CHAPTER 22

The Representation of Truth and Knowledge

22.1 Beliefs within Beliefs

What we are concerned with in this chapter are possible ways of representing the belief that a statement is true. We are not concerned with whether particular statements are true, or with the proper methods of deducing true statements from other true statements. The question is - how do the representations of the following statements differ from each other?

'John  believes  that  Mary  likes  him.'
'John  knows  that  Mary  likes  him.'
'John  does  not  know  that  Mary  likes  him.'
'John  believes  inco"ectly  that  Mary  likes  him.'



In section 20.2 we introduced a way of representing someone's internal representation (or beliefs) as a kind of box into which we place the representation of his/her representation. On the lid of the box we can write down who this representation belongs to (let us say 'John') and anything else which we believe to be true about it, including, perhaps, our belief that the contents of the box are incorrect (untrue) even if John believes the contents to be true. If the box belonging to John contains another box (containing, let us say, Mary's beliefs) then what is written on the top of the box is what John believes to be true about Mary's beliefs. If we want to represent what we think are Mary's beliefs then we must create yet another box, and place it outside the box belonging to John but inside our box (which is the whole system).

The closest we can come to the representation of an absolute truth is the representation of what we believe. If we have a representation of John's beliefs, and we want to represent the fact that we believe John's beliefs are true, then we can simply represent the same beliefs within our own box, and note the fact that the contents of John's box correspond to our own beliefs, i.e. 'John thinks.X and we think X therefore John is correct' (in our opinion).

Here, then, we have the difference between the representation of 'John thinks that Mary likes him' and 'John knows that Mary likes him'. For 'John thinks...' we simply have John's box with the appropriate contents, whereas for 'John knows ...' we have not only got John's box, but we have our own box containing a corresponding set of representations and an explicit note to the effect that they agree.

In dealing with a sentence such as 'John does not know that Mary likes him' we can have our own 'box' with the the representation of Mary liking John. Elsewhere we have a representatio of John's thoughts (John's 'box' within ours) and a third element which indicates that these do not agree. It appears that the agreement between 'boxes' should be represented explicitly so that it can be negated without actually representing the contents of 'John's box'.

It is obvious that boxes representing people's beliefs can be nested indefinitely in order to represent a statement such as 'John believes that Fred believes that Mary believes that ...'

22.2 Representing the Knowing of Things not known to us

The idea of creating a correspondence between John's beliefs and ours, in order to indicate that John's beliefs are true, works well enough in many circumstances but comes to grief when we want to represent the information that John knows something which is not known to us. For example, 'John knows Mary's telephone number'. It is not appropriate, even if we know what Mary's telephone number is, to replace the thing which John knows by the number in question, and it is impossible if we do not know what the number is. Knowing a telephone number is more than having a number in your head. The representation of the word 'telephone' must contain within it all the functionality of the device we call a 'telephone', and that representation will contain a representation of someone having something in their head (or in their box), an element X. The possession of this X will allow them to carry out a procedure on the telephone which will cause it to allow them to converse with the person at the other end of the telephone. Clearly we are leaning very heavily on our ability to represent causal links.

The difference between the two kinds of knowing is really the difference between 'Knowing THAT something is true' and 'knowing HOW to do something'. Because of the nature of a telephone, knowing a telephone number is equivalent to 'knowing how'.

Representing something which someone knows and which we do not know can always be converted into the representation of something which produces results which are known to us. If I know that a friend knows all about advanced physics (which I do not), I know that he can pass examinations in physics (which I could not). I do not need to represent the knowledge in his head which enables him to do these things.

22.3 Negative Transportation

A particular problem which has been the subject of some controversy in linguistics is called the problem of 'negative transportation'. The term 'transpor­tation' refers to the way in which the scope of negation appears to move from one level in a syntactic analysis to another level. The phenomenon is therefore seen by some as a problem for syntactic analysis. Consider the following sentences: (la)  He  thought  that  he  did  NOT  need  to  leave.
(lb)  He  did  NOT  think  that  he  needed  to  leave.
(2a)  He  knew  that  he  did  NOT  need  to  leave.
(2b)  He  did  NOT  know  that  he  needed  to  leave.
Most people agree that (la) and (1 b) mean the same thing, and most agree that (2a) and (2b) do not mean the same thing. This seems puzzling in view of the identical grammatical structures of the sentence pairs. Why should the scope of the negation appear in (la) to extend over both the thinking and the needing, whereas in (2a) the scope ofthe negation covers only the knowing and not the needing, which remains as a positive assertion? Careful examination of (la) and (1 b) usually reveals, for some people, a subtle distinction in meaning, but the problem of the complete difference between the two types of negation in (2a) and (2b) remains.

The problem can be resolved, however, by resort to belief structure representation. Consider first the positive forms of these sentences:

(la)  He  thought  that  he  needed  to  leave.
(2a)  He  knew  that  he  needed  to  leave.
In both cases we have a box with 'his' beliefs inside it. In the case of (2a) we have in addition our beliefs, which correspond to his.

The word 'know' carries within it a hidden reference to an additional representational structure of the thing which is known. Moreover the veracity of that additional structure is vouched for (by us). When we negate each sentence, the negation applies to the whole sentence (to John's beliefs); but certain elements escape negation by referring to something for which there exists other evidence of its truth. In the representation of sentence (2) the negative form (2a) 'he did not know that ...', the part of the representation which lies outside John's box (which belongs to us), escapes negation. Our representation then indicates that 'he' lacks this vital information.