surely the archetype of the “rationality” that Chapman is so down on.
I don’t think this is the case. Also Chapman isn’t down on rationality in general, he just thinks it’s not sufficient on its own—but he does think that it’s still necessary:
Rationality and meta-rationality are complementary activities. Meta-rationality is not an alternative to rationality. Neither can operate without the other; they walk hand-in-hand.
Meta-rationality is not in the business of finding true beliefs or optimal actions. That’s rationality’s job. On the other hand, getting good at meta-rationality will make you more effective at rationality, and therefore better at finding true beliefs and optimal actions.
Meta-rationality selects and adapts rational methods to circumstances, so it is meaningless without rationality. Conversely, you cannot apply rationality without making meta-rational choices. However, since meta-rationality is rarely taught explicitly, it’s common to use only the simplest, default meta-rational criteria. Those are meta-rational nonetheless: there is no universal rational method, so in any situation you have to choose one and figure out how to apply it.
Also he points out on the Bongard page itself that solving the problems does also involve rationality:
The Bongard problems are a great introduction to meta-rationality for STEM people, because they definitely involve no woo. There appears—at first—to be nothing “mushy” or “metaphysical” involved.
Solving them obviously involves rationality. It feels very similar to solving ordinary puzzles, which are paradigms of systematic cognition. This illustrates the important point that stage 5 does not reject systematicity: it uses it.
As I understand it, Chapman’s definition of rationality is something like a systematic method for solving a problem, akin to a formal algorithm where you can just execute a known series of steps and be done with it. (This would be the prototypical case of a rational method, though it’s not a clear-cut definition so methods can be more or less rational.)
His point with the Bongard problems is that you cannot solve them in such a way—whereas e.g. solving a math equation could be done by just executing some known algorithm for solving it, there’s no fixed algorithm that you could apply to solve a Bongard problem. At the same time, once you have formulated some formal (rational) criteria for how the shapes are different (e.g. “the shapes on the left have sharp angles, the shapes on the right are round”), you can apply a rational method for verifying that criteria (the rational method being to check whether all the shapes satisfy this criteria).
So while there isn’t a rational method for solving the problem, there is a rational method for verifying that a possible solution is the correct one. And the process of trying out potential rational solutions and looking for one that might work is the meta-rational activity.
His point with the Bongard problems is that you cannot solve them in such a way—whereas e.g. solving a math equation could be done by just executing some known algorithm for solving it, there’s no fixed algorithm that you could apply to solve a Bongard problem.
If we are to be pedantic, I said that solving a math equation can be done in such a way, which can arguably be interpreted as “there exists at least one math equation that can be solved in such a way”.
I don’t think this is the case. Also Chapman isn’t down on rationality in general, he just thinks it’s not sufficient on its own—but he does think that it’s still necessary:
Also he points out on the Bongard page itself that solving the problems does also involve rationality:
As I understand it, Chapman’s definition of rationality is something like a systematic method for solving a problem, akin to a formal algorithm where you can just execute a known series of steps and be done with it. (This would be the prototypical case of a rational method, though it’s not a clear-cut definition so methods can be more or less rational.)
His point with the Bongard problems is that you cannot solve them in such a way—whereas e.g. solving a math equation could be done by just executing some known algorithm for solving it, there’s no fixed algorithm that you could apply to solve a Bongard problem. At the same time, once you have formulated some formal (rational) criteria for how the shapes are different (e.g. “the shapes on the left have sharp angles, the shapes on the right are round”), you can apply a rational method for verifying that criteria (the rational method being to check whether all the shapes satisfy this criteria).
So while there isn’t a rational method for solving the problem, there is a rational method for verifying that a possible solution is the correct one. And the process of trying out potential rational solutions and looking for one that might work is the meta-rational activity.
That’s only true of some equations.
If we are to be pedantic, I said that solving a math equation can be done in such a way, which can arguably be interpreted as “there exists at least one math equation that can be solved in such a way”.