Thursday, October 04, 2007


Anti-Luminosity: The Forgotten Premise

Let a case be a world, subject and time triple < w, s, t >. Conditions either obtain or fail to obtain in each case, and are introduced by that-clauses: e.g. the condition that one is happy or that one feels cold (however, for simplicity I don't always state conditions in this cumbersome form in what follows).

A condition C is luminous iff the following holds:

For every case A, if C obtains in A, then one is in a position to know that C obtains in A.

Tim Williamson's anti-luminosity argument is meant to offer a proof that no non-trivial conditions are luminous in this sense (a condition is trivial iff it obtains in every case, or else fails to obtain in every case).

Williamson proceeds, he claims without loss of generality, by way of a reductio of the claim that the condition that one feels cold is luminous. So from the definition of luminosity, we have as our claim for reductio:

(LUM) For every case Ax, if one feels cold in Ax, then one is in a position to know that one feels cold in Ax.

Now imagine a series of times (T0, T1, T2.......Tn) between dawn and noon, each a millisecond apart. Fixing the subject and the world, we obtain a series of cases (A0, A1, A2........An) individuated by those times. One warms up very slowly, virtually imperceptibly, throughout this period. The following are also stipulated features of the case:

(COLD) In A0 one feels cold.
(WARM) In An one does not feel cold.

Williamson's two crucial premises are the following:

(REL) If in a case Ax, one knows that one feels cold, then in case Ax+1 one does feel cold.

(CON) If in a case Ax, one is in a position to know that one feels cold, then if one actively considers the matter, one knows in Ax that one feels cold.

On the assumption that one actively considers the matter of whether one feels cold in each case (A0, A1, A2........An), (LUM), (CON) and (REL) together entail the following tolerance principle for one feeling cold:

(TOL) For every case Ax, if one feels cold in Ax, then one feels cold in Ax+1.

And now Sorites reasoning will easy demonstrate the inconsistency of (TOL) with (COLD) and (WARM). So, since Williamson thinks he can independently motivate all the relevant analogues of (REL), and that (CON) is plausible, it follows that we should reject (LUM) for any non-trivial condition.

Virtually every discussion of Williamson's argument, online or in print, has focused on the reliability premise (REL). I agree that this is a weak point in the reasoning, and it should be explored, but I believe it's monopoly on attention has been deeply unfortunate - the issues surrounding (CON) have been completely neglected. Many presentations of the argument in the literature don't even acknowledge (CON) as a premise (Williamson's own presentations actually do acknowledge it). It's been the same online: in a recent discussion over at the Excluded Middle Errol Lord defines luminosity as I have above, and then when presenting Williamson's argument he writes:

'Now suppose feeling cold is luminous, which entails (2i):

(2i) If in Ax one feels cold, then in Ax one knows that one feels cold.'

(I've altered the reference to cases to be in line with that of the rest of my post here.)

I certainly don't mean to pick on Errol at all - the same move is made in several papers in print, and indeed, I only barely made things more explicit in my earlier post on this stuff. Moreover, Brueckner and Fiocco relegate the following remark to an endnote in their 2002 paper on the argument:

'Following Williamson, we will simplify things by speaking of knowing rather than being in a position to know.'

Over the next while I'll endeavor to convince you that this isn't a harmless simplification at all - we need to explore the issues surrounding (CON) just as much as those arising from (REL). (CON) is an instance of a more general principle, on which subsequent posts will focus:


In every case Ax, if one is in a position to know that condition C obtains, then if one has done everything one is in a position to do to determine whether C obtains, then one knows in Ax that C obtains.

Williamson is quite explicit that as he intends to understand the notion of being in a position to know, Determination is a necessary condition on one's being in a position to know:

'To be in a position to know p, it is neither necessary to know p, nor sufficient to be physically and psychologically capable of knowing p. No obstacle must block one's path to knowing p. If one is in a position to know p, and one has done what one is in a position to do to decide whether p is true, then one does know p.' (Knowledge and its Limits: 95)

In posts to follow, I'll discuss the role of Determination in the debates on the viability of semantic anti-realism and on the constitutive norm of assertion. Stay tuned.

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I always thought the idea here was that one is consciously and actively introspecting about whether one feels cold, such that for any case along that morning, if one is in a position to know that one feels cold, then one actually does know that one feels cold. Whether or not this sort of constant active introspection is actually possible might be a further question, but it doesn't sound incredibly implausible. The way you put it, it sounds like considering might bring one into a different case, and thus break the argument.
(CON) (If in a case Ax, one knows that one feels cold,) (then if one actively considers the matter, (one knows in Ax that one feels cold.))

Do those parens pick out the right scope of each clause? If they do, then (CON) is trivially true. If one knows in case Ax, then one knows in case Ax. Is the antecedent supposed to read "If in a case Ax one is in a position to know that one feels cold"?
Thanks Errol, I hadn't noticed that. It's just a silly typo. (CON) is the premise that links the consequent of luminosity claims - that one is in a position to know that C obtains - with the antecedent of the reliability premise - that one knows that C obtains in that case, so the 'in a position to' is crucial; I'm not sure how it went AWOL on me, but it's fixed now.
Kenny, you're right that that's how (CON) is meant to work in the argument. But Williamson needs the generalized thing on p95 if he's to claim that no non-trivial condition is luminous - that the number of books in my office is odd is a non-trivial condition, but no amount of introspection will be sufficient to pass from being in a position to know that condition obtains to knowing it obtains. Could you maybe spell out your thought in the last sentence a little more, please? I'm not quite seeing it yet.
Perhaps in case x I'm in a position to know that I feel cold, but I'm not considering the proposition that I feel cold. However, once I consider this proposition, I may now be in case y which is not the same as x. In y I may no longer be in a position to know that I feel cold (especially if some sort of contextualist thing is going on with knowledge), and in fact the very act of considering might change my situation enough that I no longer feel cold! At any rate, I'm unlikely to be in a position at y to know that I felt cold at x.
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