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.
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
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
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
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.