On the no-miracle argument for scientific realism

In the last decades, the most popular philosophical defence of scientific realism has been what is known as the ‘no miracle argument’ (NMA; Putnam 1981¹). Though there is a range of different interpretations of NMA, it typically asserts that scientific realism is ‘the best explanation’² (or perhaps, the only reasonable one) of the ‘success of science’, or more particularly, of the empirical success of modern scientific theories³. I admit that the argument is intuitively compelling, and my own discussion will probably not contradict it, strictly speaking, but I will try to show that, when considered from the point of view of a deflationary semantics, NMA transforms itself in something close to a trivial scientific claim, i.e., something that is basically a concern for scientists, rather than for philosophers.

Let’s start by considering what is that NMA tries to be an explanation for. In the most compelling cases, what it tries to explain is not the ‘general success’ of modern science (i.e., how it is that we have managed to develop a so successful science), but, more specifically, the tremendous empirical success of some theories, especially in the natural sciences, and more particularly in physics. Defenders of NMA claim that it would be almost impossible that those theories made so many and so good predictions if they were not true, or at least, very approximately true. But, what are we exactly explaining when we explain ‘the empirical success of a theory’? What kind of fact is our explanandum?

Let T be the theory whose empirical success we want to explain, and let E be the proposition (or conjunction of propositions) about the world that constitute the empirical evidence on which T is assessed. For simplicity, let’s suppose that T explains E perfectly, i.e., that T logically entails E, and that actually E has been derived from T before the truth of E has been established, so T not only explains E but predicted it. The fact that T is ‘predictively successful’ seems to consists in the conjunction of the following propositions (each of them logically independent of the others):

(1) T entails E

(2) E was deduced from T before knowing whether E is true

(3) E is true

Hence, in order to explain the ‘success’ of T, we shall have to offer an explanation of these three facts; no more, no less. However, (1) is just a ‘logical fact’: there is no difference between ‘explaining why’ T entails E and just proving that T entails E; there is nothing like a ‘substantive’ explanation in explaining (1), i.e., an explanation that has to do with how the world is, or anything we can conceive as related to ‘the problem of scientific realism’. Regarding (2), it can be decomposed into two different claims:

(2.a) E has been deduced from T

(2.b) That deduction was made before knowing whether E was true.

As in the case of (1), the fact (2.a) seems to have little to do with a substantive explanation in the sense necessary for assessing the NMA; at most, it is a psychological or historical fact about the specific people who carried out the deduction of E from T, and about the evolution of the mathematical or logical technics that allowed to perform it. The explanation of (2.b) (i.e., the explanation of why the fact referred to in (2.a) took place in a certain moment instead of another) seems also not to have anything to do with whether T or E are true: take into account that to explain (2.b) is just to explain why E was deduced from T at moment t, and possible answers to that question would be things like “because T had been invented before t, and E had not been tested before t”, or something like that. Hence, the possible explanations of (2.b) will refer to when some propositions and their truth became ‘available’ to the scientists, and so, something like ‘the truth of T’ (which is the explanans favorited by NMA) seems to play no role at all in the explanation of (2.b). At most, the fact (2), including its two components, would demand an explanation that belongs to the history of science, not to philosophy.

Lastly, we have the fact (3), i.e., the fact that E is true. What would be an explanation of that? Here is where our semantic deflationism reminds us that ‘the fact that E is true’ is just another way of expressing exactly the same fact that proposition ‘E’ expresses. Explaining (3) is just the same thing as explaining E. But for explaining E we don’t need any philosophical theory; what we need (and scientists pursue) is a scientific theory like T, one of whose goals is, obviously, to explain E (i.e., to explain fact nr. 3).

We find out something similar when we reflect on the usual way realists express, not the explanandum of NMA, but its purported explanans: it is, they say, the truth of T, or the fact that T is true (or approximately so), what ‘explains’ its empirical or predictive success. But from our deflationary semantics, there is no difference at all between ‘the fact that T is true’ and those facts about the world that we express in affirming T. Hence, ‘that T is true’ is just a different way of saying that T (when T is not taken as the name of the theory, but as the conjunction of its axioms or principles). Hence, by saying that ‘the truth of T explains its empirical success’, or that ‘the fact that T is true explains why T is empirically successful’, we are just expressing in a slightly more complicated way what we can express just by saying that T explains E, for ‘T’ asserts exactly the same as ‘the fact that T is true’, and ‘E’ asserts basically the same as ‘the empirical predictions or T are true’. In a nutshell: explaining the ‘empirical success’ of a scientific theory is just what the theory itself does, if it is empirically successful.

I want to insist in that I am not claiming that there is nothing like ‘explaining the empirical success of a theory’. What I am saying is that, when we analyse what that ‘explaining’ can consist in, we find that it is just the same thing as what the theory does with the empirical data it explains, if it is empirically successful. Hence, in order to assess whether ‘the truth of T’ is a good explanation of ‘the empirical success of T’, the only thing we could do is to see whether T is a good, or appropriate, or acceptable explanation of E. But this is a scientific problem, i.e., a problem for scientists to solve, not a ‘philosophical’ one.I am also not denying that there is something important to the intuition that ‘it is very unlikely that T is not (at least approximately) true, given how empirically successful it is’, nor to the idea that (novel) predictions are a better reason to accept the truth of the theory than (ex post) accommodations of already known facts. My point is that these intuitions are better understood as something pertaining to the process of scientific research per se, rather than to a philosophical analysis.