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What confirms a physical theory?

Guest blog by Richard Dawid, LMU Munich,
Munich Center for Mathematical Philosophy

Thanks, Lubos, for your kind invitation to write a guest blog on non-empirical theory confirmation (which I recently discussed in the book "String Theory and the Scientific Method", CUP 2013). As a long-time follower of this blog – who, I may add, fervently disagrees with much of its non-physical content – I am very glad to do so.

Fundamental physics today faces an unusual situation. Virtually all fundamental theories that have been developed during the last four decades still lack conclusive empirical confirmation. While the details with respect to empirical support and prospects for conclusive empirical testing vary from case to case, this general verdict applies to theories like low energy supersymmetry, grand unified theories, cosmic inflation or string theory.

The fact that physics is characterised by decades of continuous work on empirically unconfirmed theories turns the non-empirical assessment of those theories' chances of being viable into an important element of the scientific process. Despite the scarcity of empirical support, many physicists working on the above-mentioned theories have developed substantial trust in their theories' viability based on an overall assessment of the physical context and the theories' qualities.

In particular in the cases of string theory and cosmic inflation, that trust has been harshly criticised by others as unjustified and incompatible with basic principles of scientific reasoning. The critics argue that empirical confirmation is the only possible scientific basis for holding a theory viable. Relying on other considerations in their eyes amounts to abandoning necessary scientific restraint and leads to a relapse into pre-scientific modes of reasoning.

The critics' wholesale condemnation of non-empirical reasons for having trust in a theory's viability is based on an understanding of scientific confirmation that has dominated the philosophy of science throughout the 20th century. It can be found for example in classical hypothetico-deductivism and in most presentations of Bayesian confirmation theory. It consists of two basic ideas. First, theory confirmation is taken to be the only scientific method of generating trust in a theory's viability. Second, it is assumed that a theory can be confirmed only by empirical data that is predicted by that theory.

In my recent book, I argue that this understanding is inadequate. Not only does it prevent an adequate understanding of theory assessment in contemporary high energy physics and cosmology. It does not give an accurate understanding of the research process in 20th century physics either.

I propose an understanding of theory confirmation that is broader than the canonical understanding. My position is in agreement with the canonical understanding in assuming that our concept of confirmation should cover all observation-based scientifically supported reasons for believing in a theory's viability. I argue, however, that it is misguided and overly restrictive to assume that observations that instil trust in a theory must always be predicted by that theory. In fact, we can find cases of scientific reasoning where this assumption is quite obviously false.

A striking example is the Higgs hypothesis. High energy physicists were highly confident that some kind of Higgs particle (be it SM, SUSY, constituent or else) existed long before a Higgs particle was discovered in 2012. Their confidence was based on an assessment of the scientific context and their overall experience with predictive success in physics. Even before 2012, it would have been difficult to deny the scientific legitimacy of their assessment. It would be even more implausible today, after their assessment has been vindicated at the LHC.

Clearly, there is an important difference between the status of the Higgs hypothesis before and after its successful empirical testing in 2011/2012. That difference can be upheld by distinguishing two different kinds of confirmation. Empirical confirmation is based on the empirical testing of the theory's predictions. Non-empirical confirmation is based on observations that are not of the kind that can be predicted by the confirmed theory. Conclusive empirical confirmation is more powerful than non-empirical confirmation. But non-empirical confirmation can on its own provide fairly strong reasons for believing in a theory's viability.

At this point, I should explain why I use the term viability rather than truth and what I mean by it. The truth of a theory is a difficult concept. Often, physicist know that a given theory is not strictly speaking true (for example because it is not consistent beyond a certain regime) but that does not take anything from the theory's value within the regime where it works. What is more important that truth is a theory's capability of making correct predictions in a given regime. Roughly speaking, I call a theory viable at a given scale if can reproduce the empirical data at that scale.

What are the observations that generate non-empirical confirmation in physics today? Three main kinds of argument, each relying on one type of observation can be found when looking at the research process. They don't work in isolation but only acquire strength in conjunction.

The first and most straightforward argument is the no alternatives argument (NAA). Physicists have trust in the viability of a theory that solves a specific physical problem based on the observation that, despite extensive efforts to do so, no alternative theory that solves this problem has been found.

Trust in the Higgs hypothesis before empirical confirmation was crucially based on the fact that the Higgs hypothesis was the only known convincing theory for generating the observed mass spectrum of elementary particles within the empirically well-confirmed framework of gauge field theory. In the same vein, trust in string theory is based on the understanding that there is no other known approach for a coherent theory of all fundamental interactions.

On its own, NAA has one obvious weakness: scientists might just have not been clever enough to find the alternatives that do exist. In order to take NAA seriously, one therefore needs a method of assessing whether or not scientists in the field typically are capable of finding the viable theories. The argument of meta-inductive inference from predictive success in the research field (MIA) can provide that assessment. Scientists observe that, in similar contexts, theories without known alternatives turned out to be successful once empirically tested.

Both, the pre-discovery trust in the Higgs hypothesis and today's trust in string theory gain strength from the observation that standard model predictions were empirically highly successful. One important caveat remains, however. It often seems questionable whether previous examples of predictive success and the new theory under scrutiny are sufficiently similar to justify the use of MIA. In some cases, for example in the Higgs case, the concept under scrutiny and previous examples of predictive success are so closely related to each other that the deployment of MIA looks fairly unproblematic. NAA and MIA in conjunction thus were sufficient in the Higgs case for generating a high degree of trust in the theory. In other cases, like string theory, the comparison with earlier cases of predictive success is more contentious.

In many respects, string theory does constitute a direct continuation of the high energy physics research program that was so successful in the case of the standard model. But its evolution differs substantially from that of its predecessors. The far higher level of complexity of the mathematical problems involved makes it far more difficult to approach a complete theory. This higher level of complexity can throw the justification for a deployment of MIA into doubt. Therefore, it is important to provide a third argument indicating that, despite the high complexity of the theory in question, scientists are still capable of finding their way through the 'conceptual labyrinth' they face. The argument that can be used to that end is the argument from unexpected explanatory interconnections (UEA).

The observation on which UEA is based is the following: scientists develop a theory in order to solve a specific theory. Later it turns out that this theory also solves other conceptual problems it was not developed to solve. This is taken as an indicator of the theory's viability. UEA is the theory-based 'cousin' of the well known data-based argument of novel predictive success. The latter relies on the observation that a theory that was developed based on a given set of empirical data correctly predicts new data that had not entered the process of theory construction. UEA replaces novel empirical prediction by unexpected explanation.

The most well-known example of UEA in the context of string theory is based on the theory's role in understanding black hole entropy. String theory was proposed as a universal theory of all interactions because it was understood to imply the existence of a graviton and suspected to be capable of avoiding the problem of non-renormalizability faced by field theoretical approaches to quantum gravity. Closer investigations of the theory's structure later revealed that - at least in special cases - it allowed for the full derivation of the macro-physical black hole entropy law from micro-physical stringy structure. Considerations about black hole entropy, however, had not entered the construction of string theory. String physics offers a considerable number of unexpected explanatory interconnections that allow for the deployment of UEA. Arguably, many string physicists consider UEA type arguments the most important reason for having trust in their theory.

NAA, MIA and UEA are applicable in a wide range of cases in physics. Their deployment is by no means confined to empirically unconfirmed theories. NAA and MIA play a very important role in understanding the significance of empirical theory confirmation. The continuity between non-empirical confirmation and the assessment of empirical confirmation based on NAA and MIA can be seen nicely by having another look at the example of the Higgs discovery.

As argued above, the Higgs hypothesis was believed before 2012 based on NAA and MIA. But only the empirical discovery of a Higgs particle implied that all calculations of the background for future scattering experiments had to account for Higgs contributions. That implication is based on the fact that the discovery of a particle in a specific experimental context is taken to be a reliable basis for having trust in that particle's further empirical implications. But why is that so? It relies on the very same types of consideration that had generated trust in the Higgs hypothesis already prior to discovery. First, no alternative theoretical conception is available that can account for the measured signal without having those further empirical implications (NAA). And second, in comparable cases of particle discoveries in the past trust in the particle's further empirical implications was mostly vindicated by further experimentation (MIA).

Non-empirical confirmation in this light is no new mode of reasoning in physics. Very similar lines of reasoning have played a perfectly respectable role in the assessment of the conceptual significance of empirical confirmation throughout the 20th century. What has changed is the perceived power of non-empirical considerations already prior to empirical testing of the theory.

While NAA, MIA and UEA are firmly rooted in the history of physical reasoning, string theory does add one entirely new kind of argument that can contribute to the strength of non-empirical confirmation. String theory contains a final theory claim, i.e. the claim that, if string theory is a viable theory at its own characteristic scale, it won't ever have to be superseded by an empirically distinguishable new theory. Future theoretical conceptualization in that case would be devoted to fully developing the theory from the basic posits that are already known rather than to searching for new basic posits that are emprically more adequate. Though the character of string theory's final theory claim is not easy to understand from a philosophical perspective, it constitutes an interesting new twist to the question of non-empirical confirmation and may shed new light on the epistemic status of string theory.

For the remainder of this text, though, I want to confine my analysis to the role of the three 'classical' arguments NAA, MIA and UEA. Let me first address an important general point. In order to be convincing, theory confirmation must not be a one way street. If a certain type of observation has the potential to confirm a theory, it must also have the potential to dis-confirm it. Empirical confirmation trivially fulfils that condition: for any set of empirical data that agrees with a theory's prediction, there are others that disagree with it and therefore, if actually measured, would dis-confirm the theory.

NAA, MIA and UEA fulfil the stated condition as well. The observation that no alternatives to a theory have been found might be overridden by future observations that scientists do find alternatives. That later observation would reduce the trust in the initial theory and therefore amount to that theory's non-empirical dis-confirmation. Likewise, an observed trend of predictive success in a research field could later be overridden by a series of instances where a theory that was well trusted on non-empirical grounds turned out to disagree with empirical tests once they became possible. In the case of UEA, the observation that no unexpected explanatory interconnections show up would be taken to speak against a theory's viability. And once unexpected interconnections have been found, it could still happen that a more careful conceptual analysis reveals them to be the result of elementary structural characteristics of theory building in the given context that are not confined to the specific theory in question. To conclude, the three non-empirical arguments are not structurally biased in favour of confirmation but may just as well provide indications against a theory's viability.

Next, I briefly want to touch a more philosophical level of analysis. Empirical confirmation is based on a prediction of the confirmed theory that agrees with an observation. In the case of non-empirical confirmation, to the contrary, the confirming observations are not predicted by the theory. How can one understand the mechanism that makes those observations confirm the theory?

It turns out that an element of successful prediction is involved in non-empirical confirmation as well. That element, however, is placed at the meta-level of understanding the context of theory building. More specifically, the claim that is tested at the meta-level is a claim on the spectrum of possible scientific alternatives to the known theory. NAA, MIA and UEA all support the meta-level hypothesis that the spectrum of unconceived scientific alternatives to the theory in question is very limited. That implication can indeed be directly inferred from the fact that the metalevel hypothesis increases the probability of the observations on which NAA, MIA and UEA are based. So, at the metalevel we do find the same argumentative structure that can be found at the ground level in the case of empirical confirmation.

Let us, for the sake of simplicity, just consider the most extreme form of the meta-level hypothesis, namely the hypothesis that, in all research contexts in the scientific field, there are no possible alternatives to the viable theory at all. This radical hypothesis predicts 1: that no alternatives will be found because there aren't any (NAA); 2: that, given that there exists a predictively successful theory at all, a theory that has been developed in agreement with the available data will always be predictively successful (MIA); and 3: that that a theory that has been developed for one specific reason will explain all other aspects of the given research context as well, because there are no alternatives that could do so (UEA).

A more careful formulation of non-empirical confirmation based on the concept of limitations to the spectrum of possible alternative theories would need to say more on the criteria for accepting a theory as scientific, on how to individuate theories, etc. In this short presentation, it shall suffice to give the general flavour of the line of reasoning: non-empirical confirmation is a natural extension of empirical confirmation that places the agreement between observation and the prediction of a hypothesis at the meta-level of theory dynamics rather than at the ground level of the theory's predictions.

An instructive way of clarifying the mechanism of non-empirical confirmation and its close relation to empirical confirmation consists in formalizing the arguments within the framework of Bayesian confirmation theory. An analysis of this kind has been carried out for NAA (which is the simplest case) in "The No Alternatives Argument", Dawid, Hartmann and Sprenger BJPS 66(1), 213-34, 2015.

A number of worries have been raised with respect to the concept of non-empirical confirmation. Let me, in the last part of this text, address a few of them.

It has been argued – especially by someone who has increasingly loved to "reduce physics to sociology" – that arguments of non-empirical confirmation are sociological and therefore don't constitute proper scientific reasoning. This claim may be read in two different ways. In its radical form, it would amount to the statement that there is no factual scientific basis to non-empirical confirmation at all. Confidence in a theory on that account would be driven entirely by sociological mechanisms in the physics community and only be camouflaged ex post by fake rational reasoning. The present text in its entirety aims at demonstrating that such an understanding of non-empirical confirmation is highly inadequate.

A more moderate reading of the sociology claim is the following: there may be a factual core to non-empirical confirmation, but it is so difficult to disentangle from sociological factors that science is better off if non-empirical confirmation is discarded. I concede that the role of sociology is trickier with respect to deployments of non-empirical confirmation than in cases where conclusive empirical confirmation is to be had. But I would argue that it must always be the aim of good science to extract all factual information that is provided by an investigation. If the existence of a sociological element in scientific analysis would justify discarding that analysis, quite some empirical data analysis had to be discarded as well.

To give a recent example, the year 2015 witnessed considerable differences of opinion among physicists interpreting the empirical data collected by BICEP2. Those differences of opinion may be explained to a certain degree by sociological factors involved. No-one would have suggested to discard the debate on the interpretation of the BICEP2 data as scientifically worthless on those grounds. I suggest that the very same point of view should also be taken with respect to non-empirical confirmation.

It has also been suggested (e.g. by George Ellis and Joseph Silk) that non-empirical confirmation may lead to a disregard for empirical data and therefore to the abandonment of a pivotal principle of scientific reasoning.

This worry is based on a misreading of non-empirical confirmation. Accepting the importance of non-empirical confirmation by no means devaluates the search for empirical confirmation. To the contrary, empirical confirmation is crucial for the functioning of non-empirical confirmation in two ways. Firstly, non-empirical confirmation indicates the viability of a theory. But, as I said earlier, a theory's viability is defined as: the theory's empirical predictions would turn out correct if they could be specified and empirically tested. Conclusive empirical confirmation therefore remains the ultimate judge of a theory's viability - and thus the ultimate goal of science.

Secondly MIA, which is one cornerstone of non-empirical confirmation, relies on empirical confirmation elsewhere in the research field. Therefore, if empirical confirmation was terminated in the entire research field, that would remove the possibility of testing non-empirical confirmation strategies and, in the long run, make them dysfunctional. Non-empirical confirmation itself thus highlights the importance of testing theories empirically whenever possible. It implies, though, that the absence of empirical confirmation must not be equated with knowing nothing about the theory's chances of being viable.

Finally, it has been argued (e.g. by Lee Smolin) that non-empirical confirmation further strengthens the dominant research programs and therefore in an unhealthy way contributes to thinning out the search for alternative perspectives that may turn out productive later on.

To a given extent, that is correct. Taking non-empirical confirmation seriously does support the focus on those research strategies that generate theories with a considerable degree of non-empirical confirmation. I would argue, however, that this is, by and large, a positive effect. It is an important element of successful science to understand which approaches merit further investigations and which don't.

But a very important second point must be added. As discussed above, non-empirical confirmation is a technique for understanding the spectrum of possible alternatives to the theory one knows. One crucial test in that respect is to check whether serious and extensive searches for alternatives have produced any coherent alternative theories (This is the basis for NAA). Therefore, the search for alternatives is a crucial element of non-empirical confirmation. Far from denying the value of the search for alternatives, non-empirical confirmation adds a new reason why it is important: even if the alternative strands of research fail to produce coherent theories, the observation that none of those approaches has succeeded makes an important contribution to the non-empirical confirmation of the theory that is available.

So what is the status of non-empirical confirmation? The arguments I present support the general relevance of non-empirical confirmation in physics. In the absence of empirical confirmation, non-empirical confirmation can provide a strong case for taking a theory to be viable. This does by no means render empirical confirmation obsolete. Conclusive empirical testing will always trump non-empirical confirmation and therefore remains the ultimate goal in science. Arguments of non-empirical confirmation can in some cases lead to a nearly consensual assessment in the physics community (see the trust in the Higgs particle before 2012). In other cases, they can be more controversial.

As in all contexts of scientific inquiry, argumentation stressing non-empirical confirmation can be balanced and well founded but may, in some cases, also be exaggerated and unsound. The actual strength of each specific case of non-empirical confirmation has to be assessed and discussed by the physicists concerned with the given theory based on a careful scientific analysis of the particular case. Criticism of cases of non-empirical confirmation at that level constitutes an integral and important part of theory assessment. I suggest, however, that the whole-sale verdict that non-empirical theory confirmation is unscientific and should not be taken seriously does not do justice to the research process in physics and obscures the actual state of contemporary physics by disregarding an important element of scientific analysis.

Richard Dawid, LMU Munich

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