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.... (shrink)

2. Invariant Sensorimotor Features ("Affordances"). To say this is not to declare oneself a Gibsonian, whatever that means. It is merely to point out that what a sensorimotor system can do is determined by what can be extracted from its motor interactions with its sensory input. If you lack sonar sensors, then your sensorimotor system cannot do what a bat's can do, at least not without the help of instruments. Light stimulation affords color vision for those of us with the (...) right sensory apparatus, but not for those of us who are color-blind. The geometric fact that, when we move, the "shadows" cast on our retina by nearby objects move faster than the shadows of further objects means that, for those of us with normal vision, our visual input affords depth perception. From more complicated facts of projective and solid geometry it follows that a 3-dimensional shape, such as, say, a boomerang, can be recognized as being the same shape Ð and the same size Ð even though the size and shape of its shadow on our retinas changes as we move in relation to it or it moves in relation to us. Its shape is said to be invariant under these sensorimotor transformations, and our visual systems can detect and extract that invariance, and translate it into a visual constancy. So we keep seeing a boomerang of the same shape and size even though the shape and size of its retinal shadows keep changing. (shrink)