Chap. 5: Situated Possibilities, Induction and Necessity

According to modal empiricism, the aim of science is to produce theories constituted of unified models that would be accurate in all possible situations of their domain of application, which is to say that they are accurate as a matter of necessity. A reason for scepticism could be that this aim is unachievable, because we have no empirical access to mere possibilities and necessities. At most, our theories could register actual regularities. In chapter five of Modal Empiricism, I argue that this worry is unfounded, because knowledge of necessity and knowledge of universal regularities are both justified by the same standard, which is simple induction (this chapter is based on Ruyant 2019).

Knowledge of possibilities is mundane: for example, I know that if I had let a glass vase fall from my window one minute ago, it would have broken. The inductive epistemology presented in this chapter explains that there is nothing mysterious involved in this kind of knowledge, and so, the aim that modal empiricism attributes to science is in principle achievable. This result is made possible by the particular kind of possibilities that modal empiricism endorses.

Situated Possibilities

As I explain in this chapter, when I say that a model would be accurate in all possible situations where it would be relevant, I am not talking about other possible worlds, but about alternative ways actual situations could be. This possibilities are anchored to actual situations. They are therefore limited in range: these *possible situations* must be of the same type, they are bounded in space and time and they must have the same location, origin and background conditions than an actual situation of reference. The fact that they are possible depends on the way natural constraints on phenomena influence what is possible or not for this situation of reference.

Claiming that a model is modally adequate is making a statement of necessity, since it is a claim about a range of possibilities, namely the range of all alternative ways all situations of a given type (such that the model is relevant) could be. However, such a statement of necessity is weaker than the necessity commonly associated with laws of nature in philosophy of science. It is closer to what is sometimes called phenomenological or experimental laws.

One reason for this is that model accuracy depends on empirically accessible properties, and models, in particular idealised models, are tested against coarse-grained properties, so that it can be “blind” to counterfactual variations that are too fine-grained. By analogy, the statement “necessarily, all swans are white” can be blind to variations in whiteness, because white is a vague property.

Another reason why this kind of necessity is weaker is that associated possibilities are anchored to actual situations. By analogy, the claim that all swans are necessarily white would concern only alternative ways actual swans. born in this world, could be, and not merely possible swans that were never born in this world. To take another example, if all falling objects in this universe were located at the surface of the Earth, we could say that all objects in free fall necessarily accelerate at a rate of 9.8 m/s² towards the centre of the Earth. Even if not a fundamental law of nature, this would be true of all possible falls of actual objects, so this would be true by necessity. This kind of necessity can be thought of in terms of relative necessity, in the same way technological possibilities are not unrestricted, but depend on our technological abilities.

I will argue that if one assume that such possibilities exist, then this kind of statement of necessity can be justified by induction. But why think that these possibilities exist in the first place?

There are semantic reasons to think so. Modal discourse is ubiquitous in natural languages and in science, and denying meaningfulness to whole parts of our discourse looks like a dogmatic position. Furthermore, many of the arguments against the descriptivist semantics once entertained by logical positivists rest on modalities, notably the problem of the reduction of dispositional terms to categorical properties, or Kripke (1980)’s modal arguments for semantic externalism. One does not need to buy Kripke’s essentialism, but his arguments against descriptivism show, conclusively in my opinion, that talk about possibilities and necessity is not reducible to talk about meaning, relations between concepts or anything that can be known a priori. Since Kripke, it has became the modal sceptic’s burden to convince us that modal discourse would be meaningless, massively false or reducible to non-modal discourse, and given the centrality of modally loaded concepts in science, such as explanation and causation, this burden is quite heavy.

I have also presented in chapter four pragmatic reasons to endorse modalities: they make better sense of scientific practice, since scientists are apparently willing to test their models against various possibilities, including by creating very unnatural situations.

A final class of reasons for accepting modalities has to do with action-based views of perception, according to which possibilities for action, or affordances, would be part of our perception (see Briscoe and Grush for a review). These views are supported by cognitive research, and a natural interpretation is in terms of perception of possibilities in the world, such as the fact that a ball is catchable. If epistemology is to be informed by science, and in particular empiricism by the science of perception, then it makes sense to accept natural possibilities in our epistemology. Furthermore, the kind of situated possibilities presented here has a good compatibility with these theories, since affordances are anchored to actual objects.

The Inductive Route Towards Necessity

Induction is a mode of inference by which a regularity observed in a sample of objects is “projected” onto other unobserved objects of the same type. For example, having observed white swans, one infers that all swans are white. There are various worries about induction, including about what kinds of features and types should be considered projectible (Goodman 1954). I will return to some of these worries later, but for now, let us assume that induction, although fallible, is generally acceptable: it is rational to infer a generality from a finite set of observations, so long as no incompatible generality is as well warranted. I assume that the predicates used by scientists are projectible, which is ensured by the fact that norms of experimentation are directed towards cross-contextual stability.

As far as I know, the received view is that induction, if valid, can justify universal regularities, but not statements of necessity, because mere possibilities and necessities are not part of our experience. It follows that one has the choice between being a sceptic about modal knowledge or accepting modes of inference that go beyond induction. However, I think that this received view is false. The reason is that just as one can take exemplars in a sample to be representative of a larger set of actual phenomena, one can take these examplars to be representative of a larger set of possible phenomena. For example, the free fall of an object can be representative of all possible free falls of all objects of the same type, including those that did not or will not occur, or the observation of proteins through various manipulations can be taken to be representative of what would happen if we performed the same manipulations on any living tissue. In this respect, universal generalisations and statements of necessity are on a par.

This reasonning is allowed by a focus on situated possibilites. Thinking in terms of possible worlds would be problematic, because we only have access to one exemplar, our world, so induction cannot really get started, but this is not a problem if we think in terms of possible situations (note that my approach is somehow similar to roca-royes_mind-independence_2007).

Modal sceptics argue that we have no “modal telescope” to observe other possible worlds, and that we never experience relations of necessity nor mere possibilities: once these possibilities are realised, they are no more merely possible, but actual. However, we never observe universal regularities either, nor do we observe unobserved phenomena, and once we observe them, they are no more unobserved. So, this extension from the observed to the unobseved, which is a feature of ampliative reasonning, is no more a problem in the case of necessities than in the case of universal generalisations. There might be problems with it, concerning the notion of representativeness involved, the fallibility of this kind of reasonning, possible biases in our sample, etc. but they affect any kind of induction. Assuming that possible situations exist, claiming that actual situations are only representative of actual ones but not of possible ones of the same type would be question-begging.

I provide a technical argument in the book that goes even further: if a universal regularity is justified by induction, then the associated statement of necessity is justified as well. I show that the contrary assumption could only occur if we had reasons to think that a type of situation is never realised in the actual universe, but still possible. For example, we could remain uncertain whether all possible golden spheres of more than one kilometer are stable, but be confident that all actual golden spheres of more than one kilometer are stable, because no such sphere exists. However, the idea that no such sphere exists is itself a universal generalisation, and if it is justified by induction, then it is as much justified as the idea that such spheres are *impossible*. So, if the universal regularity is true for lack of big golden spheres, we can be confident that the statement of necessity is true as well. Or if we could fear that an alien civilisation is creating big gold spheres somewhere in the universe, then none of these statements is justified. In any case, universal generalisations and statements of necessity are on a par.

In general, when scientists are confronted with hypotheses that are incompatible for some possibility, the rational thing to do is to implement this possibility in order to decide between the two hypotheses, if only because for all they know, it could be realised somewhere in the universe. It follows that a universal generality can be justified by induction only if all its plausible modal competitors are eliminated, and in consequence, the associated statement of necessity is as much justified. I explain that this view corresponds to the way “crucial experiments” are often carried out in science.

Laws of Nature

One objection against an inductive epistemology for modalities is that we could not make the difference between lawful statements and accidental generalisations. For example, “no raven moves faster than 30 m/s” is not a law of nature, even if true, but “no object moves faster than 300000 km/s” is a law.

Goodman (1954) remarks that there is a strong connection between this distinction and induction. The fact that all coins in my pocket are silver coins is accidental, and it cannot be confirmed inductively: if I take a silver coin out of my pocket, this tells me nothing about the other coins in my pocket.

Some philosophers have argued that law-like generalisations must be arrived at by a stronger inference than induction: inference to the best explanation. The fact that all coins in my pocket are silver coins, even if true, could not be explained by a law, which is why silverness is not projectible. In contrast, the fact that all copper pieces conduct electricity could be explained, and if I observe one conducting copper pieces, I can infer that other pieces will conduct electricity too. Their conclusion is that induction rests on inference to the best explanation: first, we posit potential laws on the basis of our observations, and then we can *deduce* universal generalisations from these laws (Dretske 1977).

I believe that this is a mistake. If all coins in my pocket were silver coins during my whole life, and if no experience could defeat this fact, then this would call for an explanation. If a coin falls on heads everytime, we might suspect that it is loaded. However, we know, by induction, that coins in pockets are generally mixed and that they fall on average as many times on heads as on tails. So, I would say that “all coins in my pocket are silver coins” is actually a law candidate, but only a very bad one. The incompatible universal statement “coins in pockets are generally mixed” has much more occurrences to make its case (and if we insisted that they are as well justified, a simple experiment could tell them apart). This is the reason why silverness is not projected in the former case, and this has nothing to do with inference to the best explanation. In sum, I believe that induction is always applicable, and the fact that some regularities are accidental is itself discovered by induction.

Having said that, it should be noted that induction can justify much more than laws of nature, if ever such things exist. It can justify “no raven moves faster than 30 m/s”, for instance. But as noted earlier, the statements of necessity associated with situated possibilities are weaker than nomological necessity, so this is not surprising. As observed by Lange (2000, ch. 4), many inductive inferences concern contingent states of affairs rather than laws of nature (for example, the fact that native americans are blood type O or A), and they still support counterfactual reasoning. Furthermore, it is not clear that the fundamental laws of scientific theories are directly justified by induction: as observed by Cartwright (1983) and Giere (1999), they are rarely applied directly to the world. For instance, the fact that no object moves faster than 300000 km/s in a particular reference frame, say, the Earth, is not a law, but the consequence of a law applied in a particular context, the Earth. I think that it makes more sense to view the fundamental laws of theories as organising principles for the models of a theory than as statements of necessity.

Do We Need More?

I have argued that statements of necessity can be justified by induction. This means that whether a particular model is modally adequate can be justified by induction on experience. This removes one of the main reasons for scepticism about modalities. However, the adequacy of particular models is not enough to justify the adequacy of whole theories and their fundamental laws. This could be a reason to be a realist, in particular observing that theories are often successfully extended to new domains of experience. I address this topic in chapter 6 of Modal Empiricism. I will present this chapter in the next article.