samedi 6 août 2016

Structural realism or modal empiricism?

Welcome to this new blog dedicated to the philosophy of science. I already have two blogs, but they're in French, so I decided to make a new one in English. Not that I don't like to write in French. It's a lot easier: my style is more fluid and precise than in English. I also like the idea of keeping my home language alive, especially in philosophy, as English is increasingly becoming the only language in town. But having a blog in English will allow me to share my thoughts with a wider audience, or so I hope. (Please excuse my language mistakes and correct me any time in comments, that's how I'll improve!).

One of my purpose here will be to share in an informal way the content of my PhD dissertation, which I'm currently writing. The dissertation mainly talks about epistemological issues in science, with a little metaphysics. To be precise, I defend a position in the debate on scientific realism, which I dubbed "modal empiricism". I think it's an original position (although the term appears with the same intended meaning in a chapter by Giere in "Images of Science: Essays on Realism and Empiricism", 1985). The position can be expressed in more than one way, but here is one: our best scientific theories are correct descriptions of the relations of necessity between our observations and interventions. Here is another one: all that we know is that our theories are empirically adequate, but the empirical content of our theories is modal: it's about possible experiences.

There is a lot to say, but I think that this position has lots of virtues. For a start, let me say a word about how I came to defend it. The readers familiar with structural realism and Newman's objection can skip to the last paragraph of this post.

Structural realism and Newman's objection

Belted Rhombic Deltahedron

Structural realism is the view that our best scientific theories roughly get the structure of the world right, if not its nature. The interpretation of a theory (what count as natural kinds, fundamental processes...) can be lost in theory change, but the structure of a successful theory is usually retained, at least in part, which shows that past, abandoned theories, even if false, got something right about the world: its structure, the relations between things. Our contemporary theories, even if they're eventually replaced by better one, are probably right about the structure of the world as well.

The position originated independently, during the last century, from Poincaré and Russell, among other authors. For Poincaré, all that we can transmit through language is relations (I cannot tell you what it's like to see red, but I can tell you that tomatoes and blood have the same colour), so any objective knowledge must be about relations. For Russell, we have no direct access to the fundamental nature of reality, because we access it through our senses, but at least, given some minimal assumptions, we can be confident that the relations between our perceptions mirror the relations between external objects. Anyway, the conclusion is the same: we know about the structure of the world, or the relations between objects whose fundamental nature remains unknown.

Structural realism has been reintroduced by Worrall in the contemporary debate on scientific realism to solve the problem of theory change for scientific realism (drawing from an argument of Poincaré). It's not a full-blown realist position, since it claims that our knowledge of reality is limited to structure, but Worrall's (or Poincaré's) argument about theory change has also been adopted by so-callled ontic structural realists, who claim that the world is only a structure: basically, they get rid of inaccessible objects, or reduce them to structural aspects.

So far, so good, but there is a fatal objection against structural realism, known as Newman's objection (because it was stated by Newman, against Russell): structural realism turns out to be nothing but empiricism. At least if "relation" is understood in a logico-mathematical sense: in logic, a relation is defined by the objects it relates (its extension), and nothing more. But suffices to say that these objects exist for the relation to exist, in the mathematical sense: it can well be defined. So saying that there is a structure of relations between unknown objects is not saying much, unless we qualify these relations: if there are enough objects in the world, then any structure that could be defined from these objects exists indeed. Now if we qualify these relations, if we interpret them in a realist fashion, then we run the risk of falling prey to the problem of theory change again.

Of course, the structural realist is not only saying that there is a structure in the world, but also that it relates to our observations in a certain way. However then, she's only an empiricist, for all she says is that there is a structure of relations between observable phenomena, and enough objects in the world to fill the holes.

Is it really a problem? For a realist, it is, because empiricism is unable to explain the predictive success of our theories (in particular when it comes to their making novel, unexpected predictions): it merely states that success. However, then, that success seems miraculous. I am not quite convinced by this "no-miracle argument", and I'll have to say more in another blog post about this, but for now, let us take it for granted.

It's often believed that ontic structural realism is immune to Newman's objection, since they view relations as basic entities in the world, not mere mathematical objects. They also generally adopt a different framework: they don't consider scientific theories as sets of logical statements, but as sets of models, following the so-called "semantic conceptions of theories" (I don't think it's very different, but again, let me postpone that discussion). However this is not exactly right: Newman's objection can also be expressed in a semantic conception. It boils down to Putnam's model theoretic argument against realism. And at the end of the day, ontic structural realists face a problem that, I think, is the exact counterpart of Newman's objection: the problem of telling us the difference between mathematical and physical structure. The claim that the world is a structure is quite trivial if it's a mathematical one, for the same reasons, so ontic structural realists must qualify the structure they are talking about. In any case, getting rid of the inaccessible objects is not what could solve Newman's problem. We don't need less, but more...

Modalities to the rescue

Belted Multicrown Cube

Can we get back to the intuition of Poincaré and Russell, that the structure of our theories tells us something about the world, and not only about mere regularities in our observations? There is an interesting paper by Melia and Saatsi ("Ramseyfication and Theoretical Content", 2006) where they envisage different solutions to the problem from a formal perspective. As I see it, focusing on the formalism allow them to map precisely the different solutions available (even though they have already been proposed by other authors).

One way of expressing the structural content of theories that was used by structural realists is the Ramsey sentence: roughly, a logical sentence that expresses the content of a theory, with all theoretical terms (such as "electron" or "mass") replaced by variables. The idea is that when theoretical terms are removed, the theory is no more "interpreted": it doesn't talk about the nature of reality any more. Only the structure and the observational terms remain. However, the variables that replace theoretical terms allow for a concise, "factorized" formulation of the theory, while only retaining the "empirical theorems" could have yield an infinite number of statements. Some structural realists claims that the Ramsey sentence is exactly what we should be committed to about our theories. However, in this context, Newman's objection can be formulated as a theorem of logic, which says that a Ramsey sentence is logically equivalent to the empirical consequences of the original theory, plus a cardinal claim (enough objects to bear the structure): structural realism, thus formulated, merely says that our theories are empirically adequate. So much for the structural realist.

If Newman's objection can be framed as a theorem of logic when applied to Ramsey sentences, then the only way we could circumvent it is to see where Ramsey sentences go wrong. The formalism of Ramsey sentences makes a few assumptions: universal quantification, a strict distinction between theoretical and observational terms, and the use of extensional logic. In their paper, Melia and Saatsi consider different possible departures from this formalism (qualifying the objects or the relations we talk about, introducing observational terms that apply to unobservable objects as well, etc.). What we want is enough departure to invalidate the theorem, and not be a mere empiricist, but not as much as to be a full blown realist, and fall prey to the problem of theory change again.

Their conclusion is that nothing really works, except for one possibility: using intensional logic. The crux is that the structure of scientific theories is not extensional: it is nomological. Our theories are about modal relations: relations of necessity, in particular. That could be expressed by using modal logic, for example, and that, they say, would block Newman's objection.

Ontic structural realists (except some, such as Lyre) make a similar move to differentiate mathematical and physical structure. Physical structure, they say, is modal, or nomological, whereas mathematical structure is not. So it seems that we have a convergence of solutions.

Is it really working? En route to Modal Empiricism

Foil Crown Cuboctahedron

Does introducing modalities really block Newman's objection, and allow us to infer from our theories more than observational regularities, but some "real structure"? I was quite convinced for a long time, without really thinking about it, but now, I am not sure it works.

At least it depends what we want: if we want that our theories be about relations between real, inaccessible objects, and not only about observable phenomena, then I don't think modalities will do the job. A simple way to mimic modal logic in extensional logic is to quantify over possible worlds (something is necessary when it is true in all possible worlds). Then there is no reason why the theorem that supports Newman's objection would not apply to a theory expressed in modal logic in this way. The difference with standard structural realism is that we are not talking about actual observations only, but also about possible observations. Yet the relations are still between observable phenomena, not real objects (except for a cardinal claim). If standard structural realism collapses to empiricism, then this version collapses to a modal empiricism.

Now maybe we don't need real objects, but anything real will do to qualify as a realist, and, one could argue that when we talk about modal relations, we talk about something real, that does not supervene on actual observations. Then the position (structural realism with modalities) should be considered a brand of realism, not of empiricism, even though it does not say anything substantial about real objects entering in the structure. Basically, the position would collapse into ontic structural realism, rather than modal empiricism: our theories are about modal relations in the world.

However, there is a slight difference between the ontic structural realist, who claims that modal relations exist autonomously and that it's "all there is", and the epistemic structural realist, who claims that they are relations between possible observations and unknown objects and that it's "all we can know". Modal relations, here, are not autonomous entities, but relations between possible observations. Since the theorem implies that we say nothing substantial about real objects, the only thing that we really have to posit beyond actual observations are possible observations, and since they're still observations (or, to be precise, observable phenomena), there is no reason not to call this position empiricism.

Let us go back to Poincaré's position: he held that relations are objective because they are transmissible. Intuitively, we could think that this position is immune to Newman's objection: to be sure, the fact that two objects are of the same colour is objective, if not the corresponding qualitative experience of colours, since everyone agrees. However if we ask: "what is the intented relation?" we'll soon realise that it's a relation between perceptions different persons could have: we're saying that everyone would agree about this relations, but the relata are still observations--possible observations, that is. So Poncaré's position can be considered a version of empiricism.

If we get rid of observable phenomena, for example if we think that they reduce to structural aspects of reality, then we get ontic structural realism. But then we get problems too, and it's hard to understand how we could reach a more robust realist position by removing entities. Moreover, the "modal" qualifier becomes a bit nebulous. What is it to say that there is a "modal structure" if we don't say that some things (phenomena, observations) are actual, and others merely possible? If all possibilities are on a par in the structure (or if actuality is indexical), do we get something different from a purely mathematical structure? If something is actual, and not merely possible, isn't it somehow something "more" than the modal structure? Or does the modal structure itself says that some things are actual, and not others? Then why do we need possibilities? I won't discuss these issues here, because I want to focus on the other position, the one that retains observable phenomena (actual and possible) in our worldview, as the relata of the structure.

Is introducing modalities the right move? As I said, everything depends on what we want. If we want something "real", then introducing modalities doesn't really works: all we have is relations between observable phenomena, as any empiricist would have it. We only extended the range of observable phenomena to possible ones (but note the "able" in "observable": maybe we didn't even do that!). But if what we want is explain the empirical success of our theories (and that's what a realist really wants, after all), that might help. A commitment to modalities certainly brings us closer to realism. At least there is a possible avenue: I hope to discuss the no-miracle argument in a future blog post. However then, the position should better be called modal empiricism, not structural realism.

That is the line of thinking that initially brought me to modal empiricism. There are other reasons too: the more I think about it, the less I'm convinced that there is a continuity of structure between successive theories, beyond mere empirical structures. And as I said, I became suspicious of the no-miracle argument, too, and of abductive reasoning in general. I think modal empiricism is really what we should go for, but not in the purpose of explaining the predictive success of theories: rather because empirical adequacy is better construed in modal terms, in terms of possible experience, that is (observations and interventions). In sum, the route I follow now is quite different from the one that brought me to modal empiricism, but I hope that these arguments are still of interest.

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