2 hours ago, DavidOdden said:
“Implicit knowledge” is a form of mysticism, based on a premise of a magical automatic reason machine in the human mind. . . ."
David, in some usages of “implicit knowledge”, there is nothing mystical or magical. There is a sense of implicit useful in cognitive-development research literature (viz., Gelman and Meck 1983, 344). The child is said to have implicit knowledge of the counting principles if she engages in behavior that is systematically governed by those principles, even though she cannot state them. The child has gone far beyond learning first words (roughly months 12 to 18) by the time she is learning to count. By 30 months, the basic linguistic system has become established and is fairly stable (Nelson 1996, 106). Not until around 36 months or beyond does the child have an implicit grasp of the elementary principles of counting: assign one-label-for-one-item, keep stable the order of number labels recited, assign final recited number as the number of items in the counted collection, realize that any sort of items can be counted, and realize that the order in which the items are counted is irrelevant (Gelman and Meck 1983; Butterworth 1999, 109–16).
Gelman and Meck liken this implicitness of the counting principles at this stage of cognitive development to the way in which we are able to conform to certain rules of syntax when speaking correctly without being able to state those rules. That much seems right, but there is a further distinction I should make. The child’s implicit counting principles are being learned (and taught) as an integral part of learning to properly count aggregations explicitly, expressly. In contrast, we can (or anyway, my preliterate Choctaw ancestors centuries past could) live out our lives, speaking fine in our mother tongue, following right rules of syntax, yet without being able to state those rules; indeed, without even knowing any of the terminology of syntax. Our learning of tacit rules of syntax is not for the sake of becoming able to follow them explicitly, only tacitly.
Another sense of implicit is in more common use. That is the logicomathematical sense. It is in that sense that we say a certain theorem is implicit in a set of axioms; Hertz’ wave equation for propagation of electromagnetic radiation is implicit in Maxwell’s field equations; an inverse-cube central force law is implicit in a spiral orbit; dimension reductions are implicit in Kolmogorov superposition-based neural networks; certain measure relations are implicit in any similarity discerned in perception; or certain measure relations are implicit in a concept class. Cf. Rand (1969, 159–62); Campbell (2002, 294–96, 300–10); Boydstun (1996, 201–2).
In addition to using “implicit” in her theory of the genesis of measurements-omitted concepts (which I suppose for the concept existence requires suspension of particular measure-values along all the measure-dimensions possessed by all the kinds of existents there are), Rand used “implicit” in describing a cognitive growth in our infant comprehension from existence to identity to unit.*
References
Boydstun, Stephen. 1996. Volitional synapses (Part 3). Objectivity 2(4):183–204.
Butterworth, Brian. 1999. What Counts: How Every Brain is Hardwired for Math. New York: Free Press.
Campbell, Robert L. 2002. Goals, values, and the implicit: Explorations in psychological ontology.
Journal of Ayn Rand Studies. 3(2):289–327.
Gelman, Rochel, and Elizabeth Meck. 1983. Preschoolers’ counting: Principles before skill.
Cognition 13:343–59.
Nelson, Katherine. 1996. Language in Cognitive Development. Cambridge: Cambridge University Press.
Rand, Ayn. [1969] 1990. Transcripts from Ayn Rand’s epistemology seminar. Edited by L. Peikoff and H. Binswanger. Appendix to Introduction to Objectivist Epistemology. Expanded 2nd edition. New York: Meridian.