Reductionism,emergence, and effective field theories

In recent years, a “change in attitude” in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.     

Einstein and the Kaluza–Klein particle

In his search for a unified field theory that could undercut quantum mechanics, Einstein considered five-dimensional classical Kaluza–Klein theory. He studied this theory most intensively during the years 1938–1943. One of his primary objectives was finding a non-singular particle solution. In the full theory this search got frustrated, and in the x⁵-independent theory Einstein, together with Pauli, argued it would be impossible to find these structures.     

Suppressing spacetime emergence

One of the primary tasks in building a quantum theory of gravity is discovering how to save spatiotemporal phenomena using a theory which, putatively, does not include spacetime. Some have taken this task a step further and argue for the actual emergence of spacetime from a non-spatiotemporal ontology in the low-energy regime. In this paper, it is argued that the account of spacetime emergence presented in Huggett and Wüthrich (2013) and then assumed in Baron (2019), Crowther (2016), Wüthrich (2017), and Wüthrich and Lam (2018) fails to accomplish the task to which it is set. There is a prima facie contradiction between the scale-independent ontology of spacetime in GR and the scale-dependent account of emergence proposed by this literature. One can avoid this contradiction but only at the cost of changing the target of emergence and by endorsing a perspectival theory of ontology – a view I call “ontic-perspectivism”. Though this paper explicitly addresses spacetime emergence, many of the following arguments are applicable to other accounts where objects of ontology, or their properties, are claimed to emerge in the low-energy regime.     

“Local–Global”: the first twenty years

This paper investigates how and when pairs of terms such as “local–global” and “im Kleinen–im Grossen” began to be used by mathematicians as explicit reflexive categories. A first phase of automatic search led to the delineation of the relevant corpus, and to the identification of the period from 1898 to 1918 as that of emergence. The emergence appears to have been, from the very start, both transdisciplinary (function theory, calculus of variations, differential geometry) and international, although the AMS-Göttingen connection played a specific part. First used as an expository and didactic tool (e.g. by Osgood), it soon played a crucial part in the creation of new mathematical concepts (e.g. in Hahn’s work), in the shaping of research agendas (e.g. Blaschke’s global differential geometry), and in Weyl’s axiomatic foundation of the manifold concept. We finally turn to France, where in the 1910s, in the wake of Poincaré’s work, Hadamard began to promote a research agenda in terms of “passage du local au general.”     

Kuhn, the correspondence theory of truth and coherentist epistemology

Kuhn argued against both the correspondence theory of truth and convergent realism. Although he likely misunderstood the nature of the correspondence theory, which it seems he wrongly believed to be an epistemic theory, Kuhn had an important epistemic point to make. He maintained that any assessment of correspondence between beliefs and reality is not possible, and therefore, the acceptance of beliefs and the presumption of their truthfulness has to be decided on the basis of other criteria. I will show that via Kuhn’s suggested epistemic values, specifically via problem-solving, his philosophy can be incorporated into a coherentist epistemology. Further, coherentism is, in principle, compatible with convergent realism. However, an argument for increasing likeness to truth requires appropriate historical continuity. Kuhn maintained that the history of science is full of discontinuity, and therefore, the historical condition of convergent realism is not satisfied.     

Emergence in holographic scenarios for gravity

‘Holographic’ relations between theories have become an important theme in quantum gravity research. These relations entail that a theory without gravity is equivalent to a gravitational theory with an extra spatial dimension. The idea of holography was first proposed in 1993 by Gerard ׳t Hooft on the basis of his studies of evaporating black holes. Soon afterwards the holographic ‘AdS/CFT’ duality was introduced, which since has been intensively studied in the string theory community and beyond. Recently, Erik Verlinde has proposed that even Newton׳s law of gravitation can be related holographically to the ‘thermodynamics of information’ on screens. We discuss these scenarios, with special attention to the status of the holographic relation in them and to the question of whether they make gravity and spacetime emergent. We conclude that only Verlinde׳s scheme straightforwardly instantiates emergence. However, assuming a non-standard interpretation of AdS/CFT may create room for the emergence of spacetime and gravity there as well.     

A tale of three theories: Feyerabend and Popper on progress and the aim of science

In this paper, three theories of progress and the aim of science are discussed: (i) the theory of progress as increasing explanatory power, advocated by Popper in The logic of scientific discovery (1935/1959); (ii) the theory of progress as approximation to the truth, introduced by Popper in Conjectures and refutations (1963); (iii) the theory of progress as a steady increase of competing alternatives, which Feyerabend put forward in the essay “Reply to criticism. Comments on Smart, Sellars and Putnam” (1965) and defended as late as the last edition of Against method (1993). It is argued that, contrary to what Feyerabend scholars have predominantly assumed, Feyerabend's changing attitude towards falsificationism—which he often advocated at the beginning of his career, and vociferously attacked in the 1970s and 1980s—must be explained by taking into account not only Feyerabend's very peculiar view of the aim of science, but also Popper's changing account of progress.     

The rhetorical strategy of William Paley’s Natural theology (1802): Part 1, William Paley’s Natural theology in context

This article reconstructs the historical and philosophical contexts of William Paley’s Natural theology (1802). In the wake of the French Revolution, widely believed to be the embodiment of an atheistic political credo, the refutation of the transmutational biological theories of Buffon and Erasmus Darwin was naturally high on Paley’s agenda. But he was also responding to challenges arising from his own moral philosophy, principally the psychological quandary of how men were to be kept in mind of the Creator. It is argued here that Natural theology was the culmination of a complex rhetorical scheme for instilling religious impressions that would increase both the virtue and happiness of mankind. Philosophy formed an integral part of this strategy, but it did not comprise the whole of it. Equally vital were those purely rhetorical aspects of the discourse which, according to Paley, were more concerned with creating ‘impression’. This facet of his writing is explored in part one of this two-part article. Turning to the argumentative side of the scheme, part two examines Paley’s responses to David Hume and Erasmus Darwin in the light of the wider strategy of inculcation at work throughout all his writings.     

The methodological origins of Newton’s queries

This paper analyses the different ways in which Isaac Newton employed queries in his writings on natural philosophy. It is argued that queries were used in three different ways by Newton and that each of these uses is best understood against the background of the role that queries played in the Baconian method that was adopted by the leading experimenters of the early Royal Society. After a discussion of the role of queries in Francis Bacon’s natural historical method, Newton’s queries in his Trinity Notebook are shown to reveal the influence of his early reading in the new experimental philosophy. Then after a discussion of Robert Hooke’s view of the role of queries, the paper turns to an assessment of Newton’s correspondence and Opticks. It is argued that the queries in his correspondence with Oldenburg on his early optical experiments are closely tied to an experimental program, whereas the queries in the Opticks are more discursive and speculative, but that each of these uses of queries represents a significant Baconian legacy in his natural philosophical methodology.     

Mechanisms,the interventionist theory,and the ability to use causal relationships

In the area of social science, in particular, although we have developed methods for reliably discovering the existence of causal relationships, we are not very good at using these to design effective social policy. Cartwright argues that in order to improve our ability to use causal relationships, it is essential to develop a theory of causation that makes explicit the connections between the nature of causation, our best methods for discovering causal relationships, and the uses to which these are put. I argue that Woodward's interventionist theory of causation is uniquely suited to meet Cartwright's challenge. More specifically, interventionist mechanisms can provide the bridge from ‘hunting causes’ to ‘using them’, if interventionists (i) tell us more about the nature of these mechanisms, and (ii) endorse the claim that it is these mechanisms—or whatever constitutes them—that make causal claims true. I illustrate how having an understanding of interventionist mechanisms can allow us to put causal knowledge to use via a detailed example from organic chemistry.     

Formal and physical equivalence in two cases in contemporary quantum physics

The application of analytic continuation in quantum field theory (QFT) is juxtaposed to T-duality and mirror symmetry in string theory. Analytic continuation—a mathematical transformation that takes the time variable t to negative imaginary time—it—was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean approaches within mainstream QFT (e.g., Wilsonian renormalization group methods, lattice gauge theories) and the Euclidean field theory program for rigorously constructing non-perturbative models of interacting QFTs. A crucial difference between theories related by duality transformations and those related by analytic continuation is that the former are judged to be physically equivalent while the latter are regarded as physically inequivalent. There are other similarities between the two cases that make comparing and contrasting them a useful exercise for clarifying the type of argument that is needed to support the conclusion that dual theories are physically equivalent. In particular, T-duality and analytic continuation in QFT share the criterion for predictive equivalence that two theories agree on the complete set of expectation values and the mass spectra and the criterion for formal equivalence that there is a “translation manual” between the physically significant algebras of observables and sets of states in the two theories. The analytic continuation case study illustrates how predictive and formal equivalence are compatible with physical inequivalence, but not in the manner of standard underdetermination cases. Arguments for the physical equivalence of dual theories must cite considerations beyond predictive and formal equivalence. The analytic continuation case study is an instance of the strategy of developing a physical theory by extending the formal or mathematical equivalence with another physical theory as far as possible. That this strategy has resulted in developments in pure mathematics as well as theoretical physics is another feature that this case study has in common with dualities in string theory.     

Un-conventional wisdom: theory-specificity in Reichenbach's geometric conventionalism

The standard account portrays Hans Reichenbach's argument for geometric conventionalism as based upon general epistemological concerns of verifiability. As such, his version of conventionalism ought to be equally well applicable to all theories that posit a geometric structure to space–time. But when Reichenbach's writings from the period between the publication of Relativitätstheorie und Erkenntnis Apriori and Axiomatik der Raum-Zeit-Lehre, i.e., between 1920 and 1924, are examined, a very different picture emerges. The argument for the conventionality of geometry that appears in these writings is tied to discussions of the theory of general relativity and Reichenbach explicitly argues that geometry in Minkowski space–time is not conventional once the definition of simultaneity is put in place. In light of this, the received interpretation of Reichenbach's position needs to be replaced with a theory-specific picture of geometric conventionalism. This change has interesting consequences for both the standard arguments against Reichenbach's view and for questions in Reichenbach scholarship.     

John Hunter and his approach to pathology

Given the old conception of the relation greater than, the proposition that the whole is greater than the part is an immediate consequence. But being greater in this sense is not incompatible with being equal in the sense of one-one correspondence. Some who failed to recognize this formulated invalid arguments against the possibility of infinite quantities. Others who did realize that the relations of equal and greater when so defined are compatible, concluded that such relations are not appropriately taken as quantitative relations, at least, not in general. If suitable quantitative relations were to be defined, there was a possibility of retaining either the traditional definition of greater and finding another concept of equality, or of retaining the concept of equality as one-one correspondence and defining greater than so that it is incompatible with equality in this sense. The former alternative was implicitly taken by Bolzano, who never succeeded in defining suitable quantitative relations. The latter alternative was taken by Cantor, and is the basis of his great success in constructing a mathematical theory of the transfinite.     

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.     

Ramsey sentences, structural realism and trivial realization

Several recent authors identify structural realism about scientific theories with the claim that the content of a scientific theory is expressible using its Ramsey sentence. Many of these authors have also argued that so understood, the view collapses into empiricist anti-realism, since an argument originally proposed by Max Newman in a review of Bertrand Russell’s The analysis of matter demonstrates that Ramsey sentences are trivially satisfied, and cannot make any significant claims about unobservables. In this paper I argue against both of these claims. Structural realism and Ramsey sentence realism are, in their most defensible versions, importantly different doctrines, and neither is committed to the premises required to demonstrate that they collapse into anti-realism.     

Francesco Patrizi’s two books on space: geometry, mathematics, and dialectic beyond Aristotelian science

Francesco Patrizi was a competent Greek scholar, a mathematician, and a Neoplatonic thinker, well known for his sharp critique of Aristotle and the Aristotelian tradition. In this article I shall present, in the first part, the importance of the concept of a three-dimensional space which is regarded as a body, as opposed to the Aristotelian two-dimensional space or interval, in Patrizi’s discussion of physical space. This point, I shall argue, is an essential part of Patrizi’s overall critique of Aristotelian science, in which Epicurean, Stoic, and mainly Neoplatonic elements were brought together, in what seems like an original theory of space and a radical revision of Aristotelian physics. Moreover, I shall try to show Patrizi’s dialectical method of definition, his geometrical argumentation, and trace some of the ideas and terms used by him back to Proclus’ Commentary on Euclid. This text of Proclus, as will be shown in the second part of the article, was also important for Patrizi’s discussion of mathematical space, where Patrizi deals with the status of mathematics and redefines some mathematical concepts such as the point and the line according to his new theory of space.     

(Mis)Understanding scientific disagreement: Success versus pursuit-worthiness in theory choice

Scientists often diverge widely when choosing between research programs. This can seem to be rooted in disagreements about which of several theories, competing to address shared questions or phenomena, is currently the most epistemically or explanatorily valuable—i.e. most successful. But many such cases are actually more directly rooted in differing judgments of pursuit-worthiness, concerning which theory will be best down the line, or which addresses the most significant data or questions. Using case studies from 16^th-century astronomy and 20^th-century geology and biology, I argue that divergent theory choice is thus often driven by considerations of scientific process, even where direct epistemic or explanatory evaluation of its final products appears more relevant. Broadly following Kuhn's analysis of theoretical virtues, I suggest that widely shared criteria for pursuit-worthiness function as imprecise, mutually-conflicting values. However, even Kuhn and others sensitive to pragmatic dimensions of theory ‘acceptance’, including the virtue of fruitfulness, still commonly understate the role of pursuit-worthiness—especially by exaggerating the impact of more present-oriented virtues, or failing to stress how ‘competing’ theories excel at addressing different questions or data. This framework clarifies the nature of the choice and competition involved in theory choice, and the role of alternative theoretical virtues.     

Why history matters to philosophy of physics

Naturalized metaphysics remains the default presupposition of much contemporary philosophy of physics. As metaphysics is supposed to concern the general structure of reality, so scientific naturalism draws upon our best physical theories to attempt to answer the foundational question “par excellence ” viz., “how could the world possibly be the way this theory says it is?” A particular case study, Hilbert's attempt to analyze and explain a seeming “pre-established harmony” between mind and nature, is offered as a salutary reminder that naturalism's ready inference from physical theory to ontology may be too quick.     

Foundations of quantum gravity: The role of principles grounded in empirical reality

When attempting to assess the strengths and weaknesses of various principles in their potential role of guiding the formulation of a theory of quantum gravity, it is crucial to distinguish between principles which are strongly supported by empirical data – either directly or indirectly – and principles which instead (merely) rely heavily on theoretical arguments for their justification. Principles in the latter category are not necessarily invalid, but their a priori foundational significance should be regarded with due caution. These remarks are illustrated in terms of the current standard models of cosmology and particle physics, as well as their respective underlying theories, i.e., essentially general relativity and quantum (field) theory. For instance, it is clear that both standard models are severely constrained by symmetry principles: an effective homogeneity and isotropy of the known universe on the largest scales in the case of cosmology and an underlying exact gauge symmetry of nuclear and electromagnetic interactions in the case of particle physics. However, in sharp contrast to the cosmological situation, where the relevant symmetry structure is more or less established directly on observational grounds, all known, nontrivial arguments for the “gauge principle” are purely theoretical (and far less conclusive than usually advocated). Similar remarks apply to the larger theoretical structures represented by general relativity and quantum (field) theory, where – actual or potential – empirical principles, such as the (Einstein) equivalence principle or EPR-type nonlocality, should be clearly differentiated from theoretical ones, such as general covariance or renormalizability. It is argued that if history is to be of any guidance, the best chance to obtain the key structural features of a putative quantum gravity theory is by deducing them, in some form, from the appropriate empirical principles (analogous to the manner in which, say, the idea that gravitation is a curved spacetime phenomenon is arguably implied by the equivalence principle). Theoretical principles may still be useful however in formulating a concrete theory (analogous to the manner in which, say, a suitable form of general covariance can still act as a sieve for separating theories of gravity from one another). It is subsequently argued that the appropriate empirical principles for deducing the key structural features of quantum gravity should at least include (i) quantum nonlocality, (ii) irreducible indeterminacy (or, essentially equivalently, given (i), relativistic causality), (iii) the thermodynamic arrow of time, (iv) homogeneity and isotropy of the observable universe on the largest scales. In each case, it is explained – when appropriate – how the principle in question could be implemented mathematically in a theory of quantum gravity, why it is considered to be of fundamental significance and also why contemporary accounts of it are insufficient. For instance, the high degree of uniformity observed in the Cosmic Microwave Background is usually regarded as theoretically problematic because of the existence of particle horizons, whereas the currently popular attempts to resolve this situation in terms of inflationary models are, for a number of reasons, less than satisfactory. However, rather than trying to account for the required empirical features dynamically, an arguably much more fruitful approach consists in attempting to account for these features directly, in the form of a lawlike initial condition within a theory of quantum gravity.