Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ames!amdahl!nsc!andrew From: andrew@nsc.nsc.com (andrew) Newsgroups: comp.ai Subject: Re: A Definition of "Symbol," "Symbolic," and "Symbol-Manipulation" Summary: isomorphism and reductionism Keywords: syntax, semantics, formality, systematicity, interpretability Message-ID: <10208@nsc.nsc.com> Date: 25 Mar 89 02:43:50 GMT References: Organization: National Semiconductor, Santa Clara Lines: 114 I posted the message enclosed below on comp.ai.neural-nets some days ago, but have had zero response. Having read this net, maybe I've found a home. You are discussing ideas (Chinese Room -related) which are exactly in the field of my inquiry; i.e. symbols and their attributes. Here's your context: 1. Steven Harnad: "(there exist) ..iconic and categorical (feature-filtered) representations of object categories". "connectionism contributes to feature-filtering.. forms the categorical representations" 2. Karl Kluge: "Denotation seems to be `an arbitrary property of symbols in an instantiated executing formal system, unlike the syntax and operational semantics of the symbols.' " 3. Ray Allis: "..but, at bottom, symbols are associated with non-symbols. The non-symbols are what we compare to detect similarity and difference, to discover analogy, to think." All these refer to symbols, attributes, features and the central role of the recognition of isomorphism. My note is prompted by recent developments in neural-net research. There are now known to exist architectures capable of extracting features from input datasets (in a non-supervised fashion) whose properties are mathematically, physically and biologically attractive and/or plausible. These features are either Gabor functions or the eigenvectors of the input autocorrelation. These features are nice because: mathematically - known formal statistics of data physically - eigenvectors/states are often used to describe fundamental features of physical systems biologically - learning rules are purely local - learning is proven to converge, and to converge correctly - random noise input produces feature representations similar to those found in the early vision processing receptive fields of certain mammals. (They are not nice because convergence is not realtime - yet). The note is: 1) Proposing a relationship between isomorphism and feature extraction 2) Questioning what is the best way to think about attributes. ========================================================================== Could somebody out there in philosophy land please enlighten me as to the "currently favoured" way to describe "the attribute of a thing" ? (a little like Plato and "the whiteness of cream", except that's not my name). Why I am asking this (hopefully not too idiotic) question: 1) Many people agree that the understanding of isomorphism is critical to the understanding of cognition and intelligence. 2) The existence of isomorphisms seems only possible if attributes exist, else, without predicates (attributes), we have only the crassness (sorry, holism) of Zen "direct-pointing" whereby things just are, and all share none or the same attribute! (kick the pot, Bunto). East/West diverges here... 3) The existence of attributes seems only possible when a feature extraction process is performed, by which attributes are *created* as a direct result of the interaction of the perceiver with the environment (_vide_ the old saw about the Eskimo's words for snow), or with his/ her own structure (the predisposition of infants to eye/nose/mouth forms). The isomorphism issue thus seems decomposable to that of the qualities of predicates, and therefore to the mechanisms of feature extraction. (?comments?). Note - I'm not suggesting that this pins down what an isomorphism *is*, but maybe gives some leverage/ connection. As to the qualities of predicates, there seem to me to be two ways to go: 1) a simple, "non-relational" predicate, like "whiteness" or "how many" 2) a set membership predicate, like "is a member of" or "has .. members". These 2 ways seem to be related in that 1) appears to be subsumable under 2) in a recursive fashion (i.e. "is a member of the set of white things"); nevertheless, it seems that maybe property inheritance and suchlike are excess baggage for a general definition of what an attribute "is". Is 2) an inclusive definition? ========================================================================= I realise that "attribute" opens a whole can of worms, and I would like to keep this definition as down-to-earth as possible, in line with the bottom-up approach of nets. For example, attributes like "understanding" are so high-level (emergent) that they are not relevant here. One note on symbols, however: from the abovementioned reductionist perspective, symbols evaporate! becomes becomes . The feature set is all that is, all the way from just inside the "transducer surface" to just inside the "effector surface". Analytic deduction of "symbols" from patterns of activation equivocates to just one more level of , based on . Reasonable? Analytic deduction of "understanding" from patterns of activation equivocates to (cf. the fire/chemistry or the clock/physics analogies) the ability to associate up to a prescribed "level" in the feature set of known physical laws. One can replace the word "associate" by "recognise an isomorphism" here, of course. ============================================================================ DOMAIN: andrew@logic.sc.nsc.com ARPA: nsc!logic!andrew@sun.com USENET: ...{amdahl,decwrl,hplabs,pyramid,sun}!nsc!logic!andrew Andrew Palfreyman 408-721-4788 work National Semiconductor MS D3969 408-247-0145 home 2900 Semiconductor Dr. P.O. Box 58090 there's many a slip Santa Clara, CA 95052-8090 'twixt cup and lip ============================================================================