What is a scientific speculation? What epistemic attitude should one take towards speculation in science? These are two of the central, hitherto little discussed, questions Achinstein seeks to shed light on in his book. With regards to the second question, Achinstein identifies three views held by scientists and philosophers about speculation: first, a conservative view, according to which one ought not to speculate at all in science—Newton’s hypotheses non fingo is a case in point; second, a moderate view, according to which one may speculate, but only if one subjects one’s speculations to empirical tests—Achinstein associates this view with Whewell and Popper; third, a liberal view, according to which one may speculate ‘like mad’, without any constraints—he associates this view with Feyerabend. Achinstein himself ends up rejecting all three of these views in favour of what he calls a ‘pragmatic view’ of speculation in science. Before going into further detail, let us see how Achinstein answers the first question about the nature of speculation.
Achinstein characterizes the act of speculating as the introduction of assumptions or hypotheses in one’s theorizing without knowing there is evidence for those assumptions or hypotheses (p. 1). His main focus is ‘truth-relevant’ speculations, in which speculators believe that the assumptions or hypotheses used are (approximately) true or at least possible candidates for truth. Achinstein believes that these kinds of speculations are also what the scientific community really cares about (p. 23). His first stab at a definition of speculation is:
(Spec) hypothesis h is a (truth-relevant) speculation for person P if and only if P does not know that there is evidence that h. (p. 20)
According to this ‘no knowledge of the existence of evidence’ conception of speculation (p. 26), if I strongly believe that there is evidence for h and I have very good justification for my belief, I still speculate if I don’t know that there is evidence for h.
Achinstein spends quite some time discussing how the claim that P speculates depends on the kinds of conceptions of evidence one presupposes. Making use of some of his previous work on evidence, he settles on two kinds of conceptions of evidence in particular: the ‘Bayesian’ conception of evidence (B-evidence), according to which e is evidence that h if and only if p(h/e) > p(h), and his own preferred conception of evidence (A[chinstein]-evidence), according to which some fact e is potential evidence that h if and only if p(E(h, e)/e) > ½, whereby E(h, e) is an ‘explanatory connection’ between h and e. Now, this means that according to the B-conception of speculation, if P knows that there is some e that increases the probability of h, then h is not a speculation for P. Achinstein believes this is too weak. In contrast, on the A-conception h is not a speculation only if there is an explanatory connection between h and e, and if the posterior probability of this explanatory connection is higher than ½. Achinstein considers the somewhat arbitrary threshold of ½ ‘reasonably high’, since, with it, e must make h ‘at least more probable than not’ (pp. 29–30). Furthermore, Achinstein believes that objective rather than subjective probabilities are ‘the most important and interesting ones’ for the purposes at hand and that an explanatory connection is essential for a good conception of evidence. He even recommends that B-evidence be ‘upgraded’ so as to include a ½ threshold, objective probabilities, and an explanatory connection (pp. 30–1). With these clarifications of the concept of evidence in hand, Achinstein amends (Spec):
(Scientific Spec): h is a (truth-relevant) scientific speculation for P (with respect to the truth of h) if and only if P does not know that there is explanatory evidence that h (A-evidence or explanatory B-evidence). (p. 45)
Returning to the question of what epistemic attitude one ought to take towards speculation, Achinstein dismisses the conservative view on the grounds that even Newton, one of its main proponents, did not abide by it. He finds the moderate view problematic, because it doesn’t give any guidance as to when ‘verifications’ (or better, empirical tests) of speculations need to happen (pp. 49ff). Instead, Achinstein suggests that there are other standards than empirical tests for good speculations. These standards are ‘pragmatic standards that depend on the aims and epistemic situation of the speculator and the evaluator, which can vary from one scientist and context to another’ (p. 50). But what are these standards? Achinstein is disappointingly unclear on this. One might have thought that pragmatic standards are such that speculations are to be evaluated according to how well they work, how successful the theorizing is in achieving certain theoretical goals (however that is to be defined), and perhaps also by how theoretically virtuous the relevant pieces of theorizing are. But no such specifics are provided. What’s more, his notion of speculation doesn’t seem to play much of a role in arguing for his pragmatic view.
I find Achinstein’s definition of speculation also rather dissatisfying. First, on this account there is no way to distinguish speculation from other forms of theorizing. I consider speculation to be an extremely ‘thin’ form of theorizing where there is no or very little evidence for the hypotheses used. This is quite different from theorizing in which one has ‘good reason to think that something is (or that there is) evidence’ for one’s theorizing (p. 27). Achinstein believes it’s a strength that his account covers both forms of theorizing, but I think a good account of speculation should not deem empirically justified theorizing speculative. For example, he is happy to regard Newton’s celebrated law of gravitation as a speculation (pp. 22, 159). I think that’s clearly wrong.
My second major concern relates to the agent-relativity of Achinstein’s account, which makes the answer to the question about whether somebody speculates dependent on their state of knowledge. Suppose that I’m like Trump and don’t believe (and therefore don’t know) that there is evidence for man-made climate change. Am I speculating about climate science, as Achinstein’s account would entail? No, I’m just ignorant of all the evidence that there is for man-made climate change. But Achinstein’s account has no way of distinguishing such cases of ignorance from genuine speculations.
Third, I believe that Achinstein’s relativization of speculation to different conceptions of evidence is a red herring. Whether somebody is speculating shouldn’t depend on philosophical debates about the nature of evidence. In particular, it shouldn’t depend on a philosopher’s seemingly arbitrary decision for one or the other threshold for what counts as evidence. Although a good account of speculation should correctly sort the clear cases (see my first complaint), speculation, like so many natural language terms, may just be inherently vague and prohibit the drawing of strict boundaries.
Strangely, the discussion of speculation is restricted entirely to the first chapter, which constitutes about a fifth of the book. This is followed by two chapters on simplicity as a potential guide to truth, and a chapter each on conformational holism and the idea of a ‘theory of everything’ (in which he includes both string theory and panpsychism). Achinstein considers these topics instances of speculations ‘about the world and about methods for gaining scientific knowledge about the world’, or simply ‘philosophical speculations’ (p. 66). He argues that all of these speculative ideas should be rejected.
I found the connection between speculation and those other topics a little forced. A more natural way of connecting speculation to simplicity at least would have been to treat simplicity as a possible constraint on theorizing without much evidence. Nonetheless, I consider the treatment of simplicity to be the most valuable part of the book, therefore in the last part of this review, I’ll focus on this.
In his first chapter on simplicity, Achinstein discusses the ontological claim that nature is simple and the epistemological claim that simplicity is a guide to truth (regardless of whether or not nature is simple). For the ontological claim, he argues, there is little justification, at least when understood as a ‘global’ rather than a ‘local’ claim about particular parts of reality; some parts of the world may indeed be simple, others not (pp. 83–4). He mostly discusses inductive arguments in support of the epistemological claim and finds them wanting—rightly so. An interesting claim that Achinstein makes in this context is that initially simple theories tend to become more complex over time (he mentions the ideal gas law as one example among others) (pp. 93f). What he seems to overlook, though, is that our descriptions of the phenomena become ever more complex too, which leaves open the possibility that our best theories of those more complex descriptions are in fact the simplest. Achinstein then discusses various ways probabilistic accounts—Bayesianism, Sober’s likelihood account, and Sober’s use of Akaike’s theorem—may justify the epistemological claim. His assessment of each account is quite short but fair. This first chapter on simplicity ends with an assessment of Reichenbach’s straight rule of induction—recently advocated by Kevin Kelly—as an example of simplicity as an ‘epistemic strategy’.
In his second chapter on simplicity, Achinstein analyses in quite some depth Newton’s ‘rules for the study of natural philosophy’, which Newton employed to derive the law of gravity in Book III of the Principia. Some of these rules appeal to simplicity. Achinstein argues, however, that simplicity plays no substantial epistemic role in the derivation and suggests that it is either redundant (because simplicity goes along with empirical arguments) or merely pragmatic. I’m not quite convinced.
Newton seems to use simplicity whenever he seeks to establish the identity of terrestrial gravitational forces as the centripetal forces keeping the planets and their moons in their orbits (let’s call this ‘force identity’). This is interesting, because one of Newton’s major achievements was to unify in one theory terrestrial and celestial motion, which on the prior Aristotelian view were fundamentally distinct: celestial motion was ‘special’—namely, circular and eternal—whereas the ‘natural place’ of terrestrial motion was linear and directed towards the earth.
In support of force identity, Newton makes the following argument: If the force holding the moon in its orbit around the earth were different from the force acting on unsupported objects on earth, and if the moon were close enough to the earth (charmingly, Newton says, ‘so near the earth as almost to touch the tops of the highest mountains’), then the two forces should combine and the moon should fall to the earth twice as fast as it actually would. But since the moon wouldn’t fall twice as fast to the earth, force identity is true. Now, that’s quite a counterfactual to digest, but Achinstein is confident that this argument is empirical (p. 148). What’s more, Newton’s argument actually presupposes that the motion of heavenly bodies like the moon decomposes into inertial and centripetal forces, and that the moon would behave just like any other terrestrial object when it’s close enough to the earth’s gravitational field. In other words, the argument presupposes force identity and Newton therefore cannot use the moon argument to support force identity, on pain of circularity. Hence, his moon argument is best considered illustrative. The rules of simplicity, which Newton explicitly appeals to when assuming force identity, have a substantial epistemic role to play after all—contra Achinstein.
Although Achinstein has not convinced me of his account of speculation, he is to be commended on for identifying a hitherto neglected topic worthy of philosophers’ attention. A further step in the development of a more appropriate account of speculation would be to focus less on empirical constraints and more on the many other signposts scientists have at their disposal when speculating.
Samuel Schindler Aarhus University firstname.lastname@example.org
 Achinstein defines an explanatory connection between h and e as either h correctly explains why e is true, or e correctly explains why h is true (sic), or some hypothesis correctly explains why both h and e are true. The latter condition seems particularly problematic, since there could be common cause of h and e, and the relation between h and e merely correlational. As an addition to the explanatory connection, Achinstein requires that e be true and that e does not entail h.