Markman & Dietrich (1998a) repeat that domain-independent abstract mediating (DIAM) states are rare, as if this somehow creates problems for the position I introduced (Bringsjord, 1998a). This is incorrect. One can cheerfully affirm that DIAM states are rare, but WHY are they so? Markman & Dietrich (and everyone else thinking and writing about such matters in cognitive science) seem to think the answer involves the nature of cognizers. This too is incorrect. That domain-independent abstract mediating states are rare is due to the way we accidentally educate our youth.
2. The goal is to put on the table a new position concerning DIAM states and WHY they are rare; namely:
(F) Whether or not DIAM states turn up in a given cognizer, and the
extent to which they turn up, hinges on the education received by
that cognizer. Those (rare) people suitably educated in formal
logic usually instantiate DIAM states when faced with logical
problems ranging from the simple ones dominating the psychology of
reasoning literature, to more difficult ones the solutions to which
result in high academic honors.
For example, professional logicians, by virtue of their education, routinely enjoy DIAM states. My informal study, reported in my original commentary (1998a) and conducted, as reported in that commentary, in response to a challenge from Johnson-Laird (personal communication; see Johnson-Laird & Savary 1995), certainly shows that some (suitably educated) people have DIAM states. After all, what evidence could be stronger than the direct observation of subjects drawing out a deductive solution to a problem like Johnson-Laird's, exclusively in the formal syntax of first-order logic? If Markman & Dietrich are still inclined to resist the data I present, I would draw their attention to the data formally presented in a recent paper, which reports on successful efforts to educate students in such a way as to produce in them (efficacious, from the standpoint of problem solving) DIAM states (Bringsjord 1998b). Another year-long experiment intended to furnish additional confirmation of (F) is in progress.
3. Notice that if (F) is true, then it's simply a coincidence that DIAM states are rare. Consider the following thought-experiment, in which, by hypothesis, (F) is the case. Instead of Earth, let's talk of the planet Wearth (pronounced to rhyme with 'worth'). On Wearth, all human children without significant cognitive deficiencies are educated so as to routinely exploit DIAM states. Starting in the 1st grade, students learn the propositional calculus -- alongside arithmetic of the sort their counterparts learn on Earth. At the start of the 3rd grade, children on Wearth crack into quantifier logic, and are given problem after problem that yields to first-order logic. For every conventional math word problem children receive on Earth, children on Wearth get five word problems to be solved by formal logic. At the sixth grade, Wearth children are taught n-order extensional logic, and the simplest of intensional logics, and are asked to provide formal proofs in these systems alongside the usual "plug and chug" calculation seen on Earth for elementary algebra, geometry, and calculus. Wearth will produce many cognizers with DIAM states; such states will not be rare at all. Again, that OUR cognitive scientists need to search hard for DIAM states is just a coincidence, a function of the way we teach our young. (For reasons that are well outside the scope of this commentary, I happen to believe this way is bad and should be supplanted with Wearth-like pedagogy.)
4. One last point. Markman & Dietrich (1998a) believe it may be possible that the logically sophisticated subjects involved in my studies are calling upon their experiences with previously seen problems. There is a simple reason why this possibility can be ruled out: the problems in question are new. This can be verified by simply asking the subjects if they have seen either the particular problem facing them, or problems of the same general type, and by constructing problems that are checked against extant problems in the literature. (The problem Johnson-Laird gave me for his challenge is ingenious in no small part because it is of a new type, and he hadn't published it anywhere before sending it to me for my use.)
Bringsjord, S. (1998a) Domain-Independent Abstract Mediating States and AI. PSYCOLOQUY 9(53). http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?9.53 ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.53.representation-mediation.2.bringsjord
Bringsjord, S. (1998b) In Defense of Logical Minds. Proceedings of the 20th Annual Meeting of the Cognitive Science Society. (Mahwah, NJ: Lawrence Erlbaum), pp. 173-178.
Johnson-Laird, P. and Savary, F. (1995) "How to Make the Impossible Seem Probable," in Proceedings of the 17th Annual Conference of the Cognitive Science Society (Hillsdale, NJ: Lawrence Erlbaum Associates), pp. 381-384.
Markman, A.B. & Dietrich, E. (1998a) Domain Independent Mediating States are Rare PSYCOLOQUY 9(56). http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?9.56 ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.56.representation-mediation.3.markman
Markman, A.B. & Dietrich, E. (1998b). In Defense of Representation as Mediation. PSYCOLOQUY 9(48) http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?9.48 ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.48.representation-mediation.1.markman