The Justifiability of Belief in Theories

As said, Agazzi correctly characterizes the problem of scientific realism as that concerning the reality of the unobservables postulated by theories (§ 5.1.4). But this problem has various aspects, such as whether it is possible to refer to unobservables, or whether the terms referring to them are eliminable, or whether discourse about them can be true or false, or whether knowledge of them is the aim of science.

Their position, in his view, is based on the “Radical-empiricism argument” (p. 290), which illicitly infers

from the easily admissible thesis (a) that every existence claim about the world must explicitly be linked with sense experience... to the already more controversial thesis (b) that such claims must ultimately rest on sense experience, but even to the extreme thesis (c) that every existing entity must be directly ascertainable by sense experience (p. 291).^[58]

Van Fraassen, for instance, holds that the only ultimate justification of beliefs can be unaided sense observation. But to this severely restrictive position Agazzi replies that justification also comes from the rational arguments, by which statements about the unobservables can be inferred from statements about the observable reality (§ 5.5.2).

3.1 Explanatory Arguments

The most important of those rational arguments are the abductive ones, based on the need to explain the observable phenomena thorough unobservable causes or structures:

A general characteristic of our knowing activity (that we find also in everyday life) is that in order to explain...

Occam’s razor (entia non sunt multiplicanda praeter necessitatem) is certainly a wise intellectual principle, but it also admits of a ‘counterpart’ which is no less wise (entia non sunt diminuenda praeter necessitatem). The conjunction of these two principles says that we must have good reasons both for introducing and for denying entities, properties, and so on (p. 299).

We introduce hypotheses (i.e. conjectures) to explain facts (i.e., states of affairs estab­lished beyond reasonable doubt, though, like every claim, subject to the possibility of error).... Scientific knowledge, like every form of human knowledge, walks on two legs, experience and reason! (p. 359).

A theory usually postulates other entities and speaks of their properties and processes in order to explain the laws. But in such a way these entities could hardly be denied a right of citizenship among the referents of the science involved (pp. 361-362).

Thus, even without explicitly mentioning it, Agazzi accepts the inference to the best explanation (see Lipton 1991) as the backbone of theoretical reasoning in science.

Antirealists typically deny the need for explanation or think, like Van Fraassen, that something can be explained by deducing it from a hypothesis, even with­out believing in the truth of the latter. In reply Agazzi asks: “would we honestly accept, as an explanation of a fact, a hypothesis which we know to be false, but which accidentally happens to be such that we can logically deduce this fact from it?” (p. 296). In fact, mere acceptance of a theory without belief is possible from a pragmatic point of view, not from a cognitive one (§ 5.5.3).

A particularly effective argument is the “no miracles argument” of Smart (1968, p. 150), Sellars (1962, p. 97), Boyd (1983), Putnam (1975a, p. 73; 1978, pp. 19-21), and others: only a miracle could explain the success of science, unless we acknowledge that theories are largely true (§ 5.6).

Hacking (1983) and Giere (1988) supported entity realism by arguing that unob­servables (like electromagnetic waves or microparticles) certainly exist, since we produce and manipulate them (e.g., by television sets, microwave ovens, X-rays generators, particle accelerators etc.). Agazzi employs the same argument: “The specific ‘criterion of reality’ for scientific objects that technology introduces... is the fact that technology makes use of such objects, and it is obviously not possi­ble to make use of something that does not exist” (p. 309). But in this formulation the argument risks to be understood as a petitio principii, since the premise that we manipulate and use waves or microparticles is not based on direct perception, but on the very belief in the truth of theories which this argument is supposed to justify. But the same reasoning becomes fully plausible when phrased as another variant of the “no miracle” argument, as Agazzi does elsewhere: “if we succeed in operating on reality, letting ourselves be guided by a science, it follows that this science has picked out some actual properties of reality” (p. 285).

Larry Laudan objected in his famous (1981) that many theories that enjoyed large success in the past, later proved to be wrong, hence success is not evidence of truth. Agazzi replies in two ways: first, by endorsing what is commonly called deployment realism,^[59] today the most accredited form of scientific realism: as a conjunction of a certain number of statements, a theory can be called “false” when even just one of them is false.

It may well happen that a particular theory which turns out not to be adequate from sev­eral points of view and is therefore replaced by another, remains partially adequate from certain points of view; and this is enough to afford an understanding of its predictive suc­cess. This success depends on those parts of the theory which were adequate (p. 301).

Only when the postulated referents are characterised through properties which actually play a logical (and not just a psychological) role in explanation and, especially, in predic­tion, can they be credited with a solid ontological status (p. 302).

It might be objected that often a theory succeeds in predicting certain phenomena precisely because they were known in advance, and the theory has been formulated in order to accommodate them. So, there is no compelling evidence of its truth. The reply is that in other cases theories predict phenomena previously unknown, or not used in the construction of the theory, and then the partial truth of the theory is the only plausible explanation (see Alai 2014a). While Agazzi does not explicitly consider this objection, he notices that “We are even more obliged [to believe in an object postulated by the theory] if it is possible for us to derive from the existence of this object, in a logically cogent way, certain previously unobserved features that we actually observe in conformity with our prescriptions” (284).

Agazzi’s second reply to Laudan’s historical objection is that in some cases a theory replaces another without contradicting it, but by introducing a new domain of objects (p. 302). But on this point, a keynote in Agazzi’s epistemology, I shall come back shortly.

3.2 How Do We Know that Unobservable Entities Exist?

A different antirealist objection is reported by Agazzi as follows:

There are certain measurements that we can perform in order to attribute to [an electron], let us say, a mass, a charge, a spin, and so on.

To this he replies by his doctrine of objectification:

This seemingly reasonable argument is actually involved in the old superstition of epistemological dualism which, in this case, consists in conceiving of the electron as a kind of ‘substance’ that lies ‘behind’ its properties, and which is such that we never encounter it, while we are able to encounter its properties. If one thinks this way, however, one conceives of the electron as a ‘thing’ and not as an ‘object,’ and one has removed one­self from physics by this very fact. If we instead conceive of the electron as an object, it must be conceived of not as something to which properties are attached, but as something which is constituted by these properties. An object is to be considered as the ‘structured’ totality of the objectively affirmable properties and not as a mysterious substratum of these properties. This might sound as a Humean positivism, but it is not, since we do not maintain that such properties are exclusively our perceptions: they are ontological aspects of reality and may even be perceptually not attainable (p. 283).

An object is a complex structured reality, as we have pointed out, and there is no reason to pretend that the all the properties that go into this structure be observationally testable. [Therefore] the distinction between a realism of properties and a realism of entities... is useless since, in science, entities (objects) are (as we have maintained) nothing but struc­tured sets of properties (p. 284).

But I don’t think this reply is successful, because the objection could also be phrased as follows: for Agazzi each abstract object must have a concrete refer­ent.

In the case of some objects it may be that none of the properties attributed to them is empirically testable. In such a case we are nevertheless obliged to admit the existence of such objects for theoretical reasons. We are even more obliged if it is possible for us to derive from the existence of this object, in a logically cogent way, certain previously unobserved features that we actually observe in conformity with our prescriptions. The ‘realist’ import of scientific applications acquires relevance, though not in the grossly pragmatist sense according to which success is the best guarantee of truth. Rather... in the more rigorous sense according to which if we succeed in operating on reality, letting ourselves be guided by a science, it follows that this science has picked out some actual properties of reality... (pp. 284-285).

3.3 The Problem of Incommensurability

In the 1960s and 1970s a strong threat to realism came from Kuhn’s (1962) and Feyerabend’s (1975) claim that the theoretical change brought about by “scientific revolutions” is so radical to make theories “incommensurable”: since the meaning of each term is contextual, i.e. determined by its relations to all other terms, a term does not have the same meaning when occurring in different theories. So, theories cannot be rationally compared, and there cannot be any rational justification for believing one theory rather than any other.

Agazzi tackles this problem by two complementary strategies, which now we shall briefly examine: (A) as far as alternative theories share at least some basic predicates, we can identify some common referents, hence rationally compare them; (B) if instead they don’t share any referent, they are incommensurable, but not incompatible, since they deal with different objects. In both cases, therefore, there can be progress.

(A) The first strategy was followed in the 1970s and in the 1980s by the best advocates of scientific rationality (Putnam 1975b; Brown 1977, 1988; Shapere 1981, 1984, etc., beside Agazzi himself: 1976a, 1976b): meaning has two components, sense and reference; and while senses are contextual, so varying across theories, as claimed by Kuhn and Feyerabend, referents are not, and can be univocally identified across theories, if these share some basic predicates. For instance, even if a theory classifies whales as mammals and another as fishes, it is clear that they refer to the same animals, since they attribute them many common properties. Equally, it is clear that Avogadro’s “molecules” and Dalton’s “atoms” were the same objects, as they shared many properties (§§ 3.2, 3.3, 5.3.5).

But while thus attributing a key role to reference, Agazzi keeps a descriptivist theory, according to which reference is fixed by properties, or descriptions. On this account, whenever two entities postulated by different theories share many proper­ties, but not the vast majority of them, it remains undetermined whether they are the same entity differently described, or two distinct entities described in partially similar ways. The problem is even more serious in the case of “theoretical” terms (i.e., terms for unobservable entities), because Agazzi grants that “their entire meaning depends on the context of the theory, being influenced in particular by the logical relations existing with the operational as well as the other theoretical predi­cates. Therefore, they are endowed with only a ‘contextual meaning’” (p. 379). There follows that there is meaning variance, just as claimed by contextualists, hence theories cannot be rationally compared.

This problem can be overcome only by (i) embracing a referential theory of meaning also for theoretical terms, and (ii) accepting a “causal” theory of refer­ence, as suggested by Putnam (1975b), according to which reference is directly fixed to what a given entity actually is, not to a (possibly wrong) description of it. This may happen either by ostension (in the case of observation terms, like ‘gold’), or through the causal role played by the referent (in the case of theoretical terms). Thus reference, even of theoretical terms, can be identified non-descrip- tively, hence independently of the theory, so that shared referents can be identified.

As concerns basic observational predicates and the operational procedures, contextualists like Kuhn and Feyerabend held, and Agazzi grants, that “these pro­cedures are certainly bound to some non-empirical context (the context which allowed for the design and use of the instruments, the context depending on the ‘historical’ and the ‘hermeneutic’ dimensions of science)” (p. 379), hence also their interpretation is theory-laden. But like Stegmuller (1976, Chap. 3), Pera (1982, Chap. IV.3), Shapere (1984), Kosso (1992, Chap. IX), and others, Agazzi points out that the context on which the interpretation of basic predicates and operational procedures depends need not be that of the theory under scrutiny: hence, its evaluation can still be objective. In other words, the theoretical/non the­oretical distinction is theory-relative, and what matters is that the empirical basis of a given theory be non-theoretical with respect to it (§ 7.2.5).

(B) Agazzi’s second strategy in facing the problem of radical theoretical change hinges on his doctrine of objectivity: if two theories share the same operational predicates, and there is an operational sentence implied by one and denied by the other, they are comparable and incompatible (pp. 380-381). But if

two theories contain operational predicates which are not completely identical... they do not speak about the same objects, and because of that they are to be considered as incom­parable or incommensurable, by resorting to our criteria (p. 381).

It is then clear that two ‘rival’ theories can both remain true, each obviously about its own objects (...), so that they are not really rival (p. 286).

In the history of science there are several theories which have established a rich set of true sentences about certain specific domains of objects, and this truth is never destroyed by the fact that other theories have proposed new systems of true sentences about new domains of objects (p. 381).

There follows that in any case theories can be true, and there can be progress: when successive theories share referents, progress is linear: in particular, it is cumulative if the superseding theory includes the superseded one, and non-cumulative if the former contradicts the latter.^[60] Instead, when there is a complete change of objects we have non-linear progress, which is cumulative in the sense that knowledge about the new objects is added to the knowledge of the old ones, even if “this progress cannot be understood as a purely logical fact.... theory change very often means the opening of a new domain of inquiry... and this is by no means a matter of pure logic” (p. 382; §§ 7.2.7, 7.2.8; p. 286).

The idea of a radical change of objects strikes me as crucial in understanding the relations among different disciplines dealing with partially overlapping domains: for instance, psychology and neurophysiology both deal with our mental life, and they are not incompatible, but complementary. Perhaps, as suggested by Agazzi (p. 286), in this way one can also plausibly explain at once the radical contradiction and the pacific coexistence we observe between classical and quantum mechanics: for quantization, indeterminacy and casual behaviour pertain to the micro-world, while continuity, determinacy and causality pertain to the macro-world.

In general, however, it seems difficult to apply this idea to the relationships among different theories of the same discipline: it is implausible that in order to speak of the same objects two theories must share all the operational predicates, as claimed by Agazzi. In fact, as shown by the causal theories of reference, the descriptions given through operational predicates are not definitions of the terms, but just ways to fix their referents: as it was rightly objected to Bridgman’s oper- ationism, when we measure mass by different methods we are not measuring different properties, but the same property (Suppe 1977, p. 19). Probably, therefore, in typical cases of “scientific revolution” we have theories purporting to deal with identical or largely overlapping domains of observable objects, but postulating dif­ferent theoretical objects and properties. Moreover, the theoretical objects postu­lated by a theory are not introduced in addition to the different objects postulated by the rival theory, but in the place of them. For instance, Newtonian mechanics and general relativity deal with the same observable objects (like planets and stars), and with some common theoretical properties (like mass); but the former claims that there is action at distance, and space has no causal powers, while the latter denies that there is action at distance, and claims that space has causal powers. So, they cannot be both (completely) true.

3.4 The “Pessimistic Meta-Induction”

In recent years, however, an even more serious threat to realism and to the idea of progress has been the so called “pessimistic meta-induction”: since no theory older than, say, a hundred years is now believed to be true any more, probably in the next hundred years or so even all presently accepted theories will be rejected. So, how could we ever justifiably believe in the truth of some theory? (§ 8.1.5; Putnam 1978, p. 25).

Agazzi formulates this problem as the question: “How can scientific theories be true if they are usually refuted after a more or less short life?” But literally understood, the question is not difficult: except for verificationists, theories might well be refuted, yet true; in fact, all of them could be both refuted and true. The trouble is, theories are not just refuted, but mutually incompatible; so, they cannot be all true. Of course, we don’t need that all of them are true, only that some are; above all, we need to be able to (fallibly) distinguish the (probably) true ones from the (probably) false ones, i.e., we want to be justified in believing some of them. But how can we believe in those which now appear as most plausible, if the pessi­mistic meta-induction convinces us that all of them will be discarded in a hundred years or so?

Popper held that successive theories, though false, approximate truth more and more. But for Agazzi this is not an acceptable solution, for it presupposes a sub­stantialist conception of truth, which in turn entails epistemological dualism, i.e. the idea that we don’t know reality, but an intermediate entity called ‘truth’ (pp. 287, 391, 392).

But I think the mere grammatical practice of treating ‘truth’ as a substantive term does not, by itself, have this wrong implication: ‘knowing the truth’ is usu­ally understood as a short for ‘knowing of some particular statements that they are true’, i.e. ‘knowing the truth about some particular facts’; and this, by seman­tic descent, simply means ‘knowing some particular facts’. So, ‘approximating the (total) truth’ is a short for ‘knowing an ever larger number of facts’. The real prob­lem with the Popperian idea of an increasing number of known truths (i.e., facts) is rather that if really all theories were shown to be completely false, as claimed by antirealists, later theories would contain the same number of truths (zero!) as the earlier ones.

Agazzi tries to counter the pessimistic induction by the semantic principle of the eternity of truth: “If a sentence does not change, and its referents do not change, then its truth (or falsity) does not change” (p. 402). Now, this is obvious, but the problem is that once a sentence has been refuted, the evidence is that it was (and still is) false, and this may happen to all scientific statements. Granted, in some cases

the purported falsifications must be interpreted neither as an elimination of their respec­tive referents nor as a discovery of false assertions made about these referents, but as a change of referents... and with it so too change the objects to which theories refer.... But it is then clear that two ‘rival’ theories can both remain true, each obviously about its own objects (or referents as one may prefer), so that they are not really rival (p. 286; § 7.2.7).

But as I noticed earlier, these are limiting cases, for in general theories of the same discipline make incompatible claims about the same things.

3.5 Are Refuted Theories Still True?

Earlier I noticed that Agazzi’s idea that theories apply only to the restricted domain of their own objects might be just a misleading way of putting the obvi­ous point that a theory does not speak of everything, which is compatible with the absoluteness of truth. But here it turns out that he understands it in a more radical way, resembling Kuhn’s and Feyerabend’s relativism: that prima facie rival theo­ries actually speak of different objects is not just an occasional contingency, but it must necessarily be always the case.

In fact, he argues that a theoretical sentence of theory T con be refuted only by endorsing its contradiction, which in turn means accepting a theory T’ contradict­ing T. But two theories contradict each other only if they have the same referents, and because of the theory-ladennes of terms, this happens only very seldom (p. 403). (This is like saying that, e.g., a theory entailing ‘phlogiston exists’ and one entailing ‘phlogiston does not exist’ are not contradictory, since ‘phlogiston’ does not refer to the same entity in those theories). It follows that

the condition for the eternity of truth is always fulfilled for, two theories being necessarily different, either they give rise to the unproblematic situation comparable to that of two sen­tences being ‘complementarily’ true of the same referent, or to the even less problematic situation of two sentences being true of two different referents. Our puzzling conclusion is therefore that no falsification of a theory is properly possible, and in such a way the entire objection is met (p. 404).

But this conclusion is really too embarrassing to be acceptable: it contradicts Agazzi’s own attempt to preserve the comparability of theories by showing that meaning vari­ance applies to senses but not to referents, and as a consequence it wrecks realism: if all theories are automatically true, then they are merely analytic, and empirical science is void of any factual content (against Agazzi’s own claim that only formal sciences are semantic, while natural sciences are apophantic). Even the weaker thesis that no theory is refutable entails the impossibility of distinguishing truth from falsity, hence of justifying any scientific belief, hence of knowing anything.

The Author fully appreciates the paradoxical character of his claim, and he asks: “Do we really believe that Ptolemaic astronomy is still true,^[61] that the corpus­cular theory of light was not disproved by experimental results on the velocity of light, that Newtonian mechanics was not disproved by relativistic and quantum mechanics, and so on?” (p. 404).

And he answers: “yes!”: Ptolemaic astronomy was only about the relative motions of the Sun and the Earth, because at the time they couldn’t observe their absolute motions; hence, it is still true (p. 404). But this is to reduce the content of theories to their empirical claims, so giving into antirealism: what scientific realism is all about is that theories have a non-observable content, and we can believe in its truth.

The corpuscular and wave theories of light, says Agazzi, describe different aspects of the same “thing”, in fact now they are both employed to account for the optical phenomena known today:

the corpuscular theory was (and is) true of the corpuscular aspects of light... and the wave theory was (and is) true of the undulatory aspects of light, and finally... our present wave-particle theory of light is true of light as we objectify it in present-day physics. [Only,] after a certain time an objectification meets its ‘limits,’ and without being proven false, it is proven partial. (p. 405).

But this overlooks that the two theories were incompatible, for claiming that light is a wave implies denying that it is made up of particles, and vice versa. Moreover, while our current theory has some aspects of both, it denies that either one was a correct model of light. Nor these three theories intend to describe different domains, for all of them aim to explain the nature of that radiation by which we see the world. One could deny that they contradict each other only by reducing them, again, to their empirical content, thereby ignoring the explanatory aim of science, and conceiving progress as a mere accumulation of empirical data.

Concerning relativistic and quantum mechanics, Agazzi denies that they rep­resent a progress with respect to classical mechanics, or that they offer a more approximately true description of the same objects. On the contrary, they talk about utterly different objects, because

objects are ‘clipped out’ of things by operational predicates which are defined on the basis of operational procedures. Every operational procedure is given (or, better, is characterised) by a certain order of approximation or margin of error.. This means that. it makes no sense to carry out calculations leading, for example, to the expression of the length of a body as being equal to 5.00021 cm. if the instrument on which the length calculations are based in that context only admits of a margin of error of one millimetre. The alleged accu­racy would simply lead to a meaningless statement... because if the meaning of the opera­tional predicate has been introduced by means of a measurement limited by a certain order of approximation, it is clear that we are not using this meaning (or we are misusing it) if we pretend that it is bound to a different order of approximation (pp. 405-406).

I think quantum mechanics is where Agazzi’s idea of a domain shift applies best, but this interpretation is possible even without embracing the old verificationistic and operationistic view of meaning he presupposes here: the measurements made by a particular instrument do not define the meaning of terms, which is constituted by both sense and referent. Measurements only contribute (together with other properties described by the theory and by common sense) to constitute the sense, but reference is a relation to things themselves, independently of our definitions. The statement that the length is 5.00021 cm. may be true or false, but it is certainly meaningful, whether we can control it or not. Measurements are only criteria for checking the truth of such attributions, and two instruments with approximation margins of respectively 1 and 0.01 mm still measure the same property.^[62]

Summing up, the pessimistic meta-induction cannot be countered by appeal to the relativity of truth or of objects. But Agazzi could successfully reply by the same strategy he endorsed earlier (pp. 301-302), that of deployment realism: rather than claiming that rejected theories remain totally true, but only about the objects defined by them (i.e., about mere Kantian phenomena), he could argue that they remain partially true of all reality, understood as independent of the criteria employed to identify their referents. A theory which is overall false may still make some true claims (both empirical and theoretical). Since those claims can be iden­tified through the essential role they played in the prediction of novel effects, they can be safely (although fallibly) believed.

Agazzi accounts for the cumulative nature of science by claiming that since a theory is true only relatively to its objects, after a sufficient number of checks it becomes practically certain and immune to falsification (pp. 408-409). But what makes scientific knowledge relatively stable is rather that those claims which are singled out as approximately true by their deployment in successful predictions are typically preserved by later theories, so cumulated over time.