We shall henceforth restrict our considerations about the EE thesis to gen-uine rivals. We defined the empirical equivalence of two theories T and T0 as the equality of their empirical contents: EC(T) = EC(T0). This can be construed as meaning that T and T0 entail the same observational sentences.
The following formulation of the EE thesis is thus obtained:
(EE1) T has genuine rivals that entail the same observational con-sequences.
It is actually probable that given a theory T entailing a body of evidence E, there will be a theory T0 entailing E as well. But this kind of empirical equivalence cannot support the strong underdetermination thesis (SUD) which threatens scientific realism. The reason, as Quine puts it, is that all statements face the ‘tribunal of experience not individually but only as a corporate body’
(Quine 1953: 41). This is the so-called Quine-Duhem thesis.5 The consequence of this holism is that what is tested is not a hypothesis or theory alone, but a whole ‘theoretical group’, including auxiliary assumptions about the laboratory instruments used in testing it, about the background conditions, etc. Thus, in fact, E is entailed not by T alone, but by T & A, where A denotes an admissible set of auxiliary assumptions: T & A → E. But we saw Laudan and Leplin (1996) arguing that “auxiliary information providing premises for the derivation of observational consequences from theory is unstable in two respects: it is defeasible and it is augmentable.” Thus, assuming that the empirical equivalence ofT andT0 takes place under the same class of auxiliary assumptions – i.e., T & A is empirically equivalent to T0 & A – then as the class of auxiliaries changes, the consequences of its conjunction with T, and, respectively, T0, change too. If A becomes A0, then T & A0 does not, in general, deductively entail the same observable consequences asT0 &A0 does.
Accordingly, the empirical consequences of a theory “must be relativized to a
5The term ‘Quine-Duhem thesis’ coined in contemporary philosophy of science enjoys wide acceptance. Nonetheless, the detailed examination by Donald Gillies (1998: 302–17) of Duhem’s and, respectively, Quine’s contributions proves that these contain contradictory elements. On the one hand, Quine extends his holism to all statements, in all scientific disciplines. He maintains that even the claims of logic and mathematics are not immune to revision. Thus, “revision of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics (Quine 1953: 43). On the other hand, Duhem exempts from revision logic and mathematics, as well as certain empirical disciplines – e.g., physiology. Besides, unlike Quine, Duhem believes that scientific methodology cannot rely on logic alone. Good scientists are led by a ‘bon sense’ in resolving theoretical disputes (cf.
Duhem 1945: 217).
particular state of science” (Laudan and Leplin 1996: 58). The point is also made by Leplin:
The judgement that rival theories are identical in their observational com-mitments must be historically indexed to the auxiliary information avail-able for drawing observational consequences from theories, and to the technology and supporting theory that determine the range of things ac-cessible to observation. (Leplin 2000: 397)
It can thus be seen that EE1 allows the incoming evidence to favorT overT0. This refutes SUD’s claim that no possible evidence can justify the choice ofT overT0. Obviously, a stronger version of the EE thesis is needed by supporters of underdetermination.
Kukla (1998) has made an interesting move to block Laudan and Leplin’s argument from the “instability of auxiliary assumptions”(henceforth IAA). He appropriates Leplin’s suggestion of time-indexing the auxiliary assumptions:
“every indexed theory has empirical equivalents under the same index.” (Kukla 1998: 63). Thus, according to Kukla, forT andT0 to be empirically equivalent at timetis for them to entail the same observations under the common index At, the class of auxiliary assumptions accepted at time t. As Devitt (2003) indicates, this yields the following formulation of the EE thesis:
(EE2): T has genuine rivals which are such that whenT and any of the rivals are conjoined withAtthey entail the same observations.
Prima facie, Kukla’s approach does not bring forth any substantial difference from the previous situation: if T &At is empirically equivalent toT0 &At, it does not follow thatT &At0 will be empirically equivalent toT0 &At0, where t0 > t. Thus, the effectiveness of the IAA-argument is undeterred, so that EE2
is as inapt as EE1 to entail SUD.
Kukla then emphasizes that to believe at timetthatT andT0 are empiri-cally equivalent is to believe that they are atemporally empirically equivalent:
The point is that we know that, whatever our future opinion about aux-iliaries will be, there will be timeless rivals to any theory under those auxiliaries. (Kukla 1998: 63)
This is logically equivalent to claiming that there are empirically equivalent total sciences, meaning, the “conjunction of any ‘partial’ theory and all ac-ceptable auxiliary theories we deem to be permissible.” (1998: 45). If that was correct, then EE2 would indeed lead to SUD, for IAA could at most establish that partial theories can be discriminated by their empirical consequences.
IAA would simply not apply to total sciences, because as Boyd indicates, “to-tal sciences are self-contained with respect to auxiliary hypotheses.” (Boyd
1984: 50). In other words, a total science entails by itself all its observational consequences, since all needed auxiliaries are already part of it.
Nonetheless, the way in which Kukla construes the notion of a total science is problematic. For one thing, he seems to take it that once accepted, a theo-retical sentence will not be ever rejected. This is the only way to make sense of his claim that “it doesn’t matter which partial theory we begin with – the end result will be the same [i.e., a total science]” (1998: 64). This does not square with the lesson which the debates about the dynamics of theories taught us, namely that science cannot be understood as a continuously growing corpus of accepted statements; there is a good deal of rejection of old statements taking place, too. What is true about them is often taken over by new formulations, corresponding to new interpretations and new mathematical formalisms. We saw earlier that scientific realism copes well with that.
Besides, the “end result” envisaged by Kukla could only be contemplated at the “end of time”, by checking the list of all accepted assumptions in the history of science. Until then, we have to live with new auxiliary assumptions appearing every minute. For a fan of the concept of a total science, IAA emerges now as a result of our ignorance about what the list of all accepted assumptions will look like on the Judgement Day.
Finally, and more to the point, it is significant to note that Kukla speaks of two or more – possibly infinitely many – total sciences. But granted that we could somehow fix the above mentioned difficulties, it is obvious that talk of two or more total sciences begs the question of underdetermination by assuming thatall scientific theories face empirically equivalent rivals. But this already means to assume that SUD is true, whereas SUD is supposed to follow from EE2.
We may thus conclude that Kukla’s time-indexing maneuver cannot cir-cumvent the IAA-argument. In order to establish SUD, a considerably stronger version of theEE thesis seems necessary:
(EE3): For every theory T and for any possible evidence E, there are genuine rivals of T entailing the same evidence E under the same body of auxiliaries.
If that was the case, all theories would be indistinguishable by all possible evidence. This would indeed be a hard time for the empirical sciences, since any claim to objectivity would have to be suspended. Fortunately, there is no reason to believe that EE3 is in place. Besides, as will be argued below, even if it were true, EE3 could not be used to establish SUD.
Note first that there are interesting cases of theories empirically equiva-lent under all possible evidence. Earman (1993) gives the example of a
four-dimensional formulation of the Newtonian mechanics which is empirically in-discriminable from a mechanics adopting a non-flat affine structure and relin-quishing gravitation. Poincar´e (1902) mentions empirically indistinguishable theories about the structure of space. Let us take a more detailed look at one of the cases of underdetermination constructed by Newton-Smith and Lukes (1978) with respect to the structure of space-time. The example concerns the dense and, respectively, continuous characters of space and time as they are represented in different mechanical theories. In a rigorous axiomatization of the Newtonian mechanics, space and time are postulated to be continuous.
That is, the points along an interval are mapped onto the real numbers. The motion of a particle can thus be represented by continuous functions from real numbers representing time, to real numbers representing spatial coordinates.
We can also define higher-order kinematic notions, like velocity and acceler-ation, obtained by successive derivations of the position function. However, given the limited – to some finite number of decimals – accuracy of our mea-surements, we can only ascertain a dense structure of space and time, that is, spatial and temporal coordinates isomorphic to intervals of rational numbers.
In different words,
the conjecture is ... that different hypotheses about space and time (mere density versus continuity) are compatible with all actual and possible measurements. While it is no doubt simpler to represent space and time continuous rather than merely dense, it might be that this is merely a matter of convenience, and that no measurement data can decide the matter. (Newton-Smith 2000: 535)
The computational difficulty of the dense representation comes from the fact that it makes derivation impossible. Therefore, the corresponding mechanics –Notwen’s mechanics, as Newton-Smith calls it – deals with average velocities and accelerations which are mere approximations of the Newtonian, instanta-neous values. One can also argue that Notwen could employ the full range of mathematical techniques used by Newton. Thus again, considering the sets of measurements made from either perspective, the two mechanical theories seem to be empirically equivalent:
Notwen’s theory with its postulation of merely dense space and time and Newton’s theory with continuous space and time are clearly incompatible.
However the theories are empirically equivalent in the sense that an ob-servation counts for (against) Newton if and only if it counts for (against) Notwen. Notwen and Newton will test their theories by measuring the values of the parameters and plugging these values into the equations to generate predictions. ...the measured values with which they both begin will be represented by rational numbers. In a world in which Notwen’s
theory is successful a test of Notwen’s theory will involve predictions of ra-tional values for parameters which subsequent measurement supports. In this test Newton may predict the parameter to have a nearby non-rational value. On the other hand, if Newton’s theory is borne out Notwen can find a valuehwhich is such that his theory is confirmed by the observa-tion confirming Newton. ...Thus, the choice between these theories is an empirically undecidable matter. (Newton-Smith and Lukes 1978: 85)
One can anticipate that the realist will want more than a mere fit with the observational data to be considered as empirical grounds for assessing the verisimilitude of a theory. Sometime in the future, it may be that one of the two mechanical theories (but not the other) will be embedded into a more general theory of a wider scope, with a high degree of empirical success. Ac-cording to Zahar (1973), this has been the case with the Special Relativity theory on the one hand, and the Lorenz ether-drift theory, on the other hand.
In 1905, in light of the evidence existent at that time, the two theories were empirically equivalent. Nonetheless, Special Relativity was later preferred on the grounds of its compatibility with the General Relativity theory. We believe that this is what actually happens most of the time in the history of science with empirically equivalent theories: one of them is embedded in a new, more general theory, and thus benefits from indirect confirmation and from an ex-tended range of applications; the rival one loses more and more supporters, until it is practically abandoned. As will be seen in the chapter 7, this was the fate of the S-matrix theory in high energy physics.
Newton-Smith and Lukes retort that “there is no reason to assumea priori that the best total physical theory (if there be such a theory) will decide between the rival hypotheses or that there is a unique best total theory as opposed to two empirically equivalent total theories.” (Newton-Smith and Lukes 1978: 86). This answer clearly evokes Kukla’s appeal to total sciences.
For the reasons just presented, I deem this move untenable.
Newton-Smith (1999, personal correspondence) also suggests that there may be a peculiarity of the space-time theories which allows the construction of interesting cases of empirical equivalence. There is no doubt something in it, since most examples of empirical equivalence have been constructed via mathematical transformations on the structure of space-time. But there are also exceptions. As Cushing (1990; 1994) indicates, quantum mechanics has two empirically equivalent interpretations: the dominant, Copenhagen inter-pretation, and Bohm’s interpretation. Also, for decades, quantum field theory was considered to be empirically equivalent to the S-matrix theory of strong interaction, until the latter was abandoned without being falsified (see chapter 7). However, returning to EE3, there is surely no reason to admit thatall the-ories are empirically equivalent. In fact, there are in scientific practice quite
few theories having empirically equivalent rivals in the sense of EE3. Most cases of empirical equivalence are of the EE1 sort, which, as we have seen, is benign to scientific realism.
Assuming that EE3 is in place, would this actually entail SUD? In line with Leplin (1997), we argue that EE3cannot be used to infer SUD, because if SUD is true, then EE3 is undecidable. In other words, the argument purports to show that UD entails the negation of EE (UD → ¬EE), which is logically equivalent to¬UD∨ ¬EE. From the disjunction of these negations it follows that EE and UD cannot both be true. With one stroke, Leplin elegantly blocks the impetus of the entire underdetermination argument.
Here is the key phrase of the argument – though rather cryptic with respect to the consequences Leplin wants to extract from it:
Because theories characteristically issue in observationally attestable pre-dictions only in conjunction with further, presupposed background the-ory, what observational consequences a theory has is relative to what other theories we are willing to suppose. As different presupposition may yield different consequences, the judgement that theories have the same observational consequences – that they are empirically equivalent – depends on somehow fixing the range of further theory available for presupposition. And this UD ultimately disallows. (Leplin 1997: 155)
Leplin states that every epistemologist, realist or antirealist, has to employ some epistemic standards to appraise the admissibility of the auxiliaries con-joined with a given theory. Those auxiliaries which are independently war-ranted by empirical evidence are deemed admissible. Given theory T and a set of admissible auxiliaries A, we conjoin T & A to derive the prediction P (T &A→P). Depending onP’s truth-value, we expectT to be confirmed or disconfirmed. Certainly, this demands that Ahad been independently tested, and better supported than T. Otherwise, given the Quine-Duhem problem, the confirmation fromP would be distributed indeterminately on both T and A. This would make uncertain the use of A to the purpose of testing T, for the auxiliaries would “be subject to the same immunity to probative evidence as afflicts theory in general.” (Leplin 1997: 155). If no theory can be pre-ferred over its empirically equivalent rivals, as SUD urges, then the epistemic standards for the admissibility of A cannot be met. If there is no basis for choosing A over of some empirically equivalent set of auxiliary assumptions, then there is no fact of the matter as to what the empirical consequences of T are. Consequently, there is no possibility to establish whether the empirical consequences ofT, and respectively, of its empirically equivalent rivals, are the same. In other words, assuming SUD entails that EE3 cannot be established.
As Leplin phrases it, “EE cannot be used to obtain UD, because if UD is true then EE is undecidable.” (Leplin 1997: 155).
In summary, the formulations of EE are either too weak to lead to SUD, or so strong as to undermine SUD itself. The former (EE1 and EE2) are not problematic to scientific realism, while the latter (EE3) has no reason to be accepted.