What Does Understanding Consist in?

Monday, 10 July 2017

What Does Understanding Consist in?

My aim in this paper is to address certain questions about intentionality in the form of understanding, the most important of which are the following. Is understanding an event or process, as when I say that I now understand or that I did understand but no longer do? If understanding can occur at a particular time, when we need not be manifesting it, then it must involve dispositions, so that we understand a rule, for instance, if we are disposed to follow it correctly. But should I say that my understanding consists in following the rule, or being thus disposed, or that it is in this way that I manifest my understanding, which itself is a mental state?

 If understanding is a mental state, how is it connected with the overt behaviour by which it may be publicly manifested? Surely the one can occur without the other. Again, if there is such a mental state how is it connected, not with behaviour but with thoughts and mental images? Can I not have a mental image of a word, say, without understanding the word? Clearly I can, but perhaps if I understand the word then this informs my mental image of it. Similarly, if a word is on the tip of my tongue, and if all at once I have it, then surely that eureka experience is inseparable from my sudden realisation that it is the right word. Could it be, then, that understanding is irreducible, so that it cannot be reduced to its behavioural manifestations or to mental content if in each case they are non-cognitively described?

            Also, there is a question about incorrigibility: If I sincerely claim that I have toothache, then arguably I cannot be mistaken, which I can be if I claim to understand the word ‘toothache’; but this makes sense only if the argument is that I cannot be mistaken provided that I understand the word ‘toothache’ or the sentence ‘I have toothache’. But surely I understand the sentence ‘I have toothache’, said by me of myself, only if I do have toothache. And now it follows logically, but trivially, that I cannot be mistaken in my claim to have toothache. The question, then, is whether any statement about oneself can be incorrigible in a non-trivial sense.

            That, in the form of questions, is the problem of intentionality applied to the concept of understanding, and since we are not going to have time to cover all of it, what I suggest is that I focus on the occurrent and dispositional aspects of understanding and on the question of whether it is irreducible.

            If we start with Wittgenstein on understanding, we may first of all ask whether it has to be manifested in overt behaviour, in line with his dictum that inner processes stand in need of outward criteria. He says that to understand a formula we need to be able to apply it according to public standards of correct use, so that it is not enough just to have it in our minds, for we also need to be suitably disposed with regard to public application of the formula.

 Let us try to construct a counter-example. Suppose that a monolingual Frenchman and myself have the following English sentence, which I shall call sentence A, in our minds: ‘How many 7’s are there in the set of natural numbers between 1 and 99 inclusive?’ Suppose I have just read this sentence and understand it, whereas the Frenchman has been taught to uncomprehendingly read it aloud and has memorised it. If we now ask what makes the difference between us, then one answer is that unlike him I have the dispositions appropriate to understanding. It would seem, too, that these need not be behavioural dispositions, for it could be that without saying or writing anything I have the following thought, which I shall refer to as sentence B: ‘How many 7’s? Let me see: 7, 17, 27 – hang on, one 7 for every ten numbers, ten tens in a hundred, therefore the answer is ten 7’s.’ To have this thought is to actualise one of the dispositions I need to have when entertaining sentence A if I am to understand it.

            Of course, I could have actualised a behavioural disposition, for instance by writing down sentence B, but the point is that I did not need to, contrary to what Wittgenstein seems to be saying. But now, let us take this further: should I say that my understanding of sentence A, which the Frenchman lacks, consists only in my being suitably disposed? The trouble here is that it is easy to imagine that the Frenchman has been taught to parrot not only the question but also the answer, so that he, too, has sentence B in his mind. Perhaps, then, there is an essential difference which so far we have overlooked, and an obvious candidate concerns the qualitative difference in the experience of thinking or speaking the sentences. When the Frenchman has them in his mind, he experiences them as I would a Russian script that I have learnt by heart. If we imagine my having some limited interaction with Russians, then it could be that I am taught to speak a particular Russian sentence in response to being prompted in Russian, so that in speaking the sentence I do have dispositions but with no understanding of what I say or am disposed to say.

            It is arguable, then, that there is a qualitative difference in the experiences of entertaining a sentence with and without understanding, and this would fit with the fact that if to understand a sentence is to be suitably disposed with regard to other sentences, then they too have to be understood. Thus, I understand sentence A if, for instance, I am disposed to respond with sentence B, but only if I understand sentence B in its turn There is a strong indication here that understanding should be regarded as being irreducible, which is to say that I understand sentence A, ‘How many 7’s are there in the set of natural numbers between 1 and 100?’ if I take it to ask how many 7’s there are in the set of natural numbers between 1 and 100, there being no other way of putting it. It is true that sentence A is susceptible of a non-semantic description, as when I refer to it as consisting of a string of letter sequences, the first of which is H,O,W; but this is just what the uncomprehending Frenchman would have to say, whereas it is open to me to add that my understanding of the sentence informs my experience of it, so that unlike the Frenchman I ‘see’ it, in inverted commas,  not as a string of letters but as a statement, a sentence charged with meaning, this being the qualitative difference which was mentioned earlier.

That is the position I wish to defend, for instance against the charge that no matter how I ‘see 'sentence A, it is always possible that I do not understand it. It is true, of course, that mistakes are made, and in fact sentence B gives the wrong answer to question A, the correct answer being nineteen, not ten. An easy mistake, unlike that of thinking I understand sentence A when in fact I do not. To bring out this point, imagine that I am reading a story which, if it is to make any sense, must contain, apart from correct English, a great deal of detailed scene-setting and narrative continuity, so that the locations and the lives of the characters become familiar to me, as in real life. This means that every line of text generates and confirms my expectations, for instance with regard to the consistent use of names of people and places. Imagine all that, as with any story, and now try to entertain the possibility that I am completely mistaken in thinking that I understand a single word of it. This would be tantamount to its being not me but the Frenchman who is looking at every word of every line and thinking that he understands when in fact the words mean nothing to him at all.

            It would, of course, be very foolish of me to entertain such a possibility, but worse than that it would also be incoherent. The reason, to go back to sentence A, even though it is much shorter than the average story, is that if I seriously doubt whether I understand it, just because it is logically possible that I do not, then I must also question my grasp of the sentences by which I express that doubt; hence its incoherence.

            To argue as I have done  is to analyse understanding from a first-person point of view, leaving work to be done with regard to other people’s understanding. Let us consider, then, a behaviouristic account of it. Suppose, for instance, that I judge that another person understands the even number sequence, 2, 4, 6, 8 and so on, given his actions and what they indicate about those to which he is disposed. Then it could be argued, as indeed it is, that his understanding is constituted by his behaviour, not by any inner states and processes which it manifests and reveals. This is not to deny that to credit him with understanding is to imply the existence of conscious processes guiding his actions, otherwise my computer would understand the game of noughts and crosses.

Relevant here is the undoubted fact that other animals show awareness of their environment, as with dogs and bats, even if the grasp of arithmetical sequences would seem to have eluded them thus far. Anthropomorphism apart, we have no insight into the cognitive processes of a dog fetching its lead or of a bat hanging very cleverly upside down. All that we can say, or so the theory goes, is that understanding, even if it requires consciousness, consists in overt behaviour, particular inner processes being unknowable in the case of other animals and inessential in the case of people.

            Now, it has to be admitted that such a theory may seem plausible, at least until its full implications are brought out and a comparison made with a first-person view of what it is to understand. As already argued, it is very obvious that the facts of my own understanding are inimical to any analysis that disregards or sidelines conscious processes of cognition, including those that enter into my judgement of another person’s understanding. Thus the first-person point of view is inescapable, so that our task is to reconcile it with the third-person point of view, one approach to which is to assimilate them to each other as much as possible.

            Suppose, for instance, that I come across a book I remember reading; then what I cannot do, of course, is to recall my actual cognitive processes at that time, an ignorance of detail which also extends to what I know of another person when I think that he is reading a text. What I can say, however, is that he scans every word of every line, that his understanding informs his reading experience, that for each word he has numerous dispositions as a condition of understanding it. This is to say that I attribute to him, as to myself, the essence of what it is to read and to understand.

            What, though, of the fact that what it is to understand is governed by correctness conditions, so that the concept of understanding is normative? Kripke's argument, as discussed in previous posts, is that if understanding is dispositional, then from a first-person point of view, which is that of the individual, one cannot distinguish between dispositions as they are and as they ought to be. This, for many theorists, is the crux of the matter, especially if it is realised that the argument, if valid, also applies to occurrent understanding, all of which may lead us to expect the distinction to be clear-cut. But now, the problem here is that in appreciating the distinction, I necessarily take a first-person stance, since I can take a third-person stance only in the trivial sense, in the present context, of speaking in the third person or making reference to other people. Kripke would seem to disagree, for he speaks of the practice of the community, which he opposes to that of the individual, the former being such that the practice of the community is, as it were, self-complying, there being no distinction between that practice as it is and as it ought to be..Arguing against him, I claimed that nothing could then count as the practice of the community in Kripke's sense, for there would be no way of specifying such practice in the case of any particular word. None of this is without relevance, but my present point is that the distinction in question is grasped by individuals, of which I am one, so that it is filtered through my own thoughts, including those by which I distinguish between my own linguistic practice and that of the wider community. The first-person point of view is inescapable, even when one's reference is to the practice of a community.

            If this is correct, and again harking back to previous posts, then Kripke must be wrong, and the distinction between practice as it is and as it ought to be must be one that the individual can apply to his own reasoning. Consider, then, the previous question of the  number of 7's between 1 and 99, the answer I gave being nineteen, and suppose that I seek confirmation, to which end I reason as follows. There are nine digits between 1 and 9, after which there are ninety binary numbers, the total number of digits therefore being 189. There are nine zeroes, the other digits all having the same frequency, so that there must be twenty of each. So nineteen is the wrong answer, this being my conclusion if I can pinpoint my mistake. Ah, now I have it: I overlooked the fact that 77 has two 7's, not one.

            Thus it is that I incorporate standards of correctness into my own system of reasoning and belief, further to which is the fact that it is only within a sytem in which I take for granted my understanding, if it seems to me that I understand, that I can doubt my understanding in particular cases, all of which is clearly illustrated in the example just given.

Answer to Last Week's Puzzle

Here is the puzzle again:

The Problem of More Hats and Wearers
There are four men, Arthur, Brett, Chad and Lionel, who is blind, and six hats: 3 red, 2 black, 1 white. As before, they each wear a hat they cannot see, and they can see one another, apart from Lionel, and hear one another. Each sighted man in turn now says that he does not know the colour of his hat. Then Lionel says that he does know. 
What is his hat colour and how does he know?

Solution to problem of more hats and wearers:
Arthur says he does not know (the colour of his hat), so it cannot be that Brett, Chad and Lionel are wearing two black hats and a white one, otherwise Arthur would say that his hat is red.
Now Brett says he does not know (the colour of his hat), so it cannot be that Chad and Lionel are wearing the two black hats, otherwise Brett would know that his hat must be red, since it could not be white.
By the same token, Chad and Lionel cannot be wearing a black and a white hat, otherwise Brett would know that his hat must be red, since it could not be black, and nor could it be white, there being only one white hat. 
And now Chad says he does not know (the colour of his hat), so it cannot be that Lionel is wearing a black hat, otherwise Chad would know that his own hat must be red, since it could not be black or white; and by the same token, Lionel cannot be wearing a white hat, otherwise Chad would know that his own hat must be red, since it cannot be black, and there is only one white. Therefore, Lionel’s hat is red, a deduction which he has made when he says he knows the colour of his hat.

This Week's Puzzle

            99        45        39        36        28        21

72        27        18        21        ?          13        7

The above two rows of numbers are connected in such a way that the ? stands for a particular number. What is it? Note that the '7' is not a typo.