The Independence Condition for Robustness and the Spiral Synergy of Robustness-as-Stability and Robustness-as-Consilience

However, one might object that the different kinds of testing strategies presuppose each other in a vicious circle. Is there a vicious circle here? The answer to this question will throw into proper perspective the objection raised by the indepen­dence condition for robustness.

From an operational point of view, it is easy to acknowledge that there are not only vicious circles, but also fruitful ones, in which self-correcting or spiral pro­cedures take place, with qualitatively new results that each procedure alone could not produce. Everyday life offers plenty of examples. Forging a hammer is a well-known example in this context. One must not already have a hammer to make a new one, for tools that are more rudimentary can be used. Even though similar from some points of view (e.g. from the point of view of beating and forging), they are however different from different points of view (e.g. relatively to their impact resistance). So as one does not already have a hammer to forge a hammer, so robustness in the first sense must not be already definitively founded to reinforce robustness in the second sense, and vice versa.

In the famous fable “The Father and His Sons”, Aesop gives another beautiful example taken from practical life:

A father had a family of sons who were perpetually quarrelling among themselves. When he failed to heal their disputes by his exhortations, he [...] one day told them to bring him a bundle of sticks. When they had done so, he placed the faggot into the hands of each of them in succession, and ordered them to break it in pieces. They tried with all their strength, and were not able to do it. He next opened the faggot, took the sticks separately, one by one, and again put them into his sons' hands, upon which they broke them easily. (Aesop [1867]).

The fable has an obvious moral and political meaning (“union gives strength”, as Aesop himself commented according to a different version (cf.

As we have seen, even though similar in their intersubjective testability, the two senses of robustness do realize testability in different contexts. This difference makes it possible that each element supports the other (or others) to obtain a novel effect, in a fruitful spiral. Tests that are robust in one sense of robustness may be based on tests that are robust in the other sense, and vice versa, according to a principle of reciprocal and growing integration. Even though they are reciprocally connected, methods that are robust in different senses can work together to validate empirical claims practically and operationally. Thus, there is no vicious circle here.

This last consideration puts us in a position to deal with the second objection we have still to consider: robustness-as-consilience in science (and the “no-miracle” argument for scientific realism) can be credited with epistemic warrant only if the multiple kinds of available and consilient evidence are independent; but, even if it were true that any single piece of evidence was highly reliable, it still would be very difficult, if not impossible, to ascertain when the independence condition for robustness is satisfied.

Obviously, it is impossible to settle once for all that different causal chains, though experimental—operationally well-established, are independent. In this sense, I fully agree with Nickles: “no improvements in robustness can render [...] processes or their products invulnerable to failure” (Nickles 2012, 329).

If we interpret the independence condition for robustness in this weakened form, and if what we have said until now about intersubjective reproducibility as inter­preted from an experimentalist point of view is generally correct, the following two considerations seem to be sufficient to obtain a fairly satisfying answer to the objection with which we are concerned.

First, Whewell's too-simple view that—as in the case of the Newtonian unifi­cation of various disparate laws of mechanics—the consilience of “rules springing from remote and unconnected quarters” can only be explained by the truth of the theory that made it possible (Whewell [1840]1847, Vol. 2, 65) is untenable, at least at the present state of the philosophical discussion. However, as already mentioned, when both kinds of robustness are properly balanced and are progressing in a fruitful circle, we get, for the time being, rather convincing technical-experimental evidence. In other words, what Whewell stresses in this passage is sufficient to give us reasons to believe that scientists have acquired some knowledge about nature that they can provisionally accept today and reason from. And this is what scientists must do if they wish to avoid always coming back to the same point from which they started. In this way, the independence of different pieces of evidence or sources of knowledge is treated as if, at least for the time being, it were exceptionless, that is, it is used as a hypothetical and heuristic starting point of later efforts in scientific knowledge. While scientists, at any moment of scientific development, may chal­lenge the particular content of any one claim about the independence of different pieces of knowledge that they have taken as their starting point, they nevertheless have to assume this independence as a regulative ideal for the growth of scientific knowledge (unless there is good reason to suspect there is a common cause able to explain it).

A second point to notice is this. That two fields of our experience are inde­pendent is a relative belief or claim, and more precisely one which is relative to the development of our knowledge. The (empirical-experimental) proof that some pieces of evidence were mistakenly believed to be independent necessarily pre­supposes new ‘robust’ findings, robust in both senses of the word, though in dif­ferent proportion in the different cases. This also is a fallible judgment, and its reliability is relative to robustly reproducible experiences. More generally, any process of testing needs some kind of ‘base’, and in fact, at any particular time, thanks to the mentioned synergy (or robustness of higher order), we can have at our disposal a great number of reliable findings we are not willing, although only provisionally, to put in question.

To maintain that different kinds of robustness will have to cooperate, so far as possible, with one another does not mean that there can be no tension between the two aspects of robustness here considered. On the contrary, the fact that the two senses have to cooperate presupposes that they can be at odds or in tension with each other. Thus, what Nickles notices about robustness as stability—that [r] obustness in one dimension can render a system more vulnerable to catastrophic change in another dimension” (Nickles 2012, 329)—holds also for the relationship between robustness-as-stability and robustness-as-consilience. However, in attempting to solve possible tensions and to build synergy (or, if you prefer, robustness of higher order), it is again plain that, if we wish to remain within the boundaries of scientific discourse, we must recur to arguments that are always robust in both senses of the word, though probably in different proportion.

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