Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!rutgers!princeton!mind!harnad From: harnad@mind.UUCP (Stevan Harnad) Newsgroups: comp.ai,comp.cog-eng Subject: Re: The symbol grounding problem Message-ID: <958@mind.UUCP> Date: Thu, 2-Jul-87 11:51:40 EDT Article-I.D.: mind.958 Posted: Thu Jul 2 11:51:40 1987 Date-Received: Sat, 4-Jul-87 06:08:56 EDT References: <764@mind.UUCP> <768@mind.UUCP> <770@mind.UUCP> <6174@diamond.BBN.COM> <956@mind.UUCP> Organization: Cognitive Science, Princeton University Lines: 76 Summary: Invertibility is graded only in an uninteresting sense Xref: mnetor comp.ai:604 comp.cog-eng:174 On ailist cugini@icst-ecf.arpa writes: > why say that icons, but not categorical representations or symbols > are/must be invertible? Isn't it just a vacuous tautology to claim > that icons are invertible wrt to the information they preserve, but > not wrt the information they lose?... there's information loss (many > to one mapping) at each stage of the game: 1. distal object... > 2. sensory projection... 3. icons... 4. categorical representation... > 5. symbols... do you still claim that the transition between 2 > and 3 is invertible in some strong sense which would not be true of, > say, [1 to 2] or [3 to 4], and if so, what is that sense?... Perhaps > you just want to say that the transition between 2 and 3 is usually > more invertible than the other transitions [i.e., invertibility as a > graded category]? [In keeping with Ken Laws' recommendation about minimizing quotation, I have compressed this query as much as I could to make my reply intelligible.] Iconic representations (IRs) must perform a very different function from categorical representations (IRs) or symbolic representations (SRs). In my model, IRs only subserve relative discrimination, similarity judgment and sensory-sensory and sensory-motor matching. For all of these kinds of task, traces of the sensory projection are needed for purposes of relative comparison and matching. An analog of the sensory projection *in the properties that are discriminable to the organism* is my candidate for the kind of representation that will do the job (i.e., generate the performance). There is no question of preserving in the IR properties that are *not* discriminable to the organism. As has been discussed before, there are two ways that IRs could in principle be invertible (with the discriminable properties of the sensory projection): by remaining structurally 1:1 with it or by going into symbols via A/D and an encryption and decryption transformation in a dedicated (hard-wired) system. I hypothesize that structural copies are much more economical than dedicated symbols for generating discrimination performance (and there is evidence that they are what the nervous system actually uses). But in principle, you can get invertibility and generate successful discrimination performance either way. CRs need not -- indeed cannot -- be invertible with the sensory projection because they must selectively discard all features except those that are sufficient to guide successful categorization performance (i.e., sorting and labeling, identification). Categorical feature-detectors must discard most of the discriminable properties preserved in IRs and selectively preserve only the invariant properties shared by all members of a category that reliably distinguish them from nonmembers. I have indicated, though, that this representation is still nonsymbolic; the IR to CR transformation is many-to-few, but it continues to be invertible in the invariant properties, hence it is really "micro-iconic." It does not invert from the representation to the sensory projection, but from the representation to invariant features of the category. (You can call this invertibility a matter of degree if you like, but I don't think it's very informative. The important difference is functional: What it takes to generate discrimination performance and what it takes to generate categorization performance.) Finally, whatever invertibility SRs have is entirely parasitic on the IRs and CRs in which they are grounded, because the elementary SRs out of which the composite ones are put together are simply the names of the categories that the CRs pick out. That's the whole point of this grounding proposal. I hope this explains what is invertible and why. (I do not understand your question about the "invertibility" of the sensory projection to the distal object, since the locus of that transformation is outside the head and hence cannot be part of the internal representation that cognitive modeling is concerned with.) -- Stevan Harnad (609) - 921 7771 {bellcore, psuvax1, seismo, rutgers, packard} !princeton!mind!harnad harnad%mind@princeton.csnet harnad@mind.Princeton.EDU