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  1.  31
    A. C. Paseau (2016). What’s the Point of Complete Rigour? 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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  2.  75
    A. C. Paseau (2013). An Exact Measure of Paradox. 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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  3.  23
    A. C. Paseau (forthcoming). JOHN P. BURGESS Rigor and Structure. British Journal for the Philosophy of Science:axv046.
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  4. A. C. Paseau (2013). David Papineau. Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets. Oxford: Oxford University Press, 2012. ISBN 978-0-19965173-3. Pp. Xix + 224. [REVIEW] Philosophia Mathematica (1):nkt006.
  5.  25
    A. C. Paseau (2015). Did Frege Commit a Cardinal Sin? 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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  6.  20
    A. C. Paseau & Ben Saunders (2015). Fairness and Aggregation. 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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  7.  23
    A. C. Paseau (forthcoming). A Measure of Inferential-Role Preservation. Synthese:1-22.
    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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  8.  17
    A. C. Paseau (2013). The Overgeneration Argument(S): A Succinct Refutation. 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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  9.  6
    A. C. Paseau (forthcoming). Erratum To: A Measure of Inferential-Role Preservation. Synthese:1-1.
    Erratum to: Synthese DOI 10.1007/s11229-015-0705-5In line 3 of footnote 8 on page 4, ‘allow’ should be ‘disallow’.In line 8 of page 5, \ should be \ and \ should be \. Similarly for lines 1, 2, 3, 7, 8, 13 and 14 of page 6.The entry in row 20 column 6 of the table on page 5 should be 1 rather than 0.The entry \ in row 30 column 5 of the table on page 5 should be \.In line 27 (...)
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  10.  14
    A. C. Paseau (2012). James Robert Brown. Platonism, Naturalism, and Mathematical Knowledge. New York and London: Routledge, 2012. Isbn 978-0-415-87266-9. Pp. X + 182. [REVIEW] Philosophia Mathematica 20 (3):359-364.
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  11. A. C. Paseau (ed.) (2017). Philosophy of Mathematics. 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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