Dear oh dear. AI Researcher Yudkowsky is continuing to perpetuate the same old reductionist mistakes on 'Overcoming Bias': http://www.overcomingbias.com/2008/09/excluding-the-s.html#more

This is the reason I've long since given up on the poor fellow. He writes: "different levels of organization can have separate representations in human maps, but the territory itself is a single unified low-level mathematical object." He thinks the territory is: "a single unified low-level mathematical object". Nice one. I've love to hear what Bruno thinks of that silly notion. Of course, as other readers in the thread pointed out, mathematical objects themselves cannot be located at any particular location or time in space or time ; if mathematical objects objectively exist (as Yudkowsky himself implies in his sentence), then, their very existence would represent a stark failure of reductionism. Neither inifinite sets nor uncomputable numbers can be identified with any computable physical processes: http://plato.stanford.edu/entries/platonism/ Of course, the reason mathematicians have to keep coming up with new original concepts is precisely because no single-level mathematical description is sufficient to encompass mathematical truth - as Godel himself proved. Mathematics itself operates on many levels of abstraction. Yudkowsky asks: "What experimental observations would you expect to make, if you found yourself in such a universe?" (where reductionism is false) But we *are* in just such as universe! What do you think Set Theory or Category Theory is? IT IS THE UNIVERSE MAPPING ITSELF It is an 'inner model' or 'map' of mathematics. If the Platonist/ Tegmark view is correct, then the universe itself contains a plethora of mathematical objects at different levels of abstraction, and objectively existing interfaces between them are required, if the consistency of reality is to be maintained. Sets and Categories are objectively existing high-level maps of lower-level level mathematical objects --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---