The article provides a compact review of the early modern science views of the nature of science, scientific method and knowledge, rationality and objectivity with respect to masculinity and femininity. Following primarily Galileo and Bacon's work, the author is interested in pointing out the most important ideas of the historically fixed ways of how people imagined the acquisition of knowledge, presented nature, understood the role of researchers, as well as what metaphors they applied in defining knowledge. Due to the vast (...) and diverse material, the aim is not to sketch a complete and detailed portrait of the ideal of modern science, but to explore to what extent gender-related issues were of any significance here. (shrink)

Timelines is an inquiry into the nature of time, both as an apparent feature of the external physical world and as a fundamental feature of our experience of ourselves in the world. The principal argument of Timelines is that our coventional ideas about time are largely mistaken and that what we think of as independent physical time is actually our calibration of a certain relation between events. Namely, the relation between time-keeping events and the causal sequential differences of physical processes (...) which are real and independent of us. (shrink)

I consider a number of reasons one might think we should only accept epistemic dilemmas in our normative epistemology as a last resort and argue that none of them is compelling.

According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...) allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (shrink)

Both biosemiotics and evolutionary epistemology are concerned with how knowledge evolves. (Applied) Evolutionary Epistemology thereby focuses on identifying the units, levels, and mechanisms or processes that underlie the evolutionary development of knowing and knowledge, while biosemiotics places emphasis on the study of how signs underlie the development of meaning. We compare the two schools of thought and analyze how in delineating their research program, biosemiotics runs into several problems that are overcome by evolutionary epistemologists. For one, by emphasizing signs, biosemiotics (...) needs to delineate a semiotic threshold, which is a problem not encountered by evolutionary epistemologists. Instead, the latter recognizes that all organisms are knowers that evolve knowledge, which they recognize to extend toward phenomena produced by organisms such as behavior, cognition, language, culture, science, and technology. Secondly, biosemiotics attempts at continuing adaptationist notions on how organisms relate to their environment, while especially Applied Evolutionary Epistemology comes to redefine the nature of the organism–environment relationship in such a way that it recognizes the spatiotemporal boundedness of existence, which in turn makes adaptationist accounts obsolete. (shrink)

Symmetries in physics are a guide to reality. That much is well known. But what is less well known is why symmetry is a guide to reality. What justifies inferences that draw conclusions about reality from premises about symmetries? I argue that answering this question reveals that symmetry is an epistemic notion twice over. First, these inferences must proceed via epistemic lemmas: premises about symmetries in the first instance justify epistemic lemmas about our powers of detection, and only from those (...) epistemic lemmas can we draw conclusions about reality. Second, in order to justify those epistemic lemmas, the notion of symmetry must be defined partly in epistemic terms. 1 Symmetry-to-Reality Reasoning1.1 A rough introduction to symmetry1.2 The symmetry-to-reality inference1.3 Two questions1.4 Two answers1.5 Preliminary clarifications2 Against Redundancy2.1 Redundancy2.2 Is absolute velocity redundant?2.3 Some redundancies3 Against Objectivity4 From Symmetry to Detection4.1 The epistemic approach4.2 The Occamist norm4.3 From symmetry to detection5 The Meaning of ‘Symmetry’5.1 A framework5.2 Formal definitions5.3 Ontic definitions6 Epistemic Definitions6.1 Taking observation seriously6.2 How things look6.3 Observation sentences6.4 Observational equivalence7 Symmetry as an Epistemic Notion 7.1 Observational equivalence and metaphysics7.2 The Occamist norm revisted7.3 Consequences8 Conclusion. (shrink)

Simone Weil is widely recognized today as one of the profound religious thinkers of the twentieth century. Yet while her interpretation of natural science is critical to Weil's overall understanding of religious faith, her writings on science have received little attention compared with her more overtly theological writings. The present essay, which builds on Vance Morgan's Weaving the World: Simone Weil on Science, Necessity, and Love (2005), critically examines Weil's interpretation of the history of science. Weil believed that mathematical science, (...) for the ancient Pythagoreans a mystical expression of the love of God, had in the modern period degenerated into a kind of reification of method that confuses the means of representing nature with nature itself. Beginning with classical (Newtonian) science's representation of nature as a machine, and even more so with the subsequent assimilation of symbolic algebra as the principal language of mathematical physics, modern science according to Weil trades genuine insight into the order of the world for symbolic manipulation yielding mere predictive success and technological domination of nature. I show that Weil's expressed desire to revive a Pythagorean scientific approach, inspired by the "mysterious complicity" in nature between brute necessity and love, must be recast in view of the intrinsically symbolic character of modern mathematical science. I argue further that a genuinely mystical attitude toward nature is nascent within symbolic mathematical science itself. (shrink)

Interest in thought experiments (TEs) derives from the paradox: “How can findings that carry conviction result from a new experiment conducted entirely within the head?” Historical studies have established the importance of TEs in science but have proposed disparate hypotheses concerning the source of knowledge in TEs, ranging from empiricist to rationalist accounts. This article analyzes TEs in think‐aloud protocols of scientifically trained experts to examine more fine‐grained information about their use. Some TEs appear powerful enough to discredit an existing (...) theory—a disconfirmatory purpose. In addition, confirmatory and generative purposes were identified for other TEs. One can also use details in transcript data, including imagery reports and gestures, to provide evidence for a central role played by imagistic simulations in many TEs, and to suggest that these simulations can generate new knowledge using several sources, including the “extended application” of perceptual motor schemas, implicit prior knowledge, and spatial reasoning operations, in contrast to formal arguments. These sources suggest what it means for TEs to be grounded in embodied processes that can begin to explain the paradox above. This leads to a rationalistic view of TEs as using productive internal reasoning, but the view also acknowledges the historical role that experience with the world can play in forming certain schemas used in TEs. Understanding such processes could help provide a foundation for developing a larger model of scientific investigation processes grounded on imagistic simulation (Clement, 2008). (shrink)

This paper aims to characterise properly entanglement as an external relation obtaining between multiple quantum degrees of freedom. In particular, we argue that the entanglement relation is a unique relation fully characterised by mutual information, i.e. a quantity standardly used as a measure of entanglement. This analysis leads us to propose a new metaphysical account of entanglement, which we call Relational Entanglement Tesseract. Such an account characterises entanglement for both bipartite and multipartite cases, and, at the same time, it satisfies (...) what we argue are three important desiderata of any metaphysical account of entanglement. (shrink)

This book brings together papers from a conference that took place in the city of L'Aquila, 4–6 April 2019, to commemorate the 10th anniversary of the earthquake that struck on 6 April 2009. Philosophers and scientists from diverse fields of research debated the problem that, on 6 April 1922, divided Einstein and Bergson: the nature of time. For Einstein, scientific time is the only time that matters and the only time we can rely on. Bergson, however, believes that scientific time (...) is derived by abstraction, even in the sense of extraction, from a more fundamental time. The plurality of times envisaged by the theory of Relativity does not, for him, contradict the philosophical intuition of the existence of a single time. But how do things stand today? What can we say about the relationship between the quantitative and qualitative dimensions of time in the light of contemporary science? What do quantum mechanics, biology and neuroscience teach us about the nature of time? The essays collected here take up the question that pitted Einstein against Bergson, science against philosophy, in an attempt to reverse the outcome of their monologue in two voices, with a multilogue in several voices. (shrink)

Change is endemic in nature yet scientists seek stability amidst change. When proposals fail scientists shift their focus and look for stability elsewhere. Scholars who study the development of science also seek stability in the scientific process. Here I explore the interaction between stability and change in nature as we understand it through the sciences and in the practice of scientific research. The concluding part argues that the search for stability meets a human intellectual need but this is compatible with (...) our finding what is actually there. Cases in which a previously accepted part of science is rejected or revised in response to contrary data indicates that we do not predetermine outcomes of observations and experiments. Still, the belief that there are loci of stability in nature is a working hypothesis. While it has been fruitful, only future scientific developments can determine if this will continue to hold. (shrink)

Abstract The historical evolution of the principle of relativity from Galileo to Einstein is briefly traced, and purported difficulties with Einstein's formulation of the principle are examined and dismissed. This formulation is then compared to a precise version formulated recently in the geometrical language of spacetime theories. We claim that the recent version is both logically puzzling and fails to capture a crucial physical insight contained in the earlier formulations. The implications of this claim for the modern treatment of general (...) dynamical symmetries are discussed. (shrink)

Let's begin with an old example. In De Rerum Naturua , Lucretius presented a thought experiment to show that space is infinite. We imagine ourselves near the alleged edge of space; we throw a spear; we see it either sail through the ‘edge’ or we see it bounce back. In the former case the ‘edge’ isn't the edge, after all. In the latter case, there must be something beyond the ‘edge’ that repelled the spear. Either way, the ‘edge’ isn't really (...) an edge of space, after all. So space is infinite. (shrink)

In a recent paper in this journal, Kosso ([2000]) discussed the observational status of continuous symmetries of physics. While we are in broad agreement with his approach, we disagree with his analysis. In the discussion of the status of gauge symmetry, a set of examples offered by 't Hooft ([1980]) has influenced several philosophers, including Kosso; in all cases the interpretation of the examples is mistaken. In this paper, we present our preferred approach to the empirical significance of symmetries, re-analysing (...) the cases of gauge symmetry and general covariance. Direct and indirect empirical significance Global and local continuous symmetries Gauge symmetry 3.1 Local gauge symmetry 3.1.1 Discussion of the first claim 3.1.2 Discussion of the second claim 3.2 Global gauge symmetry Space-time symmetries Direct and indirect empirical significance again Conclusion. (shrink)

ArgumentThe main thesis of this paper is that Copernicus's avoidance of all admission that scripture was contravened inDe revolutionibusand his composition of its new Preface in 1542, as well as the non-publication of Rheticus'sTreatise on Holy Scripture and the Motion of the Earth, were influenced by the early information they received on the failure of the 1541 Regensburg Protestant-Catholic colloquy, among the major consequences of which were significant increases in the problems concerning publishing works which contravened scripture. This is supported (...) by examining Rheticus's first letter to Paul Eber in conjunction with the documents on the Regensburg colloquy and on censorship in Nuremberg, as well as with the existing literature on Copernicus and his context. In view of the main thesis, Copernicus's apparent dedication of the work to the Pope merits additional explanation, and the second thesis is that components of explanations for several aspects of those parts of the Preface that relate to the Papacy and to theologians can be provided via comparisons with previous diplomacy between Warmia and the Papacy which occurred or was being referred to during Copernicus's time. This is supported by examining these parts of the Preface in the light of a selection of the relevant documents. (shrink)

I present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such (...) as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised. (shrink)

Scientific risk evaluations are constructed by specific evidence, value judgements and biological background assumptions. The latter are the framework-setting suppositions we apply in order to understand some new phenomenon. That background assumptions co-determine choice of methodology, data interpretation, and choice of relevant evidence is an uncontroversial claim in modern basic science. Furthermore, it is commonly accepted that, unless explicated, disagreements in background assumptions can lead to misunderstanding as well as miscommunication. Here, we extend the discussion on background assumptions from basic (...) science to the debate over genetically modified (GM) plants risk assessment. In this realm, while the different political, social and economic values are often mentioned, the identity and role of background assumptions at play are rarely examined. We use an example from the debate over risk assessment of stacked genetically modified plants (GM stacks), obtained by applying conventional breeding techniques to GM plants. There are two main regulatory practices of GM stacks: (i) regulate as conventional hybrids and (ii) regulate as new GM plants. We analyzed eight papers representative of these positions and found that, in all cases, additional premises are needed to reach the stated conclusions. We suggest that these premises play the role of biological background assumptions and argue that the most effective way toward a unified framework for risk analysis and regulation of GM stacks is by explicating and examining the biological background assumptions of each position. Once explicated, it is possible to either evaluate which background assumptions best reflect contemporary biological knowledge, or to apply Douglas' 'inductive risk' argument. (shrink)

Do the hard problem of consciousness and the simulation argument potentially resolve each other? Here we will argue for four possible views: that consciousness may be possible only (a) outside of, (b) inside and/or outside of, (c) inside of, or (d) interfacing with simulations. The first two of these views have been developed at length by David Chalmers and are used as jumping off points to introduce and develop the latter two views here. If any one of these views could (...) be proven true, it would simultaneously both support a kind of account of properties of consciousness and also provide a kind of sign as to whether or not we are indeed living in the kind of immersive computer simulation that Nick Bostrom hypothesizes about. However, given that none of these views are proven true but all are plausible, these considerations should tend to neutralize our credence that we are either simulated or not simulated, by themselves giving us no sign one way or the other. (shrink)

Arguments from perceptual variation challenge the view that colors are objective properties of objects, properties that objects have independent of how they are perceived. This paper attempts, first, to diagnose one central reason why arguments from perceptual variation seem especially challenging for objectivists about color. Second, we offer a response to this challenge, claiming that once we focus on determinate colors rather than the determinables they determine, a response to arguments from perceptual variation becomes apparent. Third, our nominal opponents are (...) relationalist (like Cohen in The red and the real: an essay on color ontology, Oxford University Press, Oxford, 2009) and we will argue that the main argument for rejecting objectivism commits the relationalist to a position that is more radical than the one he would wish to endorse. Fourth, we suggest that insight into which properties could be relational may be found by looking to our best scientific theories. (shrink)

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, (...) requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz. (shrink)

Aristotle ends Metaphysics books M–N with an account of how one can get the impression that Platonic Form-numbers can be causes. Though these passages are all admittedly polemic against the Platonic understanding, there is an undercurrent wherein Aristotle seems to want to explain in his own terms the evidence the Platonist might perceive as supporting his view, and give any possible credit where credit is due. Indeed, underlying this explanation of how the Platonist may have formed his impression, we discover (...) Aristotle's own understanding of what we today might call the mathematical structure of nature. Mathematicals are, to Aristotle, abstractions of order, symmetry, and definiteness, which are in turn aspects of the formal cause of goodness and beauty. This is a lens through which an Aristotelian could view modern mathematical physics as an important aspect of natural philosophy, and which is foundational for an Aristotelian philosophy of mathematics. (shrink)

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of (...) mathematics and the relationship of mathematics to physics. (shrink)

The ArgumentOne of the earliest arguments for Copernicanism was a widely accepted fact: that on a horizontal plane a body subject to no external resistance can be set in motion by the smallest of all possible forces. This fact was contrary to Aristotelian physics; but it was a physical argument (by abduction) for the possibility of the Copernican world system. For it would be explained if that system was true or at least possible.Galileo argued: only nonviolent motions can be caused (...) by the smallest of all possible forces; hence resistance-free horizontal motions are nonviolent; this confirms Copernicanism insofar as it designates the rotations of celestial spheres (being resistance-free horizontal motions) as nonviolent.Galileo's argument was compatible with (and supportive of) the specific Copernican version of impetus mechanics; but it was also compatible with a (somewhat qualified) principle of inertia. Thus it promoted decisively the transition from impetus mechanics to classical inertial mechanics. (shrink)

The paper examines Wesley Salmon’s claim that the primary role of plausibility arguments in the history of science is to impose constraints on the prior probability of hypotheses. A detailed look at Copernicanism and Darwinism and, more briefly, Rutherford’s discovery of the atomic nucleus reveals a further and arguably more important role of plausibility arguments. It resides in the consideration of likelihoods, which state how likely a given hypothesis makes a given piece of evidence. In each case the likelihoods raise (...) the probability of one of the competing hypotheses and diminish the credibility of its rival, and this may happen either on the basis of ‘old’ or ‘new’ evidence.Keywords: Copernicanism; Darwinism; Atom models; Bayesianism; Likelihoods; Probability arguments. (shrink)

We introduce the question whether there are specific kinds of writing modalities and practices that facilitated the development of modern science and mathematics. We point out the importance and uniqueness of symbolic writing, which allowed early modern thinkers to formulate a new kind of questions about mathematical structure, rather than to merely exploit this structure for solving particular problems. In a very similar vein, the novel focus on abstract structural relations allowed for creative conceptual extensions in natural philosophy during the (...) scientific revolution. These preliminary reflections are meant to set the stage for the following contributions in this volume. (shrink)

This article investigates and resolves the question whether gauge symmetry can display analogs of the famous Galileo’s ship scenario. In doing so, it builds on and clarifies the work of Greaves and Wallace on this subject.

This paper addresses and proposes to resolve a longstanding problem in the philosophy of physics: whether and in what sense Albert Einstein’s Chasing the Light thought experiment was significant in the development of the theory of special relativity. Although Einstein granted this thought experiment pride of place in his 1949 Autobiographical Notes, philosophers and physicists continue to debate about what, if anything, the experiment establishes. I claim that we ought to think of Chasing the Light as Einstein’s first attempt to (...) problematize the very idea of the electromagnetic ether frame, and that it thereby contributed to his eventual adoption of one of special relativity’s two foundational axioms: the “light postulate”. This interpretation requires the assumption that Einstein had presupposed special relativity’s other axiom, the “principle of relativity”, when initially considering Chasing the Light. This argument is novel insofar as it provides evidence that such a presupposition by Einstein is both conceptually and historically plausible. Moreover, this paper directly challenges John D. Norton’s compelling claim that Chasing the Light is best understood as a refutation of emission theories of light propagation; while both interpretations of the experiment are conceptually coherent, I argue that the interpretation found in this paper is supported more straightforwardly by historical evidence. (shrink)

In the article two viewpoints on the mind’s influence on perception are considered. One of them was developed on the assumption that perception is a nonproblematic source of knowledge about the world, which is free from mind’s influence— perception as a mirror-image. Another viewpoint is perception as action, i.e. active search and gathering the relevant information, its processing and evaluation. First viewpoint has dominated in philosophy for a long time, the second one has been developing in psychology from the 80th (...) of the 20th century. The aim of the paper is to examine some philosophically significant corollaries from both positions concerning objectiveness, epistemological status of an observation, truth, meaning of name. Analysis showed that perception as action is non-compatible with many traditional concepts, and it goes both against empiricism and against realism as it involves some critical arguments, e.g. theory ladenness of observations, underdetermination of theory by facts, the historical development of a scientific fact. (shrink)

The aim of this paper is to investigate the transition in natural science from the search for the essence of matter to the search for the laws to which matter is subject. Starting about 1600, this transition meant a change of perspective, the introduction of a new metaphysical view of the world. A scientific worldview has at least four components, its ontology, epistemology, logic and heuristic, which I shall discuss with respect to the idea of natural law.

Recent literature on epistemic innocence develops the idea that a defective cognitive process may nevertheless merit special consideration insofar as it confers an epistemic benefit that would not otherwise be available. For example, confabulation may be epistemically innocent when it makes a subject more likely to form future true beliefs or helps her maintain a coherent self-concept. I consider the role of confabulation in typical cases of interpersonal gaslighting, and argue that confabulation will not be epistemically innocent in such cases (...) even if it does preserve a coherent self-concept or belief-set for the subject. Analyzing the role of confabulation in gaslighting illustrates its role in on-going interpersonal relationships, and augments already growing evidence that confabulation may be quite widespread. The role of confabulation in gaslighting shows that whether confabulation confers epistemic benefits will depend greatly on the interpersonal context in which it is deployed, while whether a coherent self-concept is epistemically beneficial will depend to a great extent on the content of that self-concept. This shows that the notion of an epistemically harmful or beneficial feature of a cognitive process can and should be further clarified, and that doing so has both theoretical and practical advantages in understanding epistemic innocence itself. (shrink)

There are two classical and opposite positions about scientific discovery: the one that conceives scientific discovery activity as fully rational and the one that conceives scientific discovery activity as fully irrational. In the first case, machines are regarded as able to perform the scientific discovery process whereas, in the second case, machines are considered unable to perform any part of the scientific discovery process.We adopt a third intermediate approach that envisages a new role for machines, which are conceived as descriptions (...) of the results of scientific discovery activity. More precisely, the purpose of the paper is to illustrate the multilevel structure of a machine, called creative dynamic agency, that represents the articulated and incremental description of the product of scientific discovery process. The multilevel architecture reflects the composition relation that holds among phenomena described by creative agents that compose creative dynamic agency. (shrink)

We study a long-recognised but under-appreciated symmetry called dynamical similarity and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton’s principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the (...) minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology. (shrink)

Alexander’s "Infinitesimal. How a dangerous mathematical theory shaped the modern world"(London: Oneworld Publications, 2015) is right to argue that the Jesuits had a chilling effect on Italian mathematics, but I question his account of the Jesuit motivations for suppressing indivisibles. Alexander alleges that the Jesuits’ intransigent commitment to Aristotle and Euclid explains their opposition to the method of indivisibles. A different hypothesis, which Alexander doesn’t pursue, is a conflict between the method of indivisibles and the Catholic doctrine of the Eucharist. (...) This is a pity, for the conflict with the Eucharist has advantages over the Jesuit commitment to Aristotle and Euclid. The method of indivisibles was a method that developed in the course of the seventeenth century, and those who developed ‘beyond the Alps’ relied upon Aristotelian and Euclidean ideals. Alexander’s failure to recognize the importance of Aristotle and Euclid for the development of the method of indivisibles arises from an unwarranted conflation of indivisibles and infinitesimals. Once indivisibles and infinitesimals are distinguished, we observe that the development of the method of indivisibles exhibits an unmistakable sympathy for Aristotle and Euclid. Thus, it makes sense to consider an alternative explanation for the Jesuit abhorrence of indivisibles. And indeed, indivisibles but not infinitesimals conflict with the doctrine of the Eucharist, the central dogma of the Church. (shrink)

The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.

This paper defines what is and what is not science. These novel science definitions demonstrate that illustrations, like mathematics, can be scaler, real, not real, valid, and invalid. These definitions identify non-inertial reference frame logic inconsistencies, emphasizing the continued search for relative movement definitions. This search leads to Aristotle’s primary circular and secondary rectilinear movement concepts defining the at-rest reference frame, motion, and relative movement. These three novel movement definitions are confirmed using Ptolemy’s dropped ball observation, Michelson-Morley’s null result, a (...) dropped ball on a rotating platform Coriolis effect, and light’s Doppler shift. The novel relative movement definitions demonstrate Ptolemy’s dropped ball and Michel-son-Morley’s reflected light represent motion in an at-rest reference frame. The novel relative movement definition reveals the Coriolis effect and light’s Doppler shift describe the same physical process. Two future experiments are suggested to confirm the novel movement definitions. Developing the novel relative movement concepts will require applying mathematics to circular movement velocity concepts, such as rotational inertia and angular velocity. (shrink)

On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...) clarifying discussions in philosophy of mathematics and contributing towards a more refined view of mathematical practice. (shrink)

“Much as I dislike the idea of ages, I think a good case can be made that science has now moved from an Age of Reductionism to an Age of Emergence, a time when the search for ultimate causes of things shifts from the behavior of parts to the behavior of the collective” (Laughlin 2005 , p. 208). This quotation by Nobel laureate in physics, Robert B. Laughlin, in his recent book, A Different Universe , raises interesting scientific and philosophical (...) issues. Bench chemists continue successfully to synthesize new compounds and report results through quantitative and structural analyses of constitutive elements. The whole continues to be understood by analysis of the parts. The relatively recent science of emergence comes with a different perspective: how to explain novel, irreducible, and unpredictable appearances in cosmic evolution? New wholes seem to be more that the sum of their parts. How do these wholes come to exist? Do classical concepts of matter satisfy the science of emergence? Descriptions of nature’s phenomena that challenge classical interpretations of the “Age of Reductionism” are presented to stimulate possible new scientific and philosophical concepts for an age of reductionism and emergence. (shrink)

This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated Galileo’s characterization of freefall. The first part of the paper reviews the historical context leading up to Fermat’s proof. The second part illustrates how a physical and a mathematical insight enabled Fermat’s result, and that a simple modification would satisfy any of Fermat’s critics. The result is an illustration of how a purely theoretical argument can settle an apparently empirical debate.