I’m not an atheist. I’m a Christian. I don’t have an objection to bringing up teleology.

Are you asking if I can, (without sneaking in a reference to meaning) explain what a representation of something is, or specifically what a representation of a goal is?

It seems possible that my choice of the word “representation” gave a different impression than I intended. I meant basically the same thing as “encoding”. If that’s the meaning you got from it, then cool, my word choice didn’t cause a miscommunication.

If I have a computable function from finite bit strings to Turing machines, this defines an encoding scheme for Turing machines. A system of representations of Turing machines.

Is that “sneaking in a reference to meaning”? In a sense that implies a notion of “goal”? If so, not in a way that I think matters to the point.

Perhaps one could say that, by describing it as being an encoding scheme of Turing machines, that I am therefore saying it is an encoding scheme for Turing machines, as in, with the purpose/goal of specifying a Turing machine. This, I think has some truth to it, but it doesn’t imply that some artifact which relates to such an encoding scheme in some way, has that as its goal, so much as, me describing something in terms of an encoding of Turing machines, says something about my goals. Namely, I want to talk about the thing in a way relating to Turing machines.

If what you were challenging me to define without a hidden reference to meaning/purpose was specifically a system of representations of goals, then,

well, if by “meaning” you just mean like, “statements and predicates and such”, then, I would say that defining what it means for something to be a scheme for representing goals, should, yes, require referring to something like a correspondence between (encodings/representations) and, something like predicates or conditions about the world or orderings on potential configurations of the world or something like this. Which, in some sense of “meaning”, would, I think, include at least an implicit reference to that sense of “meaning”.

So, if that’s your claim, then I would agree?

But, I don’t think that would imply much about the overall goal of a system.

If I purchase a DVD player which has as parts various microcontrollers which technically are capable of general computation, just because it has some processors in it that could hypothetically execute general-purpose programs, doesn’t prevent the overall purpose of the DVD player from being “to play DVDs”.

Of course, there’s a (probably big) difference between “encoding a program” and “encoding a goal”.

But, in the same way that a device can have components capable of general computation, if only the program were swapped out, without the use of the device intended by the manufacturers being “do general computation”,

I would think that a system could be such that, considered in terms of a particular encoding scheme for goals, if some part of it which (viewed in terms of that scheme) stores some encoding of some goal, and if modified to have an encoding of a variety of other goals (viewed in terms of the encoding scheme) would result in the goal being furthered by the system,

That doesn’t imply that the goal the system was designed to achieve, nor the goal which it currently pursues, is “be able to pursue any goal in this encoding scheme”?

(... wow I phrased that badly... I should edit the wording of this, but going to post it as is first because phone low on power.)

It seems fairly likely to me at this point that I’ve misunderstood you? If you notice a way I’ve likely misunderstood, please point it out.