On Sun, Jul 5, 2020 at 11:09 AM Ben Goertzel <b...@goertzel.org> wrote:
> As you perhaps know I am a big fan of imaginary logic, having started in > this direction due to some correspondences w/ Lou Kauffmann (G. Spencer > Brown's collaborator) in the mid-1980s ... > I'm not at all surprised which is why I said NOR DCGs should ring all kinds of bells with you. But I am a _bit_ surprised I don't find you on the Laws of Form yahoo group mailing list, which I administer (although that mailing list is not very active). Lou Kauffman is prolific but has not, to the best of my knowledge, pursued Tom's construction of imaginary logics from real valued spinors. I know he and Tom were very well acquainted because I had dinner with him at Tom's house in Palo Alto circa 2000, and Tom was the original editor of the Alternative Natural Philosophy West's journal, in which Lou published some articles. Lou told me that he didn't think my "obsession" with "time" was on target regarding imaginary logic -- which struck me as quite odd given his obvious affinity for GS Brown. However, this may have been due to the general trend among the LoF folks to place "distinction" as prior to both time and space -- with a kind of "space time" emerging without priority. Under Tom's notion of a kind of negative valued quantum logic in which imaginary logic is only one kind of "spinor", I can see why they may take that view. But if so, I would have expected Lou to pursue Tom's quantum logic. But I remain suspicious of such impartiality between space and time. Sure, quantum laws are symmetric in time and space. Yet we literally "observe" time (thence space) into "existence" in the sense that observation itself breaks the symmetry. Tom regarded "the collapse of the wave function" consequent to "observation" to be tortured metaphysical nonsense. I never quite groked that. My understanding of Tom's metaphysics is inadequate. However as you probably also know, type theory is now far beyond its roots > w/ Russell & Whitehead etc., and there are type-theoretic treatments of > Anti-Foundational Set Theory and so forth... one could use type-checking on > quantifier logic extensions of imaginary logic etc. ... > Yes and I haven't followed that work so my understanding is also inadequate to critique it. However, the development of the field strikes me as analogous to trying to come up with a dynamical mode of description in terms of kinematics: Newton in terms of epicycles. *** > In other words, trying to represent physical dimensions in the theory of > types is getting the cart before the horse. You have to go back to the > foundation of logic and build up from there to discover that computation is > a dynamical system involving imaginary logic, and that "typing" is merely > checking that two "objects" have commensurable dimensions (ie: they possess > matching relational substructures required by a given operator). > *** > > Sure, that makes sense. I.e. of course you can represent > physical dimensions etc. in type theory in various ways, but if I > understand correctly, what you're suggesting is a more foundational > approach that will build up to certain particular types that are important > for physics and mind in a structured and rational way... > Yes. As I alluded above, it seems to me that the formal foundation of computation, thence the theory of computation, thence AIT, thence notions of intelligence, would benefit from a metaphysics derived from attempts to make sense of physics in terms of some sort of quantum logic. > A question in terms of AGI systems design is whether this sort of > foundational thinking on specific types and structures etc. needs to be > part of the infrastructure of one's system, or whether one can/should have > a more generalized infrastructure and use it for research/experimentation > on specific types and structures... > Well I'm rather partial to formal tools which enable us to think about "the empirical world" (using Russell's term) so that attempts at a "top down theory of universal intelligence" like AIXI, are more consilient with Reality. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T044a258b4a99cfd7-Mda121bee0bec8118cd9651fb Delivery options: https://agi.topicbox.com/groups/agi/subscription
