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  1.  89
    Trumping Naturalism Revisited.A. C. Paseau - 2024 - In Sophia Arbeiter & Juliette Kennedy (eds.), The Philosophy of Penelope Maddy. Springer. pp. 267-290.
    Whenever science returns a confident and univocal answer to a question, Trumping Naturalism enjoins us to accept it. The majority of contemporary philosophers are sympathetic to this sort of position. Indeed, several have endorsed it or something very close to it. Arguments for Trumping Naturalism, however, are scant, the principal one being the Track Record Argument. The argument is based on the fact that in cases of conflict, science has a better track record than non-scientific forms of inquiry such as (...)
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  2. Lakatos and the Euclidean Programme.A. C. Paseau & Wesley Wrigley - forthcoming - In Roman Frigg, Jason Alexander, Laurenz Hudetz, Miklos Rédei, Lewis Ross & John Worrall (eds.), The Continuing Influence of Imre Lakatos's Philosophy: a Celebration of the Centenary of his Birth. Springer.
    Euclid’s Elements inspired a number of foundationalist accounts of mathematics, which dominated the epistemology of the discipline for many centuries in the West. Yet surprisingly little has been written by recent philosophers about this conception of mathematical knowledge. The great exception is Imre Lakatos, whose characterisation of the Euclidean Programme in the philosophy of mathematics counts as one of his central contributions. In this essay, we examine Lakatos’s account of the Euclidean Programme with a critical eye, and suggest an alternative (...)
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  3. (1 other version)Non-deductive justification in mathematics.A. C. Paseau - 2023 - Handbook of the History and Philosophy of Mathematical Practice.
    In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? -/- The answer is an emphatic yes, as I explain in this article. I argue that non-deductive justification is in fact pervasive in mathematics, and that it (...)
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  4. Reducing Arithmetic to Set Theory.A. C. Paseau - 2009 - In Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan. pp. 35-55.
    The revival of the philosophy of mathematics in the 60s following its post-1931 slump left us with two conflicting positions on arithmetic’s ontological relationship to set theory. W.V. Quine’s view, presented in 'Word and Object' (1960), was that numbers are sets. The opposing view was advanced in another milestone of twentieth-century philosophy of mathematics, Paul Benacerraf’s 'What Numbers Could Not Be' (1965): one of the things numbers could not be, it explained, was sets; the other thing numbers could not be, (...)
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  5. Logos, Logic and Maximal Infinity.A. C. Paseau - 2022 - Religious Studies 58:420-435.
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  6. Ancestral Links.A. C. Paseau - 2022 - The Reasoner 16 (7):55-56.
    This short article discusses the fact that the word ‘ancestor’ features in certain arguments that a) are apparently logically valid, b) contain infinitely many premises, and c) are such that none of their finite sub-arguments are logically valid. The article's aim is to motivate, within its brief compass, the study of infinitary logics.
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  7. Dissemination Corner: One True Logic.A. C. Paseau & Owen Griffiths - 2022 - The Reasoner 16 (1):3-4.
    A brief article introducing *One True Logic*. The book argues that there is one correct foundational logic and that it is highly infinitary.
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  8. Focussed Issue of The Reasoner on Infinitary Reasoning.A. C. Paseau & Owen Griffiths (eds.) - 2022
    A focussed issue of The Reasoner on the topic of 'Infinitary Reasoning'. Owen Griffiths and A.C. Paseau were the guest editors.
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  9.  99
    What is Logical Consequence? [REVIEW]A. C. Paseau - 2024 - Philosophia Mathematica 32 (3):385-400.
    An essay review of Gila Sher's *Logical Consequence*.
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