Abstract
Infinity, in various guises, has been invoked recently in order to ‘explain’ a number of important questions regarding observable phenomena in science, and in particular in cosmology. Such explanations are by their nature speculative. Here we introduce the notions of relative infinity, closure, and economy of explanation and ask: to what extent explanations involving relative or real constructed infinities can be treated as reasonable?
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Notes
The nature and role of ‘unobservables’ or ‘theoretical entities’ in scientific theories has been one of the most crucial points of disagreement in the (at least) last six decades of debates regarding realism and antirealism in the philosophy of science—or arguably since the debate between Mach and Boltzmann on the atomic theory of gasses. It is not our intention to explore its nuances, but we rather start from the realist assumption that (some kinds of) unobservables do indeed play an essential explanatory role in science.
It is important to note that, as opposed to current completeness, the notion of all time completeness of theories is problematic in principle, given that all theories need to stand to be corrected by future observations and, in this sense, must remain open.
It is important to differentiate between those subatomic particles that are directly visible, such as electrons, and those that are only “observable” in an inferential way, as is the case with most such particles—such as Higgs. Such differentiation does not construe observables and unobservables as ontologically distinct (thus opening the door to instrumentalist skepticism); the different terms merely reflecting a methodological difference in our access to them (non-inferential or inferential).
See e.g. Greene (2011) for a number of such scenarios.
It is not easy to give an uncontroversial answer to the question of which branch of physics initiated the contemporary speculative discussion of a plurality (i.e. very large or infinity) of universes. While the Everett interpretation of quantum mechanics dates back to the mid-1950s, and surely had a non-negligible influence outside quantum physics (essentially re-injecting the millennia-old idea of a plurality of worlds with scientific respectability), the concept of Multiverse which emerged after the rise, in the 1980s, of the eternal inflation scenario (Linde 1986; Vilenkin 1983), developed in relative independence from quantum mechanical interpretations. More recently, the so called String Landscape has provided another avenue for postulating a vast number of universes, corresponding to the large number of possible false vacua allowed by String Theory. For the purposes of this paper, it will suffice to note that, being underpinned by an incomplete theory and lacking any observational support or confirmed predictions, such an idea remains speculative. For a comprehensive history of the idea of Multiverse in the XX century, see Kragh (2011). The word multiverse, on the other hand, is usually traced back to William James’ 1895 essay “Is Life Worth Living”, where the American philosopher employs the term in the context of his moral philosophy.
See the classic work of Alexandre Koyre, and his well-known thesis of a crucial passage, specific of modernity, from the closed world to the infinite universe (Koyre 1957).
This is true at least regarding the spatial extent of the Universe. It is interesting to ask if it is possible to establish observationally whether the Universe was in fact past eternal (see for e.g. Mulryne et al. 2005).
For a critique of the intelligibility of the notion of an actual, physical infinite set see Stoeger et al. (2004). Note that our argument does not depend on this ontological assumption: we are more concerned with the epistemological issue of what does and what doesn’t count as an explanatory hypothesis, bracketing the ontological question.
We shall leave the discussion of infinite turn in Philosophy for a future article.
For a recent philosophical defence of the Everettian hypothesis see Wallace (2012).
See, for example, Ellis (2011) for arguments by other authors not proponents of the Multiverse idea.
It is known that dynamical systems can have multiple attractors, but it is extremely difficult to imagine a dynamics arising from a physical theory which gives rise to \(10^{100}\)–\(10^{500}\) number of compactified end states. In fact it is very likely that the number of viable compactifications is in fact far smaller, which raises the question of how they are selected!
Compare the way in which inflation ‘predicts’ eternal inflation and the formation of an infinite number of universes with the way in which General Relativity predicted the (now observationally confirmed) existence of gravitational waves, or the way in which the wave theory of light predicted a bright spot at the centre of a shadow cast by a round object. Note that inflation itself was originally postulated as an inference to the best explanation, in order to account for the observed lack of magnetic monopoles, the flatness of spacetime, and the homogeneity and isotropy of the observable universe. It aims at doing so by offering the description of a physical mechanism responsible for inflation. While 1) the fundamental theory underpinning such a mechanism is not yet fully understood, and 2) there remains the possibility that other non-inflationary explanations might be given in the future for the observations that originally motivated it, we look favourably upon it because, unlike multiverse theories, inflation offers a speculative finite causal explanation (see the next section).
This urge at having a ‘total’ explanation of reality, which is implicitly assumed to be complete and therefore closed, has had a long history in human history.
A recent intervention on the topic of scientific method is that of Dawid (2013), who in the specific context of a defence of the scientific respectability of String Theory, makes the case, more generally, for an enlargement of our criteria for the acceptance of a theory to encompass non-empirical ones. Briefly, Dawid proposes three standards for non-empirical assessment: (1) the No Alternatives Argument, holding that our acceptance of the adequacy of a new theory should increase where no plausible alternatives are present; (2) the Unexpected Explanations Argument, holding that our acceptance of the adequacy of a new theory should increase where it is able to offer explanations for phenomena it was not originally formulated to deliver; (3) the Meta-Inductive Argument, holding the more a new theory is capable of being embedded into a whole of currently accepted and established theories the more we are entitled to believe it. We leave a more detailed discussion of this proposal for a later publication, as it seems to us that a key problem with this it is that, in the absence of experimental verification, there is a danger that the determination of whether these criteria are satisfied becomes subjective. However, provisionally accepting these criteria for the sake of argument, it seems to us that even then the multiverse hypothesis fails, not meeting criteria 1, 2 and arguably even 3.
We here subscribe to a notion of explanation as essentially tied to causation. Wesley Salmon is the philosopher traditionally indicated as re-injecting the concern with causation in the philosophy of explanation, under the general principle that ‘explanatory knowledge is knowledge of the causal mechanisms...that produce the phenomena with which we are concerned’ (Salmon 1989). A more recent account, arguing for a manipulatist account was defended by Woodward (2003), according to whom the distinction between description and explanation resides in the latter offering information in principle useful for manipulation. While the practicality of manipulation is obviously out of the question in a cosmological setting, Woodard observes that the notion can be generalised through the notion of an impersonal ‘intervention’ and understood counterfactually: ‘an explanation ought to be such that it can be used to answer what we call a what-if-things-had-been-different question: the explanation must enable us to see what sort of difference it would have made for the explanandum if the factors cited in the explanans had been different in various possible ways, that is to say if an intervention in cause X would have brought about a change in effect Y. The Multiverse scenario clearly fails to meet this criterion for being an explanation: the conditions leading to the present universe in fact were (are?) distributed across a very large (or infinite) space of actually existing possibilities where either everything vacuously explains everything else, or nothing explains anything at all.
Thus we want to ward ourselves against a potential misreading of our argument: we fully endorse the secularising drive of cosmological de-centring, and the ejection of anthropocentric notions from physical cosmology, but these cannot be used as a premise for scientific inquiry).
A non-zero cosmological constant of an appropriate size could in principle account for the observed puzzling late acceleration of the Universe, while being compatible with all other known cosmological observations. A crucial question is why does this constant take the value it has. Here we are leaving aside the fundamental question of whether this is the only way to explain the late acceleration of the Universe (see e.g. Clifton et al. 2012; Tsujikawa 2010; Clifton et al. 2012) for other scenarios for possible explanations of the late acceleration).
We are not claiming that all explanations need be causal explanations. But we are claiming that, in fields like fundamental physics and cosmology causal explanations in fact are the kinds of explanation which are required for an understanding of the phenomena.
As well as, regrettably, religious ones.
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Acknowledgments
We would like to thank Andreas Brandhuber, Peter Cameron, Bernard Carr, George Ellis, Roy Maartens and Sanjaye Ramgoolam for helpful discussions and comments.
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Tavakol, R., Gironi, F. The Infinite Turn and Speculative Explanations in Cosmology. Found Sci 22, 785–798 (2017). https://doi.org/10.1007/s10699-016-9499-2
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DOI: https://doi.org/10.1007/s10699-016-9499-2