Let me begin to explain my position by taking a very simple example from an IQ test. Please note that while the example is simple, the problems raised in considering it are equally applicable to more complicated examples.
We are given a test to find a quasi-synonym for a word - this word I will designate XO. We are asked to choose from XI, X2, X3, and X4, the word that is closest in meaning to XO, and we are given the further information that there is only one correct answer.
If there is only one correct answer, then it might be possible to find a procedure for testing the words to find the correct one. There is, in fact, a test for true synonymity, but not, as far as I am aware, any test for near synonymity. But I am prepared to assume that such a procedure for testing words might be possible, even if it has yet to be devised.
But if such a procedure is possible, then a computer, with sufficient information and programming, would be able to supply an answer, and do this every time; in this respect we have defined intelligence in such a manner that a computer could be constructed to be intelligent - indeed, more so than we. But is there any point in taking an intelligence test defined in this way? Is it a measure of intelligence, or good programming? Clive Sinclair would, no doubt, see no distinction between intelligence and programming, but I cannot accept his dogmatic assertions on the matter in the absence of any scientific proof. Given the hypothesis that intelligence is not to be equated with programming, then this line of reasoning leads to the conclusion that the intelligence test cannot measure intelligence.
The alternative is that no procedure is possible for determining the correct word - it is simply a matter of having the necessary intelligence to see the correct answer? But how can we be certain that our choice is correct? We cannot resort to procedures, for none are possible according to our premise. We are left with a very badly defined "intuition" which knows that it is correct but cannot explain why. I am sure that such intuitions do exist - Format's "last theorem" being a good example. But I think that IQ tests are a very unsatisfactory way of measuring this - if they are to retain their scientific claims. Can we measure intelligence in tests which have no validation outside of human intuition? Is this to be seriously considered a scientific basis - with complete absence of proof?
The conundrum may now be stated: if there are objective procedures to ascertain the validity of solutions to an IQ test, then a computer, or its theoretical equivalent - a Turing machine - could be programmed to supply correct answer; in this case, unless we are prepared to equate intelligence with programming, we would be advised to speak of a test of programming rather than intelligence. On the other hand, if no objective procedures of this sort do exist, then it would seem that any claim that the test measures intelligence is grounded in some notion of intuition, and cannot be given any absolute status; any measurements and data which are forthcoming would be closer to the detailed number work of a proper astrology (- not the newspaper version -) than a science using measurements - like astronomy. We are closer to the number mysticism of Pythagoras than the mathematics of Euclid.
As I distrust the idea that intelligence is to be equated with programming, I do not believe that there is a solution to the above dilemma; consequently, I do not accept the validity of IQ tests. I do not, however, disbelieve in the idea of intelligence, although, like Sir Peter Medawar, I doubt that it can be easily quantified. As I see it, intelligence involves both the ability to use programming (as in logical and mathematical skills) and the ability to criticise and improve upon those skills. Moreover, while the first part of this analysis is a necessary foundation, it is the working out of the second - as we see in the history of science - that is the real test of intelligence.
The argument, as outlined above, can still apply if there is more than one correct answer to the IQ puzzle set - we simply replace the idea of "objective procedure to determine the validity of the solution" by the idea of "objective procedures to determine the validity of membership of the solution set".