That sounds like a fairly standard way of distinguishing between intuitiionist and classical conceptions. For me, the problem boils down to whether or not you allow for *actual* infinities or only possible infinities. If you take a doing like "choose a token, apply unary_1 to it, then apply binary_1 to the original token and the output of unary_1", the result will be a theorem. And there's no, in principle, distinction between the doing and the theorem. But if you then say, "do that forever". Then the result isn't really a theorem because there's really no result. You'd have to add something else ... like a convergence operator. But convergence is persnickety. A better operator would be a similarity/distance operator.
Marcus' "try random stuff, possibly reproduce" allows for options in "reproduce" of strong or weak similarity. (Obviously, for copying a software app, you need pretty strong similarity, but perhaps not when you have complex gen-phen maps.) So it seems reasonable to include similarity operators, but not convergence operators. Then instead of "do that forever", you have "do that until similarity_1 < ε". Even if similarity_1 is NOT monotonic, you can stop when you find a procedure that's close enough to a copy to halt. And that feels like a theorem to me. Of course, there's no reason those derived theorems have to already be present at the very start of the process. The machine can have a "priming" period where it has to "prove" a bunch of theorems that will *eventually* detect the "order". So Nick's "already possessed" is technically wrong, which is what Marcus points out. But, in some sense, those provable theorems are *already* expressible in the prior language. So Nick is spiritually right. But re: self discovery as corollary to world discovery -- It seems like Wolpert's paper argues against that: https://arxiv.org/abs/0708.1362 The idea that there can only be a single strong inference device in the world implies an asymmetry between world and self discovery. But I can't really pretend to grok the contents of that paper. Maybe someone else here can? On 12/1/20 8:09 AM, jon zingale wrote: > It is a little strange to read "possessed a theory" from Nick because he > staunchly avoids language like "has consciousness". That said, I read him > here as saying that discovery of the self is a corollary to discovery of the > world. From my own perspective, theories are derived from (founded upon?) > doings, but are not the same thing as doings. Tryings are perhaps more > subtle, they evoke for me something like proto-theorems or lemmas. -- 2₵ > On 11/30/20 1:24 PM, [email protected] wrote: >> I was arguing that given, say, a string of numbers, and no information >> external to that string, that no AI could detect “order” unless it already >> possessed a theory of what order is. I found the discussion distressing >> because I thought the point was trivial but all the smart people in the >> conversation were arguing against me. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
