On Mon, Nov 5, 2012 at 11:38 PM, Aaron Hosford <[email protected]> wrote: ch of the confusion and failure generated by Boolean logic, the most commonly used and least versatile form of "fully functional" logic, arises from the failure of Boolean logic to recognize the distinction between different kinds of false statements (pieces of language). Boolean logic only recognizes statements that are false because their opposites are true. But it completely disregards the existence of statements which cannot be mapped to reality to verify their truth. These sorts of statements are not false because their opposites are true, but because they are meaningless. This lack of distinction (a bias towards perceiving truth and falsehood but not meaninglessness) is the source of many mathematical and logical paradoxes.
I do not agree with that. Logic can be, uh, pointed at meaningless and therefore incorporate that as a possible situation that can be found in a model. The real problem, as I see it, is that the model would have to be too complicated to be truly useful as a complete model of every possibility. So instead we have to incorporate models of variations of unknowns or undefineds into our models and then rely on bounded models so that the logical 'discussion' (so to speak) might be used effectively. This turns deductive logic into inductive logic and makes the effective use of logic conjectural. Jim Bromer Jim Bromer On Mon, Nov 5, 2012 at 11:38 PM, Aaron Hosford <[email protected]> wrote: > Mike, here's something for you to chew on: > > I like to think of the term "random" as meaning the absence of a * > detectable* pattern, due to biases and/or blind spots of the observer or > perspective. Under this definition, it is implicit that anything can be > seen as random or non-random given an appropriate observer or perspective. > > I think our minds are simply filters for reality, designed to pluck out > the most common and useful patterns through appropriate biases. We look for > the patterns we do because they help us accomplish our evolutionary > purpose. When something looks random to us, it simply means we can't > identify a pattern, not that there isn't one. > > Mathematics is a language for representing the sort of patterns the human > mind tends to perceive. It is, in other words, a language for representing > reality in terms of our intrinsic human perceptual biases. We have integer > arithmetic because we perceive discrete, countable units in the universe. > We have calculus because we perceive continuous phenomena such as curves, > areas, volumes, and flows in the universe. We have geometry and topology > because we perceive shapes and invariances of shape in the universe. We > have logic because we perceive a mapping between situations and their > descriptions (language, including math) in the universe. And we find > commonalities and relationships between the various branches of > mathematics, described in the terms of logic because logic is the language > we use to talk about languages, including those of mathematics. > > Much of the confusion and failure generated by Boolean logic, the most > commonly used and least versatile form of "fully functional" logic, arises > from the failure of Boolean logic to recognize the distinction between > different kinds of false statements (pieces of language). Boolean logic > only recognizes statements that are false because their opposites are true. > But it completely disregards the existence of statements which cannot be > mapped to reality to verify their truth. These sorts of statements are not > false because their opposites are true, but because they are meaningless. > This lack of distinction (a bias towards perceiving truth and falsehood but > not meaninglessness) is the source of many mathematical and logical > paradoxes. > > As for your "irregular forms", Mike, what all this boils down to is that > if the regularity of some aspect of the world isn't visible to mathematics, > it isn't visible to *people*. Mathematics simply codifies what our brains > already do. When we notice a regularity in reality, we create a branch of > mathematics to describe it. If we don't see a regularity in a portion of > reality, we call it random and mentally disregard it. I am identifying > concepts themselves as human-perceivable regularities in the world, in case > that isn't readily apparent. Thus if we can conceptualize something, it > must be regular in our minds, and either a branch of mathematics exists to > describe those regularities, or we can create one. (These new branches of > math always start out as human language and become steadily more formalized > as we become more certain about what the regularities are and how to more > effectively describe them in language.) > > So, in summary: > 1) A concept is a human-perceivable regularity. > 2) Mathematics is a highly refined language for describing > human-perceivable regularities. > Therefore: > 3) Mathematics is a highly refined language for describing concepts. > > Mathematics (and language in general) is how we tell each other about the > world. If something can't be described in terms of mathematics, it's > because it either can't be perceived, or we have identified a new branch of > mathematics that needs to be created. Eventually, we will have covered all > the filtering biases evolution has built into our minds, and mathematics > will be sufficient to describe all concepts the human mind can perceive > without further additions to the language. > > > > > > > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/10561250-164650b2> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
