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.

Situations

Uranus
By concrete situation, I mean a potential object of experience. It can be, for example, an experimental situation in a laboratory involving tiny particles, or the solar system.

What characterises a situation is it is concrete, occurent and bounded in space and time (we don't make experiments of infinite duration). By concrete and occurent, I mean that we do not refer to situations abstractly: we refer to them directly or indirectly from our own epistemic position, for example by ostentation ("these planets", "this experimental set-up"). Situations are not linguistic or representational entities: they are in the world. We experience them from our particular perspective, and we can describe them using our preferred language, but our experience or our descriptions of them, do not necessarily exhaust what there is to know about them.

However, as I said, we can describe concrete situations using a language (and in particular the theoretical vocabulary of our theories: we can say "this is an electron in an electromagnetic field"). This implies that situations have objective (or at least intersubjective) characteristics that we can bring out through observation and manipulation. These are the characteristics that allow us to know when a theoretical model applies and when it makes good predictions.

These objective characteristics concern, in particular, the type of system, the way it interacts with its environment, the way it is measured, its initial conditions and the measurement results. Any physical property that can be detected with measuring apparatus can count as an objective characteristic of a situation, even if it's not directly observable: the important point is that scientists would agree that the theory assigns this property to this situation (even if they believe the theory is false). We can view a theoretical vocabulary ("electron", "momentum", "acid", "pulsar") as a classification of situations into types, on the basis of some of their objective characteristics. The classification depends on our theories, and it might not "cut nature at its joints" (or only approximately), but it is still objective. Thus, we bypass all the difficulties mentioned in the last post about the notion of observability (except for its modal aspect, but we will return to this later).

We don't have to say much more about situations. My aim here is not to propose an ontology: situations need not be fundamental entities; they might be regions of space-time, or collections of events, or what have you. I want to stay as much neutral as possible on metaphysical issues, and just assume the minimum required to account for empirical confrontation.

Also note that there is some level of arbitrariness in what situations we consider: for example, we can consider a single planet of the solar system in a gravitational field, or the same planet and the sun, and other planets too. We can consider its evolution during one year, or during a thousand years. All these are distinct situations to which different models will apply. This shows that situations are organised mereologically: some situations contain others, either compositionally or temporally. But we do not need to say more, beyond this fact, and the fact that they have objective characteristics.

There are similarities between what I call a situation and the concept of situation invoked by some authors in the philosophy of language (Barwise and Perry, Kratzer, ... see this SEP entry). It was introduced to solve some difficulties with possible worlds semantic, in particular with intentional locutions ("John sees that Albert is eating" doesn't seem equivalent to "John sees that Albert is eating and that either Bill is sleeping or he's not", but that's what a possible world semantic would entail). These authors put emphasis on the indexical aspects of most propositions in natural languages. When one says "everyone is sleeping", one does not mean "everyone in the universe" but, for example, "everyone in this house except us". Universal, eternal propositions that do not depend on the context of utterance are not the rule, but the exception in natural languages, so according to them, the meaning of utterances is best analysed in terms of situations. In the same way, I would put emphasis on the indexical aspects of theoretical models. When it comes to empirical confrontation, particular models whose domain of application is determined in context are the rule, and putative "models of the universe" are even less than exceptions: there is no such thing outside of abstract philosophical discussions. Talk of situations reflects this fact.

Application and prediction

Jupiter 130115
I hope that what I mean by situation is clearer now. Let us turn to model application and predictions.

A model applies to a situation if it is the right kind of system in the right initial conditions and measured the right way, as specified in the model. It makes good predictions if the measurement results we would obtain would correspond to the predictions of the model (or if the results are statistically significant in the case of probabilistic predictions). All these aspects derive from the objective characteristics of situations I mentioned above.

Knowing that a model applies and makes good predictions requires some practical skills: only competent scientists can do that. This fact could seem problematic, but I think this is merely a way to show respect to the complexities and contextuality of scientific experimentation. I do not think that applicability and predictions can be formulated in the form of systematic correspondence rules between theory and experience, as logical empiricists thought, so the best we can do is to refer to the transcription of experience into a theoretical language that experimenters carry out. Yet we can be confident that this transcription is robust, and object of consensus among scientists, even when they believe in different hypotheses or theories (see the SEP entry on scientific observation for more on this, or, if you read French, this entry).

One consequence is that we have to resort to modalities to address situations that are not actually experienced (the fall of a stone on a distant planet) and still maintain that our theories are empirically adequate for these situations as well. We must say something like: "competent scientists would recognise that such model applies, and that it makes good predictions". As discussed in the last post, this problem is shared by van Fraassen's definition in terms of observable, and I think resorting to modalities is unavoidable for an empiricist who is sceptical about purely a priori, or linguistic conceptions of observation. Now obviously, this is only a problem for someone who thinks that modal statements have no truth values.

Having said that, we can note certain epistemic constraints on applicability and predictability for our definition of empirical adequacy to work properly. It's not necessary that only one model applies to a particular situation: some aspects in our models are conventional (the choice of a reference frame), and models are more or less idealised. However, we should at least assume two constraints:

Non-circularity of application
we should not decide whether or not a model applies to a concrete situation on the basis of its predictive success (otherwise no theory could ever fail to be empirically adequate).
Non-ambiguity of predictions
the conditions of application of models to situations should allow us to select, for each theory, a class of models that all make approximately the same predictions (otherwise no theory would be empirically adequate, because they'd make contradictory predictions for the same situations).

In sum, the conditions of application of models must not be too liberal, so as to avoid systematic failure of theories for some models, but not too restrictive, so as to allow that any model can still fail in its prediction. This is ensured if applicability concerns the type of system and its initial conditions, at the beginning of an experiment, while predictions concern measurement results we would obtain later on.

Let us take the example of a situation that involves observing our solar system. We first need to observe the trajectory of planets to determine the mass of the sun. Now if we accepted that models with the wrong value for the mass of the sun were applicable to the solar system, the predictions of the theory would be ambiguous. When we observe the trajectories to determine the mass of the sun, we must consider that we are not really testing the empirical adequacy of the theory: we are merely determining which models apply. That's not enough to claim that the selected models make good predictions: once the mass of the sun is determined, we must observe the trajectories of planets a bit longer to make sure that the predictions of the models are correct.

Revising the conditions of applicability of models in front of an experimental failure can happen (such as when we posited the existence of Neptune to account for the failure of our models of the solar system to describe Uranus's orbit), but then, as Lakatos observes, this revision should yield new predictions (we later observed Neptune). The hypothesis of Neptune should not count as a prediction of the theory, rather as a determination of which model of the theory applies to our solar system, and one of the corresponding prediction is that this planet can be observed by other means.

These points only reflect good practices of scientific experimentation: we expect that theories make novel, unambiguous predictions, and that they could eventually fail in their predictions. These are conditions for our theories to be empirically adequate. Yet these aspects were not present in van Frassen's definition of empirical adequacy.

Different versions of empiricism

Full Disk of Saturn
All this in order, we can say that a model is empirically adequate if it makes good predictions whenever it applies to a concrete situation, and that a theory is empirically adequate if all its models are (either they never apply, or they make good predictions when they do). Meanwhile, we haven't mentioned any notion of observable, but we still focus on empirical confrontation only. We take into account experimental interventions, not only observations, since the notion of applicability does not necessarily rest on pure observation. Finally, and more importantly, we do not need a model of the universe. That does not mean that our notion of empirical adequacy is restricted to what is actually experienced: as for van Fraassen's, it can concern anything that could be experienced in the universe. But we do not need a cosmic application for our theories to believe that they are empirically adequate everywhere and at any time. Thus we stay closer to scientific practice.

As an end note, I would like to highlight one interesting feature of this definition: that it allows us to conceive of different versions of empiricism in a quite straightforward way. I take empiricism to be the view that we are only in a position to know that our best theories are empirically adequate, and nothing more. The definition of empirical adequacy I proposed quantifies over concrete situations, and indeed, one can imagine different domains of quantification for situations:

Sceptical empiricism
Our theories are empirically adequate for all situations experimented so far
Manifest empiricism
Our theories are empirically adequate for all situations that we did, or will experiment
Factual empiricism
Our theories are empirically adequate for all actual situations in the universe, i.e. for all situations that we could experience in principle, even if we don't
Modal empiricism
Our theories are empirically adequate for all possible situations
Giere proposes a similar taxonomy (in "Images of science", edited by Churchland, 1984) with slightly different labels. These versions of empiricism differ in the level of induction that they are willing to accept as rationally justified, or as required for making sense of scientific practice.

The position that I defend is the last one: I think that we are justified in thinking that our theories are empirically adequate for all situations that could arise in the world.

I am talking about physical possibilities here (not about epistemic possibilities, since obviously, it is conceivable that our theories fail to be empirically adequate), so a commitment to physical necessity is required to be a modal empiricist. Empiricists are generally suspicious about physical necessity, and I'll have to justify in future posts why this commitment does not conflict with an empiricist stance. I think that empirical adequacy is actually better cast in modal terms, and that it is the best way to account for scientific practice (we already have the beginning of an argument here: modalities are required to extend empirical adequacy to non experienced situations).

I will also have to say more about what possible situations are. The concept of a possible situation seems prima facie at odds with the idea that situations are concrete entities in the world, not abstract entities, but we can think of possible situations as alternative proceedings of actual situations, or as proper parts of these alternative proceedings. We can also think of them as conceptual tools to talk about physical necessity (just as possible worlds semantic does not commit us to the concrete existence of other possible worlds).

Meanwhile, I can give an intuitive idea of what modal empiricism amounts to. Imagine you throw a ball, and observe its trajectory. Factual empiricism claims that our best theories will predict with great accuracy this trajectory. Modal empiricism claims that too, but it also claims that our best theories would have predicted the ball's trajectory, had we thrown it a bit earlier, or a bit later than we actually did. We are not saying that our theories are true descriptions of the world beyond the objective features of our experience, so this is still an empiricist position, but we do not restrict ourselves to actual experiences, or to possible experiences of actual situations: our theories are empirically adequate for all possible experiences of all possible situations.

I think this position is quite intuitive, and that it has lots of virtues when in comes to responding to the different arguments on scientific realism (including the infamous no-miracle argument). That will be the main topic of the posts to follow.

4 commentaires:

  1. Having practiced yoga and meditation for 20+ years I tend to lean skeptical on this issue, but given your definition of empirical adequacy I can accept your Modal Empiricism. Although in your definition of empirical adequacy, I would probably relax “its predictions are correct” to “there is broad consensus that its predictions are approximately correct.” I especially like the manner in which you integrate situation semantics into your definition; I think this is a key element whose relevance is made explicit in Special and General Relativity. It was John L. Austin who introduced situation semantics in his 1950 paper, “Truth:”

    http://www.aristoteliansociety.org.uk/pdf/austin.pdf

    This is really what I find so interesting about Kevin Knuth’s “Observor-Centric Foundations” (hopefully you read Knuth’s paper):

    https://arxiv.org/abs/1310.1667

    Although Knuth is a physicist, he started out working at NASA’s Ames Research Center exploring how to develop an autonomous robot that could navigate unfamiliar terrain, i.e. the surface of Mars, by searching a space of questions. So Knuth’s “Observor-Centric” approach really emerged from his study of how agents, with finite resources and limited knowledge, should properly go about making sound inferences, which is at the heart of science. What I find so compelling is that his method is so general, he’s used it successfully in virtually every sub-field of physics, information theory, decision theory, etc., and that it leads invariably to a contextually meaningful calculus. A context is a situation and meaningful is semantics – situation semantics!

    One minor point, perhaps irrelevant, in your critique of structural realism there is the line, “At least if ‘relaation’ is understood in a logico-mathematical sense: in logic, a relation is defined by the objects it relates (its extension), and nothing more.” This is true as far as general definitions go, for instance, in mathematics a relation R is generally defined as a subset of A X B or A X A, where A and B are sets, but relations, from the perspective of situation semantics, are informed by their symmetries: commutativity; associativity; transitivity; reflexivity; anti-symmetry; etc. Is this distinction meaningful or relevant? You define a theory as a set of models; David Bohm defines a model as a system of concepts; to me, a system of concepts is a set of related entities!?! And in your introduction you express your position with, “our best scientific theories are correct descriptions of the relations of necessity between our observations and interventions.” Perhaps I’m just playing the devil’s advocate here, but I can’t help but wonder if there isn’t a better way to capture the essence of a theory? I don’t have an answer, of course, but I do have a suggestion.

    If you think about what scientists do, in general, it seems to me that they distill information from situations via observation and experiment; they then organize that information, they put it in order, as Knuth demonstrates over and over, where order is a relation; they then utilize that organized information as a basis to form plausible but speculative hypotheses; they then test those hypotheses with further observation and experiment, and on and on it goes. Now the essential element which informs this whole process is, naturally, information! And what is information? This is a question posed by David Deutsch; he pointed out that the same information can be stored on a variety of media and then asked, “What is the general form of information?” I believe Ben Goertzel gives the correct answer. Goertzel, following, to a degree, Gregory Bateson, proposes that pattern is the general form of information; pattern informs – literally, forms from within.

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    1. Thank you for your insightful comments.

      I had heard about information-theoretic approaches to quantum mechanics, they are interesting approach indeed.

      Regarding the formal properties of relations: yes of course, and this is precisely in terms of these characteristics (transitivity, reflexivity) that Russell expressed his structural realism. His view is that we have knowledge of this "second-order" structure, i.e. the formal characteristics of relations, since we have no direct access to the objects related.

      Models have a quite precise definition in Tarski's work, as set-theoretic entities: bare objects and n-ary relations (defines extensionnaly), and a mapping between these elements and a vocabulary (proper names and predicates).

      What bothers me with the concept of information is that sometimes, the intentional aspect associated with it (information *for* someone, *about* something) seems completely eluded. I'm not sure how to make sense of it.

      Now the idea of patterns is used indeed by structural realists (e.g. Ladyman's "everything must go", where he takes inspiration from Dennett). It has affinities with the concept of multiple realisability employed in discussions on reduction and emergence. This is precisely the kind of observation Connes makes, about our cells being replaced but the "pattern" remaining. Many authors defended that higher-level properties, such as biological properties, should be identified functionnally, not by their constitution, because of multiple realisability. Now I wonder what happens if we extend this view down to the fundamental level: obviously, we get something like an ontic structural realism, in line with Ladyman etc. But again, I can't help thinking that something is missing in this picture (qualitative aspects perhaps?) and that it borders mathematic platonism dangerously...
      This is why I refer to observation and interventions: not that the view couldn't be refined by metaphysical speculations, but I think we should always keep the link with experience.

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  2. If you’re not familiar with Goertzel, he trained as a Dynamical Chaos theorist but his objective from the outset was AGI research; his cross-disciplinary knowledge is quite impressive – and I believe he’s conversant in French! Anyway, he developed a philosophy of mind in conjunction with a complex systems model exemplifying his philosophy and, in order to speak intelligiently about his philosophy, he developed a philosophical framework which he calls Pattern Theoretics. In Pattern Theoretics pattern is the fundamental entity.

    Goertzel defines a pattern in an entity Z as an entity X, generally a subset of Z, and a process Y, such that the structural complexity of X, where structural complexity is a measure of all the pattern in an entity, plus the structural complexity of Y, plus the structural complexity of applying Y to X, is less than the structural complexity of Z, and Y applied to X yields a reasonable approximation of Z. A good example: let Z = N, the set of all naturals, let X = 0, and let Y be “apply the successor function to X recursively,” i.e. . . . S(S( . . . (S(S(0))) . . . )) . . . . Another good example: Einstein’s field equation for the curvature of space-time!

    Consider the following from George Ellis:

    https://arxiv.org/ftp/arxiv/papers/1212/1212.2275.pdf

    “Causation: The nature of causation is highly contested territory, and I will take a pragmatic view:

    Definition 1: Causal Effect If making a change in a quantity X results in a reliable demonstrable change in a quantity Y in a given context, then X has a causal effect on Y.

    Example: I press the key labelled “A” on my computer keyboard; the letter “A” appears on my computer screen.

    Existence: Given this understanding of causation, it implies a view on ontology (existence) as follows: I assume that physical matter (comprised of electrons, protons, etc.) exists. Then the following criterion for existence makes sense:

    Definition 2: Existence - If Y is a physical entity made up of ordinary matter, and X is some kind of entity that has a demonstrable causal effect on Y as per Definition 1, then we must acknowledge that X also exists (even if it is not made up of such matter).

    A: Causal Efficacy of Non Physical entities: Both the program and the data are non-physical entities, indeed so is all software. A program is not a physical thing you can point to, but by Definition 2 it certainly exists. You can point to a CD or flashdrive where it is stored, but that is not the thing in itself: it is a medium in which it is stored. The program itself is an abstract entity, shaped by abstract logic. Is the software “nothing but” its realisation through a specific set of stored electronic states in the computer memory banks? No it is not because it is the precise pattern in those states that matters: a higher level relation that is not apparent at the scale of the electrons themselves. It’s a relational thing (and if you get the relations between the symbols wrong, so you have a syntax error, it will all come to a grinding halt). Furthermore it is not the same as any specific realisation of that pattern. A story can told (and so represented in sound mediated by air vibrations), printed in a book, displayed on a computer screen, attended to in ones mind, stored in one’s memories; it is not the same as any of these particular representations, it in itself is an abstract thing that can be realised in any of these ways; and it is the same with computer programs: they are abstract entities that can be physically realised in many different ways, bit no particular one of them is the same as the story itself. They are its varied representations. This abstract nature of software is realised in the concept of virtual machines, which occur at every level in the computer hierarchy except the bottom one [17]. But this tower of virtual machines causes physical effects in the real world, for example when a computer controls a robot in an assembly line to create physical artefacts.”

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  3. With that fresh in mind, consider the following from Alain Connes, Connes being considered, as you probably know, a foremost authority on Quantum Field Theory. The following is from, “The Riemann Hypothesis,” by Karl Sabbagh:

    “It is quite amazing to realize that our simpleminded materialistic conception of external reality is really built on quicksand, and that after a while the only real thing you can cling to is much more abstract. Just let me give you a concrete example of that. If you take one individual, most of his cells are actually replaced totally over a period of several years, so what is he? Is he a collection of cells? Certainly not, because precisely these cells are replaced. But what he is is something quite different – it’s a scheme. The only thing that is pertinent is the scheme, the organization. Quantum mechanics is extremely striking in that respect, because it makes it clear that even if you try to cling to external matter as being reality, you will find that as soon as you go to the sufficiently small, then precisely because of quantum mechanics you will come across inconsistencies, so you can’t rely on that as being the ultimate reality.”

    Of course Connes is a mathematical realist; he believes that the physical world exists within an “archaic mathematical reality” and that we simply acquire knowledge of that archaic reality by projecting our intellect onto it. Buddhists would agree with Connes with regards to mental constructs, such as mathematics and dreams, being as real as the physical world, but unlike Connes, who explicitly reifies mathematics, Buddhists go the opposite way and say that the physical is just as insubstantial as the mental; nothing exists unto itself, it’s simply emergent pattern. Goertzel’s definition of emergence, within his Pattern Theoretic framework, is rather enlightening in this regard. I, of course, am a Buddhist, following the Madhyamaka tradition.

    I certainly believe in an objective reality but we, as embodied minds, are separated from that reality by our sensory-perceptual mechanism. Situation semantics corresponds to sensory percepts, not necessarily to objective reality. Our theories make predictions by extending patterns perceived in logical ways. As neuroscience and cognitive science seem to indicate, logic, in this sense, is defined by the environment our senses perceive, so this should not, really, be surprising. I think many people find it surprising because they reify their self, their ego, and establish in that reification an definite boundary between self and other where no such boundary exists; they think of themselves and their logic as being somehow separate from the environment. But the world our senses perceive is comprehensible simply because we define comprehensibility relative to the world our senses perceive! Object reality and inter-subjective reality are separated by layers and layers of the comprehensible and these layers of the comprehensible represent some kind of superposition of objective reality and subjective (inter-subjective) perception. How exactly this works I find somewhat mysterious but I’m convinced pattern plays a fundamental role. Perhaps you could utilize Goertzel’s Pattern Theoretics to more fruitfully express what the essence of theory is.

    If you’re interested in Pattern Theoretics I would recommend Goertzel’s books: The Structure of Intelligence; The Evolving Mind; Chaotic Logic; From Complexity to Creativity; The Hidden Pattern.

    The first four can be found here:

    http://wp.goertzel.org/books/;

    The Hidden Pattern here:

    http://www.goertzel.org/HiddenPattern_march_4_06.pdf.

    You can probably get the gist of things simply by reading Chaotic Logic and The Hidden Pattern.

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