The game tree really does have Real Options and Real Choices.
Yes, but cash out what you mean. Physical chess programs do not have Physically Irreducible Choices, but do have real choices in some other sense. Specifying that sense, and why it is useful to think in terms of it, is the goal.
The way you capitalize “Physically Irreducible Choices” makes me think that you’re using a technical term. Let my try to unpack the gist as I understand it, and you can correct me.
You can shoehorn a Could/Would/Should kernel onto many problems. For example, the problem of using messy physical sensors and effectors to forage for sustanance in a real-world environment like a forest. Maybe the choices presented to the core algorithm include things like “lay low and conserve energy”, “shift to smaller prey”, “travel towards the sun”. These choices have sharp dividing lines between them, but there isn’t any such dividing line in the problem. There must something outside the Could/Would/Should kernel, actively and somewhat arbitrarily CONSTRUCTING these choices from continuousness.
In Kripke semantics, philosophers gesture at graph-shaped diagrams where the nodes are called “worlds”, and the edges are some sort of “accessibility” relation between worlds. Chess fits very nicely into those graph-shaped diagrams, with board positions corresponding to “worlds”, and legal moves corresponding to edges. Chess is unlike foraging in that the choices presented to the Could/Would/Should kernel are really out there in chess.
I hope this makes it clear in what sense chess, unlike many AI problems, does confront an agent with “Real Options”. Why would you say that chess programs do not have “Physically Irreducible Choices”? Is there any domain that you would say has “Physically Irreducible Choices”?
But at this point, you are thinking about semantics of a formal language, or of logical connectives, which makes the problem more crispy than the vague “could” and “would”. Surprisingly, the meaning of formal symbols is still in most cases reduced to informal words like “or” and “and”, somewhere down the road. This is the Tarskian way, where you hide the meaning in the intuitive understanding of the problem.
In order to formalize things, we need to push all the informality together into “undetermined words”. The standard examples are Euclidean “line” and “point”. It’s entirely possible to do proof theory and to write proofs entirely as a game of symbols. We do not need to pronounce the mountain /\ as “and”, nor the valley \/ as “or”. A formal system doesn’t need to be interpreted.
Your sentence “Surprisingly, the MEANING of formal symbols is still in most cases reduced to informal words like “or” and “and” somewhere down the road.” seems to hint at something like “Surprisingly, formal symbols are FUNDAMENTALLY based on informal notions.” or “Surprisingly, formal symbols are COMPRISED OF informal notions.”—I will vigorously oppose these implications.
We step from the real world things that we value (e.g. stepper motors not banging into things) into a formal system, interpreting it (e.g. a formal specification for correct motion). (Note: formalization is never protected by the arguments regarding the formal system’s correctness.) After formal manipulations (e.g. some sort of refinement calculus), we step outward again from a formal conclusion to an informal conclusion (e.g. a conviction that THIS time, my code will not crash the stepper motors). (Note: this last step is also an unprotected step).
Yes, but cash out what you mean. Physical chess programs do not have Physically Irreducible Choices, but do have real choices in some other sense. Specifying that sense, and why it is useful to think in terms of it, is the goal.
The way you capitalize “Physically Irreducible Choices” makes me think that you’re using a technical term. Let my try to unpack the gist as I understand it, and you can correct me.
You can shoehorn a Could/Would/Should kernel onto many problems. For example, the problem of using messy physical sensors and effectors to forage for sustanance in a real-world environment like a forest. Maybe the choices presented to the core algorithm include things like “lay low and conserve energy”, “shift to smaller prey”, “travel towards the sun”. These choices have sharp dividing lines between them, but there isn’t any such dividing line in the problem. There must something outside the Could/Would/Should kernel, actively and somewhat arbitrarily CONSTRUCTING these choices from continuousness.
In Kripke semantics, philosophers gesture at graph-shaped diagrams where the nodes are called “worlds”, and the edges are some sort of “accessibility” relation between worlds. Chess fits very nicely into those graph-shaped diagrams, with board positions corresponding to “worlds”, and legal moves corresponding to edges. Chess is unlike foraging in that the choices presented to the Could/Would/Should kernel are really out there in chess.
I hope this makes it clear in what sense chess, unlike many AI problems, does confront an agent with “Real Options”. Why would you say that chess programs do not have “Physically Irreducible Choices”? Is there any domain that you would say has “Physically Irreducible Choices”?
But at this point, you are thinking about semantics of a formal language, or of logical connectives, which makes the problem more crispy than the vague “could” and “would”. Surprisingly, the meaning of formal symbols is still in most cases reduced to informal words like “or” and “and”, somewhere down the road. This is the Tarskian way, where you hide the meaning in the intuitive understanding of the problem.
In order to formalize things, we need to push all the informality together into “undetermined words”. The standard examples are Euclidean “line” and “point”. It’s entirely possible to do proof theory and to write proofs entirely as a game of symbols. We do not need to pronounce the mountain /\ as “and”, nor the valley \/ as “or”. A formal system doesn’t need to be interpreted.
Your sentence “Surprisingly, the MEANING of formal symbols is still in most cases reduced to informal words like “or” and “and” somewhere down the road.” seems to hint at something like “Surprisingly, formal symbols are FUNDAMENTALLY based on informal notions.” or “Surprisingly, formal symbols are COMPRISED OF informal notions.”—I will vigorously oppose these implications.
We step from the real world things that we value (e.g. stepper motors not banging into things) into a formal system, interpreting it (e.g. a formal specification for correct motion). (Note: formalization is never protected by the arguments regarding the formal system’s correctness.) After formal manipulations (e.g. some sort of refinement calculus), we step outward again from a formal conclusion to an informal conclusion (e.g. a conviction that THIS time, my code will not crash the stepper motors). (Note: this last step is also an unprotected step).