24 found
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  1.  28
    Non-metric Propositional Similarity.A. C. Paseau - forthcoming - Erkenntnis:1-22.
    The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘\ is closer in meaning to \ than \ is to \’ and thereby give a precise account of comparative propositional similarity facts. Notably, (...)
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  2.  16
    Arithmetic, Enumerative Induction and Size Bias.A. C. Paseau - 2021 - Synthese 199 (3-4):9161-9184.
    Number theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states that every even number greater than 2 is the sum of two primes. Enumerative inductive evidence for such conjectures usually consists of small cases. In the absence of supporting reasons, mathematicians mistrust such evidence for arithmetical generalisations, more so than most other forms of non-deductive evidence. Some philosophers have also expressed scepticism about the value of enumerative inductive evidence in (...)
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  3.  17
    Is English Consequence Compact?A. C. Paseau & Owen Griffiths - 2021 - Thought: A Journal of Philosophy 10 (3):188-198.
    Thought: A Journal of Philosophy, Volume 10, Issue 3, Page 188-198, September 2021.
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  4.  76
    A Measure of Inferential-Role Preservation.A. C. Paseau - 2019 - Synthese 196 (7):2621-2642.
    The point of formalisation is to model various aspects of natural language. Perhaps the main use to which formalisation is put is to model and explain inferential relations between different sentences. Judged solely by this objective, a formalisation is successful in modelling the inferential network of natural language sentences to the extent that it mirrors this network. There is surprisingly little literature on the criteria of good formalisation, and even less on the question of what it is for a formalisation (...)
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  5.  54
    Isomorphism Invariance and Overgeneration.Owen Griffiths & A. C. Paseau - 2016 - Bulletin of Symbolic Logic 22 (4):482-503.
    The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of ‘logical constant’ which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider five (...)
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  6.  53
    Did Frege Commit a Cardinal Sin?A. C. Paseau - 2015 - Analysis 75 (3):379-386.
    Frege’s _Basic Law V_ is inconsistent. The reason often given is that it posits the existence of an injection from the larger collection of first-order concepts to the smaller collection of objects. This article explains what is right and what is wrong with this diagnosis.
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  7.  55
    The Overgeneration Argument(S): A Succinct Refutation.A. C. Paseau - 2014 - Analysis 74 (1):ant097.
    The overgeneration argument attempts to show that accepting second-order validity as a sound formal counterpart of logical truth has the unacceptable consequence that the Continuum Hypothesis is either a logical truth or a logical falsehood. The argument was presented and vigorously defended in John Etchemendy’s The Concept of Logical Consequence and it has many proponents to this day. Yet it is nothing but a seductive fallacy. I demonstrate this by considering five versions of the argument; as I show, each is (...)
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  8.  78
    What’s the Point of Complete Rigour?A. C. Paseau - 2016 - Mind 125 (497):177-207.
    Complete inferential rigour is achieved by breaking down arguments into steps that are as small as possible: inferential ‘atoms’. For example, a mathematical or philosophical argument may be made completely inferentially rigorous by decomposing its inferential steps into the type of step found in a natural deduction system. It is commonly thought that atomization, paradigmatically in mathematics but also more generally, is pro tanto epistemically valuable. The paper considers some plausible candidates for the epistemic value arising from atomization and finds (...)
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  9. An Exact Measure of Paradox.A. C. Paseau - 2013 - Analysis 73 (1):17-26.
    We take seriously the idea that paradoxes come in quantifiable degree by offering an exact measure of paradox. We consider three factors relevant to the degree of paradox, which are a function of the degree of belief in each of the individual propositions in the paradox set and the degree of belief in the set as a whole. We illustrate the proposal with a particular measure, and conclude the discussion with some critical remarks.
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  10.  14
    Compactness Theorem.A. C. Paseau - 2022 - Internet Encyclopedia of Philosophy.
    The Compactness Theorem The compactness theorem is a fundamental theorem for the model theory of classical propositional and first-order logic. As well as having importance in several areas of mathematics, such as algebra and combinatorics, it also helps to pinpoint the strength of these logics, which are the standard ones used in mathematics and arguably … Continue reading Compactness Theorem →.
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  11.  12
    Logos, Logic and Maximal Infinity.A. C. Paseau - 2022 - Religious Studies 58 (2):420-435.
    Recent developments in the philosophy of logic suggest that the correct foundational logic is like God in that both are maximally infinite and only partially graspable by finite beings. This opens the door to a new argument for the existence of God, exploiting the link between God and logic through the intermediary of the Logos. This article explores the argument from the nature of God to the nature of logic, and sketches the converse argument from the nature of logic to (...)
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  12.  9
    The Compactness Theorem.A. C. Paseau, and & Robert Leek - 2022 - Internet Encyclopedia of Philosophy.
    The Compactness Theorem The compactness theorem is a fundamental theorem for the model theory of propositional and first-order logic. As well as having importance in several areas of mathematics, such as algebra and combinatorics, it also helps to pinpoint the strength of these logics, which are the standard ones used in mathematics and arguably … Continue reading Lunder →.
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  13.  6
    Lunder.A. C. Paseau, and & Robert Leek - 2022 - Internet Encyclopedia of Philosophy.
    The Compactness Theorem The compactness theorem is a fundamental theorem for the model theory of propositional and first-order logic. As well as having importance in several areas of mathematics, such as algebra and combinatorics, it also helps to pinpoint the strength of these logics, which are the standard ones used in mathematics and arguably … Continue reading Lunder →.
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  14.  32
    Propositionalism.A. C. Paseau - 2021 - Journal of Philosophy 118 (8):430-449.
    Propositionalism is the claim that all logical relations can be captured by propositional logic. It is usually regarded as obviously false, because propositional logic seems too weak to capture the rich logical structure of language. I show that there is a clear sense in which propositional logic can match first-order logic, by producing formalizations that are valid iff their first-order counterparts are, and also respect grammatical form as the propositionalist construes it. I explain the real reason propositionalism fails, which is (...)
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  15.  63
    Fairness and Aggregation.A. C. Paseau & Ben Saunders - 2015 - Utilitas 27 (4):460-469.
    Sometimes, two unfair distributions cancel out in aggregate. Paradoxically, two distributions each of which is fair in isolation may give rise to aggregate unfairness. When assessing the fairness of distributions, it therefore matters whether we assess transactions piecemeal or focus only on the overall result. This piece illustrates these difficulties for two leading theories of fairness before offering a formal proof that no non-trivial theory guarantees aggregativity. This is not intended as a criticism of any particular theory, but as a (...)
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  16.  48
    Justin Clarke-Doane* Morality and Mathematics.Michael Bevan & A. C. Paseau - 2020 - Philosophia Mathematica 28 (3):442-446.
    _Justin Clarke-Doane* * Morality and Mathematics. _ Oxford University Press, 2020. Pp. xx + 208. ISBN: 978-0-19-882366-7 ; 978-0-19-2556806.† †.
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  17. David Papineau. Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets. Oxford: Oxford University Press, 2012. ISBN 978-0-19965173-3. Pp. Xix + 224. [REVIEW]A. C. Paseau - 2013 - Philosophia Mathematica (1):nkt006.
  18.  36
    Justin Clarke-Doane*Morality and Mathematics.Michael Bevan & A. C. Paseau - forthcoming - Philosophia Mathematica.
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  19.  35
    Isomorphism Invariance and Overgeneration – Corrigendum.O. Griffiths & A. C. Paseau - 2017 - Bulletin of Symbolic Logic 23 (4):546-546.
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  20.  41
    Philosophy of the Matrix.A. C. Paseau - 2017 - Philosophia Mathematica 25 (2):246-267.
    A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.
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  21.  50
    JOHN P. BURGESS Rigor and Structure.A. C. Paseau - 2016 - British Journal for the Philosophy of Science 67 (4):1185-1187.
  22.  35
    The Laws of Belief: Ranking Theory & its Philosophical Applications, by Wolfgang Spohn.A. C. Paseau - 2017 - Mind 126 (501):273-278.
    The Laws of Belief: Ranking Theory & its Philosophical Applications, by SpohnWolfgang. New York: Oxford University Press, 2012. Pp. xv + 598.
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  23.  2
    Philosophy of Mathematics.A. C. Paseau (ed.) - 2016 - Routledge.
    Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and the (...)
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  24.  37
    James Robert Brown. Platonism, Naturalism, and Mathematical Knowledge. New York and London: Routledge, 2012. Isbn 978-0-415-87266-9. Pp. X + 182. [REVIEW]A. C. Paseau - 2012 - Philosophia Mathematica 20 (3):359-364.