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Bertrand Russell famously defended a principle of acquaintance taken to govern some or all forms of propositional cognition—for example judging that p or supposing that p. One of the central statements and defences of the principle occurs in ‘Knowledge by Acquaintance and Knowledge by Description’ (Proceedings of the Aristotelian Society 1910–11; reprinted in Mysticism and Logic (1917; references to the 1986 reissue)). The statement of the principle, in italics, and defence occur in the following brief passage:

Whenever a relation of supposing or judging occurs, the terms to which the supposing or judging mind is related by the relation of supposing or judging must be terms with which the mind in question is acquainted. This is merely to say that we cannot make a judgement or a supposition without knowing what it is that we are making our judgement or supposition about. It seems to me that the truth of this principle is evident as soon as the principle is understood…” (211, Russell’s italics)

Two preliminary comments about this passage are in order. The first is that Russell seems to suppose that the subjects of judging and supposing are minds rather than things with minds—i.e. thinkers. I won’t comment further on that supposition here. The second is that Russell appears to take instances of judging or supposing to be occurrences—plausibly, episodes or events, rather than e.g. states or processes. (209) A question therefore arises about the generality of the principle of acquaintance. Is the principle intended to apply to all forms of propositional cognition? First, does Russell think that all instances of propositional cognition—including for example instances of believing or knowing—are episodic, or does he allow that some such instances are states? Second, if Russell were willing to allow that some forms of propositional cognition are not episodic—because, for example, their instances are states—, would he take the principle of acquaintance to apply also to the states? In the first instance, it would be natural to assume that Russell intended the principle to apply to all forms of propositional cognition. Hence, since Russell says nothing explicitly to restrict the principle’s application, it would be natural to take Russell to be committed to holding either that all forms of propositional cognition are episodic or that the principle applies to cognitive states as well as episodes.

The principle then claims the following:

(PA) In any case in which a subject, S, cognizes that p, then for all constituents C of the proposition that p, S is acquainted with each of C.

The defence of the principle takes the following form (ignoring issues about unrestricted generalisation over propositions):

(P1) For all S, p, if S cognizes that p, then S knows what it is that they are making their cognizing about.

(P2) For all S, p, if S knows what it is that they are making their cognizing about, then for all constituents C of the proposition that p, S knows each of C.

(P3) For all S, p, and constituents C of the proposition that p, if S knows each of C, then S is acquainted with each of C.

(C4) For all S, p, and constituents C of the proposition that p, if S cognizes that p, then S is acquainted with each of C. [≈ (PA)]

Russell takes (P1) to be obvious. (P2) and (P3) are the most natural ways of attempting to mediate a straightforward transition to Russell’s conclusion, (PA), via its plausible equivalent, (C4).

One serious problem with this version of Russell’s argument is that (P2) is undefended, and looks suspiciously close to an application of (PA). For knowing what it is that one is making one’s cognizing about is not obviously a matter of knowing, in the sense of being acquainted with, the elements that one’s cognizing is about. Rather, where it is a fact that one is making one’s cognizing about the elements C, knowing what it is that one is making one’s cognizing about is knowing that fact: it is knowing that one is making one’s cognizing about the elements C. In that case, (P2) looks to depend on a principle to the effect that propositional knowledge is subject to an analogue of (PA), so that knowing that one is making one’s cognizing about the elements C requires knowing (in the acquaintance sense) each of C.

Now a fairly standard manoeuvre at this point would be to suggest that Russell really meant for his appeal to the subject’s knowing what it is that they are cognizing about to be an appeal to the subject’s knowing that which they are cognizing about. Although Russell appears to be wrong that there is a natural reading of the “knowing what” construction that takes the required reading, he may have been mislead by the availability of an analogous reading of the “seeing what” construction. For although there are readings on which seeing what is before one is a matter of seeing that such-and-such, there are also readings on which it is a matter of seeing that which is before one. For instance, one might see what is before one either in seeing that a computer screen is before one, or in seeing the computer screen. Thus, what Russell should have exploited is the following replacement for (P1):

(P1’) For all S, p, if S cognizes that p, then S knows that which that they are making their cognizing about.

A natural concern about (P1’) is that it is too close to (PA) to serve in argumentative defence of the latter principle. It may be that Russell nonetheless took (P1’) to be obvious. However, that won’t help others to get themselves into a position from which they also take it to be obvious.

At that stage, one might be tempted to give up, as hopeless, the attempt to reconstruct Russell’s argument. Instead, one might accept that Russell’s attempt to defend (PA) fails, and then try to diagnose the source of his error. Given the materials we have, a natural diagnosis would be the following. The premise Russell needs, (P1’), is not independently plausible. However, it might be argued that the premise to which he appeals, (P1), is independently plausible. If that were right, then we could understand why Russell might take that premise to be obviously correct. We would then be in a position to explain his presentation of the erroneous argument as due to his slipping unconsciously between appeals to knowing what and knowing that which.

That diagnosis might be correct. However, it appeals, in passing, to the claim that (P1) is plausible. Now it might be that people are in fact inclined to find (P1) plausible. But further reflection on that premise raises a number of delicate issues.

Let’s continue on the assumption that (P1) is supposed to hold with respect to all forms of propositional cognition, including propositional knowing. Then we have the following.

(P1) For all S, p, if S cognizes that p, then S knows what it is that they are making their cognizing about.

(P2’) For all S, if S knows what it is that they are making their cognizing that p about, then for some appropriate true proposition, that q, that answers the question, what is S making their cognizing about?, S knows that q. [Plausible approximate account of knowing what.]

(P3’) For all S, p, if S knows that p, then S cognizes that p. [From the opening assumption.]

The apparent availability of this derivation presents the proponent of (P1) with two potential difficulties for (P1). The first difficulty is that the derivation is recursive, so regressive. Suppose

(P4) S cognizes that that patch is red.

From (P1), we have:

(P5) S knows what it is that they are making their cognizing about.

(P6) An appropriate answer to the question, what is S making their cognizing about?, is that S is making their cognizing about that patch’s being red. [Plausible account.]

(P7) S knows that S is making their cognizing about that patch’s being red. [From (P2’)]

(P8) S cognizes that S is making their cognizing about that patch’s being red. [From (P3’)]

(P5) S knows what it is that they are making their cognizing about. [Reiteration.]

(P9) An appropriate answer to the question, what is S making their cognizing about?, is that S is making their cognizing about S’s making their cognizing about that patch’s being red.  [Plausible account.]

(P10) S knows that S is making their cognizing about S’s making their cognizing about that patch’s being red. [From (P2’)]

(P11) S cognizes that S is making their cognizing about S’s making their cognizing about that patch’s being red. [From (P3’)]

And so it goes. In combination with (P2’) and (P3’), (P1) is regressive, and imposes cognitive conditions on cognizers that seem on their face highly implausible. In order to cognize that p, one must engage in cognition at the next level in the hierarchy that is directed onto elements that may be absent from the proposition that p, including cognition directed at the cognition taking place at the previous level in the hierarchy. Moreover, a subject’s cognizing that p requires that they suffer indefinitely many pieces of cognition, each about about pieces of cognition that are lower in the hierarchy. Perhaps those consequences are defensible. If they are not, the defender of (P1) will need to reject either (P2’) or (P3’). I take no stand here on which of those options constitutes their optimal response.

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