Wittgenstein's Philosophical Investigations: The Muddle of Understanding as a Mental Process
Wittgenstein writes that "perhaps you will say . . . understanding itself is a [mental] state" (PI, 146). Wittgenstein presents this supposition--that the demonstration or viable accompaniments to understanding are symptomatic of an underlying mental state--in order to reduce the notion to absurdity. I shall point out this reductio and reasoning in rejecting the notion the understanding and knowledge are mental processes. Wittgenstein's resolution to the notion is to get us to think of understanding and knowledge as dependent upon the particular circumstances of the language-game. Mental states, according to Wittgenstein, have two distinct qualities about them: they have some amount of temporal duration and can be readily predicated of the individual at the time they occur. Thus, we say of someone that "he has been in continuous pain . . . he was depressed . . . he was in great excitement" and so on (p. 59e, n.(a)). To denote the temporal duration of the mental state we say further that he was depressed for the "whole day" or someone was in continuous pain "since yesterday."
Our grammatical use of the verbs "to know" and "to understand" fool us into thinking that they are used to denote mental states. It seems to us that the discovery by B of A's formula was first in the understanding because we feel the momentary sensation that we "know" the solution. It appears to us then that understanding and knowledge are mental processes with some amount of temporal duration (PI, 151). Yet Wittgenstein feels that it is absurd to suggest that we have a mental picture for some length of time of the alphabet or of a multiplication table for the number 9 (PI, 148). In the case of (143) it is conceivable that the formula may occur to B (or A may at some point impatiently provide the solution to him) and B may still not understand (152).
If understanding is a mental state, then there must be more to it than the "characteristic accompaniments" that visibly manifest themselves when understanding occurs. Understanding seems to be hidden behind the characteristic accompaniments that emerge symptomatically from it. Understanding, it seems, is a shadow which lies just behind the characteristic accompaniment (PI, 153; 194). Now we are in the muddle for "how can the process of understanding have been hidden from B, when he said 'Now I understand'[?]" (153). If understanding is a mental state then it should have some amount of temporal duration during which time we should be able to easily identify that understanding within ourselves. If understanding is a hidden shadow behind the visible accompaniments, then we certainly cannot justify predicating of ourselves some feeling, activity, or state which is otherwise unknown to us. Further, a thing which we are having difficulty finding within ourselves is not something that enjoys a duration in time. If understanding is a mental process or state, then we should be able to see it inwardly or access it the way we do the sensations of pain or the melody of a piece of music. Therefore, Wittgenstein concludes, understanding is not a mental state (154).
Wittgenstein's reductio hinges on showing the inconsistency between a mental state, which has some amount of duration of time, and understanding which seems to be instantaneous. In (148) Wittgenstein asks "When do you know[?]. . . Always? . . . is what you call 'knowledge' a state of consciousness or a process[?]" When B exclaims "Now I can go on!" this sudden realization of understanding occurs within an instant. It has no perceptible beginning and our sudden realization has long-since faded by the time we realize that it had even occurred.
We are fooled by our use of grammar and run into trouble when we try to think of understanding as a mental process of some duration in our mind. Wittgenstein's reference to Augustine--in which time is something that Augustine knows provided that no one asks him--helps to illustrate the problematic nature of understanding (PI, 89). It seems an odd question to ask when we were first aware of the rules of chess in their entirety. If asked, we cannot say exactly when we knew all of the rules of chess and we do not experience a period of understanding during which we become consciously aware of all of these rules while moving a single chess piece (p. 59e, n.(b)). Sometimes we doubt that we are able to whistle a tune in its entirety, but discover to our satisfaction that after beginning the first few notes we can. On other occasions, we're mistaken when we believe that we do know the tune when in fact we sometimes discover that we do not or have forgotten it (PI, 184).
Wittgenstein's resolution in (154) argues that understanding and knowledge rely upon the particular circumstances in which they are being demonstrated. Rather than be misled by the grammar of these verbs, we should instead inquire into the circumstances which provide the justification for our concluding that we know how to go on. Certainty of knowledge will be embedded within the language-game itself; there are criteria used to determine whether or not understanding has taken place and these criteria vary from circumstance to circumstance (PI, 182). Wittgenstein argues that "the criteria which we accept for . . . 'being able to', 'understanding', are much more complicated than might appear at first sight" (PI, 182).
Wittgenstein seems correct in pointing out that the circumstances will reveal whether or not I know whether I can go on. If knowledge is a mental state then I should know, upon mental introspection, whether or not I am able to recite the first ten lines to the Iliad. I could confidently assert that I can and just as the mental state of pain is incontrovertible to me so too should be the presence of these lines within my mind. Yet, after reciting "Sing, goddess, the anger of Peleus' son Achilleus" it suddenly occurs to me that I cannot go on. Or perhaps I can and finish without difficulty under some circumstances but forget the lines next week under completely different circumstances. Maybe in the first case I was alone with someone in intimate surroundings so that the words came naturally to me while in the latter case I was at a podium in front of hundreds of people. Wittgenstein wants to point out that knowing something is very much dependent upon the particular circumstances that we find ourselves in when we are asked to demonstrate that knowledge. Because of the circumstances of the latter case--I was nervous or perhaps I was suffering from jet lag or couldn't sleep the night before--I failed to remember the poem. Yet under different circumstances, such as when I get a good night's sleep, the lines of the poem are known to me when I recite them. So it seems that my original statement of knowing the first ten lines of the Iliad was a "signal" or an almost reflexive indicator that I believed that I could go on if asked to do so (PI, 180). Given the circumstances that I get a good night's rest I can say that I can recite the first ten lines of the Iliad.
In the case of B's struggle to derive the correct formula from A's sequence of numbers, Wittgenstein seems correct in arguing that the statement "I can go on!" is a signal of B's understanding while the actual outcome depends upon the success or failure of B's attempt to go on. We might say that B's understanding of the formula depends upon whether or not he knows algebra, is familiar with a base-10, place-value decimal system, and so on. The circumstances of B's familiarly with algebra and decimal numbers provide the criteria for asserting that B can go on. Therefore, B's understanding is predicated upon these circumstances and criteria, not the mental machinations that are said to precede the final solution to A's formula.