Friday, October 28, 2005

Platonic Forms, Symbol Grounding, and Invariant Representations 

Human societies are composed of many people, each a biological organism similar to the rest. Each of these persons has a similar mind and perceptual and motor system. As each person grows from infancy, he or she learns invariant representations of the world. And all of us live in a similar world. Simultaneously, each is taught words to be associated with these representations. When these words are expressed by one person, they evoke similar invariant representations in the minds of those who receive these expressions. This simultaneous activation of invariant representations in two or more minds around a verbal or written symbol is a semantic event. We say the symbol, the word, is grounded. It is grounded in the mutual collection of memories out of which the essence of the thing was extracted. The essence is that which is invariant. It is the form of the thing that remains constant throughout all the memories. Plato looked for these and for a time thought they may really exist outside our minds. Later nominalists refuted him by insisting that words are simply associated with a collection of particulars similar in some respect. The problem of symbol grounding suggests that both are needed. The invariant essence wouldn't really exist at all were it not for the collection of memories out of which it formed. But likewise, there would be no collection, no grouping without the essential form which holds between it's elements.

Before machines can be said to participate in semantic events, symbols exchanged in conversations will need to be grounded in memories of the particulars necessary to produce the constant form so represented. There is a company formed to build such machines. Numenta claims it will develop a memory machine that can develop invariant representations in a way that is similar to the way the human neocortex does. "The Numenta technology, called Hierarchical Temporal Memory (HTM), is based on a theory of the neocortex described in Jeff Hawkins' book titled "On Intelligence" (with co-author Sandra Blakeslee)." But "It may well take several years before products based on HTM systems are commercially available."

Until then the semantic web will have to keep looking for ways to ground symbols, that is, URI in other ways.

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Prior Art

Socrates

"We are in the habit, I take it, of positing a single idea or form in the case of the various multiplicities to which we give the same name. Do you not understand?" "I do." "In the present case, then, let us take any multiplicity you please; for example, there are many couches and tables." "Of course." "But these utensils imply, I suppose, only two ideas or forms, one of a couch and one of a table." "Yes." "And are we not also in the habit of saying that the craftsman who produces either of them fixes his eyes on the idea or form, and so makes in the one case the couches and in the other the tables that we use, and similarly of other things? For surely no craftsman makes the idea itself. How could he?" "By no means."
Plato, Republic X, page 596a


David Hume

"This convention is not of the nature of a promise: For even promises themselves, as we shall see afterwards, arise from human conventions. It is only a general sense of common interest; which sense all the members of the society express to one another, and which induces them to regulate their conduct by certain rules. I observe, that it will be for my interest to leave another in the possession of his goods, provided he will act in the same manner with regard to me. He is sensible of a like interest in the regulation of his conduct. When this common sense of interest is mutually expressed, and is known to both, it produces a suitable resolution and behaviour. And this may properly enough be called a convention or agreement betwixt us, though without the interposition of a promise; since the actions of each of us have a reference to those of the other, and are performed upon the supposition, that something is to be performed on the other part. Two men, who pull the oars of a boat, do it by an agreement or convention, though they have never given promises to each other. Nor is the rule concerning the stability of possession the less derived from human conventions, that it arises gradually, and acquires force by a slow progression, and. by our repeated experience of the inconveniences of transgressing it. On the contrary, this experience assures us still more, that the sense of interest has become common to all our fellows, and gives us a confidence of the future regularity of their conduct: And it is only on the expectation of this, that our moderation and abstinence are founded. In like manner are languages gradually established by human conventions without any promise. ..." - A Treatise of Human Nature, Chapter 74 by David Hume


John Locke

"...Semeiotike, or the doctrine of signs; the most usual whereof being words, it is aptly enough termed also Logike, logic: the business whereof is to consider the nature of signs, the mind makes use of for the understanding of things, or conveying its knowledge to others. For, since the things the mind contemplates are none of them, besides itself, present to the understanding, it is necessary that something else, as a sign or representation of the thing it considers, should be present to it: and these are ideas. And because the scene of ideas that makes one man's thoughts cannot be laid open to the immediate view of another, nor laid up anywhere but in the memory, a no very sure repository: therefore to communicate our thoughts to one another, as well as record them for our own use, signs of our ideas are also necessary: those which men have found most convenient, and therefore generally make use of, are articulate sounds. The consideration, then, of ideas and words as the great instruments of knowledge, makes no despicable part of their contemplation who would take a view of human knowledge in the whole extent of it. And perhaps if they were distinctly weighed, and duly considered, they would afford us another sort of logic and critic, than what we have been hitherto acquainted with." - AN ESSAY CONCERNING HUMAN UNDERSTANDING by John Locke 1690