Peter Milne University of Stirling
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  1. Peter Milne (2013). Not Every Truth has a Truthmaker II. 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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  2. Peter Milne (2013). Operations Are Punctuation Marks'. In Peter Sullivan Michael Potter (ed.), Wittgenstein's Tractatus. History and Interpretation. Oup. 97.
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  3. Peter Milne (2012). Belief, Degrees of Belief, and Assertion. Dialectica 66 (3):331-349.
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  4. Peter Milne (2012). Indicative Conditionals, Conditional Probabilities, and the “Defective Truth-Table”: A Request for More Experiments. 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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  5. Peter Milne (2012). Probability as a Measure of Information Added. 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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  6. Peter Milne (2011). Sensibility and the Law: On Rancière's Reading of Lyotard. Symposium: The Canadian Journal of Continental Philosophy 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 lawof the Other. Reading the sublime through the figure of (...)
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  7. Peter Milne (2010). Subformula and Separation Properties in Natural Deduction Via Small Kripke Models. 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 Lindenbaumlmarck.
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  8. Joseph S. Fulda & Peter Milne (2009). The Mathematical Pull of Temptation Revisited. Acta Analytica 24 (2):91-96.
    In this paper, we defend and extend a (simple) mathematical model of akrasia.
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  9. Peter Milne (2009). What is the Normative Role of Logic? 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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  10. Peter Milne (2008). Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events. Studia Logica 90 (3):425 - 453.
    Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an approximation (...)
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  11. Peter Milne (2008). Russell's Completeness Proof. History and Philosophy of Logic 29 (1):31-62.
    Bertrand Russell’s 1906 article ‘The Theory of Implication’ contains an algebraic weak completeness proof for classical propositional logic. Russell did not present it as such. We give an exposition of the proof and investigate Russell’s view of what he was about, whether he could have appreciated the proof for what it is, and why there is no parallel of the proof in Principia Mathematica.
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  12. Peter Milne (2007). Existence and Identity in Free Logic: Two Comments. Mind 116 (464):1079-1082.
    Professor Tennant and I agree on much regarding the proof-theoretic semantics of free logic. Here I point to two issues, one on which we disagree, the other on which I find it hard to say how closely we may agree. The first concerns the exact content of Tennant's Rule of Atomic Denotation. The second concerns the nature of assumptions whose formal counterparts contain parametric occurrences of names.
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  13. Peter Milne (2007). Existence, Freedom, Identity, and the Logic of Abstractionist Realism. 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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  14. Peter Milne (2007). Omniscient Beings Are Dialetheists. Analysis 67 (295):250–251.
  15. Peter Milne (2007). On Gödel Sentences and What They Say. 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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  16. Peter Milne (2007). On Gödel Sentences and What They Say. 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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  17. Peter Milne (2005). Not Every Truth has a Truthmaker. 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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  18. W. Aitken, L. Alberucci, D. J. Anderson, J. A. Barrett, K. Bimbó, B. Brown, E. Dresner, P. Milne, M. Peterson & G. Priest (2004). Freund, MA, 237 Glanzberg, M., 27 Hawthorne, J., 89 Jané, I., 437 Ju, S., 481. Journal of Philosophical Logic 33 (641).
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  19. Peter Milne (2004). Algebras of Intervals and a Logic of Conditional Assertions. 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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  20. Peter Milne (2003). Bayesianism V. Scientific Realism. Analysis 63 (4):281–288.
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  21. Peter Milne (2003). The Simplest Lewis-Style Triviality Proof Yet? Analysis 63 (4):300–303.
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  22. Peter Milne (2002). Harmony, Purity, Simplicity and a “Seemingly Magical Fact”. The Monist 85 (4):498-534.
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  23. Peter Milne (2001). Book Review. The Taming of the True Neil Tennant. [REVIEW] Mind 110 (438):569-577.
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  24. Peter Milne (2001). The Design Inference: Eliminating Chance Through Small Probabilities. British Journal for the Philosophy of Science 52 (4):801-808.
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  25. Peter Milne (2000). Is There a Logic of Confirmation Transfer? 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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  26. P. Milne (1999). Beaney, M.-Frege. Philosophical Books 40:30-32.
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  27. Peter Milne (1999). Tarski on Truth and its Definition. Proceedings of the Aristotelian Society 99:141-167.
    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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  28. Peter Milne (1999). Tarski, Truth and Model Theory. 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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  29. Peter Milne (1998). Disjunction and Disjunctive Syllogism. Canadian Journal of Philosophy 28 (1):21 - 32.
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  30. Peter Milne (1997). Bruno de Finetti and the Logic of Conditional Events. 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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  31. Peter Milne (1997). Quick Triviality Proofs for Probabilities of Conditionals. Analysis 57 (1):75–80.
  32. Peter Milne (1996). Log\ documentclass {aastex}\ usepackage {amsbsy}\ usepackage {amsfonts}\ usepackage {amssymb}\ usepackage {bm}\ usepackage {mathrsfs}\ usepackage {pifont}\ usepackage {stmaryrd}\ usepackage {textcomp}\ usepackage {portland, xspace}\ usepackage {amsmath, amsxtra}\ usepackage [OT2, OT1]{fontenc}\ newcommand\ cyr {\ renewcommand\ rmdefault {wncyr}\ renewcommand\ sfdefault {wncyss}\ renewcommand\ encodingdefault {OT2}\ normalfont\ selectfont}\ DeclareTextFontCommand {\ textcyr}{\ cyr}\ pagestyle {empty ... [REVIEW] Philosophy of Science 63:21-26.
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  33. Peter Milne (1996). Log[P(H/Eb)/P(H/B)] is the One True Measure of Confirmation. Philosophy of Science 63 (1):21-26.
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  34. Peter Milne (1996). On Tennant's Intuitionist Relevant Logics. Australasian Journal of Philosophy 74 (1):175 – 181.
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  35. Peter Milne (1995). A Bayesian Defence of Popperian Science? Analysis 55 (3):213 - 215.
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  36. Peter Milne (1995). On the Completeness of Non-Philonian Stoic Logic. History and Philosophy of Logic 16 (1):39-64.
  37. Peter Milne, Donald Gillies, Peter Kosso & Alan Musgrave (1995). 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. [REVIEW] Philosophical Quarterly 45 (180):379.
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  38. Peter Milne (1994). Classical Harmony: Rules of Inference and the Meaning of the Logical Constants. 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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  39. Peter Milne (1994). Intuitionistic Relevant Logic and Perfect Validity. Analysis 54 (3):140 - 142.
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  40. Peter Milne (1994). Review: The Physicalization of Mathematics. [REVIEW] British Journal for the Philosophy of Science 45 (1):305 - 340.
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  41. Peter Milne (1993). Counterparts and Comparatives. Analysis 53 (2):82 - 92.
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  42. Peter Milne (1993). Inference to the Best Explanation. Philosophy and Phenomenological Research 53 (4):970-972.
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  43. Peter Milne (1993). The Foundations of Probability and Quantum Mechanics. 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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  44. Peter Milne (1993). Minimal Doxastic Logic: Probabilistic and Other Completeness Theorems. Notre Dame Journal of Formal Logic 34 (4):499-526.
  45. Modal Metaphysics & Peter Milne (1992). Ron Bontekoe. International Philosophical Quarterly 32 (2).
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  46. Peter Milne (1992). Languages of Possibility: An Essay in Philosophical Logic. Philosophical Books 31 (4):222-224.
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  47. Peter Milne (1992). Modal Metaphysics and Comparatives. Australasian Journal of Philosophy 70 (3):248 – 262.
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  48. Peter Milne (1992). The Analytic Tradition: Meaning, Thought and Knowledge. Philosophical Books 33 (1):20-22.
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  49. Peter Milne (1991). Annabel and the Bookmaker: An Everyday Tale of Bayesian Folk. Australasian Journal of Philosophy 69 (1):98 – 102.
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  50. Peter Milne (1991). A Dilemma for Subjective Bayesians — and How to Resolve It. Philosophical Studies 62 (3):307 - 314.
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  51. Peter Milne (1991). Conditionalisation and Quantum Probabilities. Australasian Journal of Philosophy 69 (2):214 – 218.
  52. Peter Milne (1991). Verification, Falsification, and the Logic of Enquiry. 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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  53. Graham Oddie & Peter Milne (1991). Act and Value: Expectation and the Representability of Moral Theories. 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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  54. Peter Milne (1990). Scotching the Dutch Book Argument. 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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  55. Graham Oddie & Peter Milne (1990). Act and Value. Theoria 57:42-76.
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  56. Peter Milne (1989). Frege, Informative Identities, and Logicism. British Journal for the Philosophy of Science 40 (2):155-166.
  57. Peter Milne (1989). Schlesinger On Justified Belief And Probability. Analysis 49 (January):11-16.
    George schlesinger has characterized justified belief probabilistically. I question the propriety of this characterization and demonstrate that with respect to it certain principles of epistemic logic that he considers plausible are unsound.
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  58. Peter Milne (1989). Science Without Unity: Reconciling the Human and Natural Sciences. Philosophical Books 30 (1):62-63.
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  59. Peter Milne (1988). Reply to Currie. Mind 97 (387):457-460.
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  60. Peter Milne (1987). Physical Probabilities. Synthese 73 (2):329 - 359.
    A conception of probability as an irreducible feature of the physical world is outlined. Propensity analyses of probability are examined and rejected as both formally and conceptually inadequate. It is argued that probability is a non-dispositional property of trial-types; probabilities are attributed to outcomes as event-types. Brier's Rule in an objectivist guise is used to forge a connection between physical and subjective probabilities. In the light of this connection there are grounds for supposing physical probability to obey some standard set (...)
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  61. Peter Milne (1986). Benenson, F. C. [1984]: Probability, Objectivity and Evidence. Routledge and Kegan Paul. Hardback £19.95. Pp. Xii+284. [REVIEW] British Journal for the Philosophy of Science 37 (1):123-126.
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  62. Peter Milne (1986). Can There Be a Realist Single-Case Interpretation of Probability? Erkenntnis 25 (2):129 - 132.
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  63. Peter Milne (1986). Frege's Context Principle. Mind 95 (380):491-495.
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  64. Peter Milne (1986). Hartry Field on Measurement and Intrinsic Explanation. British Journal for the Philosophy of Science 37 (3):340-346.
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  65. Peter Milne (1985). A Note on Popper, Propensities, and the Two-Slit Experiment. British Journal for the Philosophy of Science 36 (1):66-70.
  66. Peter Milne (1984). Reviews. [REVIEW] British Journal for the Philosophy of Science 35 (1):312-313.
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  67. Peter Milne (1983). A Note on Scale Invariance. British Journal for the Philosophy of Science 34 (1):49-55.
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  68. Peter Milne (1983). Reviews. [REVIEW] British Journal for the Philosophy of Science 34 (3):312-313.
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  69. Peter Milne, Notes on Teaching Logic.
    hese notes don’t reach any conclusions. Their purpose is to point to issues one needs to think through seriously when thinking about logic teaching. They indicate some of the relevant literature where some of these issues are addressed, but they also raise points that seem to have been overlooked. They aim to promote informed discussion. That indeed was their origin: they are descended from an internal discussion document prepared a few years ago when the then Department of Philosophy at the (...)
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  70. Peter Milne, Betting on Fuzzy and Many–Valued Propositions.
    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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  71. Peter Milne, Tractatus 5.4611: 'Signs for Logical Operations Are Punctuation Marks'.
    I examine the ideas leading up to Wittgenstein's pronouncement at Tractatus 5.4611 that signs for logical operations are punctuation marks.
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