dimanche 23 juillet 2017

Comments on Dewar's paper on Ramsey sentences

Dewar has written a rich and enthusing paper on Ramsey sentences and Newman's problem. This is a topic I've worked on for my Master and PhD dissertation, but the paper is a bit technical, and as I am not very familiar with the formalism used, it took me two or three careful reads to understand what the author was trying to do. Now it seems to me that the author attempts to formalise in model theory some of Melia and Saatsi's arguments on Newman's problem for structural realism. Then he suggests that the whole Ramsey approach is inappropriate to extract the structural content of a theory, and that we should focus on the notion of definition instead.

Let me recall what all this is about, and give a personal exegesis of the paper. Then I will give some comments and criticisms.

A bit of context

First a bit of context. Recall that the structural realist answers the pessimist meta-induction by claiming that our theories are, if not true, at least “structurally true”. But what is structure? One way to express it is Ramsey sentence formalism: structure is what remains from theoretical equations when theoretical predicates are not interpreted, and this is expressed by replacing them with predicate variables over which one quantifies existentially. All we say is that theoretical predicates refer to “something out there” that realises the structure of the theory, but that “something” need not be natural properties. In particular, they can be multiply realisable by natural properties.

Then comes Newman's objection: if you're too liberal on what counts as “something” (for example, if you accept that any arbitrary set of objects is an admissible property, any collection of couples a relation, and so on) then any structure you want is realised in the world somehow, given that there are enough objects. We just have to “pick” the right structure by arbitrary grouping some objects, and any theory is structurally true (if it match our observations at least). So one should better add constraints on what structures are admissible.

Melia and Saatsi wrote a paper where they examine various solutions to this problem. In particular, they examine how qualifying the structure we are talking about (we're talking about “real” relations, not any structure) could help. They consider limiting it to “natural” properties and relations, or to “qualitative” properties and relations (any arbitrary logical combination of natural properties), and they argue that the former is too strict for structural realism because properties deemed natural do not always survive theory change, and that the latter is too liberal, because if the world is sufficiently asymmetric, any extension we want can be picked by a unique qualitative property and so any theory would have its structure realised somehow.

Summary of the paper (1): definitions

Dewar's paper is mostly focused on these arguments, that he addresses in model theory through the angle of definitions, and through the angle of structural equivalence.

Here is a personal summary of my understanding of the paper (I apologise for imprecisions).

The idea is to define a structure (called a frame) that will limit admissible extensions for predicates (the "somethings" theoretical predicates are allowed to refer to). We can imagine that this frame corresponds to a natural structure out there in the world: a domain of objects, and natural groupings of these objects into natural properties and relations. At first, we don't expect any particular constraints on them: they are natural only because nature says so. Now one could say that a theory T is structurally true if one can map its predicates to some "natural" elements of this structure, and if T is true given this mapping.

But that seems too strict: we would intuitively think a theory whose predicate correspond to the negation of a natural property still gets the structure of the world right. So we can liberalise our account by accepting that the predicates of T would not refer to natural properties, but could ideally be defined in terms of natural properties. This is done by extending the frame to all extensions that could be "defined" from natural extensions (in technical terms, the frame is closed under definability, and we get Henkin semantics). The idea is that T gets the structure of the world right, because if we interpret its theoretical vocabulary suitably in terms of natural properties, by means of definitions, then T is true (that would allow for multiple realisation if we accept second-order formula, I guess).

What's interesting with this approach is that it allows you to put more or less liberal constraints on what counts as an admissible “definition from natural properties”. A strict constraint would be that theoretical predicates perfectly match natural properties. More liberal constraints would involve different kinds of definability of theoretical predicates in terms of natural ones (for example through negation). But If admissible definitions are too liberal, then any theory will come out structurally true for a suitably chosen set of definitions, and we run into Newman's problem.

In sum, the notion of definition helps us consider different degrees between quasi-realism (theoretical predicates refer to natural properties only) and quasi-empiricism (theoretical predicates refer to anything so long as the theory is empirically adequate) in the context of Ramsey sentences.

Now the author is not interested in truth, but in theoretical equivalence, so my presentation is not completely faithful, but we can recover the author's idea from it. The idea would be something like: T1 and T2 are structurally equivalent if, whatever the frame is out there, they would come out either both true or both false in this account. Either there is a definition from natural properties that makes them true, or not, but they are always both true or both false “in the same worlds”. However I find it less easy to grasp, and in the following, I will transpose the author's arguments in terms of truth rather than theoretical equivalence, because they work just as well (it's just that the question is different: in one case, are our theories structurally true in some meaningful sense, in the other, what is the structural content of a theory). I will also employ a loose, syntactical language (talking of "natural predicates") instead of a more rigorous semantic account from time to time, for the sake of simplicity.

Summary of the paper (2): collapse problems

In the paper, the author considers a particular class of admissible definitions: if my understanding of its formal account is correct, it requires that definitions be explicit (a predicate should be strictly equivalent to a formula expressed in "natural vocabulary" and observational vocabulary), they should be first order formula, and they should not contain proper names referring to particular objects. As the author explains, this last constraint is sound, because any extension could be defined if we allowed reference to any particular object. He then recovers Melia and Saatsi's result: this constraint is insufficient if the world is asymmetric (loosely speaking, if different objects of the world cannot have exactly the same properties and respective relations), because then, any object can be picked by a qualitative definition: it is identifiable by its place in the structure, so to speak, and in turn, any extension can be defined (the author adds precautionary notes that might, I guess, have to do with complications due to his focus on theoretical equivalence rather than truth).

Finally the author gives another reason why this kind of definition is too liberal: there are theories that are not notationally equivalent (not mere reformulations of one another through explicit definitions), but that would be structurally equivalent with this account, because (my formulation) they are structurally true in exactly the same worlds. He gives an example of this that I will discuss below.

Could we bring more constraints on definitions to avoid the problem? The author gives reasons to be pessimistic: the notion of definition proposed is already quite strict for a structural realist, but even with this strict notion, we already get into troubles. According to the author, the problem is not so much with what definitions we allow, than with the fact that opening the domain of admissible extensions to those which are definable immediately gives us more than what we wanted (in particular, theories that are mutually interpretable, yet not notationally equivalent because interpretations are different in one sense or the other: these theories will be structurally equivalent under this account). In sum, the problem is with the Ramsey sentence approach in the associated semantics: it cannot capture what we would mean by structural equivalence, so it's not the proper tool to extract the structural content of our theories, even if we qualify a domain of properties and relations they are talking about. And the author finishes by suggesting that we should abandon this idea of extracting structural content through semantic frameworks and Ramsey sentences, in favour of a direct account of structural equivalence in terms of definition.

I wasn't convinced by this last part, as I will explain below.

Discussion

Let me now give brief comments on this. First, I think examples from actual science or other literature in philosophy of science could have made some arguments more palatable, although they (mostly) support the author's points.

Take the idea that a theory expressed with the negative of a natural predicate should still count as structurally true (my formulation). That's very plausible by structural realists standards. For example, think of positrons which were initially thought of as “holes” in a sea of electrons. If positrons are natural entities, then this old theory somehow uses a “negative” predicate (the absence of an electron). Yet the structural realist should want this theory to be structurally correct because it was empirically successful and made novel predictions (see Pashby). Now whether this is true for any definition, however contrived, remains to be seen in my opinion.

The notion of definition introduced also reminds me of Nagel's bridge laws to account for inter-theory reduction, and in some sense, structural realists want old theories to “reduce” to new ones. But it is widely recognized that Nagel's account of inter-theory reduction is too strict. Moving to an account such as Kim's, that is, understanding one theory's predicates as functional (higher-order predicates, identifying “causal profiles”) rather than strictly definable by bridge laws would require more liberal definitions, at least, second-order formula and probably implicit definitions instead of explicit ones. And that's certainly a move that the structural realist should make, in particular if they wish to account for special sciences revealing “real patterns” (as Ladyman and Ross). Now structural realists often mention Post's correspondence principle, that a new theory should “degenerate” into the old one under some limit, as Newtonian mechanics is a limiting case of the theory of relativity when the speed of light goes to infinity. But arguably, this correspondence principle cannot be captured by the strict definitions considered in the paper because “degenerate” involves some approximations and limits. This supports the author's point, in that even too strict notions of definition lead us into troubles.

Finally, one could relate the discussion on the world being asymmetric, which allows for a qualitative identification of any real object, to theoretical symmetries in physics, which are often mentioned by structural realists. Theoretical symmetries are not world symmetries: they relate different models, not a single model to itself (so for example, physics is CPT invariant, but that doesn't mean that there is a twin earth of anti-matter going backward in time somewhere in the universe). Yet world symmetries could count as a sub-part of theoretical symmetries (permutation symmetry for bosons in quantum mechanics could count as such a “world symmetry”).

There is a parallel here to make with notational equivalence. Newtonian physics is translation invariant, from which we could infer that “having position x” in a model could be translated into “having position y” in another without loss of cognitive content. The two models are notationally equivalent, or structurally equivalent. But the point I wish to make is that if structuralist authors are generally tempted to eliminate the “surplus structure” associated with symmetries, including world symmetries, they eliminate symmetries from their models and they will ultimately consider that the world's structure, what's really out there, has to be represented by an asymmetric model. Then we are pretty sure to run into the troubles mentioned in the paper: any “real object” must be identifiable qualitatively (and indeed, ontic structural realists put emphasis on the idea that individuals are identified by their position in the structure!), but that makes any theory structurally true with qualitative definitions. Again, these observations strengthen the author's points.

Now intuitively, I would say that the way to go for a structuralist is to bring restrictions on admissible definitions. The author thinks it's not the right way to go, but I am not really convinced. For sure, the notion of definition proposed is already too strict in some respects. But not in others. Newman's problem is that we could find very contrived and ad-hoc mappings to qualitative properties to make any theory structurally true, so perhaps we should consider the virtue of theoretical simplicity: we want our theories to be informative, we want them to describe the structure of the world with few axioms. Then we could introduce different levels of definability, according to how many logical operators they use for example, and associated to each, we'd have different degrees of structural equivalence: the less contrived our definitions must be, the closer two theories are structurally speaking. Then the structuralist can argue that science progresses toward closer structural equivalence to an ideally true theory of the world...

Criticisms

This brings me to criticism of the final part of the article. Dewar provides a trivial example of theories that do not seem structurally equivalent, intuitively speaking, yet are equivalent because one can be interpreted as a qualitative reformulation of the other, and conversely. Translated in natural language, the first theory T1 says that there is at least one property P in the world (a property P such that any object is either P or not, which is trivial). The second T2 says that there are properties Q and R such that any object that is Q is also R.

How are T1 and T2 structurally equivalent? Well, imagine T1 is true. Then we can make T2 true by defining Q and R as equivalent to P. Now imagine T2 is true. Then we can make T1 true by defining P in any way we want in terms of Q and R (since T1 is trivial). This means that T1 and T2 can always be made true in the same worlds: they are structurally equivalent. But they are not notationally equivalent, and according to the author, they shouldn't be considered structurally equivalent.

Here I disagree. The two theories are not notationally equivalent, but their Ramsey sentences are already structurally equivalent if we assume that P, Q and R are natural properties! (in technical terms, using frame semantics, not Henkin semantics). So we don't even need to make any kind of definitions admissible to see them as equivalent. And that makes sense from a structuralist perspective. We want our theories to be true for “important properties and relations” in the world. Now saying that there is at least one important property (T1) and saying that there is one important property that implies the other (T2) is not saying much: indeed, if T1 is true, T2 is, and conversely, and T2 doesn't say anything important beyond T1 unless we interpret its predicates further. The two theories are inequivalent if they are interpreted, but unless we use observational terms (which is not the case here), what else shall we say about their properties that wouldn't count as more structure? That Q and R are different properties perhaps? That could be logically translated, and then the two theories would no more be equivalent. So contrarily to the author, I think the Ramsey sentences formalism is the right tool to understand what we mean by structural equivalence (or resemblance), and notational equivalence is the wrong tool. T2 cannot be seen as a mere reformulation of T1, but it only adds anything to T1 if we assume metaphysical stuff (an “interpretation” of Q and R) that the structuralist shouldn't care about if it cannot be translated into structure.

Here is an example to make my point. Take Galilean and Newtonian physics: both theories are mutually interpretable (make “position x” equivalent to “metric relation x to the centre of gravity of the universe” and Newtonian physics is true in every Galilean world) although Newtonian physics is not notationally equivalent to Galilean physics, because it has more structure (every object has a “true” position in space-time, which cannot be retrieved from Galilean physics). Now remarking that the two theories are mutually interpretable, hence structurally true in exactly the same worlds for some qualitative reformulation, is certainly of interest for the structural realist. It means that by structuralist standards, absolute space-time in Newtonian physics is a metaphysical component that adds nothing to the structure of the theory.

In light of this, I think the author's complaint could be an artefact of his focus on structural equivalence rather than truth. Notational equivalence is an interesting notion concerning the way our theories are presented, but it is not necessarily so interesting when it comes to know which theories are true or not. Notational equivalence goes both ways, from one theory to another and conversely, but truth only goes one way: from the world to our theories. Having a definition of our theoretical terms from natural properties is quite enough to think that our theories get part of the structure of the world right. Now perhaps we won't have the notion of formal equivalence the author seeks, but all these semantics that the author is using were precisely designed for a purpose: having a formal grasp of the notion of truth, not of theoretical equivalence.

mercredi 18 janvier 2017

Modal empiricism as pragmatic realism

So far I explained why modal empiricism is the best position on epistemological grounds:

All this is fine, but epistemology is only one side of the questions over scientific realism. The other side, which is too often neglected in my opinion, is the semantic side, in the broad sense: what exactly is scientific representation about? How does it relate to reality? Shall we interpret the content of scientific theories as descriptions of the world, or as mere tools to make accurate predictions?

Three accounts of meaning

F21. Venous enlargement in hepatic cirrhosis. Alfred Kast Wellcome L0074357
This was the central question in philosophy of science during most of the 20th century. Logical empiricists viewed scientific theories as linguistic statements and attempted to provide an analysis of their meanings.

It is common nowadays, following the semantic view of theories, to think of scientific theories as a collection of models rather than a set of statements, but although models played an important role in the argument of the previous posts, I think the statement view is roughly correct, and roughly equivalent to the semantic view.

The semantic view was a sane reaction to the idealistic conceptions of logical empiricism. Its main import is that it emphasised the role models play in empirical confrontation, as mediators between the theory and experience. But as an attempt to bypass semantic questions, I think it is misguided, because models need to be expressed in a language to have a domain of application, and axioms unify various models in a coherent scheme, so the best way to express the content of a theory is with axioms expressed in a theoretical language.

Now comes the main question of the semantic side of scientific realism: how shall we interpret this theoretical language? There are roughly three options:

structuralism:
theoretical terms are mere placeholders in the conceptual structure of the theory
reductionism:
theoretical terms should be analysed by their intensional or extensional relations to our experience, or their function in experience
essential realism:
theoretical terms directly refer to natural properties and relations, or essences

Note that the question is not about what theories achieve to do, but about what they purports to do: about their meaning, or about what would make them true if they were true. The emphasis on linguistic aspects the logical empiricist entertained is not misguided. After all, meaning is generally analysed in terms of truth conditions: the meaning of a statement is what would make this statement true. There are three traditional theories of truth, which roughly correspond to our three options: coherentism, according to which truth is coherence with a conceptual scheme, pragmatism, according to which truth has to do with the ideal success of a statement, or our capacities to assess this statement, and correspondence, according to which truth is correspondence to reality. In sum, the locus of truth-conditions, and meaning, is either in our representations only, in experience, or in an independent reality. (One could add deflationist theories of truth but I forget them here because they do not really shed light on meaning.)

To many authors, only a correspondence theory can sustain genuine realism: the others would rather lead us to various forms of empiricism, relativism or idealism. Kripke's defence of essential realism has been influential, which is a reason why the focus in philosophy of science moved away from semantic aspects, toward epistemic aspects: given that our theories purports to refer to natural properties, or to correspond to reality, how would we know that they succeed? A correspondence theory of truth introduces a gap between the content of our representations and our capacities to know that they are true, and this is where realists resort to abductive reasoning to fill the gap. The fact that this is problematic is a good reason not to forget about other options, and to keep an eye on philosophy of language. Interestingly, pragmatics became a big subject there, with an emphasis on the role of intentional aspects and context on meaning, and direct reference is not uncontroversial anyway.

This account seems unfair to structuralists, because structural realists would typically accept a correspondence theory of truth, but apply it to the structure directly. In a sense, this is a way to accommodate coherentist aspects (for the vocabulary) with a correspondence truth (for the structure). Now I'm not sure it works: Putnam's model-theoretic argument is a good argument against this kind of view. Structural realism is unstable. It must tell us what the relata of the structure are. If they're elements of experience, this is just empiricism. If they're natural properties, this is just standard realism. If they're identified by the structure only, this is a mathematical platonism, not so far from idealism, and this is vacuous as a realism (because any mathematical structure exists, abstractly: no big deal). So, basically, we fall back on one of our three options.

What about modal empiricism?

F19. Carcinoma scirrhosum diffusum ventriculi. Alfred Kast Wellcome L0074358
So what all this has to do with modal empiricism? Aren't semantic and epistemic questions independent?

Well, a first remark is that I defended that modal empiricism is not realism, because it rests on an inductive, not abductive epistemology. But the contrast between empiricism and realism is not initially a contrast in which inferences are valid or not, but in whether one holds our theories to be true, or merely empirically adequate. Could an induction on possible situations be enough to know that our theories are true after all? Couldn't modal empirical adequacy collapse to truth?

Another remark is that modal empiricism does not entertain a distinction between what is observable or not. Empirical adequacy is expressed in terms of application and predictions, which concern the objectivable aspects of situations. I emphasised how active intervention was necessary to test theories when they posit unobservable entities, such as proteins. On the surface, the arguments are similar to the arguments in favour of entity realism. Again, couldn't modal empiricism be enough to claim that these entities exist? If these entities are identified by their causal role (functionally that is) and if causal relations can be empirically assessed, they certainly exist for the modal empiricist.

Finally, note that essences and intensions are often analysed in modal terms. If interpreting a theory amounts to describe the essential properties it refers to, or to give it an intension, and if, as I have argued, modal statements are not underdetermined by experience, then perhaps the interpretation of a theory is not underdetermined either?

Take Quine's example of renates (creatures with kidneys) and cordates (creatures with a heart). Both have the same extension (all animals with a kidneys have a heart) but a different intension. We could take this intension as a description of their essence. Imagine a theory that says that renates are hairy and another that says that cordates are hairy. For a standard empiricist, both have the same empirical consequences, although they're different theories, but not so for a modal empiricist: we could intervene in the world to differentiate them (through genetic manipulations, say: create a cordate that is not are renate). But then, the interpretation of the theory matters for possible predictions, and we might as well be realists. Ok, but what if we discover that the manipulations are impossible? What if the genes that code for kidneys also code for hearts? Well, we'd have discover that renates and cordates are identical, as a matter of natural necessity. But we can still be realists, and claim to have discover the essence of cordates and renates. Again, the interpretation matters.

All this works so long as our theoretical terms somehow keep in touch with empirical observations. But what linguistic resources do we have, beyond experience and modalities, to interpret our theories? So it seems that modal empiricism is just standard realism.

Pragmatic truth and internal realism

F8. Serosa intestinorum et mesentarium. Cholera. Alfred Kast Wellcome L0074374
What is puzzling is that we defended that modal empiricism is better than realism because it does not fall prey to a pessimistic meta-induction. So what has gone wrong?

The answer, I think, lies in the theory of truth one adopts, and incidentally, on the modalities involved. Correspondence truth introduces a gap between our epistemic abilities and the truth of our theory. But for the empiricist, no correspondence truth is involved. Theoretical terms are always interpreted in how they relate to experience. They matter only insofar as they change the conditions of application and prediction of theoretical models. We are talking about possible conditions here, and modal relations are involved, but no metaphysical necessity or possible worlds: only physical necessity, possible situations in the actual world, i.e. situations that we could implement by intervention.

This is some kind of reductionist account of meaning associated with a pragmatist theory of truth: following pragmatist truth, saying that our theories are modally adequate, or saying that they're true makes no practical difference.

There is an important difference with essential realism, which is that the meaning of theoretical terms will change from theory to theory, contra Kripke. Here, a theoretical term could be ideally analysed in terms of its modal relations to conditions of application and good prediction for the theory, i.e. in terms of its functional role in experimentation. This account seems similar to logical empiricists verificationism, or to operationalism, but the modal aspect and the pragmatic aspect of this construal (in particular, the fact that it does not rest on a distinction between observable and unobservable, and that the notion of application can incorporate pragmatic or contextual aspects) can help overcome the difficulties of these standard positions (such as the reduction of dispositional terms). But the problem of theoretical change remains: observations and interventions are theory-laden, so can't a new theory change the conditions of application of our theoretical terms? Then Kripke's arguments would apply: generally, we are willing to say that we could discover that gold is not yellow (because this is an illusion for example). Gold is not identical with its manifestations: it is what causes these manifestations. Similarly, we would be willing to accept that the way we apply terms like "electron" in experiments is misguided, in light of a new theory. The term "electron" cannot be analytically synonymous with some conditions of application, even extending to possible conditions of application.

I don't think this is a problem if we reject a strict notion of analyticity: indeed, the meaning of theoretical terms will change from theory to theory. However, experimental practices generally survive theory change. We can measure temperature with a thermometer, whether we endorse classical thermodynamics or statistical physics. The reason for this is a continuity in empirical adequacy. So, precisely, modal empiricism has the resources to answer Kripke's arguments: we keep using the same terms because they approximately play the same causal role, and we can be confident that they will continue to do so because our theories are modally adequate. The meaning of "mass" changes from Newtonian gravitation to general relativity, and the rest mass we attribute to the sun changes slightly, but not drastically. If it were to change drastically, i.e. if we discovered that our theories are not modally adequate, well, we would stop using the term "mass" because it would not apply any more. So modal empiricism is not analytic, but still, it guarantee a pragmatic continuity in theoretical term use.

By the way, this is a nice way to associate intensional and essentialist aspects: if experimentation is theory laden, then the intension of theoretical terms will tend to fixate on projectible predicates, i.e. to "group" objectivable aspects in such a way that necessary relations can be attributed to these groups. They mimic essential properties, because the "analytical" necessity associated with their intension (and the structure of the theory) will tend to match physical necessity. Or in a Quinean vein, there is no strict distinction between analytic and synthetic necessity, and meaning itself can be discovered empirically.

The conclusion of this is that modal empiricism, equipped with a pragmatic theory of truth, is just realism: not genuine realism for the aficionados of correspondence truth, but, at least, pragmatic realism (or perhaps internal realism).

Conclusion

F15 Typhus abdominalis, necrosis superficialis Alfred Kast Wellcome L0074365
Of course, one can choose the semantic theory that one wishes in order to make any epistemological position a realist position that says that our theories are true. The logical empiricists did just that with their verificationist theory of meaning. The advantage of modal empiricism is that its commitment to modalities allows for a richer semantic theory that can mimic semantic realism, and thus can probably retain its benefits. The modal empiricist can use theoretical language just as a realist would do. But if pressed on metaphysical or semantic questions, the modal empiricist will not claim that theoretical terms refer to natural properties or that theories correspond to reality: they're only applicable in bounded domains of experience, and they're interpreted relatively to our epistemic position, not in terms of absolute existence. Their meaning is just the functional role they play in experience, and it can be adjusted in front of new theories. That's how the modal empiricist can use a realist language, and at the same time maintain its advantages over realism in front of anti-realist arguments.

jeudi 3 novembre 2016

Why Empiricists should Endorse Modalities (2) Scientific Rationality

In the previous post, I explained why, assuming that there is necessity in the world, relations of necessity are perfectly knowable on the basis of experience, without any recourse to abductive reasonning. That certainly works in favour of an endorsement of natural modalities for the empiricist: at least, epistemic arguments against it are not conclusive. But still, an empiricist could resist this kind of commitment by assuming that there is no necessity in the world from the start. She could interpret modal discourse in a pragmatic way, rather than assume that modal statements have truth values. In this post, I want to explain why she shouldn't.

As I said in the previous post, I don't think that the existence of necessity in the world itself (as opposed to relations of necessity if there is necessity in the world) can be confirmed or disconfirmed by experience. However, no position really comes without some general metaphysical framework, and this includes all empiricist positions: the idea that all knowledge comes from experience is not itself confirmed or disconfirmed by experience. The idea that our theories will continue to be empirically adequate in the future is not confirmed or disconfirmed by experience. The empiricist is only willing to assume the minimum necessary, and to refrain from speculations. One could frame this as some kind of transcendental argument: we need some basic assumptions to make sense of the world, but we shouldn't assume more.

This is exemplified by van Fraassen's defense of constructive empiricism. He does not say that his position is itself confirmed by experience, but he rephrases empiricism as a position about the aim of science, as a collective endeavour: its aim, according to van Fraassen, is to produce empirically adequate theories (not true theories). A scientist can well be a realist, but needs not be to be a good scientist. However, a scientist must at least assume that our theories are empirically adequate, and will continue to be in the future. Now if one thinks that scientific practice is a rational activity, one should also believe that our best theories are empirically adequate. This is a minimum.

I think this is the correct way of thinking about epistemological positions. But I think that it supports modal empiricism rather than constructive empiricism.

mardi 25 octobre 2016

Why empiricists should endorse modalities (1): modal knowledge

Let us take stock. In the posts so far (linked below in order),

  • I presented modal empiricism: the view that our best scientific theories are empirically adequate for all possible situations to which they would apply.
  • I detailed the conception of empirical adequacy on which the position rests. It is not cast in terms of a model of the universe, as usually, but in terms of situations to which different models apply, and, I think this conception is more connected to scientific practice than the usual ones.
  • This conception of empirical adequacy does not commit us to modal empiricism, but I explained how modal empiricism is able to answer the no-miracle argument, while retaining the advantages of empiricism when it comes to theory change.
  • Finally, I explained why, according to me, scientific realism is misguided: it rests on (meta-)abduction for its justification, but abduction, however central it is in scientific practice, is not a principle of justification, but a strategic device to select good hypotheses: hypotheses that we should test first, that is. It doesn't exempt us from further empirical tests if we want to justify these hypotheses. But scientific realism cannot itself be tested empirically.

What makes modal empiricism a version of empiricism, not of scientific realism, is that in contrast with realism, the modalities to which it is committed are arrived at by induction on possible situations, not by abduction. Relations of necessity are no explanations to regularities, but regularities extended to the possible.

samedi 24 septembre 2016

Against abduction

Abduction (or "inference to the best explanation") is the cornerstone of scientific realism. There are always many different theories, or hypothesis that could account for some given phenomena, but scientists make their choice on the basis of non-empirical criteria, such as simplicity: they choose the best explanation. According to a realist, this means one likely to be true. This, in essence, is abductive reasoning: an inference from non-empirical, explanatory virtues to truth, or to likelihood. Furthermore, the realist claims that her position, that our best scientific theories are approximately true, is itself the best explanation to their predictive success. That's what we could call a meta-abduction: a justification of abduction (best explanations are true) by means of abduction (that best explains their success, so it's true). So it's clear that abduction is essential to realism, perhaps its definite characteristic. But is abduction a valid form of inference?

samedi 3 septembre 2016

Is empirical success a miracle?

In the previous post, I detailed my conception of empirical adequacy: a theory is empirically adequate if for every model of the theory, for all situations to which the model would apply, the model would make correct predictions. Depending on the range of situation we consider (situations actually experimented, actual situations we could experiment in principle...) on can derive different versions of empiricism. Modal empiricism is the view that our theories are empirically adequate for all possible situations.

In this post, I would like to explain why modal empiricism can respond to the no-miracle argument for scientific realism, and why it is not threatened by a meta-induction argument. But before that, we must examine the different kinds of induction that are involved in our definition.

lundi 22 août 2016

Empirical Adequacy: a Proposal

In the last post, I criticised van Fraassen's definition of empirical adequacy. According to van Fraassen, a theory is empirically adequate if it has at least one model such that all observable phenomena fit inside (they correspond to the empirical substructures of the model). My criticisms were the following: it rests on a problematic distinction between observable and unobservable, it does not take into account interventions and manipulations, which are central in scientific experimentation, and it refers to an hypothetical model of the universe, which is unnecessary and disconnected from scientific practice.

Can we do better? I think we can if we directly refer to scientific experimentation instead of coming up with an abstract reconstruction of empirical adequacy. Empirical adequacy should simply be framed in terms of the good predictions of models when they apply to various situations. Thus I suggest the following definition:

A theory is empirically adequate exactly if, for all its models, and for all concrete situations in the world, if the model applies to the situation, then its predictions are correct.

Here it is: that's a pretty simple definition. Now, of course, I need to expand a bit what all this means. This is the aim of the present post. But let me begin with an illustration.

Take as a concrete situation the evolution of the solar system during a certain period of time. A Newtonian model of the solar system applies to this situation if it correctly describes the planets and the sun, with their respective initial positions and masses. It makes good predictions if the evolution of the position of planets in the model correspond to the positions that we could observe in this situation. If this is so, then our model of the solar system is empirically adequate for this situation. If all models of the theory that we could apply in the world are empirically adequate for all situations to which they apply in the world, then our theory is empirically adequate.

I will now explain in more details what I mean by situation, application and prediction.