An Expedient Mind: ISSUES

AN EXPEDIENT MIND

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TRUTH

Truth, Language and Philosophy
If our robot is to use language as we do, then he cannot dodge the issue of truth. He cannot avoid using or hearing statements with words such as “It is true that …”, “It is my belief that …” and “He knows you did that”. Somehow he must be able to represent the meaning of these statements, and respond to them in a way which we would find appropriate. If he does all that, I would say that he understands the meaning of truth. Understanding truth is no trivial matter, however, for it is an issue which lies at the heart of philosophical discourse.

Truth and Prediction
I return to the central theme of my thesis - the evolutionary driving force behind the development of intellect. The intellect is a mechanism for making accurate predictions of future events. Truth is a measure of the extent to which those predictions match observation. Note that it is the observations which are in the future and which are predicted. The events and circumstances which are the subject of those observations, will often be future events etc. but that is not a requirement. It could just be that the circumstances have existed for some time, but have not yet been observed.

The Meaning and Truth of Words and Sentences
It is a phenomenon frequently remarked upon that while sentences and other multi-word phrases can be considered to be either true or false, single words, uttered in isolation, do not appear to have any truth-value at all. What I have not encountered, however, is an explanation about why that is the case.
My view is that a single #concept cannot make predictions.
An #entity, for example, identifies something. It gives us a set of potential properties. It provides potential roles it might play. but it does not identify one particular action or set of circumstances which pertain at one location at one moment in time.
A #scenario, typically, identifies an action, It tells of the roles which various potential entities can play in this action. It tells us the potential consequences (predictions). But because those #entities which are playing the roles are not identified, no predictions can be made.
It is only when these two are kinds of #concept are brought together in an #interpretation, that the deficiencies of each are made good by the presence of the other. That is when some definite statement is made about the world. It is only then that predictions can be made. And it is only when predictions are made that the issue of truth can arise.

Evaluating the Truth of a Statement
When our robot tests the “truth” of a statement, what he is actually doing is comparing two INTERNAL structures.

(1) a test-structure and
(2) a reference-structure.

Usually, when we are talking, in general terms, about the “truth” of a statement, the test-structure is the structure which represents the meaning of that statement, and the reference-structure is that structure I call {REALITY}. In our robot {REALITY} has many components - his on-going #memory-trace, his store of #concepts, his #interpretation of events, which includes his three-dimensional model of the physical environment.
Let us say that I make the statement (S1) -

S1 = “A book is lying on the table”.

He (the robot) will process the sentence “S1” and create the #interpretation structure which I denote with the expression {S1}. I nside {S1} we can find a representation of the #concept {BOOK} lying on top of the #concept {TABLE}. So his task is to compare {S1} with his {REALITY} which is constantly being updated by his interpretation of his sensory perceptions. In effect {S1} says to him - “If you turn your head in the direction of the table, you will find that your {REALITY} will then have the representation of a book lying on the table”. If that prediction turns out to be correct, then the robot will decide that that sentence S1 is “true”. Note, however, that he might believe that the statement is true even if he does not turn his head to put that verification process into effect. In these circumstances, instead of using {REALITY} to check the truth of the statement, he uses to interpretation of the statement, to update his {REALITY}. So {REALITY} can be formed vicariously, using information from a trusted source. We need ways to represent these different conditions. Historical Truth Consider the same utterance put into the past tense. S2 = “A book was lying on the table”. The truth of that statement cannot be verified by the robot by turning his head and looking. Verification in that case, is either abandoned, and the truth taken on trust, or S2 is subjected to indirect checks. To do that, the structure {S2} must be manipulated to generate some predictions. If the book is no longer lying on the table, that fact and the structure {S2} imply or predict that the book has been removed by some unseen causal factor. That prediction might generate a search for confirmation in the form of a question “Has anyone taken a book off this table?” It could also generate a search for a dust-free, book-shaped patch on the table surface. Verification, in these circumstances, resembles the investigation of a crime, in which an attempt is made to reconstruct past events from implications and currently available evidence. The simplest response, however, is to believe the statement. If that is done, the structure {S1} is incorporated into {REALITY}. Truth, in a non-linguistic context I am uneasy with the significance, which philosophy has traditionally placed on language, in relation to truth. It seems to me that any representational structure can have a truth-value. Late one misty night I was driving home on a winding Highland road. Although the road was tortuous, there were a few straight sections. When I saw the road stretching out ahead of me in a dead straight line, I put my foot down. Because of the mist, I could not actually see the road clearly, but I could see the white line which marked the centre of the road. A few seconds later I was breaking hard and frantically throwing the wheel over. That “white line”, I had discovered, was actually a tall white tree growing on the far side of a very sharp bend. It could be said that the interpretation structure which I had constructed from my sensory perceptions, had told me a lie. Fictional Reality. The term “fictional reality” may be a contradiction, but it identifies a phenomenon which requires an explanation. Consider this sentence - S3 = “Hamlet killed the King with a sword tipped with poison” Is S3 true? Most people, at least those familiar with the Shakespearean play, would say “YES”. And yet, although there was indeed a historical figure who was the Prince of Denmark and who was called Hamlet, it is very unlikely that he did the things which Shakespeare described. We can be fairly certain, in fact, that he did not stride about the battlements of Elsinore, spouting mournful soliloquys in Elizabethan English. But, in this context, that answer “YES” does not imply that these things are a historical fact. The “truth” verification process would not use {REALITY} as its reference-structure. Instead it would use a structure we might call {HAMLET} which is a representation of the action depicted in Shakespeare’s play. That suggests two verification procedures ... test-structure = {S3} reference-structure = {HAMLET} answer = “true”. We can then make a check on the validity of {HAMLET} thus test-structure = {HAMLET} reference-structure = {REALITY} answer = false The Representation of Meaning and of Truth I repeat, to test the truth of a statement, the robot will compare the structure which represents the meaning of the statement, against some reference structure which will normally but not always be {REALITY}. That idea makes a clear distinction between the meaning of a statement and its truth value. We can create the meaning structure without testing its truth value. But we cannot test its truth value without first creating its meaning structure. So truth value depends upon, or is an attribute of meaning. Meaning comes first. Truth is a dependent attribute. That contradicts a theory called “truth conditional semantics” (TCS). According to TCS the meaning of a statement is a list of the referents, which would make the statement true. If for example, the statement is “the book is on the table” then the meaning of the statement is a comprehensive list of all the books, and tables with reference to which that statement would be true. The idea has its origins in the foundations of mathematics and in that context it provides a useful tool particularly in the specification of artificial computer languages. My approach, however, requires that the meaning of a statement is determined before its truth value can be tested. So what happens if the statement makes an explicit reference to the truth value of some other statement? eg: “It is true that the book is on the table.” We can read the statement above as a double-barrelled statement like this ... statement (1): “The book is on the table” statement (2): “Statement (1) is true” And we can say that statement (2) “quotes” statement (1). The “Disquotational Theory of Truth”, holds that the quoting of a statement in that way, does not matter. According to that theory, statement (1) and statement (2) have exactly the same truth value and therefore they have the same meaning. My approach comes at it from the other direction. The two statements may indeed have the same truth value. In fact, it is obvious that if statement (1) is true, then statement (2) must also be true. But they do not, in my view, have the same meaning. My approach is to represent the meaning structure of the partial statement, “It is true that ... “ as a structure with this form [ID, TEST, REF, matcher-program, CRIT, RES=true] where ID = the identifier for this shoe-box TEST = the structure under test REF = the reference structure matcher-program = the program which will do the comparison CRIT = a set of criteria to be used by the matcher-program RES = the result obtained by the matcher-program. Because the structure has its own ID it is possible for us to refer directly to it and to all its component parts. In particular we can refer to RES(ID) and in that way gain access to the result of a matching procedure. If we now re-write that in terms of our examples S1 and S2, we get The meaning structure of S1 is {S1}. The meaning structure of S2 is {S2}. {S2} = {IT IS TRUE THAT S1} = [ID, {S1}, {REALITY}, matcher-program, CRIT, RES=true] Now that is simply a meaning structure. It is not the truth-value of S2. What it does do, however, is refer to the truth-value of S1. Even so, it is still a meaning structure. To get a truth-value for S1, the structure above must be activated. That is, the matcher-program must be activated or evaluated. That program will compare {S1} with {REALITY} using the criteria CRIT, and place the result obtained in RES. We need a way of putting that activation into effect and to do that we can introduce a new function eval. The expression eval{S2} indicates that {S2} is activated in that way and the result obtained will be the truth value of S1. So we can write RES(eval{S2}) = truth value of {S1} Notice, however, that that provides a truth-value for {S1} it does not produce the truth value of {S2}. To obtain that we would need to activate the meaning structure of another statement which asserted that “S2 is true”. To examine the truth of any statement or make an assertion about its truth, it is necessary to step up to a higher level, where one can, as it were, look down on the first from a high vantage point. From that position one can point and say “THAT STATEMENT DOWN THERE IS TRUE” The meaning structure of that high level statement is then activated and the result obtained is the truth-value of the lower level statement. The Matcher-program In the next chapter and I will tackle the very severe problems associated with designing a matcher-program to meet our requirements. Here, I will describe the issues involved, only briefly. Matching two data structures (in a way that will achieve a result within a reasonable time-span) is known to be a very difficult problem. As the size of those data structures increases, the time which a program would take to make a comparison, must also increase and it will increase much more rapidly than the size of the structures themselves. In such circumstances, the ability to achieve a satisfactory match, or prove that no such match is possible, can be compromised. Criteria The situation is made even more difficult, by the variability of the match-criteria which may be specified. We can, for example, specify that certain elements of the structures do not need to match. Or we may specify that certain elements may be deemed to match, although they do not do so, in simplistic terms. The upshot, is that the creation of a matcher-program, with suitable criteria, is THE most difficult problem in this entire exercise. Practical considerations force upon us the use of heuristic programs which will often achieve a satisfactory result, but which will not always do so. It will also be necessary to place a time limit on the matcher program. If it over-runs the deadline, or if some other emergency arises while the matcher is running, then it may be necessary to call a halt and declare a failure to find a match. Actually, it is not hard to write some kind of program. We could certainly implement something which would work in some kind of way. But it is very hard to write a program which will always produce results which we would judge satisfactory, in most circumstances. If someone did try to implement my robotic system, they would not find it impossible, but they would find an embarrassment of alternatives with which they would need to experiment. Negation by Failure When a match attempt fails we must make a decision about how such a failure should be interpreted. We could say that the result is “perhaps”, or we could take the view that failure to prove X must imply that NOT(X) is true. Both these interpretations are appropriate in some circumstances. For example, if we have a database of, say, the members of a club, and we want to find out whether X is male or female, failure to find out that X is male, should not be taken as proof that X is female. Maybe he just got missed out, or someone omitted to enter his gender. But if we want to discover if X is a member of the club, then failure to find X in the database can be taken as proof that X is not a member (provided presence in the database was considered to be the definitive proof of membership). That is what is called “negation by failure”. It is an appropriate rule, in that example, because it would be unreasonable to expect us to keep an explicit record for each person who is not a member of the club. In most cases the truth-verification procedure is not carried out. The assertion that something is “true” is often taken on trust, particularly if the information comes from a trusted source. If we insist on the robot carrying out an exhaustive test of every truth-condition, it would place on him, an impossible computational burden, and one which would rarely produce any definite result. One consequence of this is that it possible to construct the meaning structure of a nonsensical statement like “A four cornered triangle”. We can build the structure, but of course it will contain contradictory information. That will not come to light, however, until the meaning structure is evaluated. It will then be found that it is impossible to produce an actual example of the object described. It has an anomalous meaning. It is not correct, in my view, to say that it has no meaning at all. In a famous tract, the leading grammarian Noam Chomsky offered what has since become a famous example of a sentence which is both grammatical and (in his terminology) “nonsensical”. “Colorless green ideas sleep furiously” I find that term “nonsensical” somewhat ambiguous. I can’t decide whether having no sense, means having no meaning at all or having a meaning which is difficult or impossible to understand. I prefer the latter interpretation for which I use the term “anomalous”. It does have a meaning, but when we construct that meaning we find that its various components have been assigned mutually contradictory attribute values. Truth value results The RES element can take the values “true”, “false”, “perhaps”, “unknown” and “undecidable”. These values are simple indicators, or flags. They have no intrinsic significance of their own. They acquire significance when they are involved in a matching procedure or a procedure which generates predictions. “True” is used to indicate that a match has been, or can be found. “False” is used to indicate that a contradiction has been, or can be found. It may, in some circumstances, be assigned arbitrarily, if a positive result is not found within a specified time limit. (i.e. negation by failure). “Perhaps” indicates that a result has not been obtained (or not sought). “Unknown” indicates that a result is “known to be unknown”. I apologise for that clumsy Rumsfeldtian expression. The value “unknown” is introduced specifically to deal with the interpretation of questions. If someone says “Is there a book on the table?” The interpretation of the sentence will represent (A BOOK} being located on {THE TABLE} but it will also represent the truth-value of that interpretation as “unknown” (in the mind of the speaker). Because the sentence is in question form, we must also place in that speaker’s {MIND} the #scenario which predicts that the speaker would like the missing information to be supplied. It has to be “unknown”. The value “perhaps” would not meet the requirements. “Undecidable” is a more difficult idea. This arises when it is actually known to be impossible to arrive at a verification of any kind. The best example of that situation is known as the “liar paradox” which is discussed below. Finally, there is the possibility of representing a truth-value by means of a unique identifier. This facilitates references to the truth-value without assigning an actual value. The Liar Paradox - Self-Referencing and Self-Evaluating Statements S4: “This sentence is false”. That statement is one example of what is known as “the liar paradox”. It is paradoxical because it makes an assertion that contradicts itself. If the statement is untrue then what it says must be true (and vice versa). Avoiding this kind of situation is why it is always necessary to step up to a higher level before making an assertion about the truth value of a statement. The liar paradox has had an honourable role in the philosophical literature on the subject of truth, ever since, in ancient times, Epimenides the Cretian, declared “all Cretians are liars”. The puzzle for philosophy, is how to deal with the meaning and or the truth-value of such a statement. My treatment goes like this .... First we construct the meaning of statement S4. S4 = “This statement is false”. {S4} = [ID, {S4}, {REALITY}, matcher-program, CRIT, RES=“false”} That expression represents the meaning of the statement S4. It is not the truth-value of the statement S4. It asserts that if it is activated the result will be a truth-value of “false”. If we did activate it and the result was indeed “false” then the truth-value of {S4} would be “true”. And that is of course, the nature of the problem. {S4} cannot be both “true” and “false” at the same time. But there is an additional problem. In order to construct the meaning structure of {S4} its components must be evaluated. That requires that we find the truth-value of {S4} to find that we must evaluate its components ... and so on recursively for ever. The same thing would happen for sentence S5. S5: “This sentence is true”. Again we would be driven into endless recursive truth-evaluations. In this case however, we will not have that anomalous contradiction at each stage. Let us keep those two issues separate. A self-referencing sentence is always “undecidable” because its meaning structure can never be computed. A liar paradox sentence like S4 is also self-contradictory. Not only can we never construct its meaning structure, but if we made an arbitrary assignment of either “true” or “false” that would generate a logical contradiction. For S5 however, we can see quite clearly that it can have the truth value “true” but we haven’t the faintest idea what is the significance of that truth value-because we cannot represent what it means. It is not saying anything about anything. It is vacuous. Knowing and Believing The concept {KNOW} contains an explicit reference to the truth-value of some other representation. So if our robot says ... S6: “I know that John is here” ... he is making a double-barrelled assertion. S6 (a): “John is here” S6 (b): “It is true that John is here” So the robot can represent the meaning of the whole thing by creating two meaning structures ... {JOHN IS HERE}1 is placed into his {REALITY} while {JOHN IS HERE}2 is also placed inside {SELF-MIND} the structure representing his own mind. The truth of that second statement is confirmed by making a comparison with {REALITY}. If he wanted to represent the meaning of S7 “I believe that John is here” He would construct only the second of these two structures. That indicates his belief in the truth of {JOHN IS HERE} but withholds confirmation. Negation Transportation One of the best arguments for this approach, is that it deals in a straight forward and robust manner with the problem called “negative transportation”. Consider these two sentences S11: Fred believes that the world is not flat. S12: Fred does not believe that the world is flat. At first sight, these two sentences appear to have the same meaning. They’re not actually identical but they seem to express a similar fact about reality. Now consider these two sentences - S13: Fred knows that the world is not flat. S14: Fred does not know that the world is flat. It is pretty clear that these two sentences do NOT have the same meaning - or anything like it. They contradict one another. If we approach these two pairs of sentences armed only with notions of grammatical analysis, then we have a curious problem which requires an explanation. S11 and S13 have exactly the same grammatical form. The same is true of S12 and S14. The only difference, in each case, is that the word “believes” (in the first pair) has been substituted by “knows” in the second pair. What is more, each pair of sentences is an example of a form of grammatical re-arrangement called “negative transportation”. This has to be seen in the context of transformational grammar, which describes various kinds of grammatical re-arrangement which are said to “preserve meaning”. The best and most often quoted example of a transformation which preserves meaning is the passive transformation ... John kicked Fred -> Fred was kicked by John I dispute that claim about meaning being preserved (exactly) but that is a quibble which we can put on one side for the present. The point is, that these transformations are used to re-arrange sentences without damaging the meaning, in order to get them into a form which is universal to all languages - the “deep structure” grammar which an essential part of the whole theory of transformational grammar. So the question is - does negative transportation preserve meaning, or doesn’t it? Or, why does it preserve meaning when we use the word “believe” and stop doing so when we use the word “know”. MY argument goes like this - The meaning of the word “knows” makes a statement about what someone believes. It ALSO asserts some truth about the world (irrespective of what that someone may believe). That second part of this implication is absent when we use the word “believes”. When we transport the word “not” to a new location, the negation of “knows” negates the belief bit of knows, but it does not negate the factual assertion part (i.e. that the world is flat). A Counter Argument One of the theories of truth which has been much discussed in philosophy, is the idea that truth is equivalent to explanatory power. There is not much difference between that idea and my contention that truth is equivalent to the power of accurate prediction. So I take seriously the criticism levelled at the explanatory power idea by Kirkham. “ ... anything deduced from a true statement must itself be true, but not everything deduced from a statement with explanatory power will itself have explanatory power.” [Kirkham Theories of Truth p101]. My defence challenges the confidence with which Kirkham makes the first part of that assertion - that anything deduced from a true statement must itself be true. The reliability of our ability to deduce truth from truth is dependent upon the reliability of the premises - the “true” statements from which the deduction is derived. I am pretty sure that Kirkham is thinking here of formal logic systems in which deductions are derived from axioms. These are declared true at the outset. The axioms, and the rules of inference define the logic system.

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