Cognitive Science 1997—Stanford UniversitySaturday, August 9, Poster Session
A Closer Look at Nonverbal IQ Tests
John W. Oller, Jr.University of Southwestern Louisiana, Lafayette
and
Marie ChavezUniversity of New Mexico
1. Can this nonverbal IQ item or others like it be solved without instructions in a particular language?1
1The actual instructions are to find the figure on the right where the dot can be placed in the same relations to the other figures that it has in the figure on the left.
2. Arthur Jensen (1980, pp. 648ff) describes this test and Raven's Progressive Matrices as among the best nonverbal tests ever produced. Herrnstein and Murray (1994) describe Raven's Standard Progressive Matrices as "a nonverbal test that is an especially good measure of g [general intelligence]" (p. 273).
3. Jensen claims of both the Cattell and the Raven tests and, other nonverbal IQ tests, that
"virtually all subjects can catch on to the task without verbal instructions" (1980, p. 132).
4. But is this true? Can you guess the instructions or imagine how to make them understood through gestures?
5. We will show why it is not only not true for the tests in question, but it cannot be true for abstract nonverbal tests in general.
To make our case it is only necessary to examine the two kinds of sign systems that undergird conventional linguistic signs. They are:
(1) ICONS or sensory based iconic signs—i.e., the kind that originate in seeing, hearing, touching, tasting, or smelling, and
(2) INDICES or motoric indexical signs—i.e., the bodily gestures or actions that relate perceivers to perceivable objects, events, or other iconic signs, including the surface-forms of linguistic signs.
6. Can either or both of these kinds of signs, ICONS and INDICIES, be combined in pantomime and wordless drama to provide an adequate basis for solving nonverbal IQ items? Could the "correct" answers be determined and agreed upon by the test designers without using a common language?
7. It is immediately clear that sensory based ICONS alone cannot serve the required purpose because
they are private signs that cannot be transferred from one perceiver to another. Therefore, ICONS alone cannot provide the instructions to any complex nonverbal IQ test item.
8. But suppose we add INDICES into the picture. If we hand someone an object or point to one, it is true that we may cause that person to generate a sensory impression of the object that resembles our own. But how can we be sure that the desired result has been achieved?
9. The special difficulty of ICONS combined with explicit gestural INDICES can be illustrated with the help of the following photograph.
Photo of Nathanael at 11 months goes here
10. Let us assume that the preceding picture is an ordinary photograph, untampered with and created by common methods of film exposure, development, etc. Thus, it is an ICON of a particular little child created with the aid of a camera at a particular time, at a particular place, by one or more particular persons, etc. Now, consider the following questions:
(1) Could the photograph be of a more particular individual object than is shown?
(2) Could the time-space coordinates of the film exposure be more particular (unique and unrepeatable) than the segment of matter-time-space displayed in the ICON by the particular pointing of the camera, clicking of the shutter, and exposure of the film that was effected when the shot was taken?
(3) Will the child in the picture, or those involved in taking it, ever be exactly the same age again as they were when the picture was taken?
(4) Could the various INDICES required to produce the ICON, the photograph, be any more particular than they are?
11. The answers, we believe, to all the foregoing questions must be negative. No, no, no, and no.
12. Why then, if the picture and all the events associated with its production, are as particular as they can possibly be, do we not immediately know the space-time coordinates of the object? In other words, how comes it that we cannot immediately say, "Oh that is a picture of little Nathanael Murdoch. It was taken at a studio in Spang Dahlem, Germany on July 6, 1997. He was 11 months old on that date. He was taken to the Schmidt studio by his mother Laura." And so on and so forth.
13. The reason is that even the most particular ICONS that can be conceived (and none is more particular than the sort we were just considering), though they be supported in principle and in fact by utterly particular gestural acts, INDICES, created by particular individuals, at particular times and in particular places, etc., they must nevertheless always fail to achieve determinate particularity from the point of view of any observer. Let us see why this must be so.
14. The general inadequacy of ICONS is that they cannot tell anyone determinately what they are about. They are general signs exactly as well suited to absolutely any object as their resemblance to that object may justify. The trouble is that every ICON resembles all objects somewhat and many objects very well. This is demonstrated mathematically by showing that any surface can be transformed gradually into any other.
15. But suppose we had a moving picture of the shooting of the photograph. Suppose further that the moving film could be extended indefinitely before and after the event. Now we would see the pointing of the camera. We would see the positioning of the child by some caretaker. We would see the photographer shoot the picture in question, along with many others, no doubt. Etc.
(1) With all the additional INDICES—and with all the pointing, gesturing, and other movements we might like to include—added into the now moving picture, will we be able to tell the time, place, or name of the child?
(2) Will the INDICES make the particulars any more determinate than they were before?
16. The answer is still "no" in both cases. The reason is that ICONS supported by INDICES are still undetermined with respect to their natural historical particularity. That is, the history of the child, his mother, his father, his siblings, the photographer, the location where the film was exposed, the time and date, are all impossible to determine without the kinds of signs that we find in conventional linguistic symbols.
17. No matter how many sensory ICONS may be attached to gestural INDICES, the latter cannot supply determinate identities to their ICONS.
18. In fact, INDICES are universally degenerate in a peculiar respect: it is impossible to say with certainty where any given index is pointing. For instance, in Figure 2 below, what is pointed at? Is it the square? The dot in the square? The near or far corner of the square? The edge of the dot? Something beyond the square?
19. Because Figure 2 shows a universal degeneracy associated with indices, it is clear that they can never serve to determinately identify either the argument of a predication or the predicate to be asserted of that argument. Much less can gestures serve to determinately specify more complex syntactic relations between two arguments as in "Bill sold the car," or three as in "Sarah gave the book to Sue", and so forth.
20. Neither is there any determinate way to show in nonconventionalized gestures that "The dot is inside the circle and outside the square in Figure 1." Never mind the additional complexity that there is more than one square and that the larger one is to be regarded as a mere frame.
21. However, every abstract nonverbal IQ item requires determinate distinctions between arguments and determinate associations of them with distinct predicates. Such determinate distinctions, however, can only be provided by conventional linguistic signs. This holds because
(1) ICONIC signs are doubly degenerate and indeterminate—(a) they are private and non-transferrable and (b) even if they could be made transferrable through indices they are too general in their applicability; and
(2) INDICES unfortunately are degenerate with respect to their arguments—that is, an observer of a nonconventionalized gesture can never be sure what its intended argument is or just what is predicated of that argument. The case only gets worse if more than one argument is involved.
22. Therefore, without conventionalized linguistic signs it is utterly impossible to give determinate instructions for the solution of any abstract nonverbal IQ test item. It is also impossible for test writers to construct such items without recourse to a common language that will enable them to agree on a determinate solution (i.e., a "correct" answer) to the item. Neither determinate solutions to such items, nor determinately comprehensible instructions are possible without recourse to some particular natural language.
23. Because it is absurd to expect some test-taker to understand a foreign language on its first presentation, it is absurd to give the instructions to nonverbal IQ tests in any language other than the primary language of the test takers.
24. It is also false to claim that nonverbal IQ tests are "pure" measures of native intelligence uncontaminated by acquired proficiency in some particular natural language.
References
Herrnstein, R. & Murray, C. (1994). The bell curve: intelligence and class structure in American life. New York: Free Press.
Jensen, A. R. (1980). Bias in mental testing. New York: Free Press.
Oller, J. W., Jr. (1997). Monoglottosis: what's wrong with the idea of the IQ meritocracy and its racy cousins? Applied Linguistics, 18(4), 467-507.
