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  1. David Atkinson, Nonlocality Is a Nonsequitur.
    Nonlocality in quantum mechanics does not follow from nonseparability, nor does classical stochastic independence imply physical independence. In this paper an explicit proof of a Bell inequality is recalled, and an analysis of the Aspect experiment in terms of noncontextual, but indefinite weights, or improper probabilities, is given.
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  2. David Atkinson & Porter Johnson, Nonconservation of Energy and Loss of Determinism.
    An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution (...)
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  3. Jeanne Peijnenburg & David Atkinson, Probabilistic Justification.
    We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.
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  4. David Atkinson, A New Metaphysics.
    Theo Kuipers describes four kinds of research program and the question is raised here as to whether string theory could be accommodated by one of them, or whether it should be classified in a new, fifth kind of research program.
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  5. David Atkinson, Acting Rationally with Irrational Strategies.
    When the Parrondo effect was discovered a few years ago (Harmer and Abbott 1999a, 1999b), it was hailed as a possible mechanism whereby, in a kind of collaboration of failure, losing strategies could be combined to yield profit. The precise relevance of the Parrondo effect to natural and social phenomena is however still unclear. In this paper we give specific examples, first in the artificial setting of a gambling machine, and then in more natural applications to genetics and to environmental (...)
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  6. David Atkinson, Bell's Inequalities and Kolmogorov's Axioms.
    After recalling proofs of the Bell inequality based on the assumptions of separability and of noncontextuality, the most general noncontextual contrapositive conditional probabilities consistent with the Aspect experiment are constructed. In general these probabilities are not all positive.
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  7. David Atkinson, Dirac's Quantum Jump.
    This minicourse on quantum mechanics is intended for students who have already been rather well exposed to the subject at an elementary level. It is assumed that they have surmounted the first conceptual hurdles and also have struggled with the Schrödinger equation in one dimension.
     
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  8. David Atkinson, Infrared and Ultraviolet Coupling in Qcd.
    The coupled Dyson-Schwinger equations for the gluon and ghost propagators in QCD are shown to have solutions that correspond to a unique running coupling that has a nite infrared xed point and the expected logarithmic decrease in the ultraviolet. The infrared coupling is large enough to support chiral symmetry breaking and quarks are not con ned, but they cannot be isolated.
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  9. David Atkinson, Infinite Resistive Lattices.
    The resistance between two arbitrary nodes in an infinite square lattice of identical resistors is calculated. The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions. © 1999..
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  10. David Atkinson, Joint Probabilities Reproducing Three EPR Experiments On Two Qubits.
    An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.
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  11. David Atkinson, Mentale En Fysische Afbeeldingen.
    De meesten van ons kunnen zich moeiteloos beelden uit hun schooljaren voor de geest halen. Dikwijls zijn die beelden vaag en fragmentarisch, maar herkenbaar genoeg: het jongetje met het ziekenfondsbrilletje, het meisje met de afgezakte kousen, de onderwijzeres met de grote ruiten rok. Wie begiftigd is met een sterke auditieve verbeelding (en oud genoeg) kan zelfs weer horen hoe de schoolbel klingelde of hoe de kroontjespennen over het papier krasten. Sommigen zijn zelfs in staat om zich geuren te herinneren, of (...)
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  12. David Atkinson, Quantum Mechanics and Retrocausality.
    The classical electrodynamics of point charges can be made finite by the introduction of effects that temporally precede their causes. The idea of retrocausality is also inherent in the Feynman propagators of quantum electrodynamics. The notion allows a new understanding of the violation of the Bell inequalities, and of the world view revealed by quantum mechanics. Published in The Universe, Visions and Perspectives, edited by N. Dadhich and A. Kembhavi, Kluwer Academic Publishers, 2000, pages 35-50.
     
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  13. David Atkinson, Running Coupling in Nonperturbative QCD: Bare Vertices and y-Max Approximation.
    A recent claim that in quantum chromodynamics in the Landau gauge the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson- Schwinger equations are taken to be bare. The gauge invariant running coupling is shown to be uniquely determined by the equations and to have a large finite infrared (...)
     
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  14. David Atkinson, Singular Scattering Matrices.
    A nonlinear integrodifferential equation is solved by the methods of S-matrix theory.
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  15. David Atkinson, The Light of Einstein.
    The Michelson-Morley experiment suggests the hypothesis that the two-way speed of light is constant, and this is consistent with a more general invariance than that of Lorentz. On adding the requirement that physical laws have the same form in all inertial frames, as Einstein did, the transformation specializes to that of Lorentz.
     
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  16. Jeanne Peijnenburg & David Atkinson, Lamps, Cubes, Balls and Walls.
    Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf’s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in 1998 (...)
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  17. Jeanne Peijnenburg & David Atkinson (2014). The Need for Justification. Metaphilosophy 45 (2):201-210.
    Some series can go on indefinitely, others cannot, and epistemologists want to know in which class to place epistemic chains. Is it sensible or nonsensical to speak of a proposition or belief that is justified by another proposition or belief, ad infinitum? In large part the answer depends on what we mean by “justification.” Epistemologists have failed to find a definition on which everybody agrees, and some have even advised us to stop looking altogether. In spite of this, the present (...)
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  18. David Atkinson & Jeanne Peijnenburg (2013). Transitivity and Partial Screening Off. Theoria 79 (4):294-308.
    The notion of probabilistic support is beset by well-known problems. In this paper we add a new one to the list: the problem of transitivity. Tomoji Shogenji has shown that positive probabilistic support, or confirmation, is transitive under the condition of screening off. However, under that same condition negative probabilistic support, or disconfirmation, is intransitive. Since there are many situations in which disconfirmation is transitive, this illustrates, but now in a different way, that the screening-off condition is too restrictive. We (...)
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  19. Jeanne Peijnenburg & David Atkinson (2013). The Emergence of Justification. Philosophical Quarterly 63 (252):546-564.
    A major objection to epistemic infinitism is that it seems to make justification impossible. For if there is an infinite chain of reasons, each receiving its justification from its neighbour, then there is no justification to inherit in the first place. Some have argued that the objection arises from misunderstanding the character of justification. Justification is not something that one reason inherits from another; rather it gradually emerges from the chain as a whole. Nowhere however is it made clear what (...)
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  20. David Atkinson (2012). Confirmation and Justification. A Commentary on Shogenji's Measure. Synthese 184 (1):49-61.
    So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; in (...)
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  21. David Atkinson & Jeanne Peijnenburg (2012). Fractal Patterns in Reasoning. Notre Dame Journal of Formal Logic 53 (1):15-26.
    This paper is the third and final one in a sequence of three. All three papers emphasize that a proposition can be justified by an infinite regress, on condition that epistemic justification is interpreted probabilistically. The first two papers showed this for one-dimensional chains and for one-dimensional loops of propositions, each proposition being justified probabilistically by its precursor. In the present paper we consider the more complicated case of two-dimensional nets, where each "child" proposition is probabilistically justified by two "parent" (...)
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  22. Jeanne Peijnenburg & David Atkinson (2012). An Endless Hierarchy of Probabilities. American Philosophical Quarterly 49 (3):267-276.
    Suppose q is some proposition, and let -/- P(q) = v0 (1) -/- be the proposition that the probability of q is v0.1 How can one know that (1) is true? One cannot know it for sure, for all that may be asserted is a further probabilistic statement like -/- P(P(q) = v0) = v1, (2) -/- which states that the probability that (1) is true is v1. But the claim (2) is also subject to some further statement of an (...)
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  23. Jan Hilgevoord & David Atkinson (2011). Time in Quantum Mechanics. In Craig Callender (ed.), The Oxford Handbook of Philosophy of Time. Oup Oxford.
  24. Jeanne Peijnenburg & David Atkinson (2011). Grounds and Limits: Reichenbach and Foundationalist Epistemology. Synthese 181 (1):113 - 124.
    From 1929 onwards, C. I. Lewis defended the foundationalist claim that judgements of the form 'x is probable' only make sense if one assumes there to be a ground y that is certain (where x and y may be beliefs, propositions, or events). Without this assumption, Lewis argues, the probability of x could not be anything other than zero. Hans Reichenbach repeatedly contested Lewis's idea, calling it "a remnant of rationalism". The last move in this debate was a challenge by (...)
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  25. Jan-Willem Romeijn & David Atkinson (2011). A Condorcet Jury Theorem for Unknown Juror Competence. Politics, Philosophy, and Economics 10 (3):237-262.
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  26. Jan-Willem Romeijn & David Atkinson (2011). Learning Juror Competence: A Generalized Condorcet Jury Theorem. Politics, Philosophy and Economics 10 (3):237-262.
    This article presents a generalization of the Condorcet Jury Theorem. All results to date assume a fixed value for the competence of jurors, or alternatively, a fixed probability distribution over the possible competences of jurors. In this article, we develop the idea that we can learn the competence of the jurors by the jury vote. We assume a uniform prior probability assignment over the competence parameter, and we adapt this assignment in the light of the jury vote. We then compute (...)
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  27. David Atkinson & Porter Johnson (2010). Nonconservation of Energy and Loss of Determinism II. Colliding with an Open Set. 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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  28. David Atkinson & Jeanne Peijnenburg (2010). Crosswords and Coherence. The Review of Metaphysics 63 (4):807-820.
    A common objection to coherentism is that it cannot account for truth: it gives us no reason to prefer a true theory over a false one, if both theories are equally coherent. By extending Susan Haack's crossword metaphor, the authors argue that there could be circumstances under which this objection is untenable. Although these circumstances are remote, they are in full accordance with the most ambitious modern theories in physics. Coherence may perhaps be truth conducive.
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  29. David Atkinson & Jeanne Peijnenburg (2010). Justification by Infinite Loops. Notre Dame Journal of Formal Logic 51 (4):407-416.
    In an earlier paper we have shown that a proposition can have a well-defined probability value, even if its justification consists of an infinite linear chain. In the present paper we demonstrate that the same holds if the justification takes the form of a closed loop. Moreover, in the limit that the size of the loop tends to infinity, the probability value of the justified proposition is always well-defined, whereas this is not always so for the infinite linear chain. This (...)
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  30. David Atkinson & Jeanne Peijnenburg (2010). The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg. Studia Logica 94 (3):347 - 353.
    We have earlier shown by construction that a proposition can have a welldefined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls ‘solvable’. In the present reaction we investigate what Herzberg means (...)
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  31. David Atkinson & Jeanne Peijnenburg (2010). Volume Lxiii. Review of Metaphysics 63:999-1000.
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  32. Jeanne Peijnenburg & David Atkinson (2010). Lamps, Cubes, Balls and Walls: Zeno Problems and Solutions. Philosophical Studies 150 (1):49 - 59.
    Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in (...)
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  33. David Atkinson (2009). Nonconservation of Energy and Loss of Determinism I. Infinitely Many Colliding Balls. Foundations of Physics 39 (8):937-957.
    An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution (...)
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  34. David Atkinson & Jeanne Peijnenburg (2009). Justification by an Infinity of Conditional Probabilities. Notre Dame Journal of Formal Logic 50 (2):183-193.
    Today it is generally assumed that epistemic justification comes in degrees. The consequences, however, have not been adequately appreciated. In this paper we show that the assumption invalidates some venerable attacks on infinitism: once we accept that epistemic justification is gradual, an infinitist stance makes perfect sense. It is only without the assumption that infinitism runs into difficulties.
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  35. David Atkinson, Jeanne Peijnenburg & Theo Kuipers (2009). How to Confirm the Conjunction of Disconfirmed Hypotheses. Philosophy of Science 76 (1):1-21.
    Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.
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  36. David Atkinson, Jeanne Peijnenburg, Theo Kuipers, William T. Wojtach, Erik Curiel & Ronald Pisaturo (2009). 1. How to Confirm the Conjunction of Disconfirmed Hypotheses How to Confirm the Conjunction of Disconfirmed Hypotheses (Pp. 1-21). [REVIEW] Philosophy of Science 76 (1).
     
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  37. David Atkinson (2008). Achilles, the Tortoise, and Colliding Balls. History of Philosophy Quarterly 25 (3):187 - 201.
    A recent thought experiment has shed interesting new light on the core problem of Zeno’s Achilles. A ball apparently can, and cannot collide with an infinite, open set of balls. It is the purpose of this paper to make the new development accessible to the general philosophical community and to suggest a direction in which the problem may perhaps be solved.
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  38. David Atkinson & Jeanne Peijnenburg (2008). Reichenbach's Posits Reposited. Erkenntnis 69 (1):93 - 108.
    Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under (...)
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  39. Jeanne Peijnenburg & David Atkinson (2008). Achilles, the Tortoise, and Colliding Balls. History of Philosophy Quarterly 25 (3):187 - 201.
    It is widely held that the paradox of Achilles and the Tortoise, introduced by Zeno of Elea around 460 B.C., was solved by mathematical advances in the nineteenth century. The techniques of Weierstrass, Dedekind and Cantor made it clear, according to this view, that Achilles’ difficulty in traversing an infinite number of intervals while trying to catch up with the tortoise does not involve a contradiction, let alone a logical absurdity. Yet ever since the nineteenth century there have been dissidents (...)
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  40. Jeanne Peijnenburg & David Atkinson (2008). Probabilistic Justification and the Regress Problem. Studia Logica 89 (3):333 - 341.
    We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.
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  41. David Atkinson (2007). Losing Energy in Classical, Relativistic and Quantum Mechanics. Studies in History and Philosophy of Science Part B 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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  42. David Atkinson (2007). On Poor and Not so Poor Thought Experiments. A Reply to Daniel Cohnitz. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 38 (1):159 - 161.
    We have never entirely agreed with Daniel Cohnitz on the status and rôle of thought experiments. Several years ago, enjoying a splendid lunch together in the city of Ghent, we cheerfully agreed to disagree on the matter; and now that Cohnitz has published his considered opinion of our views, we are glad that we have the opportunity to write a rejoinder and to explicate some of our disagreements. We choose not to deal here with all the issues that Cohnitz raises, (...)
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  43. David Atkinson, Jeanne Peijnenburg & Theo Kuipers, How to Confirm the Disconfirmed. On Conjunction Fallacies and Robust Confirmation.
    Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for nine different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.
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  44. Jeanne Peijnenburg & David Atkinson (2007). On Poor and Not so Poor Thought Experiments. A Reply to Daniel Cohnitz. Journal for General Philosophy of Science 38 (1):159 - 161.
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  45. David Atkinson (2006). A Relativistic Zeno Effect. Synthese 160 (1):5 - 12.
    A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.
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  46. David Atkinson (2006). Does Quantum Electrodynamics Have an Arrow of Time?☆. Studies in History and Philosophy of Science Part B 37 (3):528-541.
    Quantum electrodynamics is a time-symmetric theory that is part of the electroweak interaction, which is invariant under a generalized form of this symmetry, the PCT transformation. The thesis is defended that the arrow of time in electrodynamics is a consequence of the assumption of an initial state of high order, together with the quantum version of the equiprobability postulate.
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  47. David Atkinson & Jeanne Peijnenburg (2006). Probability All the Way Up. Synthese 153 (2):187 - 197.
    Richard Jeffrey’s radical probabilism (‘probability all the way down’) is augmented by the claim that probability cannot be turned into certainty, except by data that logically exclude all alternatives. Once we start being uncertain, no amount of updating will free us from the treadmill of uncertainty. This claim is cast first in objectivist and then in subjectivist terms.
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  48. David Atkinson & Jeanne Peijnenburg (2006). Probability Without Certainty: Foundationalism and the Lewis–Reichenbach Debate. Studies in History and Philosophy of Science Part A 37 (3):442-453.
    Like many discussions on the pros and cons of epistemic foundationalism, the debate between C.I. Lewis and H. Reichenbach dealt with three concerns: the existence of basic beliefs, their nature, and the way in which beliefs are related. In this paper we concentrate on the third matter, especially on Lewis’s assertion that a probability relation must depend on something that is certain, and Reichenbach’s claim that certainty is never needed. We note that Lewis’s assertion is prima facie ambiguous, but (...)
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