Wilkins: Pizza Reductionism and Infinite Computation

Caveat: This is another one I’m posting without proofing. Please inform me of typos and inexplicable blunders.

John Wilkins is a philosopher of science with a specialization in the philosophy of biology. One of the issues that interests him is one of those old-time good ones, reductionism. He’s a reductionist.

And he’s recently proposed what he calls “pizza reductionism” as opposed to bog-standard “layer–cake” reductionism. As the phrase suggests, layer cake reductionism imagines a strict hierarchy with no jumping over levels. For example: cognition → psychology → neurobiology → biology → biochemistry → chemistry → physics. In this view all laws and processes are ultimately the laws and processes of physics and the rest (chemistry, etc.) we entertain because it’s convenient for us to do so.

Pizza reductionism does away with the strict hierarchy. While topping may be piled upon toppings in a pizza in a layer-like way—especially in one of those everything goes pizzas—it’s not a necessary feature of construction. Any topping can find itself floating directly on the sauce, or even penetrating the sauce to the solid bedrock of the crust.

Though I recognize it as an interesting one, and worth your attention if you go in for these things, this distinction is not why I’m writing this post. As someone who’s pursuing the construction of a pluralist metaphysics on certain propositions from object-oriented ontology, I’m not interested in reductionism of any kind. No, what interests me is an argument Wilkins brings up in the course of explicating the consequences of pizza reductionism.

Let’s pick up Wilkins’ thinking in midstream:

So the physical property is the key. It is what exists independent of the propensities and predilections of the observer systems. How we carve that up at scales above the microphysical is conventional. But the phenomena themselves are clearly real: observers really do see reds, feel pain and use descriptors for classes of physical states. It’s just that these are not the final story, the explanans.

In Harman’s metaphysics that explanans is the every withdrawing object. Harman takes that capacity of withdrawal as cause for arguing that the object that is the explanans is the real object while the phenomena themselves, which he calls sensual objects, are not real. So, Harman and Wilkins seem to be looking at much the same configuration of conceptual stuff, though they manipulate it with different conceptual hooks, but arrive at very different ways of developing broader patterns of reasoning about that stuff. Wilkins is a reductionist; Harman is not.

Wilkins continues:

And here we return to the methodological and epistemic versions of reduction. Alex Rosenberg (one of the last “club footed” reductionists still about, and with whom I agree) has argued (1994) that the problem with reductionism is simply computational: we just don’t have sufficient ability to work out the properties we see from first principles; neither the time nor the computational capacity.

From my point of view our lack of computational capacity is a game-stopper. If we cannot actually “work out the properties we see from first principles” then the assertion of reductionism is meaningless. It’s just an expression of blind faith and, while I do think there’s a role for blind faith in this world, I don’t think it incumbent upon to adopt someone else’s blind faith. If we can’t actually formulate the properly reduced laws and principles, then what’s the point in believing that they might exist?

Wilkins goes on to criticize the notion of emergence, which he seems to regard as fancy place-holder for explanations that have yet to be made. On that I agree with him. But I’ve got problems with his further suggestion that phenomena that seem emergent to us, as finite beings, might not seem so to a being with unbounded computational capacity.

A bit later:

In short, while the phenomenon is real (because none of the observable features that make it a phenomenon are unreal), it is also observer-relative. Laplace’s Demon might not see any such phenomenon.

So biology might not be a separate layer for a deity or demon. That might mean biology has no laws, or if it does those laws will be summaries, aggregates or placeholders for laws at the physical “level”. The so-called emergent properties and entities of biology, psychology and the rest of the supra-physical domains are just phenomena that we, as observers find important. Ontological emergence evaporates, leaving only methodological and epistemological emergence, and that is a measure of our surprise. In short, it tells us at least as much about ourselves as it does the phenomena we register surprise about.

My problem, of course, is that this Laplacian Demon with infinite computing capacity is simply a philosophical fiction. It’s the projection of blind faith into an imaginary agent.

That agent might just as well be a transcendent god. Now that’s a curious fix, isn’t? You defend a reductionist view of the world by positing the (hypothetical) existence of an all-seeing all-knowing transcendent being. Looks a lot like idealism to me.

But then Harman pretty much says that, doesn’t he?

* * * * *

Every once in a while I do think about infinite computation or, if not infinite, very very large. And when I do, I sometimes think about chess. From a certain abstract point of view chess is no more complicated than tic-tac-toe. When played with a stop rule—such as declaring a draw if no pieces have been exchanged in 50 moves—chess is a finite game. Every possible chess game can be listed in a tree with a finite number of elements.

Tic-tac-toe is also finite. As normally played the game space has nine cells. No more, no less. When a game is finished each cell will be in one of three states: filled with an X, filled with an O, or empty. The game starts with all the cells in the empty state. Once a cell changes from empty to either an X or an O, it cannot be changed back. The game ends when one player gets three of their symbols in a row. All that adds up to a finite number of possible games.

Yet tic-tac-toe is trivially easy while chess is extraordinarily difficult. What’s the difference? Computational requirements. They’re low for tic-tac-toe but very very high for chess. Not infinite, but merely very very high.

Now, if there were a way to prove that the reductionist laws actually exist, in the way that one can prove that chess is finite, that would give Wilkins’ position some teeth. It’s not at all clear to me that the addition of teeth would give it an appreciable bite, but there might be something to discuss.

But how can one arrive at a mathematical proof about the ultimate nature of the world?

Is that what I mean by abundance, that the world always exceeds our capacity to compute its laws and processes?