Information and metaphysics

There's a famous anecdote about Wittgenstein and his friend Piero Sraffa by Norman Malcolm (Ludwig Wittgenstein: A Memoir):

Wittgenstein was insisting that a proposition and that which it describes must have the same 'logical form', the same 'logical multiplicity', Sraffa made a gesture, familiar to Neapolitans as meaning something like disgust or contempt, of brushing the underneath of his chin with an outward sweep of the finger-tips of one hand. And he asked: 'What is the logical form of that?' Sraffa's example produced in Wittgenstein the feeling that there was an absurdity in the insistence that a proposition and what it describes must have the same 'form'. This broke the hold on him that a proposition must literally be a 'picture' of the reality it describes. [p57f]

Malcolm credited this as the crisis of faith that switched Wittgenstein from his view that the world has a logical form to the view that meaning and reference are constructed by linguistic communities. Now there is a new kind of logic formism, a kind of tractarian ontology, only this time it's framed as the information of the world. Same mistake, different clothing.

Wittgenstein's view was known as "logical atomism" - the real world has atomic facts that can be expressed as logical atoms, and the relation between a statement about the world - say, "f = ma" - and the world itself is that the world behaves or has structure like the proposition. I suspect Ludwig was thinking of mathematical models when he said that.

Luciano Floridi, the doyen of the philosophy of information, has a paper forthcoming in which he argues against the notion of a digital ontology, such as is promoted by Edward Fredkin, who he quotes as saying

[digital ontology] is a totally atomistic system. Everything fundamental is assumed to be atomic or discrete; and thereby so is everything else. In physics, DP [digital philosophy, what has been called in this paper digital ontology] assumes that space and time are discrete. There are two mathematical models of such systems. The first is Diophantine analysis; the mathematics of the integers. The second is automata theory; the mathematics of digital processes.

What is wrong with this claim is manifold, in my opinion. Floridi takes the ontological aspect to task - there's no reason to think that because there are discrete aspects to the physical world this means that the world is digital - discreteness is not the same as bits. Floridi notes that being able to be modelled by a digital system is not therefore support for the claim that the system being modelled is digital (a clear case of confusion the representation for the thing represented; surely the digital ontology folks have read their Peirce?). Floridi's paper is a model (sorry!) of clarity of argument. He argues that an analogue world is semantically rich, while a digital world has a foundational simplicity.

I think there is a simpler way to state this: Any digital system can be approximated to an arbitrary degree of precision by an analogue one - that's what we do with physical computers, after all. But no analogue system can be precisely modelled digitally, because no matter how precisely you measure and represent the analogue phenomena, any difference from the exactness of the digital metric used will have causal differences. Our mathematical models, when they are digital and not differential, only work to some degree of exactness, and we decide when the differences between, say, our flow simulation of an aircraft and the actual aerodynamics matter or not. In systems* and phenomena where small differences at the outset (in the boundary conditions of the description of the model) make very large differences, like the so-called "butterfly effect",** our arbitrary decisions surprise and occasionally dismay us.

Making the ontology of the world the atomistic structure of a representation of it is, I think, the worst error that was rife in a sea of errors in the twentieth century, a fallacy of Misplaced Concreteness indeed. Kant is to blame, of course. Sure, we are trapped in a linguistic prison - any time we want to represent the Welt an sich we have to do it propositionally. Does this mean the world is just propositions? of course not. It means that representation beings must represent everything they consider or know. Film at 11.

But Floridi, in a paper not yet available which he mentions on the blog and in the paper, aims to defend what he calls informational structural realism. As a quandam realist myself, I always approve of "realism" in a position's name, even when the preceding adjective is "internal". But I don't think he means by that word what I mean by that word:

ISR) Explanatorily, instrumentally and predictively successful models (especially, but not only, those propounded by scientific theories) of reality at a given LoA [level of abstraction] can be, in the best circumstances, increasingly informative about the relations that obtain between the (possibly sub-observable) informational objects that constitute the system under investigation (through the observable phenomena).

Are models informative? I think that is another point at which representation is confused for realism. Suppose I have a model of the solar system, in 1688 or so. From it I can predict where planets will be with some precision if I have the right data points. Am I informed by this? I do not think so - all the information I have is already in the model (unless I bring in ancillary information). In fact the informativeness of the model lies in when I am not able to make predictions; that is, when the model is wrong. I find that Neptune doesn't obey the model - that surprises me (and hence has an informational surprisal value) and I must make predictions; the model on its own is no more informative than the equations I (or rather Isaac) put into it. Of course, I may not understand my own model - I may not have had time or inclination to work through the implications and derive, for example, the periodicity of a pendulum or some other aspect, but the information is in the model whether I work it through or not.

In short, it is not the model that informs us; but the real, empirical, world. If a model fails to surprise us, then I would suggest it is unlikely to represent the world well. or it is God's Own Theory, but history indicates this is a bad induction to make.

Notes

* I think the notion of a "system" is itself an abstraction. There are, in my opinion, only causal fields that are more or less dense in places.

**Ghods, that was a bad film.