Your post is an illuminating attempt to explicate some usually implicit concepts.
I sort of agree with your first diagram, that it is only human thinking that overlays a direction, or any kind of linkage, on the human-made collection of abstractions. But you lose me after that.
David Deutsch convinced me that even this was a mistake. A mind of arbitrary power, given only the bottom row, could deduce all the others—granted.
This is a highly contentious speculation (Deutsch, like Penrose, is fond of them), and I am not aware of any experimental evidence for it, so I refuse to grant it until I see some. Well, I suppose there is a tiny bit of it, where advances in physics let people design new chemical processes, or when understanding biology better lets us predict some behavior patterns.
I am far more comfortable with the more pedestrian definition of reductionism, where the arrows of human analysis of these abstractions point downward, and the secondary arrows of synthesis point upward, together forming “explanations”, and, if we are lucky, testable predictions, when your secondary upward arrows lead to something not yet observed.
I don’t understand your description of the “causation” meta-abstraction. “Meta” because it seems to connect towers of abstractions together somehow. One hint is that you describe it by “how” instead of “what”, and, if I cut through your gratuitous use of pathos and evocative imagery, you seem to say that both abstraction towers and meta-abstraction connections between the abstraction towers are required for robust knowledge.
Furthermore, you seem to describe the breaks in your [what x how] mental framework as supernaturalism, which makes sense in the context, I suppose.
Hmm, I see I wasn’t clear there at all. That all levels can be deduced from one level is just what Deutsch himself isn’t granting—he argues against it! Rather, it (or something like it) is the explanation I usually see people give for why they label the bottom of the blue line as more “fundamental”; my intention was to point out with the next sentence that the complete-deducibility hypothesis doesn’t make the blue line directional even if true, because it would allow travel along the line in both directions. I definitely need to rewrite that part. (All that being said, I do think that advances in physics letting people design new chemical processes, and that sort of thing, are strong evidence that far more is possible; I find the hypothesis more plausible than you and Deutsch do.)
together forming “explanations”
It’s true the directions of my green arrows are debatable; the reason I went with upward was because the simplest way I could think of to formulate what was happening was just “X explains Y”—”many compounds explain synapse.” I agree that in a more zoomed-in view each green arrow would imply a complex up-and-down motion of analysis and synthesis.
it seems to connect towers of abstractions together somehow
Violet lines of causation connect blue lines of territory to each other, not green towers of map. Green towers are connected by red threads, which are (causal) explanation, not causation. I thought this was clear by analogy with the first two diagrams, but you’re not the only one, so it looks like I should make it more explicit.
Your post is an illuminating attempt to explicate some usually implicit concepts.
I sort of agree with your first diagram, that it is only human thinking that overlays a direction, or any kind of linkage, on the human-made collection of abstractions. But you lose me after that.
This is a highly contentious speculation (Deutsch, like Penrose, is fond of them), and I am not aware of any experimental evidence for it, so I refuse to grant it until I see some. Well, I suppose there is a tiny bit of it, where advances in physics let people design new chemical processes, or when understanding biology better lets us predict some behavior patterns.
I am far more comfortable with the more pedestrian definition of reductionism, where the arrows of human analysis of these abstractions point downward, and the secondary arrows of synthesis point upward, together forming “explanations”, and, if we are lucky, testable predictions, when your secondary upward arrows lead to something not yet observed.
I don’t understand your description of the “causation” meta-abstraction. “Meta” because it seems to connect towers of abstractions together somehow. One hint is that you describe it by “how” instead of “what”, and, if I cut through your gratuitous use of pathos and evocative imagery, you seem to say that both abstraction towers and meta-abstraction connections between the abstraction towers are required for robust knowledge.
Furthermore, you seem to describe the breaks in your [what x how] mental framework as supernaturalism, which makes sense in the context, I suppose.
Hmm, I see I wasn’t clear there at all. That all levels can be deduced from one level is just what Deutsch himself isn’t granting—he argues against it! Rather, it (or something like it) is the explanation I usually see people give for why they label the bottom of the blue line as more “fundamental”; my intention was to point out with the next sentence that the complete-deducibility hypothesis doesn’t make the blue line directional even if true, because it would allow travel along the line in both directions. I definitely need to rewrite that part. (All that being said, I do think that advances in physics letting people design new chemical processes, and that sort of thing, are strong evidence that far more is possible; I find the hypothesis more plausible than you and Deutsch do.)
It’s true the directions of my green arrows are debatable; the reason I went with upward was because the simplest way I could think of to formulate what was happening was just “X explains Y”—”many compounds explain synapse.” I agree that in a more zoomed-in view each green arrow would imply a complex up-and-down motion of analysis and synthesis.
Violet lines of causation connect blue lines of territory to each other, not green towers of map. Green towers are connected by red threads, which are (causal) explanation, not causation. I thought this was clear by analogy with the first two diagrams, but you’re not the only one, so it looks like I should make it more explicit.
It’s a fair cop! But I like it that way. ^_^