Hi Jason,
> On 25 Apr 2021, at 22:29, Jason Resch <[email protected]> wrote: > > It is quite easy, I think, to define a program that "remembers" (stores and > later retrieves ( information. > > It is slightly harder, but not altogether difficult, to write a program that > "learns" (alters its behavior based on prior inputs). > > What though, is required to write a program that "knows" (has awareness or > access to information or knowledge)? > > Does, for instance, the following program "know" anything about the data it > is processing? > > if (pixel.red > 128) then { > // knows pixel.red is greater than 128 > } else { > // knows pixel.red <= 128 > } > > If not, what else is required for knowledge? Do you agree that knowledgeability obeys knowledgeability(A) -> A knowledgeability(A) -> knowledgeability(knowledgeability(A)) (And also, to limit ourselves to rational knowledge: knowledgeability(A -> B) -> (knowledgeability(A) -> knowledgeability(B)) >From this, it can be proved that “ knowledgeability” of any “rich” machine >(proving enough theorem of arithmetic) is not definable in the language of >that machine, or in any language available to that machine. So the best we can do is to define a notion of belief (which abandon the reflexion axiom: that we abandon belief(A) -> A. That makes Belief definable (in the language of the machine), and then we can apply the idea of Theatetus, and define knowledge (or knowledgeability, when we add the transitivity []p -> [][]p) by true belief. The machine knows A when she believes A and A is true. > > Does the program behavior have to change based on the state of some > information? For example: > > if (pixel.red > 128) then { > // knows pixel.red is greater than 128 > doX(); > } else { > // knows pixel.red <= 128 > doY(): > } > > Or does the program have to possess some memory and enter a different state > based on the state of the information it processed? > > if (pixel.red > 128) then { > // knows pixel.red is greater than 128 > enterStateX(): > } else { > // knows pixel.red <= 128 > enterStateY(); > } > > Or is something else altogether needed to say the program knows? You need self-reference ability for the notion of belief, together with a notion of reality or truth, which the machine cannot define. To get immediate knowledgeability you need to add consistency ([]p & <>t), to get ([]p & <>t & p) which prevents transitivity, and gives to the machine a feeling of immediacy. > > If a program can be said to "know" something then can we also say it is > conscious of that thing? 1) That’s *not* the case for []p & p, unless you accept a notion of unconscious knowledge, like knowing that Perseverance and Ingenuity are on Mars, but not being currently thinking about it, so that you are not right now consciously aware of the fact---well you are, but just because I have just reminded it :) 2) But that *is* the case for []p & <>t & p. If the machine knows something in that sense, then the machine can be said to be conscious of p. Then to be “simply” conscious, becomes []t & <>t (& t). Note that “p” always refers to a partially computable arithmetical (or combinatorical) proposition. That’s the way of translating “Digital Mechanism” in the language of the machine. To sum up, to get a conscious machine, you need a computer (aka universal number/machine) with some notion of belief, and knowledge/consciousness rise from the actuation of truth, that the machine cannot define (by the theorem of Tarski and some variant by Montague, Thomason, and myself...). That theory can be said a posteriori well tested because it implied the quantum reality, at least the one described by the Schroedinger equation or Heisenberg matrix (or even better Feynman Integral), WITHOUT any collapse postulate. Bruno > > Jason > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgmPiCz5v4p91LAs0jN_2dCBocvnh4OO8sE7c-0JG%3DuwQ%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgmPiCz5v4p91LAs0jN_2dCBocvnh4OO8sE7c-0JG%3DuwQ%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/217C90D2-0AB9-4AD3-BBC7-A876EAA28069%40ulb.ac.be.
