Thursday, January 29, 2009

What Was Wrong With the Syntactic View of Theories Exactly?

These days most philosophers of science (PoSs) seem to subscribe to the semantic view of scientific theories, according to which scientific theories are collections of models (the question obviously become what kind of thing a scientific models is. For my take on this question see here). In the heydays of logical empiricism however, the prevailing view was the so-called syntactic view of theories, by which I mean here the view that scientific theories were collections of sentences. Logical empiricists, unfortunately, saddled this view with a host of other less plausible views about language and truth, which most philosophers today seem unwilling to accept. However arguments against such views are not arguments against what I call the syntactic view. So, was the rejection of the syntactic view a case of guilt by association or are there any serious arguments against the view itself (rather than the views that were usually held in conjunction with it)? If not, what are the arguments in favour of the semantic view (other than its supposedly being more empirically adequate)?
Thinking about it the only serious argument that I can think of that seems to target what I call the syntactic view (as I am intending it here) is the one according to which the same scientific theory can be formulated by using different sets of sentences (e.g. in English and French or in Lagrangian and Newtonian terms) and, therefore, the theory cannot be identified with any set of sentences. But what if we substitute sets of sentences with sets of propositions? (Would this work in the case of Newtonian and Lagrangean mechanics or would one have to say that the two are distinct theories?) The only obstacle I can see to this way of recasting the syntactic view this way was the logical empiricists' prejudice against propositions. But I don't see any reason to think of propositions as being more metaphysically mysterious than sentences (utterances are physical events but sentences like propositions seem to be abstract entities).
Am I missing something major?


  1. Another claim of the syntactic view is that theories are sets of sentences closed under logical consequence. So, are your propositions closed under logical consequence? If they are, then they will probably miss the autonomy that many people find attractive in talk of models. That is, the models are not logical consequences of the laws of the theory. This point doesn't really tell in favor of the original semantic view, but may be reason to shift to models are structures (or fictions)!

  2. Chris,

    Personally, I favor the view that models are fictional objects (more on this in the paper I linked in my post). But I also see models as being largely independent from theories. This is why I still feel I need an account of what a theory is and I don't see any reason to think that theories cannot be (deductively closed) sets of propositions especially if I can reap most of the benefits of the semantic view by claiming that theories have models (although they are not collections of models). The models of the theory being those fictional objects that are (mostly) consistent with the theory itself.

  3. I realise there is a common belief that our science theories are just human constructions and reality is somehow different (this gap between our ideas of things vs. the thing in itself).

    However, given that physics evolved from an illogical foundation of discrete particles to explain an interconnected reality (Newton) then it was always obvious that in time this foundation would collapse - as it did in the early 1900s with quantum physics and Einstein's relativity both telling us that matter is an extended structure of space.

    Strangely, if we just ask the question; "What is the most simple science language for describing reality", then we find that there is only one solution.

    Space must be the substance that exists and matter is formed from waves in space.

    This brings science into harmony with metaphysics, as it is describing reality from one substance (space) that we all commonly experience, and its properties (a wave medium) for wave motions of space that form matter.

    Thus our metaphysics has been simplified from the motion of matter particles in space and time - to the wave motion of space that causes matter and time.

    So this is deduced using Occam's razor / metaphysics.

    From here we can then further deduce that the wave structure of matter works.
    You can find the deductions on the website and from the work of maths physicist Milo Wolff.

    So it seems strange to me that we have ignored this most simple and obvious explanation of physical reality.

    Why is this? Any thoughts?
    Or more precisely - does anyone have any evidence that space does not exist - that matter is not formed from waves in space - the electron being a spherical standing wave in space.
    It seems to work just fine.
    Geoff Haselhurst

  4. Why not do the Davidson approach of talking about translations? I think this would resolve the problem of sentences you raise without necessarily creating the problem that propositions creates. That is consider the set of sentences in one language (or sublanguage) and simply think of the circumstances they are held to be true. Then a translation to a new set of sentences that maintains these truth values is a adequate translation.

  5. Hendry and Psillos ('How To Do Things With Theories', 2007) have considered what they call the "weak syntactic approach", where theories are (or are *represented as*) sets of propositions. Their main objections to this are (i) that this 'neglects the role of models in scientific theorizing', and (ii) that it 'neglects the fact ... that theories confront not the phenomena themselves but models of the phenomena.' I am currently attempting to argue against this somewhat, not by saying that the "weak syntactic approach" is the way forward, but that all of these approaches are just different ways to represent the messy "substrate of science" (as Hendry and Psillos put it). In other words it is *not* the case that there is something that a scientific theory is, and it's up to us to find out what. Instead different parts of what we find recorded in the annals of science can be represented in different ways for different purposes, and the only question should be whether the way we have represented a part of science on a particular occasion is appropriate *for the purpose as hand*. We can call such a representation a "theory" if we want, but nothing hangs on whether we do so.

  6. I think at least some motivation for the semantic view comes from the same sort of considerations which motivate structural realism. Here are the main two as I see them:

    - What seems to be preserved through theory change is only certain key features of the mathematical structure of theories - which objects and properties are quantified over may change substantially.

    - The role of the 'objects' in scientific theories seems to some to be just as 'place-holders' in a mathematical structure - it's the structure itself which does the explanatory work, and the structure itself which deserves ontological commitment, so the structure itself which our theories are fundamentally about.

    Roughly, if you buy into the first motivation only, you're an epistemic structural realist. If you buy into both, you're an ontic structural realist. But both considerations seem to motivate the semantic view of theories. All rather hand-waving, but I hope you get the idea.

    ps One thing missing from this post and the comments seems to be any mention of van Fraassen's extensive discussion of the semantic view.

  7. Gabriele,

    If you concede that the semantic view is "more empirically adequate" than the syntactic one, what other virtue does it require to be declared superior to the syntactic one? Do you believe the semantic view to be unnecessarily complicated or unacceptably ad hoc?

  8. Propositions are the semantic values of sentences; so conceiving of a theory as a set of propositions would just be the semantic view of theories.

    If these propositions have as constituents specific individuals, the semantic view will not be motivated by structural considerations (a la Alastair's discussion): for that we will need an equivalence class of propositions under substitution of descriptively indistinguishable individuals, indistinguishable using the properties provided by the theory, of course).

    On the other hand, given the syntactic view of theories, it will not be possible to pick out some specific model of the sentences in the theory using those resources anyway (as two models isomorphic with respect to the designators and predicates of the theory will both satisfy the theory). So I don't exactly see why this motivation for structuralism wouldn't also motivate one to the semantic theory.

  9. Of course, a lot here hangs on the questions -- what language? what models? I think part of the impetus for the move from the syntactic to the semantic view was a desire to move from the framework of first order logic to the full power of mathematics. (It's hard, e.g. to formulate general relativity in a linguistic framework where every consistent theory has a countable model. You can't have a countable manifold...) But I think one can switch from logic to math without having to switch from syntax to semantics.

    Another impetus is the way in which the equations of physics are actually used. If you take Schrödinger's equation, e.g., it's not clear what assertion it is actually making. Are there really Hamiltonians in the world? SE equation looks a lot more like a recipe for constructing models of systems.

    Also, I think it has seemed appealing to a number of authors that one can take a number of different epistemic attitudes to models: they provide accurate predictions of a given system, they describe how the system would behave if certain idealizing assumptions are made, etc. The theory, interpreted as a class of models, is neutral as to how you use and interpret the theory. A set of assertions seems a lot less flexible. There, it looks like the theory is trying to describe the world.

  10. Clark,

    I don't see the advantage of taking the Davidsonian approach over being committed to propositions, but I see the advantage of the latter over the former (among other things, one can provide a solid account of what is for an utterance of a sentence in one language to be a correct translation of an utterance of a sentence in another language).

  11. Peter,

    As I say above, it is exactly because of my belief that models de facto play a crucial role in science and are largely autonomous from theories that I'm interested in the arguments against the view that theories are sets of propositions--I still feel I owe an account of what a theory is, if it is not just a set of models. As far as I can see, all this is compatible with there being some models that are models of the theory.
    As for Hendry & Psillos's second point, I do not see why Newtonian mechanics cannot be (partly) taken as a set of propositions that are either true or false of the actual world even if, as a matter of fact, we need to use models in order to apply it to the world.
    In other words, one of the questions I am interested is if models are needed in principle or only as a matter of fact.
    (I am working on a paper in which I am trying to make all this much more clear, but I don't think it's goign to be ready any time soon.)

  12. mrogblog,

    As far as I can see, this might be good argument *for* the semantic view if you are already committed to either ESR or OSR. But, as it is, it is hardly an argument *against* the view that theories are sets of propositions. As I said, I don't see the view that theories are sets of propositions is inconsistent with the view that there are models of the theory (insofar as one does not identify the set of models of the theory with the theory).
    So, I don't see why a structural realist could not say that a theory is strictly speaking false (or at least that we cannot know it to be true) but some of its models "capture the structure of the world" (or fill the quotes with your favorite structuralist claim).
    Simplistically, my view is that, say, Newtonian Mechanics can be seen as a set of propositions that are strictly speaking false of the world but true of its models (where the second truth for me is akin to truth-in-fiction).

  13. I think the thrust of Chris Hitchcock's comment (whether he knows it or not) is that as long as you stick to first-order logic there is no difference between the syntactic and semantic view.

    Chris Hitchcock also points to the fact that first-order theories have countable models as motivation to escape the limitation of first-order logic -- but that is a red herring: the very same fact has never given set-theorists any pause, and uncountable sets are arguably their bread-and-butter to a larger extent and in a deeper manner than for anybody dealing with physics.

  14. Christopher G.,

    I probably would only say that the view I express in my previous comment has advantages over what the semantic view is often taken to say. (Arguably one could say that the most sophisticated advocates of the semantic view espouse the same view I express in the previous comment, but I still they are still too caught up in the idea that a theory can be taken to be true either of the world or of its models where the or is exclusive).

  15. Christopher H.,

    As far as I am concerned, the last advantage you mention is one of the problems I have with the the semantic view--it is too neutral when it comes to interpreting "what the theory says".

  16. Antony,

    You say: "Propositions are the semantic values of sentences; so conceiving of a theory as a set of propositions would just be the semantic view of theories".

    Under the label "the semantic view" I am discussing the view that theories are collection of models and most people would not think models to be propositions. So, I don't think those two views are the same. However, some of the comments you make suggest that there might be more similarities between them than people usially think there are (but only if you adopt a certain view of models).

  17. Aldo,

    It is not quite true that if you stick to FOL there is no difference between the semantic and syntactic views. While every set of sentences corresponds to a set of models, the converse is not true. That actually raises an interesting issue: According to the semantic view, it is in principle possible to reject specific models on an ad hoc basis. Physicists sometimes do this when they reject a solution to e.g. the Einstein field equations as 'non-physical', without giving any specific criterion (i.e. without adding a sentence to the theory). Whether that is a good thing or not is another question.

    My main point was rather that I think there is a confound here. The move from syntactic to semantic coincided with a move from FOL to richer mathematics, and to some extent the virtue of the latter was interpreted as a virtue of the former.

  18. Cricky, it does depend what you mean by "correspond". Certainly for any class C of models one can look at Th(C), the set of sentences true in all models in C. What may happen, though (as you also point out), is that Th(C) in turn might have models not in C (unless C is an elementary class). Thus to specify C one needs a language that is more expressive than FOL.

    I do agree that you do not need to switch to the semantic view to enjoy the advantages of a richer mathematics.

  19. The discussion remembers me of the fact that we can completely dispense of language... just if we had nothing to say.

    I appreciate the many interesting things about scientific knowledge that the semantic view of theories has taught us, but I have always suspected that this view was too unust to the syntactic approach. For, after all, formal structures are interesting and useful just because of the things you can SAY about them and about their relation to other structures. You cannot have scientific knowledge without language, so the study of what scientists SAY is essential.

  20. (Whoops...I'm new to this.)

    1) Gabriele (re your initial post): One argument that has been put forward in favour of the semantic view is that it's a better fit with scientific practice than the syntactic view. Perhaps this is supposed to be because scientists spend lots of time constructing things they call models (or at least, many kinds of scientists do). It also seems to have been thought by some that standard presentations of theories look a lot more like presentations of collections of models than presentations of axiomatised sets of sentences (in a formal language, even a first-order one...). Both arguments leave lots of room for trading on the multiple ambiguities in the term 'model', of course.

    Another consideration that seems to have swayed some is the idea that collections of models can be quite disunified, and that that seems truer to the things we call theories in real life (i.e., that they can have lots of relatively unconnected bits, or even conflicting bits). This is clearly closely related to the point Chris P. makes – perhaps it's even the same point.

    2) On some versions of it, at least, the syntactic view says that a theory is an axiomatised set of sentences. (The axioms might then be taken to be the laws of the theory, or perhaps its fundamental laws.) But then another objection to the view – similar to the different languages/same theory objection, of course – is that we don't want to say that different axiomatisations of the same set amount to different theories.

    Perhaps, though, the view you're considering, Gabriele, doesn't include the 'axiomatised'. In any case, one could just drop the 'axiomatised', or say that a theory is an equivalence class of axiomatised sets of sentences.

    3) Chris H. and Aldo: The sorts of issues you're discussing arise if we understand the semantic view to be the view that theories are collections of truth-making structures (objects we're calling models because they're models of some set of sentences, in Tarksi's sense or some closely related sense). Although this was certainly part of the notion of model at play in early presentations of the semantic view, I've argued that there's another picture entirely at work in Suppes's writings, and van Fraassen's (especially as time goes on, in van Fraassen's case), and that that's the picture semantic view theorists ought to go with (because it's better supported by their arguments, and more likely to achieve their aims). This other picture is just that a theory is (/is best thought of as being) a collection of mathematical structures used to represent systems from the domain of inquiry (objects we're calling models because they function as representations). And such a collection need not be a collection of all the truth-making structures for a set of sentences which can be taken to articulate the theory. (The short, published version of this is in v. II of the proceedings of PSA 2004.)

    4) Re theories as sets of propositions: I've argued that some of the things we call models are best thought of as sets of propositions (or better thought of that way than as mathematical structures, in any case). Given that, I've then toyed with the idea of a hybrid view of theories, according to which a theory is a collection of models, but the models are sets of propositions. So on this view, a theory would be a set of sets of propositions. I'm not ready to pin my colours to this suggestion, but it has some interesting pros, like the room it allows for disunification. (The relevant paper is unpublished, but on my website – see the latter half of "Models and the Semantic View, the really long version". Caveat lector– it's really long. A bit like this post.)

    Apologies for the self-advertising in (3) and (4).

  21. There is a theorem in the theory of Boolean algebras according to which for every Boolean algebra A, there is a first order theory T such that the Lindenbaum-Tarski algebra of T is isomorphic to A. So the limitations of the so-called synctatic approach depend on the limitations imposed on the set of the axioms of T (e.g. T must have a finite number of axioms, T must have a recursive set of axioms, T must ave a recursively enumerable set of axioms, and so on). Of course the theorem presupposes no such limitation, and indeed T may have any cardinality whatsoever. The semnatic approach is therefore equivalent to accept any first order theory without constraints on the acceptable set of axioms.