On Fri, Apr 30, 2021, 6:19 AM Bruno Marchal <[email protected]> wrote:
> 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)) > Using the definition of knowledge as "true belief" I agree with this. > (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. > Is this because the definition of knowledge includes truth, and truth is not definable? > 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. > So is it more appropriate to equate consciousness with belief, rather than with knowledge? It might be a true fact that "Machine X believes Y", without Y being true. Is it simply the truth that "Machine X believes Y" that makes X consciousness of Y? > > > > > > 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. > Can a machine believe "2+2=4" without having a reference to itself? What, programmatically, would you say is needed to program a machine that believes "2+2=4" or to implement self-reference? Does a Turing machine evaluating "if (2+2 == 4) then" believe it? Or does it require theorem proving software that reduces a statement to Peano axioms or similar? > 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. > By consistency here do you mean the machine must never come to believe something false, or that the machine itself must behave in a manner consistent with its design/definition? I still have a conceptual difficulty trying to marry these mathematical notions of truth, provability, and consistency with a program/Machine that manifests them. > > > 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 :) > In a way, I might view these long term memories as environmental signals that encroach upon one's mind state. A state which is otherwise not immediately aware of all the contents of this memory (like opening a sealed box to discover it's content). > 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. > Can it be said that Deep Blue is conscious of the state of the chess board it evaluates? Is a Tesla car conscious of whether the traffic signal is showing red, yellow, or green? Or is a more particular class of software necessary for belief/consciousness? This is what I'm struggling to understand. I greatly appreciate all the answers you have provided. Jason > 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]. > 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 > <https://groups.google.com/d/msgid/everything-list/217C90D2-0AB9-4AD3-BBC7-A876EAA28069%40ulb.ac.be?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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