NO Russell's paradox in the computer world!
This implements the 'library catalogue' conundrum: does one put the name of the book of names of books that do not contain their name in itself? This is the finite form of "set of all sets that do not contain themselves". It is equivalent to Turing's and Penrose's "computer program that stops when it finds a program possibly itself which does not stop".
Russell's paradox is a clear problem for traditional logic. Why? Traditional logic has an other worldly, timeless aspect. But the comfortable knish it has found in many human psyches has become a supernatural poison to others - this very timeless aspect requires the catalogues to be fixed, whereas their definition requires them to change.
Book contents(letters after book name letter) are in 2nd column below. On clicking 'REcataloge' the program compares the first letter(book name) in each of 4 books below to the rest of book's contents and makes 2 catalogues which are THEN put in bottom 2 boxes AFTER the contents of ALL 4 boxes are analyzed: Note that repeated cataloging causes N(book of books that do Not self-cite) to simply cycle between catalogues: explicit, mechanical use of TIME(temporal logic) in actual CAUSE and EFFECT keeps Russell's paradox from the computer world! B. Russell and K. Godel have humanly proved traditional human logic and arithmetic are seriously questionable - a great service to progress - super-logic demonstrates pure, exact, materialistic(non-human) logic, math, philosophy.
Cataloguing is done at different times(different button clicks).You can retype book contents at will. In Netscape2, choose 'View' then 'source' for program.
This gives humans further experience of the better clarity and reliability of simple mechanical, real time (materialistic) implementation of basic 'thoughts' that are now readily available(internet and javascript). Russell's paradox and the like show the traditional unsolvable problems one can get into by depending too much on old logic meme: human thought process is not practically observable so its dependence on time has been too easily ignored consciously, in the past.
[after email with Damjan.Bojadziev in Slovenia and reading Dennett 'Darwins Dangerous Idea', Oct97] Evolution of the human brain has arrived at a partially reliable binary transformation system optimized for complex decision speed. This speed seems to have sacrificed accurate, internal monitor of relative nerve state change times during the learning process - history has not yet created a logic meme of symbolizable time consciousness. See super-logic negative feedback neural network (-ANN) for critical, explicit, monitorable, general learning. Perhaps musical imagination is a partial example of 'internal monitor of nerve state change times'. We may have some logic of music but not currently any rhythmic logic. Perhaps my box dance is a very beginning form of visual music that could give rise to some visual, rhythmic logic, after much weird effort. There has been too little technical opportunity in the past to encourage more than a timeless logic meme. Written logic, math, philosophy has been limited to very simple, static paper and ink - dead text. Even my 'negative feedback neural net' currently uses time incompletely: its input specifies 'w' for 'wait' instead of actually measuring the time between input changes - it should be easy to implement; but then the stimulator would be required to 'get in the rhythm' with input key strokes. I am thinking of developing an example of 'internal monitor' in my -ANN. The -ANN paradigm demonstrates the power of naming or addressing individual nerves - this appears unverifiable in humans receiving normal experience - seeing a single letter stimulates thousands of nerves.Maybe very careful concentration could train many nerves to act as one? And then sets of these unified nerves could be combined in ways as rigorously as those in -ANN?
The following are 2 more additional demonstrations:
Computer cycling:
All computer programs have a finite cycling period, cannot generate any non-repeating digit sequence. Computer programs cannot compute their own period or need to: Turing's, Godel's and Penrose's theories apply to human thought(unknown, unreliable, hidden) not to simplified, finite, explicit automatons. The Russell's 'paradox' implementation here shows a special tight cycling on constant cataloguing.
Super-logic:
JavaScripted neural net interactively learns any propositional logic formula(nor, t, f) that gives it more control. By approximating biological brains, but being simple, exactly logical, completely observable and motivated to increase abstract physical variety( maximize entropy over time) it gives humans a good example that can be easily imitated to improve their basic ideas. It itself becomes conscious when it gets a model of itself that improves the reliability of its control( it automatically remembers for reuse those synapses from input to output that result, by external effect of its outputs, in changed inputs). It is an easily made child of the mind that may have a more important future in this universe than current biological beings!
E-mail author: R Massey for additions Oct 2003.
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