Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, using examples (...) from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones are: : I defend the traditional Nagelian conception of reduction ; : I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' ; : I stress the collapse of supervenience into deduction via Beth's theorem ; : I adapt some examples already in the literature to show supervenience without emergence and vice versa. (shrink)

This book argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, this book demonstrates how to build a metaphysics compatible with current fundamental physics, which, when combined (...) with metaphysics of the special sciences, can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, this book argues, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. The text assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the books' metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism versus empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds. (shrink)

We reconsider the Nagelian theory of reduction and argue that, contrary to a widely held view, it is the right analysis of intertheoretic reduction. The alleged difficulties of the theory either vanish upon closer inspection or turn out to be substantive philosophical questions rather than knock-down arguments.

The epistemic conception of scientific progress equates progress with accumulation of scientific knowledge. I argue that the epistemic conception fails to fully capture scientific progress: theoretical progress, in particular, can transcend scientific knowledge in important ways. Sometimes theoretical progress can be a matter of new theories ‘latching better onto unobservable reality’ in a way that need not be a matter of new knowledge. Recognising this further dimension of theoretical progress is particularly significant for understanding scientific realism, since realism is naturally (...) construed as the claim that science makes theoretical progress. Some prominent realist positions are best understood in terms of commitment to theoretical progress that cannot be equated with accumulation of scientific knowledge. (shrink)

The epistemic conception of scientific progress equates progress with accumulation of scientific knowledge. I argue that the epistemic conception fails to fully capture scientific progress: theoretical progress, in particular, can transcend scientific knowledge in important ways. Sometimes theoretical progress can be a matter of new theories ‘latching better onto unobservable reality’ in a way that need not be a matter of new knowledge. Recognising this further dimension of theoretical progress is particularly significant for understanding scientific realism, since realism is naturally (...) construed as the claim that science makes theoretical progress. Some prominent realist positions are best understood in terms of commitment to theoretical progress that cannot be equated with accumulation of scientific knowledge. (shrink)

Reduction between theories in physics is often approached as an a priori relation in the sense that reduction is often taken to depend only on a comparison of the mathematical structures of two theories. I argue that such approaches fail to capture one crucial sense of “reduction,” whereby one theory encompasses the set of real behaviors that are well-modeled by the other. Reduction in this sense depends not only on the mathematical structures of the theories, but also on empirical facts (...) about where our theories succeed at describing real systems, and is therefore an a posteriori relation. (shrink)

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum–classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \, and, on the other, a certain generalization of Ehrenfest’s Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization (...) establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models. (shrink)

The reduction from Einstein's to Newton's gravitation theories (and intermediate steps) is used to exemplify reduction in physical theories. Both dimensionless and dimensional reduction are presented, and the advantages and disadvantages of each are pointed out. It is concluded that neither a completely reductionist nor a completely antireductionist view can be maintained. Only the mathematical structure is strictly reducible. The interpretation (the model, the central concepts) of the superseded theory T′ can at best only partially be derived directly from the (...) superseding theory T; it is severely constrained by the mathematical structure, and it can involve qualitatively different central terms that cannot be logically related between T and T′. (shrink)

In metaphysics, the fundamental is standardly equated with that which has no explana- tion – with that which is, in other words, ‘brute’. But this doctrine of brutalism is in tension with physicists’ ambitions to not only describe but also explain why the fundamental is as it is. The tension would ease were science taken to be incapable of furnishing the sort of explanations that brutalism is concerned with, given that these are understood to be dis- tinctively ‘metaphysical’ in character. (...) But to assume this is to assume a sharp demarcation between physics and metaphysics that surely cannot be taken for granted. This paper sets out to examine the standing of brutalism from the perspective of contem- porary fundamental physics, together with theories of explanation drawn from philosophy of science and metaphysics. Focusing on what fundamental kinds the world instantiates and how physicists go about determining them, I argue that a partial explanation, in Hempel’s sense, may be given of this fundamental feature. Moreover, since this partial explanation issues, at least in part, from stipulations as to the essential nature of the kinds involved, I claim that it has as much right to be regarded as a metaphysical explanation as do grounding explanations. As such, my conclusion will be that the doctrine of brutalism can no longer be regarded as tenable: at least modulo certain plausible essentialist assumptions, it is no longer the case that no explanation can be given of the fundamental. (shrink)

Weyl symmetry of the classical bosonic string Lagrangian is broken by quantization, with profound consequences described here. Reimposing symmetry requires that the background space-time satisfy the equations of general relativity: general relativity, hence classical space-time as we know it, arises from string theory. We investigate the logical role of Weyl symmetry in this explanation of general relativity: it is not an independent physical postulate but required in quantum string theory, so from a certain point of view it plays only a (...) formal role in the explanation. (shrink)

Intertheoretic reduction in physics aspires to be both to be explanatory and perfectly general: it endeavors to explain why an older, simpler theory continues to be as successful as it is in terms of a newer, more sophisticated theory, and it aims to relate or otherwise account for as many features of the two theories as possible. Despite often being introduced as straightforward cases of intertheoretic reduction, candidate accounts of the reduction of general relativity to Newtonian gravitation have either been (...) insufficiently general or rigorous, or have not clearly been able to explain the empirical success of Newtonian gravitation. Building on work by Ehlers and others, I propose a different account of the reduction relation that is perfectly general and meets the explanatory demand one would make of it. In doing so, I highlight the role that a topology on the collection of all spacetimes plays in defining the relation, and how the selection of the topology corresponds with broader or narrower classes of observables that one demands be well-approximated in the limit. (shrink)

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

We argue for enlarging the traditional view of quantum gravity, based on ‘quantizing GR’, to include explicitly the non-spatiotemporal nature of the fundamental building blocks suggested by several modern quantum gravity approaches, and to focus more on the issue of the emergence of continuum spacetime and geometry from their collective dynamics. We also discuss some recent developments in quantum gravity research, aiming at realising these ideas, in the context of group field theory, random tensor models, simplicial quantum gravity, loop quantum (...) gravity, spin foam models. (shrink)