@misc{cogprints3024, volume = {35}, month = {May}, title = {There is no Concrete (or: Living Within One's Means)}, author = {Stevan Harnad}, year = {2003}, note = {Presented at conference on: "Access to the Abstract." University of Southern Denmark Odense, 30-31 May 2003. http://www.ecs.soton.ac.uk/{\texttt{\char126}}harnad/Temp/abstract.htm}, journal = {Ariadne}, url = {http://cogprints.org/3024/}, abstract = {We are accustomed to thinking that a primrose is "concrete" and a prime number is "abstract," that "roundness" is more abstract than "round," and that "property" is more abstract than "roundness." In reality, the relation between "abstract" and "concrete" is more like the (non)relation between "abstract" and "concave," "concrete" being a sensory term [about what something feels like] and "abstract" being a functional term (about what the sensorimotor system is doing with its input in order to produce its output): Feelings and things are correlated, but otherwise incommensurable. Everything that any sensorimotor system such as ourselves manages to categorize successfully is based on abstracting sensorimotor "affordances" (invariant features). The rest is merely a question of what inputs we can and do categorize, and what we must abstract from the particulars of each sensorimotor interaction in order to be able to categorize them correctly. To categorize, in other words, is to abstract. And not to categorize is merely to experience. Borges's Funes the Memorious, with his infinite, infallible rote memory, is a fictional hint at what it would be like not to be able to categorize, not to be able to selectively forget and ignore most of our input by abstracting only its reliably recurrent invariants. But a sensorimotor system like Funes would not really be viable, for if something along those lines did exist, it could not categorize recurrent objects, events or states, hence it could have no language, private or public, and could at most only feel, not function adaptively (hence survive). Luria's "S" in "The Mind of a Mnemonist" is a real-life approximation whose difficulties in conceptualizing were directly proportional to his difficulties in selectively forgetting and ignoring. Watanabe's "Ugly Duckling Theorem" shows how, if we did not selectively weight some properties more heavily than others, everything would be equally (and infinitely and indifferently) similar to everything else. Miller's "Magical Number Seven Plus or Minus Two" shows that there are (and must be) limitations on our capacity to process and remember information, both in our capacity to discriminate relatively (detect sameness/difference, degree-of-similarity) and in our capacity to discriminate absolutely (identify, categorize, name), The phenomenon of categorical perception shows how selective feature-detection puts a Whorfian "warp" on our feelings of similarity in the service of categorization, compressing within-category similarities and expanding between-category differences by abstracting and selectively filtering inputs through their invariant features, thereby allowing us to sort and name things reliably. Language does allow us to acquire categories indirectly through symbolic description ("hearsay," definition) instead of just through direct sensorimotor trial-and-error experience, but to do so, all the categories named and used in the description must be recursively grounded in direct sensorimotor invariants. Language is largely a way to ground new categories by recombining already grounded ones, often by making their implicit invariant features into explicit categories too. If prime numbers differ from primroses, it is hence only in the degree to which they happen to be indirect, explicit, language-mediated categories. Like everything else, they are recursively grounded in sensorimotor invariants. The democracy of things is that, for sensorimotor systems like ourselves, all things are just absolute discriminables: they number among those categories that our sensorimotor interactions can potentially afford, no more, no less. A primrose affords dicotyledonousness as reliably (if not as surely) as a numerosity of 6 (e.g., 6 primroses) affords factoring (whereas 7 does not).} }