I agree with Aaron's overall position regarding the absurdity/uselessness of the logical paradoxes - bugs of data and combinatorial games when the sensori-motor roots are forgotten or lost.
The real natural "truth" in my theory of intelligence is the degree of match between samples (complete match is "truth", mismatch is "not true"), and also, in that perspective, I think I've already raised that point here once - the axiomatic systems like e.g. geometry are not really taken without prove. They are "obvious", i.e. they are proven by their obvious match, they are not "intuitive" because they cannot be proven and are "magical", but because they are proven by a sight. And they seem to be "out of the formal system", because the logicians who think so don't think in terms of sensori-motor generalizing hierarchies.*IMHO what's obvious for mind is a part of the formal system, and the formal system includes that mind.* (The point on the logic paradoxes is a bit below, a little mathematical digression here:) The axioms and "their proves" are taken from sensory inputs and from the way the cognitive/perceptive system works, which is also a by-effect of the way the physical world works. The axioms are the simplest, shortest, most general and obvious properties of the sensory matrices' and the motor space, i.e. what can be measured where and how, and what can be done, where and how - *"sensori-motor data and operational space" *or so... It's probably correlated also to the human's/mathematicians' who have worked on that problems working memory capacity. In the geometry case, the data are for example points and lines (and circles/arcs), which in sensory terms are pixels and sequences of adjacent pixels with matching values/intensities among the ones from the line, and contrasting (different) to the ones who are not part of the line etc. etc. The properties of the Cartesian space, Analytic geometry and linear algebra are compressed into axioms, and the ruler, compass, protractor, the piece of paper, and the pencil and the marks that it lefts are used to "compute" the transformations. Then some visually easy to measure/to distinguish properties of the results are noticed (crossing lines, right angle, equilateral or isosceles triangles, a circle, crossing circles, etc.) and those cases are encapsulated as concepts and named. Etc. One example for the popular bullshit used by some philosophers to show how "artificial" and "counter-intuitive" maths is, about the points with size null: *Why a point have size/length of 0, since w haven't seen anything that has no dimensions?* It may sounds so impossible to answer, while it's obvious: A "length" is a measure between two locations, two points == two coordinates. If you are on the same location in the beginning and in the end, the distance is 0, so the length is 0. If you define something with one coordinate, one value, there is no difference. The point can be represented by two coordinates like a line, but since they are the same, that's optimized for brevity, and the difference is 0 == no difference == there's a match. Also what a "point" really means is *"the coordinates of a point"*, i.e. an *address *in the *sensori-motor data and operational space*, that is associated to something or is about to be used for something. Those coordinates are not a physical entity themselves. ... However, let's go back on the logical paradoxes, some words of mine on it from *Universe and Mind, Part 4 (Concept About the Universal Predetermination, Part 4), **aka “Teenage Theory of Universe and Mind”: * http://research.twenkid.com/agi_english/Teenage_Theory_of_Universe_and_Mind_4.pdf (...) p.23 *“The paradox” of the liar * Goodlier from the village of Good Liаrville once said, that all of his fellow villagers and himself are liars, and then he asked if he's he lying if he says this? If he lies, then he's not a liаr, therefore he doesn't lie. However, he's from Good Liаrville, therefore he's a liаr. What a “paradox”, I'm totally confused!? Really?! I'm sorry, but I even wouldn't really call this a “paradox”, but a play of words and “pseudo wisdom”. What I'd answer to this Goodlier character is: - I don't know whether you lie or not, there is not enough input data. [2012. note - and I don't really care :D] I'd tell him also that he's a liar anyway, no matter if is he lying in this very moment, because probably he's trying to trick me that he's wise (sorry, he failed). One or two sentences in this or similar “paradox” cases are not enough to imagine a definite non-ambiguous scene of what it's all about. For example, many people would believe that they know what a “liar” means once they hear the word. Well, what does a liar means? [Unfortunately], The practical value of general concepts in execution of direct [immediate, specific] actions is... fuzzy in such cases. Which one of all possible meanings and happenings [events, stories, memories, interpretations] that our mind has for a “liar” the story teller meant in this particular case? What does it mean to be “from Good Liarville”? Was Goodlier born there or he lives there, or he's a fan of the football team of the village? Or he has relatives there? Or he is originally from a village in this commune. It is possible that liars are the ones for whom one of this is true, but not all, and anyway - being a liar [in common sense] does not mean that you're lying in every single sentence. Therefore it's impossible to conclude is Goodliar lying in this very situation or not, as it's impossible to say definitely in more realistic cases from the daily live, where there are no [artificially] tangled premises and consequences [causes and effects]. In reality there are many causes and many possibilities to explain what's happening [and why]. Sometimes input data is not enough to find a [persuasive] proof only on their basis. According to my current understanding, mind works with* specific concepts, and not general;* *[Note from 2012 - "specific concepts" in this context means: based on specific and explicit records of sensori-motor data, an example is given above that section with a possible sequence of sensori-motor incremental learning; "specific concepts" here == concepts, generalized from sensori-motor data, grounded concepts, while "general" are the meaningless binary logical definitions like "lies/doesn't lie", "from the village/not from the village". The grounded concepts include the whole cognitive hierarchy at all levels and is physically feasible (mapped to reality)]* in specific concepts everything is as precisely defined as possible, while with the general concepts, there are too many undefined which easily lead to “paradoxes”, i.e. to insufficiency of input data for determining whether a statement belongs to a group [set/class]. Said otherwise, the description of the story is black and white, but we're asked what color is it. Or there are many colors on a picture, evenly spread, and we're asked to specify of what color is the picture: only one single color. Overall, in the above conditions the *asking unit* *has too low a resolution* *of perception and not* *enough memory* in order to think as precisely as the *evaluating unit *– us.* [The answer of the* *question requires from the evaluating unit to* *lower the resolution of the input and to lose* *details] * The "thing" asking the questions does not understand [discriminate, recognize, perceive] all details we do, and in order to communicate with it, we should act according to its model. We see the indefiniteness and the simultaneous “truth” and “false” [error, mismatch] of each possible actions, according to our own resolution of perception, but we should [are forced to] select from the offered possibilities. In case we're asked to select only one feature of all and there is not an “I don't know” option, then mind would create a model for selection of some of all, based on other,* lateral data; of data* *which did not come from this specific situation.* Since the device proposing us the possibilities lacks brains to differentiate black-and-white and color image or a motley and one-colored picture, then this device is forced itself to lower the resolution of perception and to delete part of its memories [records] that otherwise we would have kept [possessing higher resolution of perception]. This device may call a motley picture using the name of only one color, and may have it's definite reasons, but apparently it would not be able to make inferences about many colors placed on one-single canvas simultaneously. (...) ** Todor "Tosh" Arnaudov ** * -- Twenkid Research:* http://research.twenkid.com -- *Self-Improving General Intelligence Conference*: http://artificial-mind.blogspot.com/2012/07/news-sigi-2012-1-first-sigi-agi.html *-- Todor Arnaudov's Researches Blog**: *http://artificial-mind.blogspot.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
