Maxwell’s continuity argument

In his famous paper ‘The Ontological Status of Theoretical Entities’, Grover Maxwell (1962) attacked the received view’s distinction between a theoreti-cal and an observational language. He formulated his arguments specifitheoreti-cally against the semantic antirealism of logical positivism. But they can also be di-rected toward the epistemically antirealist distinction between observable and unobservable entities.

An important clarification is in order here. The positivist semantic distinc-tion between the observadistinc-tional and the theoretical languages is a sharp one.

Observational terms acquire their meanings by ostension, and observational sentences have definite truth-values. Theoretical terms are non-referential;

they are either to be eliminated by reduction to observational ones, or to re-ceive a meaning in virtue of their systematic role within a theory. Theoretical sentences have no truth-values. In any event, there is no ambiguity about whether a term or a sentence has a meaning or not. A term either refers or it does not; a statement has a truth value or it has not. By contrast, the epis-temic distinction between the observable and the unobservable is, as Maxwell argues, a vague one.

In light of these considerations, the classical ‘theory/observation’ distinc-tion appears to be equivocal: it is not apparent whether it is to be taken in a semantic or in an epistemic sense. However, the equivocation is not dan-gerous; it has been committed by instrumentalists, who typically take the two distinctions as being the same. The reason is that the basis of the semantic observational/theoretical distinction is the epistemic notion of observability.

That is, the referentiality relation of observational terms is grounded in their direct ascertainableness through sense experience. This motivates the ‘classi-cal’ instrumentalist to equate the observable with the non-theoretical and the theoretical with the unobservable. However, more sophisticated versions of instrumentalism will not put into question the reference of theoretical terms or the truth-values of theoretical statements. Their quarrel with realism is exclusively epistemic, about what one is warranted to believe. Faithful to the empiricist credo, van Fraassen relies on the observable as the secure epistemic basis of knowledge, while rejecting, as shall immediately be shown, a semantic

distinction between the theoretical and the non-theoretical.

This being said, we can return to Maxwell’s argument. It begins by showing that the observable/unobservable distinction is a matter of degree, so that no precise borderline can be drawn. The following extensive quote presents a celebrated gradual series of objects, beginning with theoretical unobservables and ending with easily perceptible entities:

Contemporary valence theory tells us that there is a virtually contin-uous transition from very small molecules (such as those of hydrogen) through “medium-sized” ones (such as those of fatty acids, polypeptides, proteins, and viruses) to extremely large ones (such as crystals of the salts, diamonds, and lumps of polymeric plastic). The molecules in the last mentioned group are macro, “directly observable” physical objects but are, nevertheless, genuine, single molecules; on the other hand, those in the first-mentioned group have the same perplexing properties as sub-atomic particles (de Broglie waves, Heisenberg indeterminacy, etc.). Are we to say that a large protein molecule (e.g., a virus) which can be “seen”

only with an electron microscope is a little less real or exists to somewhat less extent than does a molecule of a polymer which can be seen with an optical microscope? Although there certainly is a continuous transition from observability to unobservability, any talk of such continuity from full-blown to non-existence is, clearly, nonsense. (Maxwell 1962: 9)

There could hardly be a more informed and concise way of giving voice to the common-sense intuition that observability is a matter of degree, while existence and nonexistence are separated by a sharp ontological dichotomy. It indicates how the ontological status of an entity cannot be determined by its observational status. This is consonant with Devitt’s (1984: 4) Third Maxim, urging us to settle the ontological issue of realism before any epistemic or semantic issue.

Van Fraassen precedes his answer to the continuity argument by a few pre-liminaries. He notes, in the spirit of our considerations about the semantic and epistemic aspects of the theory/observation distinction, that the very ti-tle of Maxwell’s paper contains the problematic notion of ‘theoretical entity’.

Entities, van Fraassen contends, are observable or unobservable, whereas only terms or concepts can be theoretical. Consequently, he separates the discus-sion into two parts: on the one hand, he argues that the question should be,

“can we divide our language into a theoretical and a non-theoretical part?

On the other hand, can we classify objects and events onto observable and unobservable ones?” (van Fraassen 1980: 14).

As to the first issue, van Fraassen agrees with Maxwell against the received view that there is no way to split scientific language into a theoretical part and a

non-theoretical one. He explicitly endorses the omnipresent theory-dependency of language:

All language is thoroughly theory-infected. If we could cleanse our lan-guage of theory-laden terms, beginning with the recently introduced ones like ‘VHF receiver’, continuing through ‘mass’ and ‘impulse’ to ‘element’

and so on into the prehistory of language formation, we would end up with nothing useful. The way we talk, and scientists talk, is guided by the pictures provided by previously accepted theories. ...Hygienic recon-structions of language such as the positivists envisaged are simply not on.

(van Fraassen 1980: 14)

However, we’ll see that van Fraassen’s admission of the theory-ladenness of scientific language on the one hand, and his strict view of observability on the other hand, generate a tension which will prove to be fatal to constructive empiricism.

In fact, constructive empiricism is not affected by the way Maxwell has drawn the conclusion of his argument (that the ontological status of an entity is not determined by its epistemic status). The reason is that van Fraassen does at no place claim that only observablesexist. Once again, his distinction is epistemic, not ontological or semantic. He phrases it concisely:

...even if observability has nothing to do with science (is, indeed, too anthropocentric for that), it may still have much to do with the proper epistemic attitude to science. (van Fraassen 1980: 19)

Constructive empiricism merely claims that only reports about observable en-tities arebelievable. This conflicts in no respect with Maxwell’s gradual series, since believability is also a matter of degree. In other words, constructive em-piricists think that all other things being equal, the closer a claim is to the observable – i.e., detectable by unaided senses – end of the gradual series, the more believable it is. I take this answer to be perfectly acceptable. But others believe it is problematic.

As Kukla (1998: 131) points out, some supporters of the Bayesian theory of confirmation consider that the above answer would “dramatically reduce the difference between constructive empiricism and realism.” Kukla cites Foss (1984), according to which

If the constructive empiricist embraces the “Bayesian” solution..., then when he accepts a theory he will have various degrees of belief that each of the various theses of the theory is true. This position does not amount to being “agnostic about the existence of the unobservable aspects of the world described by science.” ... For the Bayesian sort of constructive empiricism does not suspend belief, but has quite a definite degrees of belief about each scientific thesis. (Foss 1984: 85–6)

In greater detail, the problem for the Bayesian constructive empiricism is as follows: if it is accepted that believability comes in degrees, then belief in reports about unobservables will decrease to a very low level. No theoret-ical entity can completely be deprived of a certain degree of observability, and accordingly, of a certain degree of credence. But if we admit that state-ments about unobservables have nonzero probabilities – no matter how low – then the conclusion is inescapable that there are circumstances under which these statements will become certainties. Hence, Foss concludes, “a degree-of-observability-Bayesian constructive empiricist would satisfy van Fraassen’s own definition of a scientific realist.” (Foss 1984: 86).

Of course, Foss is aware that van Fraassen does not ascribe degrees of probability to statements about unobservables. In fact, van Fraassen tells us that observability is a vague concept. As any other vague predicate of natural language, observability does not raise problems of use, but only logical difficulties.

A vague predicate is usable provided it has clear cases and clear counter-cases. Seeing with the unaided eye is a clear case of observation. (van Fraassen 1980: 16)

The idea is that observability can be disposed of as a dichotomous concept, yet with vague boundaries. So, as Kukla indicates, a Bayesian constructive empiricism can be saved by reformulating Maxwell’s continuum of degrees of observability as a progressive approach to a vague boundary:

Instead of molecules becoming increasingly less observable as they get smaller, it becomes increasingly uncertain whether they are observable.

(Kukla 1998: 131)

Foss would presumably refuse to admit that this move makes the Bayesian solution more acceptable. The closer to the vague boundary an entity is sup-posed to be, the less likely it is that the entityis observable. The predicament appears to be the same: constructive empiricism ascribes smaller and smaller degrees of beliefs to a series of claims that get closer and closer to the vague boundary between the observable and the unobservable. Formerly the de-creasing degrees of credence were assigned on the basis of dede-creasing degrees of observability. They are now assigned on the basis of decreasing probabilities that the event is observable.

Nonetheless, I agree with Kukla that there is an important difference be-tween the two cases:

If what makes the probability fall off is the entity’s degree of observ-ability, then it’s reasonable to suppose that, as Foss does implicitly, the

decreasing function from entities to probabilities never quite hits zero probability: you can always take a little bit more observability and lose a little bit more credence. But suppose instead that what makes the probability fall of is the entity’s being more and more deeply immersed in the vague boundary between observability and unobservability. Then it’s still reasonable to say that the probability gets smaller and smaller as it becomes increasingly uncertain whether the entity is observable –but only until you get to entities on the other side of the boundary. Once you get safely to the other side of a vague conceptual boundary, everything becomes clear again – the denizens of the other side are unambiguously not a part of the concept. (Kukla 1998: 132)

All that matters, as van Fraassen urges, is that observability possesses clear cases and counter-cases. We know of the probabilities in the latter case that they fall on a zero platform nearby the vague border. In the former case, the probabilities decreased continuously without reaching ground zero. This shows van Fraassen’s reformulation to be successful: the Bayesian solution can be an answer to the continuity argument while at the same time not inflating constructive empiricism into realism. Van Fraassen’s dichotomy guarantees that there is a class of theoretical claims which the constructive empiricist ought not to believe, while there is no such class for the scientific realist.

Certainly, the vague character of observability causes troubles for the ap-plication of the notion of empirical adequacy. If, following the constructive empiricist, to accept a theory is to believe what it says about the observable, what does acceptance of a theory mean as to those entities whose observabil-ity is so vague as to be in doubt? But this is a problem whose solution is not sought here.