i agree with that. knowledge doesn’t need foundations or completeness.
but then i’m not sure how to square that with the earlier no deep principle blocking formalizing judgment, just complexity point.
if knowledge starts in the middle, and we add details only as needed for the problems we’re working on, then judgment and explanation sounds open-ended rather than something captured by a final explicit formalism.
so when you say judgment is formalizable, do you mean we can keep improving formalizing parts of the process as needed? or do you mean there could in principle be a complete explicit formal account of the judgment process?
I didn’t say final or perfect. I think you need to define all your terms clearly. Thinking is computable (which basically means convertible to explicit, formal math) but also open-ended: you can keep improving your judgment as you go along. The outputs of thinking keep being reused as inputs of later thinking so things keep changing.
i think my last post was already making the relevant distinction. the unclear term here is actually formalizable.
thinking is computable is fine, but that can be true in a very thin sense. a perfectly true low-level physical theory of a baby still doesn’t by itself explain the baby’s knowledge creation. for that you need the right higher-level theory of the process.
so when you say judgment is convertible to explicit formal math, do you mean only the thin physics-level sense that whatever happens in a brain can be described mathematically after the fact? or do you mean a substantive higher-level account of judgment/explanation: how criticisms are generated, evaluated, and revised?
if it’s the first, i don’t think it answers the hard judgment problem. if it’s the second, then formalizable is the term that needs clarifying.
i agree with popper that C&R are the right abstractions. but genetic algorithms also do variation and selection without being creative in the relevant human/AGI sense.
so the actual theory of creativity has to explain what makes some C&R-like processes creative and others not.
Do you have an example algorithm you think clearly involves a replicator which can do general purpose problem solving instead of being restricted to a specific domain and set of capabilities?
no, not a clear one. current evolutionary algorithms have their search space, variation operators, and fitness function set up in advance for a specific task. that’s the domain restricted case.
i’m not saying those are the right kind of replicator. i’m saying they show that evolutionary structure by itself doesn’t specify general creativity.
so what would make a replicator general purpose instead of domain restricted?
two possible positions:
the missing difference is a specifiable property of the algorithm. we don’t know the property yet, but the form of the answer is “a condition a programmer could state in advance.”
even the form of that specification is open. we can’t yet say in advance what condition we’d be trying to state.
that sounds more like a test than a specification. saying we can handcraft versions for any domain tells us how to recognize the capacity, not what property makes it possible.
also, if a person is handcrafting the version for each domain, then a lot of the general intelligence is in the person choosing the representation, operators, and success criteria.
GAs can be handcrafted for lots of domains too: optimization, scheduling, symbolic regression, engineering design, etc. but that still doesn’t make them creative in the AGI sense.
so is there a further property that GAs lack? if yes, is that property something that could be stated in advance as a condition on the algorithm, or is the form of the condition still open?
i don’t really understand the objection. the property is that it can solve problems in any domain.
also, if a person is handcrafting the version for each domain, then a lot of the general intelligence is in the person choosing the representation, operators, and success criteria.
look at genes for an example. you could pick base pairs to solve problems in any domain. there is a gene that would do it. you can’t change representation, operators, anything else, just base pairs (the thing that evolution can control).
i’m not disputing that a fixed representation can be expressive enough. in the space of all python programs there’s presumably a class of programs that are AGI. same with the space of bitstrings.
but that only shows the space is expressive enough. it doesn’t settle what kind of problem remains.
two possible readings:
the remaining problem is complexity/search within a known explanatory framework. we already have the relevant framework, and the hard part is finding the right program/details.
the remaining problem includes a missing explanatory idea about creativity itself. C/R and evolution name the framework, but we don’t yet know what makes a process creative/general-purpose rather than domain-bounded search.
which is closer to human intelligence can be programmed using higher level abstractions idea?
which part is unclear? the claim that search-space expressiveness is different from a theory of creativity or how that applies to your genes example?
i switched to programs only because it was the same structure in a more familiar representation: a large representational space can contain AGI-like objects without that explaining creativity.
but i’m happy to stick with replicators/genes if that’s clearer. the question is still whether the remaining gap is just complexity inside C/R + evolution or a missing explanatory idea about creativity.
I thought you were asking about genetic algorithms and we were discussing some fairly narrow sub-issues but now you’re talking about search spaces and the remaining portion of some unspecified problem (in addition to not knowing the bigger picture you have in mind, I also don’t know what’s not remaining and why).
in #103 i asked whether formalizable meant thin computability or a substantive account of how judgment and creativity works. in #104 you answered with higher-level abstractions: conjectures, refutations and evolution.
i agree those are the right abstractions. the GA point was only meant to test whether those abstractions by themselves are the substantive account. GAs have variation+selection and are domain-restricted. so does evolutionary structure by itself distinguish general creativity from domain-restricted search, or is something more needed?
by remaining i mean: after we agree on computability and C/R+evolution, what still needs explaining?
is the explanation basically already there, and the hard part is finding/engineering the right replicator? or is there still a missing explanatory idea about what makes a replicator generally creative rather than domain-restricted?
There’s plenty of scope for better explanations in epistemology, and for progress in other fields to be relevant. I think it’s unknown how much progress in what fields is enough (and there are many different combinations that would work).
cool. so the gap includes better explanations in epistemology plus possibly other fields, with how much of what still open.
i want to restate the program point since you said it was unclear. it’s actually the same point as your genes example. base pairs are expressive enough that there’s a gene sequence for any problem. python programs are the same: somewhere in the space of all programs there’s AGI. but GAs also work in expressive spaces and aren’t creative. so expressiveness isn’t the thing. something else distinguishes creative processes from non-creative ones.
do you think that something else is the kind of thing that could be stated as a property of the algorithm, even if we don’t know the property yet? or do we not even know what form the answer would take?
Fitness scores aren’t actually evolution. These are evolution-inspired algorithms with some similarities to evolution. In biological evolution, some organisms have offspring and others don’t. That’s different than highest score wins. Many animals are successful per generation and success is close to binary (have offspring or not – but it’s complicated by the number of offspring and also e.g. by the quality of the mate(s)). And biological organisms replicate themselves instead of a master algorithm controlling everything and picking a winner (based on fitness score) and replicating it. The causality is different. Causing one’s own replication via mating is different than basically impressing some judges the most and then the judges cause the replication.
Ahh thanks for pointing out. I was thinking about fitness as not really being equivalent to nature but not with the binary clarity (obvious in hindsight). I also haven’t thought of these more as evolution-inspired than evolution. I guess it’s possible to write properly evolutionary algorithms (eg the kind of simulations where you actually have a group of creatures with traits that reproduce), but with other evo-inspired algs we artificially choose some ‘death’ point (like top 3 reproduce). It’s curious because actually using death is more random (sometimes it’s just luck, not directly due to genes).
I wonder if evolution could be more efficient if nature did have some more direct measure of fitness, or is lack of that kind of ‘optimization’ important?
