Is there more that one "Curie's principle"? How far are different formulations legitimate? What are the aspects that make it so scientifically fruitful, independently of how it is formulated? The paper is devoted to exploring these questions. We start with illustrating Curie's original 1894 article and his focus. Then, we consider the way that the discussion of the principle took shape from early commentators to its modern form. We say why we think that the modern focus on the inter-state version (...) of the principle loses sight of some of the most interesting significant applications of the principle. Finally, we address criticism of the principle put forward by Norton and purported counterexamples due to Roberts. (shrink)

Quantum field theories are notoriously difficult to understand, physically as well as philosophically. The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the ’t Hooft limit, in which the theory concerned often simplifies. The idea of the limit is that the number N of colours goes to infinity. The simplifications that can happen in this limit, and that we will consider, are: (...) the theory’s Feynman diagrams can be drawn on a plane without lines intersecting ; and the theory, or a sector of it, becomes integrable, and indeed corresponds to a well-studied system, viz. a spin chain. Planarity is important because it shows how a quantum field theory can exhibit extended, in particular string-like, structures; in some cases, this gives a connection with string theory, and so with its representation of gravity. Previous philosophical literature about how one theory might be emergent from, and-or reduced to, another one has tended to emphasize cases, such as occur in statistical mechanics, where the system before the limit has finitely many degrees of freedom. But here, our quantum field theories, including those on the way to the ’t Hooft limit, will have infinitely many degrees of freedom. Nevertheless, we will show how a recent schema by Butterfield and taxonomy by Norton apply to the quantum field theories we consider; and we will classify three physical properties of our theories in these terms. These properties are planarity and integrability, as in and above; and the behaviour of the beta-function reflecting, for example, asymptotic freedom. Our discussion of these properties, especially the beta-function, will also relate to recent philosophical debate about the propriety of assessing quantum field theories, whose rigorous existence is not yet proven. (shrink)

In his Analysis of Matter, Russell advocated an epistemic form of Epistemic Structural Realism which held that our knowledge of the external world is structural. This approach has been criticised by M.H.A. Newman, 137–148, 1928) and Stathis Psillos, S13–S24, 2001). The paper aims to reconstruct Russell’s version of ESR, and defend its experimental and philosophical plausibility. The basic assumption is that without getting a viable experimental handle on the linkage between the structure of perceptions and causal structure of the stimuli, (...) the so called upward path to SR couldn’t be defended conclusively. In this vein, the paper explores the resources of the recent experimental theories of perception. These help establishing a structuralist account of the perception, and provide an account for the causal linkage between the structure of perceptions and the structure of the stimuli. I argue that it is possible to settle for objectivity of this linkage according to the criteria of comprehensiveness, simplicity, and above all rationality, in a way that meets the standards of the scientific realists. (shrink)

The phenomenon of broken spacetime symmetry in the quantum theory of infinite systems forces us to adopt an unorthodox ontology. We must abandon the standard conception of the physical meaning of these symmetries, or else deny the attractive “liberal” notion of which physical quantities are significant. A third option, more attractive but less well understood, is to abandon the existing (Halvorson-Clifton) notion of intertranslatability for quantum theories.

Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. In this (...) overview we review the current state of affairs on both the philosophy and the physics side. In particular, we focus on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, we determine a set of yet to be answered questions to clarify the status of gauge symmetries. (shrink)

The celu of the philosophical literature on the hole argument is the 1987 paper by Earman \& Norton ["What Price Space-time Substantivalism? The Hole Story" Br. J. Phil. Sci.]. This paper has a well-known back-story, concerning work by Stachel and Norton on Einstein's thinking in the years 1913-15. Less well-known is a connection between the hole argument and Earman's work on Leibniz in the 1970s and 1980s, which in turn can be traced to an argument first presented in 1975 by (...) Howard Stein. Remarkably, this thread originates with a misattribution: the argument Earman attributes to Stein, which ultimately morphs into the hole argument, was not the argument Stein gave. The present paper explores this episode and presents some reflections on how it bears on the subsequent literature. (shrink)

I argue against the currently prevalent view that algebraic quantum field theory (AQFT) is the correct framework for philosophy of quantum field theory and that “conventional” quantum field theory (CQFT), of the sort used in mainstream particle physics, is not suitable for foundational study. In doing so, I defend that position that AQFT and CQFT should be understood as rival programs to resolve the mathematical and physical pathologies of renormalization theory, and that CQFT has succeeded in this task and AQFT (...) has failed. I also defend CQFT from recent criticisms made by Doreen Fraser. (shrink)

The Higgs mechanism gives mass to Yang-Mills gauge bosons. According to the conventional wisdom, this happens through the spontaneous breaking of gauge symmetry. Yet, gauge symmetries merely reflect a redundancy in the state description and therefore the spontaneous breaking can not be an essential ingredient. Indeed, as already shown by Higgs and Kibble, the mechanism can be explained in terms of gauge invariant variables, without invoking spontaneous symmetry breaking. In this paper, we present a general discussion of such gauge invariant (...) treatments for the case of the Abelian Higgs model, in the context of classical field theory. We thereby distinguish between two different notions of gauge: one that takes all local transformations to be gauge and one that relates gauge to a failure of determinism. (shrink)

I discuss Earman's program to achieve an objective account of the Higgs mechanism within the C∗ algebraic approach to quantum field theory. Pointing to three results obtained within this approach, I argue that if one follows Earman and understands the Higgs mechanism as a constraint, it appears to be a genuine quantum phenomenon that does not simply arise through the correspondence principle. This casts further this casts doubts on the validity of the Dirac conjecture that identifies first-class constraints and gauge (...) transformations and that provides a major motivation for both Earman's program and Struyve's demonstration that a gauge-invariant account of the Higgs mechanism can be accomplished at the classical level. (shrink)

The Higgs mechanism is an essential but elusive component of the Standard Model of particle physics. Without it Yang‐Mills gauge theories would have been little more than a warm‐up exercise in the attempt to quantize gravity rather than serving as the basis for the Standard Model. This article focuses on two problems related to the Higgs mechanism clearly posed in Earman’s recent papers (Earman 2003, 2004a, 2004b): what is the gauge‐invariant content of the Higgs mechanism, and what does it mean (...) to break a local gauge symmetry? (shrink)

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is outlined and (...) endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

In this paper I show how certain requirements must be set on any tenable account of scientific representation, such as the requirement allowing for misrepresentation. I then continue to argue that two leading accounts of scientific representation— the inferential account and the interpretational account—are flawed for they do not satisfy such requirements. Through such criticism, and drawing on an analogy from non-scientific representation, I also sketch the outline of a superior account. In particular, I propose to take epistemic representations to (...) be intentional objects that come with reference, semantic contents and a representational code, and I identify faithful representations as representations that act as guides to ontology. (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov– Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a (...) middle ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of (...) said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

This paper analyses the anti-reductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation.

The pairing argument aims to demonstrate the impossibility of non-spatial objects (including minds) standing in causal relations. Its chief premises are (roughly) that causation requires pairing relations between causes and effects and that pairing relations require spatial relations. Critics have argued that the first claim suffers from counterexamples involving indeterministic causation. After briefly rehearsing the pairing argument and the objection from indeterministic causation, I offer two ways of revising the pairing argument to meet the objection from indeterministic causation.

I point out a simple sense in which the standard formulation of Curie’s principle is false when the symmetry transformation it describes is time reversal.

This paper is a tour of how the laws of nature can distinguish between the past and the future, or be T-violating. I argue that, in terms of the basic argumentative structure, there are basically just three approaches currently being explored. The first is an application of Curie's Principle, together with the CPT theorem. The second route makes use of a principle due to Pasha Kabir which allows for a direct detection. The third route makes use of a Non-degeneracy Principle, (...) and is related to the energy spectrum of elementary particles. I show how each provides a general template for detecting T-violation, illustrate each with an example, and discuss their prospects in extensions of particle physics beyond the standard model. (shrink)

Pierre Curie claimed that a symmetry of a cause must be found in the produced effects. This paper shows why this principle works in Curie’s example of the electrostatics of central fields, but fails in many others. The failure of Curie’s claim is then shown to be of special empirical interest, in that this failure underpins the experimental discovery of parity violation and of CP violation in the twentieth century.

I propose a general geometric framework in which to discuss the existence of time observables. This framework allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist subject to a restriction on the vector fields that they generate. Pauli׳s prohibition on quantum time observables is derived as a corollary to this result. I will then discuss how time observables can be regained in modest extensions of quantum theory (...) beyond its standard formulation. (shrink)

In their Every Thing Must Go, Ladyman and Ross defend a novel version of Neo- Russellian metaphysics of causation, which falls into three claims: (1) there are no fundamental physical causal facts (orthodox Russellian claim), (2) there are higher-level causal facts of the special sciences, and (3) higher-level causal facts are explanatorily emergent. While accepting claims (1) and (2), I attack claim (3). Ladyman and Ross argue that higher-level causal facts are explanatorily emergent, because (a) certain aspects of these higher-level (...) facts (their universality) can be captured by renormalization group (RG) explanations, and (b) RG explanations are not reductive explanations. However, I argue that RG explanation should be understood as reductive explanations. This result undermines Ladyman and Ross’s RG-based argument for the explanatory emergence of higher-level causal facts. (shrink)

Curie’s principle asserts that every symmetry of a cause manifests as a symmetry of the effect. It can be formulated as a tautology that is vacuous until it is instantiated. However instantiation requires us to know the correct way to map causal terminology onto the terms of a science. Causal metaphysics has failed to provide a unique, correct way to carry out the mapping. Thus successful or unsuccessful instantiation merely reflects our freedom of choice in the mapping.

This article examines ontological/dynamical aspects of emergence, specifically the micro-macro relation in cases of universal behavior. I discuss superconductivity as an emergent phenomenon, showing why microphysical features such as Cooper pairing are not necessary for deriving characteristic properties such as infinite conductivity. I claim that the difficulties surrounding the thermodynamic limit in explaining phase transitions can be countered by showing how renormalization group techniques facilitate an understanding of the physics behind the mathematics, enabling us to clarify epistemic and ontological aspects (...) of emergence. I close with a discussion of the impact of these issues for questions concerning natural kinds. (shrink)

This paper explores the argument structure of the concept of spontaneous symmetry breaking in the electroweak gauge theory of the Standard Model: the so-called Higgs mechanism. As commonly understood, the Higgs argument is designed to introduce the masses of the gauge bosons by a spontaneous breaking of the gauge symmetry of an additional field, the Higgs field. The technical derivation of the Higgs mechanism, however, consists in a mere reshuffling of degrees of freedom by transforming the Higgs Lagrangian in a (...) gauge-invariant manner. This already raises serious doubts about the adequacy of the entire manoeuvre. It will be shown that no straightforward ontic interpretation of the Higgs mechanism is tenable, since gauge transformations possess no real instantiations. In addition, the explanatory value of the Higgs argument will be critically examined. (shrink)

Some physicists and philosophers argue that unitarily inequivalent representations in quantum field theory are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail and it is (...) proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. _1_ Introduction _2_ Weak Equivalence and Physical Equivalence _3_ Mathematical Overview of Algebraic Quantum Field Theory _4_ Fell’s Theorem and Philosophical Responses to Weak Equivalence _5_ Weak Equivalence in C*-Algebras and W*-Algebras _6_ Classical Equivalence and Weak Equivalence _7_ Interlude: Is Weak Equivalence Really Physical Equivalence? _8_ The Unruh Effect _9_ Time Evolution and Symmetries _10_ Conclusions Appendix. (shrink)

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a (...) long-standing debate on the subject. (shrink)

This paper presents three interesting consequences that follow from admitting an ontology of rigid bodies in classical mechanics. First, it shows that some of the most characteristic properties of supertasks based on binary collisions between particles, such as the possibility of indeterminism or the non-conservation of energy, persist in the presence of gravitational interaction. This makes them gravitational supertasks radically different from those that have appeared in the literature to date. Second, Sect. 6 proves that the role of gravitation in (...) supertasks of this kind may be highly non-trivial. Third,, the gravitational supertasks found in the first part enable us to show that indeterminism of classical mechanics with gravitation is much more general than has been supposed until now. This result is especially interesting from the philosophical viewpoint, as it links the scope of indeterminism in a theory like classical mechanics directly with the nature of its ontological hypotheses. (shrink)

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is (...) removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle. (shrink)

In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space–time does not match the generally accepted definition of a black hole (derived from his concept of null infinity). To overcome (...) this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the pde literature. As a compromise, one might say that in “generic” or “physically reasonable” space–times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an “Appendix” by Erik Curiel reviews the early history of the definition of a black hole. (shrink)

This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low probability, their very existence implies that the no-signaling (...) principle used in proofs of randomness of outcomes of quantum-mechanical measurements should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness that in various guises was investigated by Kolmogorov and others and treat Bell’s Theorem and the Free Will Theorem with their implications for randomness. (shrink)

Primitive ontology is a recently much discussed approach to the ontology of quantum theory according to which the theory is ultimately about entities in 3-dimensional space and their temporal evolution. This paper critically discusses the primitive ontologies that have been suggested within the Bohmian approach to quantum field theory in the light of the existence of unitarily inequivalent representations. These primitive ontologies rely either on a Fock space representation or a wave functional representation, which are strictly speaking unambiguously available only (...) for free systems in flat spacetime. As a consequence, it is argued that they do not constitute fundamental ontologies for quantum field theory, in contrast to the case of the Bohmian approach to quantum mechanics. (shrink)

The paper addresses a problem for the unification of quantum physics with the new Aristotelianism: the identification of the members of the category of substance. I outline briefly the role that substance plays in Aristotelian metaphysics, leading to the postulating of the Tiling Constraint. I then turn to the question of which entities in quantum physics can qualify as Aristotelian substances. I offer an answer: the theory of thermal substances, and I construct a fivefold case for thermal substances, based on (...) the irreversibility of time, the definition of thermodynamic concepts, spontaneous symmetry breaking, phase transitions, and chemical form. (shrink)

Curie’s Principle says that any symmetry property of a cause must be found in its effect. In this article, I consider Curie’s Principle from the point of view of graphical causal models, and demonstrate that, under one definition of a symmetry transformation, the causal modeling framework does not require anything like Curie’s Principle to be true. On another definition of a symmetry transformation, the graphical causal modeling formalism does imply a version of Curie’s Principle. These results yield a better understanding (...) of the logical landscape with respect to the relationship between Curie’s Principle and graphical causal modeling. (shrink)

I examine the construction process of the “Higgs mechanism” and its subsequent use by Steven Weinberg to formulate the electroweak theory of elementary particle physics. I characterize the development of the Higgs mechanism as a historical process that was guided through analogies drawn to the theories of solid-state physics and that was progressive through diverse contributions in the sixties from a number of physicists working independently. I also offer a detailed comparative study of the similarities and the differences that exist (...) between the approaches taken in these contributions. (shrink)

We study the Johansen–Ledoit–Sornette model of financial market crashes :219–255, 2000). On our view, the JLS model is a curious case from the perspective of the recent philosophy of science literature, as it is naturally construed as a “minimal model” in the sense of Batterman and Rice :349–376, 2014) that nonetheless provides a causal explanation of market crashes, in the sense of Woodward’s interventionist account of causation.

Howard argues that the existence of unitarily inequivalent representations in Quantum Field Theory presents a problem for structural realism in this context. I consider two potential ways round this problem: 1), follow Wallace in adopting the 'naive' Lagrangian form of QFT with cut-offs; 2), adapt Ruetsche's 'Swiss Army Knife' approach. The first takes us into the current debate between Wallace and Fraser on conventional vs. algebraic QFT. The second involves consideration of the role of inequivalent representations in understanding spontaneous symmetry (...) breaking and quantum statistics. In both cases, I suggest, the structural realist has sufficient room to manoeuvre. (shrink)

The orthodox characterization of spontaneous symmetry breaking in statistical mechanics appeals to novel properties of systems with infinite degrees of freedom, namely, the existence of multiple equilibrium states. This raises the same puzzles about the status of the thermodynamic limit fueling recent debates about phase transitions. I argue that there are prospects of explaining the success of the standard approach to SSB in terms of the properties of large finite systems. Consequently, despite initial appearances, the need to account for SSB (...) phenomena does not offer decisive support to claims about the explanatory and representational indispensability of the thermodynamic limit. (shrink)

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. New arguments are offered for basing the interpretation of QFT (...) on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: [email protected]. (shrink)

To systematically answer the generalized Kretschmann objection, I propose a mean to make operational a criterion widely recognized as allowing one to decide whether the gauge symmetry of a theory is artificial or substantial. My proposition is based on the dressing field method of gauge symmetry reduction, a new simple tool from mathematical physics. This general scheme allows one in particular to straightforwardly argue that the notion of spontaneous symmetry breaking is superfluous to the empirical success of the electroweak theory. (...) Important questions regarding the context of justification of the theory then arise. (shrink)

We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue.

Although the philosophical literature on the foundations of quantum field theory recognizes the importance of Haag’s theorem, it does not provide a clear discussion of the meaning of this theorem. The goal of this paper is to make up for this deficit. In particular, it aims to set out the implications of Haag’s theorem for scattering theory, the interaction picture, the use of non-Fock representations in describing interacting fields, and the choice among the plethora of the unitarily inequivalent representations of (...) the canonical commutation relations for free and interacting fields. (shrink)

According to the Standard Model of particle physics, some gauge transformations are physical symmetries. That is, they are mathematical transformations that relate representatives of distinct physical states of affairs. This is at odds with the standard philosophical position according to which gauge transformations are an eliminable redundancy in a gauge theory's representational framework. In this paper I defend the Standard Model's treatment of gauge from an objection due to Richard Healey. If we follow the Standard Model in taking some gauge (...) transformations to be physical symmetries then we face the “strong CP problem”, but if we adopt the standard philosophical position on gauge then the strong CP problem dissolves. Healey offers this as a reason in favor of the standard philosophical view. However, as I argue here, following Healey's recommendation gives a theory that makes bad empirical predictions. (shrink)

Path-dependence offers a promising way of understanding the role historicity plays in explanation, namely, how the past states of a process can matter in the explanation of a given outcome. The two main existing accounts of path-dependence have sought to present it either in terms of dynamic landscapes or branching trees. However, the notions of landscape and tree both have serious limitations and have been criticized. The framework of causal networks is both more fundamental and more general that that of (...) landscapes and trees. Within this framework, I propose that historicity in networks should be understood as symmetry breaking. History matters when an asymmetric bias towards an outcome emerges in a causal network. This permits a quantitative measure for how path-dependence can occur in degrees, and offers suggestive insights into how historicity is intertwined both with causal structure and complexity. (shrink)

A new form of skepticism is described, which holds that objectivity and understanding are incompossible ideals of modern science. This is attributed to Weyl, hence its name: Weylean skepticism. Two general defeat strategies are then proposed, one of which is rejected.