist, so discontinuous with our ordinary epistemic practices, that even the most ardent proponent of epistemic externalism would find it unpalatable.…

The ClosureRK Principle
If S has rationally grounded knowledge that p, and S competently deduces from p that q, thereby forming a belief that q on this basis while retaining her rationally grounded knowledge that p, then S has rationally grounded knowledge that q.…

The Radical Skeptical Paradox (II)
(S21) One cannot have rationally grounded knowledge that one is not a BIV.
(S22) If one cannot have rationally grounded knowledge that one is not a BIV, then one cannot have rationally grounded knowledge that E.
(S33) One has rationally grounded knowledge that E.…

The Inconsistent Radical Skeptical Triad
(I) One is unable to know the denials of radical skeptical hypotheses.10
(II) The closure principle.
(III) One has widespread everyday knowledge.…

The Underdetermination Principle
If S knows that p and q describe incompatible scenarios, and yet S lacks a rational basis that favors p over q, then S lacks knowledge that p.…

The Radical Skeptical Paradox (III)
(S31) One cannot have rational support that favors one’s belief that E over the BIV hypothesis.
(S32) If one cannot have rational support that favors one’s belief that E over the BIV hypothesis, then one does not know that E.
(S33) One knows that E.…

The UnderdeterminationRK Principle
If S knows that p and q describe incompatible scenarios, and yet S lacks a rational basis that favors p over q, then S lacks rationally grounded knowledge that p.…

The Radical Skeptical Paradox (IV)
(S41) One cannot have rational support that favors one’s belief that E over the BIV hypothesis.
(S42) If one cannot have rational support that favors one’s belief that E over the BIV hypothesis, then one does not have rationally grounded knowledge that E.
(S43) One has rationally grounded knowledge that E.…

The Inconsistent Radical Skeptical Triad**
(I**) One cannot have rational support that favors one’s belief in an everyday proposition over an incompatible radical skeptical hypothesis.
(II**) The underdetermination principle.
(III**) One has widespread everyday knowledge.

My confusion is that these seem very closely related sources of scepticism. It is not, for example, akin to the wide difference between Agrippan and Cartesian scepticism.

Now this does not help with Pritchard’s view, but it is interesting to look (at the suggestion of my ex-co-author) at Anthony Brueckner’s paper ‘The Structure of the Skeptical Argument’.

Brueckner sets out the argument for scepticism using material similar to Pritchard’s triad (give or take a NOT) starting with closure; then that we do not know the negation of the ringer; then that we do not know everyday claims.

(1A) If I know that P. then I know that -SK.
(2A) I do not know that -SK.
(3A) I do not know that P.

This is a first stab at codifying the argument. Closure is there as a big general premise but then, equally necessary, is the minor premise that we do not know the negation of the ringer. From that scepticism about everyday matters follows. But why don’t we know the negation of the ringer? For this, Brueckner invokes underdetermination. So the fuller argument is underpinned by two principles: Closure with respect to justification (CIJ) and also underdetermination (UP). Both are in play for the same argument.

(CIJ) For all S φ, ψ, if S has justification for believing that φ, and (φ → ψ), then S has justification for believing that ψ.

(UP) For all S, φ, ψ, if S’s evidence for believing that φ does not favor φ over some incompatible hypothesis ψ, then S lacks justification for believing that φ.
This underdetermination principle helps establish the result that I lack justification for believing that -SK.

This gives the fuller codification of external world scepticism thus:

(1B) If I have justification for believing that P, then I have justification for believing that -SK. [from (CIJ)]
(2B) If my evidence for believing that -SK does not favor -SK over SK, then I lack justification for believing that -SK. [from (UP)]
(3B) My evidence for believing that -SK (my sensory evidence) does not favor -SK over SK. [premise] (4B) I lack justification for believing that -SK. [from 2B, 3B]
(5B) I lack justification for believing that P. [from 1B, 4B]
(6B) I do not know that P. [from 5B]

This makes much more sense to me than Pritchard’s approach. In fact, however, Brueckner goes on first to compare underdetermination and closure and argue that they are very similar and then to reconstruct the whole argument using underdetermination alone as a kind of ‘uber’ principle. Here’s the former.

What is the difference, if any, between argument B's two underlying epistemic principles, viz. the underdetermination principle and the principle that justification is closed under entailment? It is helpful to consider the following principle, which is equivalent to (UP):
(UP') For all S, φ, ψ, if one has justification for believing that φ, and φ and ψ are incompatible, then one's evidence for believing that φ favors φ over ψ.
Now consider a principle which is equivalent to (CIJ'):
(CIJ") For all S, φ, ψ, if one has justification for believing that φ, and φ and ψ are incompatible, then one has justification for believing that -ψ.
(CIJ’') and (UP') share a common antecedent, but their consequents differ. Suppose that S has justification for believing that φ and suppose that ψ is a competing incompatible hypothesis. According to (CIJ"), S then has justification for rejecting ψ. According to (UP'), what follows from the supposition is that S's evidence for φ favors φ over ψ. What is the difference be- tween these two putative necessary conditions for S's justification for believing that φ? (CIJ") says nothing about S's evidence for believing that φ, thereby leaving it open that S's justification for φ is not evidentially based. Then S could have justification for believing both φ and -ψ without having evidence which favors φ over ψ. But in cases in which S's justification for φ is so based, do the principles differ? If (CIJ") were restricted to evidentially justified φs, then it seems that the resultant principle would be virtually equivalent to (UP').

Here’s the latter.

(1C) If my evidence for believing that P does not favor P over SK, then I lack justification for believing that P. [from (UP)]
(2C) My evidence for believing that P (my sensory evidence) does not favor P over SK. [premise]
(3C) I lack justification for believing that P. [from IC, 2C]
(4C) I do not know that P. [from 3C]

So my worry, in a nutshell, is that even without Brueckner’s reconstruction of closure in terms of underdetermination, I’m not sure that we have two forms of scepticism – akin to the distinction in kind between Agrippan and Cartesian, for example – as opposed to one codification with two underlying premises and hence two different potential points of attack for an anti-sceptic. One could attack closure – and hence the spread of the sceptical infection from a sceptical ringer back to everyday claims – or one could attack the efficacy of the sceptical ringer. If they are not distinct forms of scepticism, in the way Pritchard argues, there is no need for two simultaneous treatments. Hence the main selling point for his book looks rather odd.

(Then again, having just had my second AstraZeneca vaccine dose, I wouldn’t say no if offered the Pfizer as well.)

References

Brueckner, A. (1994) ‘The Structure of the Skeptical Argument’ Philosophy and Phenomenological Research, 54: 827-835

Pritchard, D.H. (2019) Epistemic angst: Radical skepticism and the groundlessness of our believing. Princeton: Princeton University Press.

Pritchard, D.H. (forthcoming) ‘In defence of closure’ in Jope, M. Pritchard, D.H. (eds.) New Perspectives on Epistemic Closure, London: Routledge.