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Peter Milne [83]Peter W. Milne [3]
  1. Log[p(h/eb)/p(h/b)] is the one true measure of confirmation.Peter Milne - 1996 - Philosophy of Science 63 (1):21-26.
    Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then (...)
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  2. Act and value: Expectation and the representability of moral theories.Graham Oddie & Peter Milne - 1991 - Theoria 57 (1-2):42-76.
    According to the axiologist the value concepts are basic and the deontic concepts are derivative. This paper addresses two fundamental problems that arise for the axiologist. Firstly, what ought the axiologist o understand by the value of an act? Second, what are the prospects in principle for an axiological representation of moral theories. Can the deontic concepts of any coherent moral theory be represented by an agent-netural axiology: (1) whatever structure those concepts have and (2) whatever the causal structure of (...)
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  3. Bruno de finetti and the logic of conditional events.Peter Milne - 1997 - British Journal for the Philosophy of Science 48 (2):195-232.
    This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the objects of conditional bets. (...)
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  4. Not every truth has a truthmaker.Peter Milne - 2005 - Analysis 65 (3):221–224.
    First paragraph: Truthmaker theory maintains that for every truth there is something, some thing, some entity, that makes it true. Balking at the prospect that logical truths are made true by any particular thing, a consequence that may in fact be hard to avoid (see Restall 1996, Read 2000), this principle of truthmaking is sometimes restricted to (logically) contingent truths. I aim to show that even in its restricted form, the principle is provably false.
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  5. What is the Normative Role of Logic?Peter Milne - 2009 - Aristotelian Society Supplementary Volume 83 (1):269-298.
    In making assertions one takes on commitments to the consistency of what one asserts and to the logical consequences of what one asserts. Although there is no quick link between belief and assertion, the dialectical requirements on assertion feed back into normative constraints on those beliefs that constitute one's evidence. But if we are not certain of many of our beliefs and that uncertainty is modelled in terms of probabilities, then there is at least prima facie incoherence between the normative (...)
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  6. Harmony, Purity, Simplicity and a “Seemingly Magical Fact”.Peter Milne - 2002 - The Monist 85 (4):498-534.
    In his penetrating and thought-provoking article “What Is Logic?” Ian Hacking flags an issue that he leaves undiscussed.
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  7. Classical harmony: Rules of inference and the meaning of the logical constants.Peter Milne - 1994 - Synthese 100 (1):49 - 94.
    The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified (...)
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  8. Not every truth has a truthmaker II.Peter Milne - 2013 - Analysis 73 (3):473-481.
    A proof employing no semantic terms is offered in support of the claim that there can be truths without truthmakers. The logical resources used in the proof are weak but do include the structural rule Contraction.
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  9. On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.
    Proofs of Gödel's First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable (...)
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  10.  83
    II—Peter Milne: What is the Normative Role of Logic?Peter Milne - 2009 - Aristotelian Society Supplementary Volume 83 (1):269-298.
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  11. Subformula and separation properties in natural deduction via small Kripke models: Subformula and separation properties.Peter Milne - 2010 - Review of Symbolic Logic 3 (2):175-227.
    Various natural deduction formulations of classical, minimal, intuitionist, and intermediate propositional and first-order logics are presented and investigated with respect to satisfaction of the separation and subformula properties. The technique employed is, for the most part, semantic, based on general versions of the Lindenbaum and Lindenbaum–Henkin constructions. Careful attention is paid to which properties of theories result in the presence of which rules of inference, and to restrictions on the sets of formulas to which the rules may be employed, restrictions (...)
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  12.  49
    A dilemma for subjective bayesians — and how to resolve it.Peter Milne - 1991 - Philosophical Studies 62 (3):307 - 314.
  13.  91
    A Bayesian Defence of Popperian Science?Peter Milne - 1995 - Analysis 55 (3):213 - 215.
  14. The simplest Lewis-style triviality proof yet?Peter Milne - 2003 - Analysis 63 (4):300–303.
  15.  96
    Belief, Degrees of Belief, and Assertion.Peter Milne - 2012 - Dialectica 66 (3):331-349.
    Starting from John MacFarlane's recent survey of answers to the question ‘What is assertion?’, I defend an account of assertion that draws on elements of MacFarlane's and Robert Brandom's commitment accounts, Timothy Williamson's knowledge norm account, and my own previous work on the normative status of logic. I defend the knowledge norm from recent attacks. Indicative conditionals, however, pose a problem when read along the lines of Ernest Adams' account, an account supported by much work in the psychology of reasoning. (...)
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  16. Indicative conditionals, conditional probabilities, and the “defective truth-table”: A request for more experiments.Peter Milne - 2012 - Thinking and Reasoning 18 (2):196-224.
    While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that (...)
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  17. Tarski, truth and model theory.Peter Milne - 1999 - Proceedings of the Aristotelian Society 99 (2):141–167.
    As Wilfrid Hodges has observed, there is no mention of the notion truth-in-a-model in Tarski's article 'The Concept of Truth in Formalized Languages'; nor does truth make many appearances in his papers on model theory from the early 1950s. In later papers from the same decade, however, this reticence is cast aside. Why should Tarski, who defined truth for formalized languages and pretty much founded model theory, have been so reluctant to speak of truth in a model? What might explain (...)
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  18.  39
    Information, confirmation, and conditionals.Peter Milne - 2014 - Journal of Applied Logic 12 (3):252-262.
  19.  73
    Can there be a realist single-case interpretation of probability?Peter Milne - 1986 - Erkenntnis 25 (2):129 - 132.
  20.  55
    Is there a logic of confirmation transfer?Peter Milne - 2000 - Erkenntnis 53 (3):309-335.
    This article begins by exploring a lost topic in the philosophy of science:the properties of the relations evidence confirming h confirmsh'' and, more generally, evidence confirming each ofh1, h2, ..., hm confirms at least one of h1, h2,ldots;, hn''.The Bayesian understanding of confirmation as positive evidential relevanceis employed throughout. The resulting formal system is, to say the least, oddlybehaved. Some aspects of this odd behaviour the system has in common withsome of the non-classical logics developed in the twentieth century. Oneaspect (...)
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  21. Omniscient beings are dialetheists.Peter Milne - 2007 - Analysis 67 (3):250–251.
  22.  9
    Praescriptum.Peter Milne - 2022 - Philosophy Today 66 (3):587-603.
    This takes a little-known reading of Kafka’s “In the Penal Colony” by Lyotard as the starting point for an examination of the relation between body and law. Lyotard’s late notion of the intractable serves as a frame for this examination: explicitly claimed to be an absolute condition of morals, I argue it also has political implications, which are here drawn out through the link between the intractable and the body. In Lyotard’s later writings, the body is usually associated with an (...)
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  23.  56
    Existence, freedom, identity, and the logic of abstractionist realism.Peter Milne - 2007 - Mind 116 (461):23-53.
    From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence. To prepare the way, we must first look closely at the rule of existential elimination familiar from classical and intuitionist logics and at rules governing identity. We then examine how well free logics meet the harmony and uniqueness constraints familiar from the proof-theoretic semantics project. Tennant assigns a special role to atomic formulas containing singular terms. This, we (...)
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  24.  10
    Praescriptum in advance.Peter Milne - forthcoming - Philosophy Today.
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  25.  79
    A note on scale invariance.Peter Milne - 1983 - British Journal for the Philosophy of Science 34 (1):49-55.
  26.  77
    Scotching the dutch book argument.Peter Milne - 1990 - Erkenntnis 32 (1):105--26.
    Consistent application of coherece arguments shows that fair betting quotients are subject to constraints that are too stringent to allow their identification with either degrees of belief or probabilities. The pivotal role of fair betting quotients in the Dutch Book Argument, which is said to demonstrate that a rational agent's degrees of belief are probabilities, is thus undermined from both sides.
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  27.  98
    The Physicalization of Mathematics.Peter Milne - 1994 - British Journal for the Philosophy of Science 45 (1):305-340.
  28. A note on Popper, propensities, and the two-slit experiment.Peter Milne - 1985 - British Journal for the Philosophy of Science 36 (1):66-70.
  29.  62
    Hartry field on measurement and intrinsic explanation.Peter Milne - 1986 - British Journal for the Philosophy of Science 37 (3):340-346.
  30. Tarski on truth and its definition.Peter Milne - 1997 - In Timothy Childers, Petr Kolft & Vladimir Svoboda (eds.), Logica '96: Proceedings of the 10th International Symposium. Filosofia. pp. 198-210.
    Of his numerous investigations ... Tarski was most proud of two: his work on truth and his design of an algorithm in 1930 to decide the truth or falsity of any sentence of the elementary theory of the high school Euclidean geometry. [...] His mathematical treatment of the semantics of languages and the concept of truth has had revolutionary consequences for mathematics, linguistics, and philosophy, and Tarski is widely thought of as the man who "defined truth". The seeming simplicity of (...)
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  31.  99
    Algebras of intervals and a logic of conditional assertions.Peter Milne - 2004 - Journal of Philosophical Logic 33 (5):497-548.
    Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic (...)
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  32.  56
    Modal metaphysics and comparatives.Peter Milne - 1992 - Australasian Journal of Philosophy 70 (3):248 – 262.
  33.  62
    On the completeness of non-philonian stoic logic.Peter Milne - 1995 - History and Philosophy of Logic 16 (1):39-64.
    The majority of formal accounts attribute to Stoic logicians the classical truth-functional understanding of the material conditional and exclusive disjunction.These interpretations were disputed,...
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  34.  25
    Betting on Fuzzy and Many–valued Propositions.Peter Milne - unknown
    From Introduction: In a 1968 article, ‘Probability Measures of Fuzzy Events’, Lotfi Zadeh pro-posed accounts of absolute and conditional probability for fuzzy sets (Zadeh, 1968).
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  35.  29
    Philosophy of Science in the Twentieth Century: Four Central Themes.Reading the Book of Nature: an Introduction to the Philosophy of Science.Common Sense, Science and Scepticism: a Historical Introduction to the Theory of Knowledge.Peter Milne - 1995 - Philosophical Quarterly 45 (180):379-384.
  36. Bayesianism V. scientific realism.Peter Milne - 2003 - Analysis 63 (4):281–288.
  37.  8
    On the Year of Publication of Tarski's ‘Der Wahrheitsbegriff in den formalisierten Sprachen’.Peter Milne - forthcoming - History and Philosophy of Logic:1-14.
    Drawing on recently published correspondence as well as on a survey of Polish and international philosophical activity published in 1937 and details concerning the publisher and bookseller Aleksander Mazzucato, I provide evidence that, contrary to some recent assertions (but in line with older bibliographical entries), Tarski's ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ was not published in journal form until 1936, although preprints, lacking two corrections and a small addendum, were likely available in the late months of 1935.
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  38. Probability as a Measure of Information Added.Peter Milne - 2012 - Journal of Logic, Language and Information 21 (2):163-188.
    Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways (...)
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  39.  71
    Frege's context principle.Peter Milne - 1986 - Mind 95 (380):491-495.
  40.  80
    The foundations of probability and quantum mechanics.Peter Milne - 1993 - Journal of Philosophical Logic 22 (2):129 - 168.
    Taking as starting point two familiar interpretations of probability, we develop these in a perhaps unfamiliar way to arrive ultimately at an improbable claim concerning the proper axiomatization of probability theory: the domain of definition of a point-valued probability distribution is an orthomodular partially ordered set. Similar claims have been made in the light of quantum mechanics but here the motivation is intrinsically probabilistic. This being so the main task is to investigate what light, if any, this sheds on quantum (...)
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  41.  25
    Minimal doxastic logic: probabilistic and other completeness theorems.Peter Milne - 1993 - Notre Dame Journal of Formal Logic 34 (4):499-526.
  42.  88
    Frege, informative identities, and logicism.Peter Milne - 1989 - British Journal for the Philosophy of Science 40 (2):155-166.
  43.  93
    Intuitionistic Relevant Logic and Perfect Validity.Peter Milne - 1994 - Analysis 54 (3):140 - 142.
  44.  61
    Verification, falsification, and the logic of enquiry.Peter Milne - 1991 - Erkenntnis 34 (1):23 - 54.
    Our starting point is Michael Luntley's falsificationist semantics for the logical connectives and quantifiers: the details of his account are criticised but we provide an alternative falsificationist semantics that yields intuitionist logic, as Luntley surmises such a semantics ought. Next an account of the logical connectives and quantifiers that combines verificationist and falsificationist perspectives is proposed and evaluated. While the logic is again intuitionist there is, somewhat surprisingly, an unavoidable asymmetry between the verification and falsification conditions for negation, the conditional, (...)
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  45.  47
    Methodological and conceptual challenges in rare and severe event forecast verification.Philip A. Ebert & Peter Milne - 2022 - Natural Hazards and Earth System Science 22 (2):539-557.
    There are distinctive methodological and conceptual challenges in rare and severe event (RSE) forecast verification, that is, in the assessment of the quality of forecasts of rare but severe natural hazards such as avalanches, landslides or tornadoes. While some of these challenges have been discussed since the inception of the discipline in the 1880s, there is no consensus about how to assess RSE forecasts. This article offers a comprehensive and critical overview of the many different measures used to capture the (...)
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  46.  9
    Cavaillès on Gentzen ‘ dans son poêle’: A Brief Historical Note.Peter Milne - forthcoming - History and Philosophy of Logic:1-3.
    In his biography of Gerhard Gentzen, Eckart Menzler-Trott includes an extract from a letter written by Jean Cavaillès to his friend and fellow philosopher of mathematics Albert Lautman on 3rd Septe...
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  47. Sensibility and the Law: On Rancière's Reading of Lyotard.Peter Milne - 2011 - Symposium: Canadian Journal of Continental Philosophy/Revue canadienne de philosophie continentale 15 (2):95-119.
    This paper responds to Rancière’s reading of Lyotard’s analysis of the sublime by attempting to articulate what Lyotard would call a “differend” between the two. Sketching out Rancière’s criticisms, I show that Lyotard’s analysis of the Kantian sublime is more defensible than Rancière claims. I then provide an alternative reading, one that frees Lyotard’s sublime from Rancière’s central accusation that it signals nothing more than the mind’s perpetual enslavement to the law of the Other. Reading the sublime through the figure (...)
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  48.  89
    Benenson, F. C. [1984]: Probability, Objectivity and Evidence. Routledge and Kegan Paul. Hardback £19.95. Pp. xii+284.Peter Milne - 1986 - British Journal for the Philosophy of Science 37 (1):123-126.
  49.  22
    Ron Bontekoe.Modal Metaphysics & Peter Milne - 1992 - International Philosophical Quarterly 32 (2).
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  50.  27
    Annabel and the bookmaker: An everyday tale of bayesian folk.Peter Milne - 1991 - Australasian Journal of Philosophy 69 (1):98 – 102.
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