The reflexivity of metaphysical constructivism

Reflexivity is problematic for strong metaphysical constructivism (SMC), which claims that all facts about the known and the knowable world are so-cially constructed. If we grant that this is a fact, then the meta-fact that it is a fact that all facts about the world are constructed is itself constructed, as is the meta-meta-fact that the meta-fact that the fact that all facts are constructed is itself constructed, and so on ad infinitum.

The moderate constructivist (MMC) claim is that only some facts about the world are socially constructed, while the rest are not. Even if the fact that some facts are socially constructed is itself a part of the class of socially constructed facts, its meta-fact need not be socially constructed. Collins and Yearley (1992), for example, claim thatnature is socially constructed, but that the social realm is not. In their understanding, what Newton says about the world is a construction, but when sociology of science says that Newton had such and such an interest, this is objectively true, hence not constructed. They explicitly deny reflexivity. But how could Collins and Yearley’s own position be exempt from social interests? Shouldn’t we seek the social factors that determine their own view, that Newton’s thinking being governed by interests is objectively true? And would not whatever answer we may give be in its own turn socially determined, and so on ad infinitum?

One answer is simply to deny that this is the case: Collins and Yearley’s account is not itself a scientific theory, so it does not fall under its own scope.

The situation is similar with Popper’s dictum that ‘To be scientific, a theory must be refutable’. It does not follow that this claim must itself be refutable since it might have a very different status, e.g. an a priori norm. The point may arguably be taken. A different answer is to bite the bullet and prove that even if an infinite regress is generated, it is not a vicious one. This is the strategy of the Edinburgh school (David Bloor, Barry Barnes, Steven Shapin), which developed the celebratedStrong Programmein the sociology of scientific knowledge.

The theoretical principles of the ‘Strong Programme’ were laid down in Bloor’s (1976) Knowledge and Social Imagery. The principle of Causality states that the explanation of scientific beliefs should employ the ‘same causal idiom’ as any other science (Bloor 1976: 3). Impartiality requires that both true and false (or both rational and irrational) beliefs be causally explained, while Symmetry demands that both kinds of beliefs be explained by the same type of factor. Finally, Reflexivity dictates that the program should apply to itself.

According to Bloor, there is no methodological difference between the nat-ural and the social sciences. In a sociological account of science,

[the] patterns of explanation would have to be applicable to sociology itself. It is an obvious requirement of principle because otherwise sociol-ogy would be a standing refutation of its own theories. ...the search for laws and theories in the sociology of science is absolutely identical in its procedure with that of any other science. (Bloor 1976: 5, 17)

The Strong Programme takes science to be a ‘social phenomenon’ whose meth-ods, results, and objectivity are causally influenced by social factors. This stance clearly evokes the so-called externalist approach to the history of sci-ence, according to which science in its particular configurations is essentially determined by social factors. Well-known is Paul Forman’s (1971) thesis that the German scientists during the Weimar Republic ‘sacrificed physics’ to the Zeitgeist. The readiness of quantum physicists to accept indeterminism and to find a failure of causality was the expression of a compromise they made under socio-intellectual pressures from a mystical and anti-rational public. Ni-iniluoto (1999) neatly formulates the general structure of such an externalist explanation:

The members of the community C belong to social classS.

The members ofS have the social interestI.

The members ofC believed that theoryT would promote interestI.

Therefore, the members ofC believed in theoryT. (Niiniluoto 1999: 255)

It follows that the belief in social causation falls under its own scope, being itself a byproduct of social interests.

Bloor admits that his program is referring, but denies that it is self-refuting. He does not dispute that an infinite regress is generated, but refuses to admit that this particular kind of regress is logically problematic. The point is made explicit by Kukla:

this particular regress doesn’t entail that anybody has to do an infinite amount of work. The fact that every belief is socially caused entails that there is always an additional SSK [sociology of scientific knowledge]

project to work onif one is looking for work. But this no more precipitates us into the abyss of Hell than the fact that we can always count more numbers. (Kukla 2000: 72)

I agree with Kukla that the Strong Programme is not menaced by a vicious regressus ad infinitum– it will be immediately explained why the regress is not vicious. Indeed, Barnes and Bloor present this fact as one of the strengths of their enterprise. Nevertheless, it is worthwhile making it clear, together with Brown (1989: 42), that with respect to reflexivity, the Strong Programme fails

not because of being self-referring, but because of its ambition of explaining all human action in terms of social causality while excludinginternalexplanations, i.e., the role of intra-scientific rationality. The point here is that the Strong Programme self-undermines its capacity to argue for its position:

Bloor’s claim is that it is not evidence, but instead social factors, which cause belief. If Bloor is right, then he must drop bricks on our heads or alter our class interests or some such thing. There is no point in arguing his case; for if he is right, then arguments must be causally ineffective.

(Brown 1989: 42)

Arguments of this kind led Bloor (1991) to suggest that the message of the Strong Programme has been misunderstood. He accepts that internalist expla-nations of science are possible, but emphasizes the need for social explaexpla-nations in order to understand why the scientific community accept certain reasons to support certain beliefs. He means that ‘the link between premise and con-clusion is socially constituted’. Yet Bloor is willing to admit causal empirical explanations about perception, assuming a ‘naturalistic construal of reason’.

In fact, naturalism seems to be a substitute, In Bloor account, for his previous sociologism. As he insists, cognitive science and the sociology of knowledge are

‘really on the same side’, since they are both naturalistic. (Bloor 1991: 170).

Through these concessions, Bloor’s version of the Strong Programme gains some acceptability for realism, but loses a lot of its bite. Some doubts still persist. As Susan Haack (1996) points out, the compelling nature of deduc-tive and mathematical reasoning requires no social explanation. The mere assumption that the scientist has trained his thinking by learning and practic-ing mathematics, is in place. But unless one embraces the absurd view that a mathematical apparatus is the byproduct of a social class following its egoistic interests or something like that, then the assumption is trivial.

To return to the problem of infinite regress, the relevant issue here is whether all infinite regresses are vicious. Kukla does not think so, and thus proposes the following criterion to distinguish between vicious and benign re-gresses: an infinite regress is vicious if it demands an infinite amount on events to take place in a finite amount of time. By contrast, if the infinite amount of events had an infinite time at their disposal in order to take place, the regress is benign. Reference to Zeno’s paradoxes of motion is useful in the latter case.

In the Achilles and the tortoise argument, each time that Achilles sets out to catch up with the tortoise, it turns out that by the time he arrives at the place where the tortoise was when he set off, the tortoise has moved slightly.

The argument displays poor Achilles with an endless amount of tasks to be performed in a physically finite time. Certainly, nowadays we say that as a finite space was decomposed into infinitely many parts, a finite time interval

can be mathematically decomposed into infinitely many distinct parts. If we take it that Achilles has an endless series of tasks to do, then by the same token he has an infinite amount of time at his disposal. Doing infinitely many things requires a lot of stamina, but this should not be a problem for Achilles, as he has infinitely many time intervals.⁷

An example closer to real epistemological problem-solving is given by the so-calledcommon knowledge of rationality (CKR) assumption in game theory.

The assumption is essential for enabling one to form expectations about the behavior of someone else. Formally, CKR is neatly presented by Hargreaves Heap and Varoufakis:

[CKR] is an infinite chain given by

(a) that each person is instrumentally rational (b) that each person knows (a)

(c) that each person knows (b)

(d) that each person knows (c). And so onad infinitum.

(Hargreaves Heap and Varoufakis 1995: 24)

But how can these infinitely many conditions be fulfilled in a finite time? The answer again appears to be that the finite series of tasks is performed by the involved players in infinitely many infinitesimal time intervals. Accordingly, the regress generated by CKR is not vicious.

So much for benign regresses. As to the vicious ones, considerably less work is required to show that they exist. Following Kukla again,

suppose that someone claims that he has always rung a bell before per-forming any action. If this were true, then he would have to ring a bell before imparting that information to us. Moreover, since the ringing of the bell was itself an action, he would have had to ring a bell before the last ring, and so on. Obviously, if what he told us were true, he would have had to ring the bell infinitely many times, by which I mean that no number of bell rings would prove sufficient. (Kukla 2000: 73)

Clearly, an infinite amount of labor, and hence an infinite physical time is required to perform this kind of action.

Let us now take a look at a concrete infinite-regress argument against strong metaphysical constructivism (SM C). As proposed by Niiniluoto (1991),

7One could object and say that we know the whole time interval to be finite, so that according to Kukla’s definition of a vicious regress, Achilles is in such a predicament. But so considered, we may just ignore Zeno’s analysis and take the space interval as finite too.

...a fact F exists if:

(2) there exists a laboratoryBwhereF has been constructed.

Now (2) expresses a fact,F’ say, and it exists if:

(3) there is a laboratoryB’ where F’ has been constructed, etc. Continuing in this way, either we admit at some stage that some facts exist without construction or else we are involved in an infinite regress of an endless sequence of labs B,B’,B”,. . . (Niiniluoto 1991: 151)

It is unclear what made Niiniluoto double the series of construction levels: F, F’, F” . . . , and B,B’,B”,. . . . Presumably he understands SMC in terms of one of its species, the doctrine that all scientific facts are socially constructed and that they are ontologically prior to all other facts. In any event, the viciousness of the above infinite regress consists for him in the infinite number of laboratories required to construct the series of facts F, F’, F”,. . . . The natural question arises, why should the construction of a scientific fact be itself scientific? It could be so, but it need not. Reference to laboratories is superfluous. Besides, even if scientific facts were scientifically constructed, why should we suppose that these actions take place in different laboratories?

There is no reason to urge more than a finite number of laboratories for the construction of the Fs. Therefore, I conclude that the infinite series of labs does not generate a genuine regress. The real problem resides in the infinite series of constructed events. The question which at this point can be raised, is why should theFs be distinct? Imagine a laboratory in which a brain in a vat is being induced to believe that there is a laboratory where a brain in a vat is being induced. . . , and so on,ad infinitum. Are the processes of inducing these beliefs about facts? And if they are, does their construction require an infinite amount of effort? For reasons already exposed, at least the latter question can be answered in the negative.

To be sure, this does not prove that there are not vicious cases of infinite regress concerning SMC. It only shows that each regress case requires individ-ual analysis, so that SMC cannot in general be proven to turn destructively against itself.