2.1. The conceptual framework

Sprenger and Hartmann’s (henceforth, SH) stability argument is based on a meta-level observation about a scientific discipline. They consider a scientific theory T stable if and only if (iff) there is an absence of alternative theories to T in the discipline that persists over a long period of time (SH propose that 30 to 50 years is an adequate measure, but this specific choice plays no decisive role in their argument). SH claim that the failure of scientists in the discipline to come up with and develop rivaling theories in this time indicates that there is a significant scarcity of possible alternative theories or even that there are no possible alternatives at all. On this basis, they then conclude that the epistemic status of a stable theory can be considered significantly improved.

SH understand a possible alternative to an established theory T to be a theoretical structure (conceived or unconceived) that (i) satisfies a set of (context-dependent) theoretical constraints, (ii) is consistent with available evidence, and (iii) makes distinguishable predictions for some future observation(s). Crucially, they do not consider theoretical structures that are empirically equivalent to T as alternatives because they do not satisfy (iii). For this reason, SH do not take their stability argument to bear directly on the question of whether or not T is approximately true.

The reason that they nevertheless take the argument to bear on the question of scientific realism is connected to their understanding of the NMA, which they construe as a two-step argument. First, T’s predictive success is taken to indicate that T is empirically adequate (i.e., consistent with all possibly collectible data). Second, T’s empirical adequacy is taken to indicate that T is true. Although both steps are necessary for accepting the full realist conjecture, justifying the first step of the NMA is already an important result for the realist and is in line with a realist interpretation of T. However, this step is far from trivial. According to SH, the pessimistic meta-induction (PMI) (Laudan (Reference Laudan1981)) is already a threat at this level: “Laudan’s PMI … teaches us that there have often been false theories that explained the data well (and were superseded later). In other words, empirically non-adequate theories can be highly successful” (Sprenger and Hartmann (Reference Sprenger and Harmann2019), 86).

In light of the PMI, amassing additional evidence of T’s empirical adequacy is of crucial importance for justifying the first step of the NMA. According to SH, T’s stability over time may act as support of this kind. Call this argument the stability-based NMA.Footnote ²

The stability-based NMA can be considered a synthesis of the NMA and the so-called no-alternatives argument (NAA) formalized and discussed by Dawid et al. (Reference Dawid, Hartmann and Sprenger2015). However, there is a crucial difference between what one may call the “classical” NAA presented there and the version of NAA that SH deploy in the stability-based NMA. The core role of a classical NAA is to generate trust in a theory in the absence of relevant empirical data. It is based on the observation that despite significant efforts, scientists have failed to come up with alternatives to the theory at hand. The argument infers from that observation that the spectrum of theories that makes distinguishable predictions within the current empirical horizon is probably fairly limited. Hence, the classical NAA addresses a local spectrum of alternatives and is therefore an argument in favor of the viability of a scientific theory, that is, its empirical adequacy within the current empirical horizon.

In SH’s stability-based NMA, the NAA is deployed to strengthen a realist interpretation of an already empirically well-confirmed theory. To this end, it is deployed as an argument in favor of the unrestricted empirical adequacy of T and therefore addresses the global spectrum of alternatives. This version of the NAA is consistent with the core epistemic mechanism of the classical NAA and can therefore be considered an extension of its scope toward the question of scientific realism. The extension is interesting and is in line with interpreting scientific realism as a meta-level hypothesis about the scientific research process that makes a wide range of observational predictions about that process rather than only as a post hoc explanation about an instance of predictive success.

2.2. The Bayesian model

SH model the stability-based NMA with the help of propositional variables H, S, C, A:

• H := T is empirically adequate.

• $\neg $ H := T is not empirically adequate.

• S := T is predictively successful.

• $\neg $ S := T is not predictively successful.

• C := T is not stable (scientists have developed an alternative to T).

• $\neg $ C := T is stable (scientists have not developed an alternative to T).

• A ${{\rm{\;}}_j}$ := There are exactly j possible alternatives to T that (i) satisfy the relevant theoretical constraints, (ii) are consistent with currently available data, and (iii) give distinguishable predictions for some set of future measurements or observations.

Next, SH make the following assumptions, which they consider “equally plausible for the realist and the anti-realist” (Sprenger and Hartmann Reference Sprenger and Harmann2019, 91):

• B1: The variables satisfy the (conditional) independencies in the Bayesian network structure of figure 1.

• B2: If T is empirically adequate, it will succeed: p(S $|$ H) = 1.

• B3: T is not more or less probable to be empirically adequate than any other possible alternative theory that is consistent with available evidence: p(H $|$ ${A_j}$ ) = 1/(j+1).

• B4: The probability that T is stable over time is a decreasing function of the number of possible alternatives to T:Footnote ^3, Footnote ⁴

  (1) $$p(\neg {\rm{C}}|{A_j},{\rm{S}}) = {e^{ - {1 \over 2}{{\left( {{j \over \alpha }} \right)}^2}}}.$$

• B5: The probability that there exist (additional) alternatives to T is the same no matter how many alternatives to T are already known to exist:Footnote ⁵

  (2) $$p(A \gt j|\mathop {\mathop \vee \limits_{k = j} }\limits^\infty {{\rm{A}}_k}) = p(A \gt j + 1|\mathop {\mathop \vee \limits_{k = j + 1} }\limits^\infty {{\rm{A}}_k})\ {\rm{for\ all\ }}j \ge 0.$$

Two probabilities are left unspecified by SH’s assumptions and are considered free parameters of the argument: $p(A_j$ ) and p(S $|$ $\neg $ H). The distribution across p(A ${_j}$ ) reflects one’s prior opinion on the number of alternatives to T. Given B3, this prior belief determines the core prior p(H) and is therefore considered a free parameter. p(S $|$ $\neg $ H), that is, the probability that T is successful given that T is not empirically adequate, is considered controversial on the basis of the PMI and is therefore difficult to numerically constrain.

Figure 1. SH’s Bayesian network representation of the stability-based NMA.

This situation leads to a well-known problem for the classical (non-stability-based) NMA. The inequality p(H $|$ S) $\gt $ f, where f is some relevant threshold like 0.5, can only be inferred given that values for these parameters are chosen carefully. In other words, the classical NMA only convinces those who take H to be sufficiently probable already to begin with (Howson (Reference Howson2000); Magnus and Callender (Reference Magnus and Callender2004)). However, SH’s stability-based NMA significantly improves the realist’s situation with respect to this problem, as may be demonstrated by an evaluation of the argument:

(3) $$\begin{align}p({\rm{H}}|\neg {\rm{C}},{\rm{S}}) & = {{p\left( {\neg {\rm{C}},{\rm{S}},{\rm{H}}} \right)} \over {p\left( {\neg {\rm{C}},{\rm{S}}} \right)}} \\ & ={{\mathop \sum \limits_{j = 0}^\infty p\left( {{{\rm{A}}_j}} \right)p(\neg {\rm{C}}|{{\rm{A}}_j},{\rm{S}})p({\rm{S}}|{\rm{H}})p({\rm{H}}|{{\rm{A}}_j})} \over {\mathop \sum \limits_{j = 0}^\infty p\left( {{{\rm{A}}_j}} \right)p(\neg {\rm{C}}|{{\rm{A}}_j},{\rm{S}})(p({\rm{S}}|{\rm{H}})p({\rm{H}}|{{\rm{A}}_j}) + p({\rm{S}}|\neg {\rm{H}})(1 - p({\rm{H}}|{{\rm{A}}_j}))}},\end{align}$$

where p(A ${_j}$ ) can be expressed (via B5) as a function of p( ${{\rm{A}}_0}$ ) (Sprenger and Hartmann Reference Sprenger and Harmann2019, 102–103):

(4) $$p\left( {{{\rm{A}}_j}} \right) = p\left( {{{\rm{A}}_0}} \right){(1 - p\left( {{{\rm{A}}_0}} \right))^j}.$$

B1–B5 then generate the following expression for the conditional probability of H, given $\neg $ C and S, evaluated in figure 2:

(5) $${{\mathop \sum \limits_{j = 0}^\infty {e^{ - {1 \over 2}{{\left( {{j \over \alpha }} \right)}^2}}}{1 \over {j + 1}}(p\left( {{{\rm{A}}_0}} \right)\left( {1 - p\left( {{{\rm{A}}_0}} \right){)^j}} \right)} \over {\mathop \sum \limits_{j = 0}^\infty {e^{ - {1 \over 2}{{\left( {{j \over \alpha }} \right)}^2}}}(p\left( {{{\rm{A}}_0}} \right)\left( {1 - p\left( {{{\rm{A}}_0}} \right){)^j}} \right)\left({1 \over {j + 1}} + p({\rm{S}}|\neg {\rm{H}})\left( {1 - {1 \over {j + 1}}} \right)\right)}}.$$

Figure 2. The results of SH’s stability-based NMA, with $\alpha $ = 4, contrasted with hyperplane z = 0.5.

The results of the stability-based NMA may be understood to generate a reversal of the situation with respect to the described problem of a prior commitment to realism. This argument only supports anti-realism if one very carefully chooses parameter values that retain an anti-realist position. In other words, the stability-based NMA only fails to convince the strong skeptic who considers the hypothesis that T is empirically adequate to be highly improbable to begin with.Footnote ⁶

3.1. Stability and the historical record of theory change

The driver of the improved results of the stability-based NMA is SH’s assumption B4. According to this assumption, a period of theoretical stability in a scientific discipline should only be expected given that the number of possible alternative theories in the discipline is very small. However, this is precisely the kind of assumption that anti-realists may take issue with on the basis of their understanding of the process of scientific theory building. When faced with a period of theoretical stability, they may rather conclude that scientists are not sufficiently cognitively and technically competent (with respect to mathematical machinery, for example) to come up with an alternative at all and that the relevant alternatives therefore remain unconceived (Stanford (Reference Stanford2001), (Reference Stanford2006)). Call this the problem of cognitive capacity. Another common explanation of stability associated with an anti-realist perspective on theory building is that scientists are working under the strong constraints of the current scientific paradigm (Kuhn (Reference Kuhn1962)) and therefore do not spend much resources on (genuinely) exploratory theorizing or that they simply reject rival theoretical frameworks before they have the chance to develop into fully fledged alternatives. Call this the problem of conservatism. In this light, SH’s claim that their assumptions are neutral with respect to the realist and anti-realist alike is questionable.Footnote ⁷

Now, it is true that SH only offer what they call a “possibility result” (Sprenger and Hartmann (Reference Sprenger and Harmann2019), 89), and they state that one condition on the improved results of the stability-based NMA is that the scientific discipline in question is not too conservative and that the $\alpha $ parameter (see equation [1]) therefore takes a small value. In conservative disciplines, which correspond to a larger value of $\alpha $ , stability will be expected even in light of a large number of possible alternatives, and therefore, “stability is the default state of [the] discipline and will not strongly support the NMA” (Sprenger (Reference Sprenger2016), 185). However, SH do not propose any criteria that may be used to identify conservative (or cognitively limited) disciplines. In the absence of criteria of this kind, it is not clear whether and how their possibility result can be realized. Hence, the argument is at risk of being sorted to already existing disagreements between realists and anti-realists about the process of theory building in science, and a relevant question is therefore whether SH’s argument can be understood to improve the realist’s dialectical situation at all.

A core claim of this article is that a general criterion of the described kind can be identified. This criterion is based on the brief but interesting remark of SH that in conservative disciplines, stability is the default state. The function of this statement is to stress that observations of stability are not in need of any special explanation in disciplines that are conservative. As such, it reinforces SH’s claim that they provide a possibility result. A stronger interpretation of this remark, however, is to take it to identify conservative disciplines with those that do not have a demonstrated history of theory change. Exactly in disciplines without a history of theory change, stability is default. Indeed, adopting this criterion is a natural strategy for the proponent of a stability argument because it also addresses the problem of cognitive capacity. In disciplines with a demonstrated history of theory change, scientists were, at previous points, sufficiently cognitively competent to develop alternative theory.

The general importance of this criterion may be emphasized by considering two different ways to understand stability arguments. In a naive understanding, a stability argument points to an observation of stability and asserts that realism can explain it. The issue with this understanding is that the assertion that an observation of stability is consistent with scientific realism is of marginal importance on its own. What conclusions are drawn on the basis of that observation will be determined by one’s background beliefs. Are scientists in the given field cognitively and technically competent? Are they actively trying to develop alternatives? If the answer to those questions is no, or if there are no relevant data in support of a specific answer, observations of stability may be considered trivial and hence cannot underwrite a strong argument in favor of realism. In a more sophisticated understanding, the argument identifies an observation of stability as unexpected relative to background beliefs and asserts that those beliefs therefore fail to explain it. Only at this stage is realism proposed as an explanation. This understanding may in principle lead to a strong argument.

Pointing at a historical record of theory change, as suggested here, offers a cogent basis for putting forward the latter kind of argument. Because the current period of theory assessment in many scientific disciplines is situated at the end point of a fairly consistent pattern of theory change, this pattern can be inductively projected into the future. In other words, a historical record of theory change underwrites the belief that scientists are typically cognitively capable enough, and typically liberal enough with respect to allocating resources to exploratory theorizing, to find and develop alternative theory within some (roughly) specified amount of time. Seeing this pattern broken in the current period of theory assessment is therefore genuinely surprising. The surprise value of that observation may act as the basis of a significant stability argument. Call this an enriched stability argument.

The enriched argument provides an empirical basis for assuming a fairly high degree of theoretical creativity in a scientific discipline and therefore offers a plausible justification for B4. According to SH’s formalism, this amounts to assuming a small value for the parameter $\alpha $ such that the conditional probabilities p( $\neg {\rm{C}}|{A_j},{\rm{S}})$ decrease quickly in j (see equation [1]). Conceptually, this means to assume that observations of stability would be surprising if a large number of possible alternatives were in principle available to scientists at the current stage of theory assessment. Hence, the surprise value of an observation of stability can be naturally interpreted as being based on a probability distribution of that kind. Of course, the exact specification of this distribution will vary depending on context and prior beliefs. Whether or not this distribution is sufficient, given some specified set of priors, for generating posteriors that support a realist position will depend on the specifics of each situation and therefore lies beyond the scope of this article. The core function of relying on an enriched stability argument is to adopt an argument structure where the expectation on scientists to find and develop alternative theories within a roughly specified time frame can in principle be provided an empirical basis.

The enriched argument also involves a better-motivated choice of time frame for assessments of theoretical stability. SH’s choice of 30 to 50 years is based on concerns about unfit theories being artificially sustained: “to rule out preservation of a theory by a series of degenerative accommodating moves, [stability] should be evaluated over a longer period, e.g. thirty to fifty years” (Sprenger and Hartmann (Reference Sprenger and Harmann2019), 90). However, this choice is fairly arbitrary and, moreover, does not take into account the specific context within which the stability claim is put forward. The enriched argument instead relativizes the time frame across which stability is assessed to the historical record of theory change in the discipline. If earlier periods of theory assessment all lasted well over 50 years before a rival theory was developed, concluding that a current theory is stable just because it survived for 50 years fails to underwrite the claim that the lack of alternatives is surprising. Only when a clear discontinuity with respect to the historical pattern of theory change is observed can the enriched argument get off the ground.

The plausibility of the enriched stability argument may be motivated by general considerations in the history of science that support the claim that theory change has historically been a fairly frequent occurrence. Some versions of the PMI may lend themselves well to this task; Stanford’s record of theory change in physics, chemistry, medicine, and biology (Stanford Reference Stanford2001) and Laudan’s list of theories discarded in instances of theory change (Laudan Reference Laudan1981) are promising candidates.Footnote ⁸ Both Stanford and Laudan take their lists to be representative of “a seemingly endless array of theories” (Stanford (Reference Stanford2001), 9) that “could be extended ad nauseum” (Laudan (Reference Laudan1981), 33).

Although these considerations motivate the initial plausibility of enriched stability arguments, realists who want to rely on an argument of this kind are still tasked with providing an assessment of their chosen discipline or research field that supports the claim that this field exhibits a consistent historical pattern of novel theory building. This is a nontrivial task for several reasons. Theories are seldom developed as a complete and individuated package and presented to the scientific community at a given time; they may be better understood as constructed over a long series of steps from a core concept to a fully developed theory. Hence, a clear pattern of novel theory building may be difficult to describe in terms of definite temporal units. Furthermore, theory change may occur in one subdomain of the discipline while stability is maintained in another. However, the enriched stability argument does not imply that the realist must be in the position to provide a complete account of the history of the relevant discipline but rather that an overall appraisal of the history of that discipline should justify the conclusion that there has been a fairly consistent pattern of novel theory building. Of course, whether or not that appraisal in fact supports that conclusion or not is still an important and complex empirical question.

Furthermore, even if realists are able to provide an assessment of the described kind, a critic may still point at the complex web of social and institutional factors in play in scientific theory building and hold that those factors must be taken into consideration when projecting past theoretical creativity toward the future.Footnote ⁹ For example, realists may argue that their meta-level assessment of the research strategy in a given discipline motivates ascribing a small probability of a theoretical shift in the near future, even if the discipline in the past has instantiated a fairly consistent pattern of theory change.Footnote ¹⁰ On the one hand, an enriched stability argument is based on a finite series of prior instances of theoretical creativity and is therefore structurally incapable of responding to this argument. Hence, this strategy is always a live option for the critic. On the other hand, it is based on a description of a research field that must be empirically motivated on a case-by-case basis. In this light, proponents of an enriched stability argument may just suggest that in the absence of a strong motivation of this kind, the statistical basis of their argument is sufficient to justify a future projection of theory change.

3.2. Predictive success and theoretical conservatism

In the previous section, an enriched stability argument in favor of scientific realism was described. The argument claims that observations of stability become epistemically significant with respect to realism when theory change is expected based on a historical record of theory change. As proposed earlier, the anti-realist may reject this expectation on the basis of a discipline-specific assessment of the factors at play in theory building in the discipline. However, the question of whether the anti-realist can also give a more general explanation of the current period of stability in science that is consistent with the anti-realist position arises. In other words, is there some structural explanation of theoretical stability that (i) cannot be rejected by pointing at the historical record of theory change but that (ii) does not speak strongly in favor of realism? The aim of this section is to show that an explanation of exactly this kind can be provided.

The suggested explanation is based on the concept of theoretical conservatism but provides a strong and highly general basis for assuming high degrees of conservatism in the current scientific landscape. This explanation can be constructed as a three-step line of reasoning. First, a correlation between predictive success and theoretical conservatism is asserted. Hence, large degrees of predictive success in a scientific discipline are accompanied by an expectation that the discipline will tend to constrain the distribution of resources for exploratory theorizing. Second, it is claimed that this correlation is substantial. In effect, theories in that discipline will be expected to be stable. Finally, the point is made that because the currently endorsed theories in science enjoy significantly higher degrees of predictive success compared with theories of the past, today’s scientific disciplines are probably much more conservative, and the stability of the current stage of theory assessment is therefore not very surprising. On this basis, the anti-realist then concludes that this stability cannot underwrite a strong argument in favor of scientific realism.

Now, granting strongly increasing degrees of predictive success may look to the anti-realist like conceding too much to the realist. However, if realists are forced to retreat back to classical NMA-type reasoning, they are no longer able to point at an additional independent line of justification for their position, which is the core role of a stability argument. Asserting a strong correlation between predictive success and stability is therefore an effective counterargument to the enriched stability-based NMA, as will be demonstrated formally in section 3.3. Call the problem identified by this line of reasoning the new problem of conservatism. The following three sections flesh out and further motivate the problem.

3.3. Formal analysis

How should proponents of the new problem of conservatism update their beliefs about scientific realism in light of observations of theoretical stability? In order to formally analyze this question, the concept of degrees of predictive success must first be offered a formal interpretation. Ideally, these degrees would be represented in their entirety. However, in the interest of simplicity and clarity (and keeping the structure of the formal model similar to SH’s), let S ${^E}$ be a binary propositional variable such that S ${^E}$ := T demonstrates exceptional degrees of predictive success, and let $\neg $ S ${^E}$ be its negation.

The new problem of conservatism asserts that the theoretical stability demonstrated in the current period of theory assessment is not very surprising but in fact expected, given the exceptional degrees of predictive success exhibited by our currently endorsed scientific theories. Expectancy, at the very least, must be considering something more probable than not. “Alice expects rain today” plausibly expresses (at least) that Alice considers it more probable that it will rain today than that it will not rain today. Hence, a proponent of the new problem of conservatism will subscribe to the claim that, given exceptional degrees of predictive success, the probability of stability is larger than 0.5. Formally:

(6) $$p(\neg {\rm{C}}|{{\rm{S}}^E}) = \mathop \sum \limits_{j = 0}^\infty p(\neg {\rm{C}}|{A_j},{{\rm{S}}^E})p\left( {{A_j}} \right) \gt 0.5.$$

At first glance, a natural way to modify the stability-based NMA in order to satisfy this inequality is by increasing the value of the $\alpha $ parameter as proposed by SH (see equation [1]). However, it turns out that $\alpha $ is not sufficiently flexible for this purpose. For all positive integer values of $\alpha $ , ${e^{ - {1 \over 2}{{\left( {{j \over \alpha }} \right)}^2}}}$ converges to zero in ${\rm{li}}{{\rm{m}}_{j \to \infty }}$ . Therefore, the sum $\mathop \sum \limits_{j = 0}^\infty $ p(¬C $|$ ${A_j}$ , S ${^E}$ )p(A ${_j}$ ) also converges to zero in ${\rm{li}}{{\rm{m}}_{j \to \infty }}$ . Hence, in order to retain equation (1), a proponent of the new problem of conservatism is forced to assume that the number of alternatives to T is already limited from the start. However, by accepting equation (6), one makes the claim that because of theoretical conservatism at least in part caused by T’s exceptional success, T’s stability remains quite probable even if an infinite amount of possible alternatives could in principle be found. For this reason, a subscriber to equation (6) cannot be plausibly modeled as accepting equation (1).Footnote ¹²

In order to evaluate the implications of the problem for the stability-based NMA, a new set of conditional probabilities p( $\neg $ C $|$ S ${^E}$ , A ${_j}$ ) must therefore be adopted. First, this choice should be consistent with SH’s core assumption B4 that p( $\neg $ C $|$ S ${^E}$ , A ${_j}$ ) are decreasing in j with the extreme case p(¬ C $|$ ${A_0}$ , S ${^E}$ ) = 1. Second, it should satisfy equation (6) given any possible probability distribution across A. Finally, it should be maximally generous to the realist who adopts an enriched stability argument, in order to ensure that the problem is distinguished from other considerations. Hence, p( $\neg $ C $|$ S ${^E}$ , A ${_j}$ ) should decrease quickly in j. The following distribution may be understood as the simplest formally adequate way of satisfying the described conditions (figure 3):Footnote ¹³

(7) $$p(\neg C|{A_j},{S^E}) = 1/\left( {j + 2} \right) + 0.5.$$

Adopting this distribution leads to the following expression for the posterior probability of H, evaluated in figure 4:

Figure 3. A graphical visualization of equation (7) with a visual cutoff at j = 100.

Figure 4. The results of the modified stability-based NMA.

(8) $$p({\rm H |\neg C, S}^E)={{\mathop \sum \limits_{j = 0}^\infty \left( {{1 \over {j + 2}} + 0.5} \right){1 \over {j + 1}}(p\left( {{A_0}} \right)\left( {1 - p\left( {{{\rm{A}}_0}} \right){)^j}} \right)} \over {\mathop \sum \limits_{j = 0}^\infty \left( {{1 \over {j + 2}} + 0.5} \right)(p\left( {{A_0}} \right)\left( {1 - p\left( {{A_0}} \right){)^j}} \right)\left({1 \over {j + 1}} + p({S^E}|\neg H)\left( {1 - {1 \over {j + 1}}} \right)\right)}}.$$

An apt comparison is with the classical NMA, evaluated in figure 5, which can be extracted from SH’s model with the following expression:

(9) $$p(H|{S^E}) = {{\mathop \sum \nolimits_{j = 0}^\infty {1 \over {j + 1}}(p\left( {{{\rm{A}}_0}} \right)\left( {1 - p\left( {{{\rm{A}}_0}} \right){)^j}} \right)} \over {\mathop \sum \nolimits_{j = 0}^\infty (p\left( {{{\rm{A}}_0}} \right)\left( {1 - p\left( {{{\rm{A}}_0}} \right){)^j}} \right)({1 \over {j + 1}} + p({S^E}|\neg {\rm{H}})\left( {1 - {1 \over {j + 1}}} \right))}}.$$

Figure 5. An evaluation of the classical NMA, as extracted from SH’s model.

The results show that modifying the stability-based NMA according to the new problem of conservatism generates an argument that does not amount to a substantial improvement over the classical NMA. Looking at an example makes the comparison more concrete. A fairly skeptical anti-realist may assign a quite small value to p(A ${{\rm{\;}}_0}$ ), say, 0.01. In SH’s model based on equation (1) with $\alpha $ = 4, this assignment still allows significant flexibility with respect to the other free parameter, p(S ${^E}$ $|$ $\neg $ H), which is just required to be in the interval [0, 0.75] in order to conclude p(H $|$ $\neg $ C, S ${^E}$ ) $\gt$ 0.5. In the modified argument, based on equation (7), an interval of [0, 0.13] is required, and for the classical NMA, the interval required is [0, 0.08].Footnote ¹⁴ Hence, although the modified stability-based NMA does amount to a slight upgrade to the classical NMA, the upgrade is not of substantial significance. The basic uncertainties associated with attaching numerical values to the free parameters of the NMA may be understood to offset a single minor improvement. The important conclusion is that, just like the classical NMA, the modified stability-based NMA requires commitment to quite specific parameter values in order to generate results that support scientific realism.

3.4 Who should advocate for nonconservatism?

Before concluding, a brief aside is motivated. The results of the analysis carried out previously offer a contribution to a recent exchange between Stanford (Reference Stanford2015) and Dellsén (Reference Dellsén2018) on theoretical conservatism and scientific realism. Stanford argues that realists should embrace conservatism because they consider it probable that the currently endorsed theoretical picture of the natural world is, by and large, approximately the correct one. Conversely, an anti-realist perspective on science supports a liberal strategy of allocating resources to exploratory theory building. Against Stanford, Dellsén claims that scientific realists should embrace nonconservatism even if they do not consider it probable that exploratory theorizing will generate promising new theory. Failed exploration of that kind amounts to evidence in favor of the endorsed theory because this failure is consistent with the understanding that the endorsed theory is the (approximately) correct one. The conclusion of the analysis in the present article is consistent with the view put forward by Dellsén. A conservative scientific discipline cannot act as a good basis for a strong stability argument in the context of scientific realism. Hence, for the realist, advocating nonconservatism will, in the long run, generate a stronger basis for an argument of that kind.Footnote ¹⁵

It is important to recognize, however, that this implication is connected to scientific realism. And one should not assume that the aims of science and the philosophy of realism are always fully aligned. If an emergence of conservatism in science is considered fully the result of a sociological development that is detrimental to the research process, it may look natural to advocate for nonconservatism. However, the line of reasoning followed in section 3.2 suggests that the situation is more complicated. A reason why one may propose a recent emergence of conservatism in science is the increasing degree of predictive success demonstrated by scientific theories. In this situation, conservatism may be considered a fruitful research strategy, given that a core aim of scientific research is to produce empirically successful theory.

This understanding is consistent with Tambolo and Cevolani’s (Reference Tambolo and Cevolani2023) more general claim that whether or not theoretical conservatism should be preferred in a scientific discipline depends on what the “main cognitive aim” of the discipline is and the degree to which scientists in the discipline expect currently endorsed theory to continue realizing that aim. From this perspective, it is not at all clear that advocating nonconservatism leads to a more successful scientific enterprise. Whether or not it does depends on what one considers to be part of the core aims of science against which that success is evaluated, along with to what degree the current theoretical description of the world is successful in realizing those aims.