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A Primer on Determinism

D. Reidel (1986)

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  1. Chance and determinism.Roman Frigg - 2016 - In Alan Hájek & Christopher Hitchcock (eds.), The Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press.
    Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which appear to square the circle by being chancy and deterministic at once, and the appearance is backed by well-confirmed scientific theories such as statistical mechanics which also seem to provide us with chances for deterministic processes. Is this possible, and if so how? In this essay I discuss this question for probabilities as they occur in the (...)
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  • Timelines: Short Essays and Verse in the Philosophy of Time.Edward A. Francisco - 2024 - Morrisville, North Carolina: Lulu Press.
    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 (...)
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  • Closing the Hole Argument.Hans Halvorson & John Byron Manchak - forthcoming - British Journal for the Philosophy of Science.
    The hole argument purportedly shows that spacetime substantivalism implies a pernicious form of indeterminism. We show that the argument is seductive only because it mistakes a trivial claim (viz. there are isomorphic models) for a significant claim (viz. there are hole isomorphisms). We prove that the latter claim is false -- thereby closing the debate about whether substantivalism implies indeterminism.
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  • The Block Universe: A Philosophical Investigation in Four Dimensions.Pieter Thyssen - 2020 - Dissertation, Ku Leuven
    The aim of this doctoral dissertation is to closely explore the nature of Einstein’s block universe and to tease out its implications for the nature of time and human freedom. Four questions, in particular, are central to this dissertation, and set out the four dimensions of this philosophical investigation: (1) Does the block universe view of time follow inevitably from the theory of special relativity? (2) Is there room for the passage of time in the block universe? (3) Can we (...)
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  • Minds, Brains, and Desert: On the relevance of neuroscience for retributive punishment.Alva Stråge - 2019 - Dissertation, University of Gothenburg
    It is a common idea, and an element in many legal systems, that people can deserve punishment when they commit criminal (or immoral) actions. A standard philosophical objection to this retributivist idea about punishment is that if human choices and actions are determined by previous events and the laws of nature, then we are not free in the sense required to be morally responsible for our actions, and therefore cannot deserve blame or punishment. It has recently been suggested that this (...)
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  • Hamiltonian Privilege.Josh Hunt, Gabriele Carcassi & Christine Aidala - forthcoming - Erkenntnis:1-24.
    We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of a theory over another: ceteris paribus, a more general formulation is more fundamental. We illustrate this criterion through a novel interpretation of classical mechanics, based on three physical conditions. Two of these conditions suffice for recovering Hamiltonian mechanics. A third condition is necessary for Lagrangian mechanics. Hence, Lagrangian systems are a proper subset of Hamiltonian systems. Finally, we provide (...)
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  • The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism.Mahmoud Jalloh - forthcoming - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics. Oxford: Oxford University Press.
    In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and (...)
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  • Scientific Theory Eliminativism.Peter Vickers - 2014 - Erkenntnis 79 (1):111-126.
    The philosopher of science faces overwhelming disagreement in the literature on the definition, nature, structure, ontology, and content of scientific theories. These disagreements are at least partly responsible for disagreements in many of the debates in the discipline which put weight on the concept scientific theory. I argue that available theories of theories and conceptual analyses of theory are ineffectual options for addressing this difficulty: they do not move debates forward in a significant way. Directing my attention to debates about (...)
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  • Psa 2018.Philsci-Archive -Preprint Volume- - unknown
    These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2018.
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  • Agent-Causation Revisited: Origination and Contemporary Theories of Free Will.Thad Botham - 2008 - Berlin, Germany: Verlag D Müller.
    Sometimes you make a choice. Whether or not you made it was up to you. The choice was free. But how can this be? A scientific view of the world may leave no room for free choice. Free will literature continually explodes. Yet experts still focus on control or on a power to do otherwise. Sadly, they neglect another intuitive feature of free will: being an underived source or ultimate originator. When acting freely, one is a self-determined, self-directed, sole author (...)
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  • Degrees of Freedom.Pieter Thyssen & Sylvia Wenmackers - 2021 - Synthese 198 (11):10207-10235.
    Human freedom is in tension with nomological determinism and with statistical determinism. The goal of this paper is to answer both challenges. Four contributions are made to the free-will debate. First, we propose a classification of scientific theories based on how much freedom they allow. We take into account that indeterminism comes in different degrees and that both the laws and the auxiliary conditions can place constraints. A scientific worldview pulls towards one end of this classification, while libertarianism pulls towards (...)
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  • The causal mechanical model of explanation.James Woodward - 1989 - Minnesota Studies in the Philosophy of Science 13:359-83.
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  • The Hole Argument.Oliver Pooley - 2021 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to the Philosophy of Physics. New York, USA: Routledge. pp. 145-158.
    This paper reviews the hole argument as an argument against spacetime substantivalism. After a careful presentation of the argument itself, I critically review possible responses.
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  • Eternal Worlds and the Best System Account of Laws.Ryan A. Olsen & Christopher Meacham - 2020 - In Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. World Scientific.
    In this paper we apply the popular Best System Account of laws to typical eternal worlds – both classical eternal worlds and eternal worlds of the kind posited by popular contemporary cosmological theories. We show that, according to the Best System Account, such worlds will have no laws that meaningfully constrain boundary conditions. It’s generally thought that lawful constraints on boundary conditions are required to avoid skeptical arguments. Thus the lack of such laws given the Best System Account may seem (...)
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  • The Problem of Determinism - Freedom as Self-Determination.Dieter Wandschneider - 2010 - Psychotherapie Forum 18:100-107.
    There are arguments for determinism. Admittedly, this is opposed by the fact of everyday experience of autonomy. In the following, it is argued for the compatibility of determinism and autonomy. Taking up considerations of Donald MacKay, a fatalistic attitude can be refuted as false. Repeatedly, attempts have been made to defend the possibility of autonomy with reference to quantum physical indeterminacy. But its statistical randomness clearly misses the meaning of autonomy. What is decisive, on the other hand, is the possibility (...)
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  • Chance and Determinism.Nina Emery - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to the Philosophy of Physics. New York, USA: Routledge.
    This chapter focuses on the relations between objective probabilities in physical theories at different levels. In general philosophy of probability, it is frequently assumed that a fundamental deterministic theory cannot support probabilistic phenomena at any higher level, or more generally that there cannot be non-trivial probabilities in higher-level theories that are not encoded in probabilities at the lower level. These assumptions face significant challenges from some well-understood physical theories – I focus on statistical mechanics and Bohmian mechanics – where a (...)
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  • Probability in Boltzmannian statistical mechanics.Roman Frigg - 2009 - In Gerhard Ernst & Andreas Hüttemann (eds.), Time, Chance and Reduction: Philosophical Aspects of Statistical Mechanics. Cambridge University Press.
    In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as Humean chances in David Lewis’ (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically.
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  • Causality.Jessica M. Wilson - 2005 - In Sahotra Sarkar & Jessica Pfeifer (eds.), The Philosophy of Science: An Encyclopedia. New York: Routledge. pp. 90--100.
    Arguably no concept is more fundamental to science than that of causality, for investigations into cases of existence, persistence, and change in the natural world are largely investigations into the causes of these phenomena. Yet the metaphysics and epistemology of causality remain unclear. For example, the ontological categories of the causal relata have been taken to be objects (Hume 1739), events (Davidson 1967), properties (Armstrong 1978), processes (Salmon 1984), variables (Hitchcock 1993), and facts (Mellor 1995). (For convenience, causes and effects (...)
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  • Some Consequences of Physics for the Comparative Metaphysics of Quantity.David John Baker - 2020 - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics Volume 12. Oxford University Press. pp. 75-112.
    According to comparativist theories of quantities, their intrinsic values are not fundamental. Instead, all the quantity facts are grounded in scale-independent relations like "twice as massive as" or "more massive than." I show that this sort of scale independence is best understood as a sort of metaphysical symmetry--a principle about which transformations of the non-fundamental ontology leave the fundamental ontology unchanged. Determinism--a core scientific concept easily formulated in absolutist terms--is more difficult for the comparativist to define. After settling on the (...)
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  • Strong Determinism.Eddy Keming Chen - forthcoming - Philosophers' Imprint.
    A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.” Such an extraordinary feature may appear unattainable in a world like ours. In this paper, I show that it can be achieved in a simple way and (...)
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  • Free Will in a Quantum World?Valia Allori - 2019 - In J. Acacio de Barros & Carlos Montemayor (eds.), Quanta and Mind: Essays on the Connection Between Quantum Mechanics and Consciousness. Springer Verlag.
    In this paper, I argue that Conway and Kochen’s Free Will Theorem (1,2) to the conclusion that quantum mechanics and relativity entail freedom for the particles, does not change the situation in favor of a libertarian position as they would like. In fact, the theorem more or less implicitly assumes that people are free, and thus it begs the question. Moreover, it does not prove neither that if people are free, so are particles, nor that the property people possess when (...)
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  • Hard presentism.Patrick Dawson - 2020 - Synthese 198 (9):8433-8461.
    Presentists believe that only present things exist. Their theories, at first glance, seem to offer many admirable features: a simple ontology, and a meaningful, objective status for key temporal phenomena, such as the present moment and the passage of time. So intuitive is this theory that, as John Bigelow puts it, presentism was “believed by everyone...until at least the nineteenth century”. Yet, in the last 200 years presentism has been beset by criticisms from both physicists and metaphysicians. One of the (...)
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  • General relativity needs no interpretation.Erik Curiel - 2009 - Philosophy of Science 76 (1):44-72.
    I argue that, contrary to the recent claims of physicists and philosophers of physics, general relativity requires no interpretation in any substantive sense of the term. I canvass the common reasons given in favor of the alleged need for an interpretation, including the difficulty in coming to grips with the physical significance of diffeomorphism invariance and of singular structure, and the problems faced in the search for a theory of quantum gravity. I find that none of them shows any defect (...)
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  • Classical Mechanics Is Lagrangian; It Is Not Hamiltonian.Erik Curiel - 2014 - British Journal for the Philosophy of Science 65 (2):269-321.
    One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question of whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: (...)
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  • On Shackel’s nothing from infinity paradox.Amaia Corral-Villate - 2020 - European Journal for Philosophy of Science 10 (3):1-13.
    The objective of this article is to provide a discussion that counters the infinite particle disappearance conclusion argued by Shackel, 417–433, 2018). In order to do this, clear criteria to disprove the results of the applications of his continuity principles are provided, in addition to the consideration of the fundamental Classical Mechanical principle of mass conservation as an independent and clear basis for this disproof.
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  • Physical Computation: How General are Gandy’s Principles for Mechanisms?B. Jack Copeland & Oron Shagrir - 2007 - Minds and Machines 17 (2):217-231.
    What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We (...)
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  • Accelerating Turing machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
    Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary (...)
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  • Special Sciences, Conspiracy and the Better Best System Account of Lawhood.Jonathan Cohen & Craig Callender - 2010 - Erkenntnis 73 (3):427 - 447.
    An important obstacle to lawhood in the special sciences is the worry that such laws would require metaphysically extravagant conspiracies among fundamental particles. How, short of conspiracy, is this possible? In this paper we'll review a number of strategies that allow for the projectibility of special science generalizations without positing outlandish conspiracies: non-Humean pluralism, classical MRL theories of laws, and Albert and Loewer's theory. After arguing that none of the above fully succeed, we consider the conspiracy problem through the lens (...)
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  • A better best system account of lawhood.Jonathan Cohen & Craig Callender - 2009 - Philosophical Studies 145 (1):1 - 34.
    Perhaps the most significant contemporary theory of lawhood is the Best System (/MRL) view on which laws are true generalizations that best systematize knowledge. Our question in this paper will be how best to formulate a theory of this kind. We’ll argue that an acceptable MRL should (i) avoid inter-system comparisons of simplicity, strength, and balance, (ii) make lawhood epistemically accessible, and (iii) allow for laws in the special sciences. Attention to these problems will bring into focus a useful menu (...)
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  • Toward a sound perspective on modern physics: Capra's popularization of mysticism and theological approaches reexamined.Robert K. Clifton & Marilyn G. Regehr - 1990 - Zygon 25 (1):73-104.
    Fritjof Capra's The Tao of Physics, one of several popularizations paralleling Eastern mysticism and modern physics, is critiqued, demonstrating that Capra gives little attention to the differing philosophies of physics he employs, utilizing whatever interpretation suits his purposes, without prior justification. The same critique is applied and similar conclusions drawn, about some recent attempts at relating theology and physics. In contrast, we propose the possibility of maintaining a cogent relationship between these disciplines by employing theological hypotheses to account for aspects (...)
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  • Explanation in Physics: Explanation in Physical Theory.Peter Clark - 1990 - Royal Institute of Philosophy Supplement 27:155-175.
    The corpus of physical theory is a paradigm of knowledge. The evolution of modern physical theory constitutes the clearest exemplar of the growth of knowledge. If the development of physical theory does not constitute an example of progress and growth in what we know about the Universe nothing does. So anyone interested in the theory of knowledge must be interested consequently in the evolution and content of physical theory. Crucial to the conception of physics as a paradigm of knowledge is (...)
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  • Abilities to Act.Randolph Clarke - 2015 - Philosophy Compass 10 (12):893-904.
    This essay examines recent work on abilities to act. Different kinds of ability are distinguished, and a recently proposed conditional analysis of ability ascriptions is evaluated. It is considered whether abilities are causal powers. Finally, several compatibility questions concerning abilities, as well as the relation between free will and abilities of various kinds, are examined.
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  • In defense of psychological laws.Martin Carrier - 1998 - International Studies in the Philosophy of Science 12 (3):217-232.
    It is argued that psychological explanations involve psychological generalizations that exhibit the same features as laws of physics. On the basis of the “systematic theory of lawhood”, characteristic features of laws of nature are elaborated. Investigating some examples of explanations taken from cognitive psychology shows that these features can also be identified in psychological generalizations. Particular attention is devoted to the notion of “ccteris‐paribus laws”. It is argued that laws of psychology are indeed ceteris‐paribus laws. However, this feature does not (...)
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  • Explanatory loops and the limits of genetic reductionism.Martin Carrier & Patrick Finzer - 2006 - International Studies in the Philosophy of Science 20 (3):267 – 283.
    We reconstruct genetic determinism as a reductionist thesis to the effect that the molecular properties of cells can be accounted for to a great extent by their genetic outfit. The non-reductionist arguments offered at this molecular level often use the relationship between structure and function as their point of departure. By contrast, we develop a non-reductionist argument that is confined to the structural characteristics of biomolecules; no appeal to functions is made. We raise two kinds of objections against the reducibility (...)
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  • Reconsidering relativistic causality.Jeremy Butterfield - 2007 - International Studies in the Philosophy of Science 21 (3):295 – 328.
    I discuss the idea of relativistic causality, i.e., the requirement that causal processes or signals can propagate only within the light-cone. After briefly locating this requirement in the philosophy of causation, my main aim is to draw philosophers' attention to the fact that it is subtle, indeed problematic, in relativistic quantum physics: there are scenarios in which it seems to fail. I set aside two such scenarios, which are familiar to philosophers of physics: the pilot-wave approach, and the Newton-Wigner representation. (...)
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  • The Zombie Attack on the Computational Conception of Mind.Selmer Bringsjord - 1999 - Philosophy and Phenomenological Research 59 (1):41-69.
    Is it true that if zombies---creatures who are behaviorally indistinguishable from us, but no more conscious than a rock-are logically possible, the computational conception of mind is false? Are zombies logically possible? Are they physically possible? This paper is a careful, sustained argument for affirmative answers to these three questions.
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  • Confessions of a (Cheap) Sophisticated Substantivalist.Carolyn Brighouse - 2020 - Foundations of Physics 50 (4):348-359.
    I illustrate a challenge to a view that is a response to the Hole Argument. The view, sophisticated substantivalism, has been claimed to be the received view. While sophisticated substantivalism has many defenders, there is a fundamental tension in the view that has not received the attention it deserves. Anyone who defends or endorses sophisticated substantivalism, should acknowledge this challenge, and should either show why it is not serious or explain how to respond to it.
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  • Animals, zombanimals, and the total Turing test: The essence of artificial intelligence.Selmer Bringsjord - 2000 - Journal of Logic Language and Information 9 (4):397-418.
    Alan Turing devised his famous test (TT) through a slight modificationof the parlor game in which a judge tries to ascertain the gender of twopeople who are only linguistically accessible. Stevan Harnad hasintroduced the Total TT, in which the judge can look at thecontestants in an attempt to determine which is a robot and which aperson. But what if we confront the judge with an animal, and arobot striving to pass for one, and then challenge him to peg which iswhich? (...)
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  • An Argument for P = NP.Selmer Bringsjord - 2017 - Minds and Machines 27 (4):663-672.
    I articulate a novel modal argument for P=NP.
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  • Ignorance of the own past.Thomas Breuer - 1998 - Erkenntnis 48 (1):41-48.
    It is shown that for an inside observer it is impossible to distinguish all states in which a system was at some past time. This holds for classical and quantum systems, but an assumption of determinism is essential in the proof.
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  • On Representational Redundancy, Surplus Structure, and the Hole Argument.Clara Bradley & James Owen Weatherall - 2020 - Foundations of Physics 50 (4):270-293.
    We address a recent proposal concerning ‘surplus structure’ due to Nguyen et al.. We argue that the sense of ‘surplus structure’ captured by their formal criterion is importantly different from—and in a sense, opposite to—another sense of ‘surplus structure’ used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.’s arguments about Yang-Mills theory and on the hole argument.
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  • Fitness, probability and the principles of natural selection.Frederic Bouchard & Alexander Rosenberg - 2004 - British Journal for the Philosophy of Science 55 (4):693-712.
    We argue that a fashionable interpretation of the theory of natural selection as a claim exclusively about populations is mistaken. The interpretation rests on adopting an analysis of fitness as a probabilistic propensity which cannot be substantiated, draws parallels with thermodynamics which are without foundations, and fails to do justice to the fundamental distinction between drift and selection. This distinction requires a notion of fitness as a pairwise comparison between individuals taken two at a time, and so vitiates the interpretation (...)
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  • Downward causation in fluid convection.Robert C. Bishop - 2008 - Synthese 160 (2):229 - 248.
    Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, inter-level relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates for emergence and downward causation. Rayleigh–Bénard convection is an example of a nonlinear system that, I suggest, yields important insights for metaphysics and philosophy of science. In this paper I propose convection as a model for downward causation in classical (...)
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  • Anvil or onion? Determinism as a layered concept.Robert C. Bishop - 2005 - Erkenntnis 63 (1):55 - 71.
    Kellert (In the Wake of Chars, University of Chicago press, Chicago, 1993) has argued that Laplacean determinism in classical physics is actually a layered concept, where various properties or layers composing this form of determinism can be peeled away. Here, I argue that a layered conception of determinism is inappropriate and that we should think in terms of different deterministic models applicable to different kinds of systems. The upshot of this analysis is that the notion of state is more closely (...)
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  • Criticism and Revolutions.Mara Beller - 1997 - Science in Context 10 (1):13-37.
    The ArgumentIn this paper I argue that Kuhn's and Hanson's notion of incommensurable paradigms is rooted in the rhetoric of finality of the Copenhagen dogma — the orthodox philosophical interpretation of quantum physics. I also argue that arguments for holism of a paradigm, on which the notion of the impossibility of its gradual modification is based, misinterpret the Duhem-Quine thesis. The history of science (Copernican, Chemical, and Quantum Revolutions) demonstrates fruitful selective appropriation of ideas from seemingly “incommensurable” paradigms (rather than (...)
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  • Branching space-time.Nuel Belnap - 1992 - Synthese 92 (3):385 - 434.
    Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.
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  • Can We Justifiably Assume the Cosmological Principle in Order to Break Model Underdetermination in Cosmology?Claus Beisbart - 2009 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 40 (2):175-205.
    If cosmology is to obtain knowledge about the whole universe, it faces an underdetermination problem: Alternative space-time models are compatible with our evidence. The problem can be avoided though, if there are good reasons to adopt the Cosmological Principle (CP), because, assuming the principle, one can confine oneself to the small class of homogeneous and isotropic space-time models. The aim of this paper is to ask whether there are good reasons to adopt the Cosmological Principle in order to avoid underdetermination (...)
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  • Paraconsistency and its relation to worldviews.Diderik Batens - 1998 - Foundations of Science 3 (2):259-283.
    The paper highlights the import of the paraconsistent movement, list some motivations for its origin, and distinguishes some stands with respect to para-consistency. It then discusses some sources of inconsistency that are specific for worldviews, and the import of the paraconsistent turn for the worldviews enterprise.
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  • Nonconservation of Energy and Loss of Determinism II. Colliding with an Open Set.David Atkinson & Porter Johnson - 2010 - Foundations of Physics 40 (2):179-189.
    An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behaviour that corresponds to the potentially infinite system is (...)
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  • Losing energy in classical, relativistic and quantum mechanics.David Atkinson - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (1):170-180.
    A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.
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