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Mill, mathematics, and the naturalist tradition

In John Skorupski (ed.), The Cambridge Companion to Mill. New York: Cambridge University Press. pp. 57--111 (1998)

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  1. Mill and Acton on Liberty, Nationality and Multinational States.Tim Beaumont - 2023 - Nations and Nationalism 29 (4):1196–1211..
    Mill's System of Logic (1843) indicates that the definition of ‘nationality’ he offered in Considerations on Representative Government (1861) is not a throwaway comment but a carefully considered causal hypothesis tailored to his politico-ethological research programme. This matters because Lord Acton's critique of Mill's claim that free institutions are almost impossible in multinational states ignored the definition, thereby obscuring subsequent scholars' vision of the conceptual dimension of this famous dispute. Although Mill struggled in his politico-ethological endeavour, he was sufficiently confident (...)
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  • Mathematics as a science of non-abstract reality: Aristotelian realist philosophies of mathematics.James Franklin - 2022 - Foundations of Science 27 (2):327-344.
    There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article lays out and compares these (...)
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  • Mereological Nominalism.Nikk Effingham - 2018 - Philosophy and Phenomenological Research 100 (1):160-185.
    Philosophy and Phenomenological Research, EarlyView.
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  • El alcance del escepticismo moral.Martín Farrell - 2013 - Análisis Filosófico 33 (1):47-66.
    El escepticismo moral sostiene que las proposiciones morales no son verdaderas ni falsas de acuerdo al criterio de verdad por correspondencia, y que el criterio de verdad por coherencia no es aplicable en moral. Para refutarlo, habría que mostrar la existencia de hechos morales, o demostrar que la coherencia es suficiente para una buena teoría moral. El artículo sostiene que esto no puede hacerse. Moral skepticism maintains that moral propositions are no true, nor false, according with the correspondence theory of (...)
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  • Fregean One-to-one Correspondence and Numbers as Object Properties.Boris Grozdanoff - 2009 - Principia: An International Journal of Epistemology 13 (3):327-338.
    The paper critically examines an unpopular line of Frege’s view on numbers in the Foundations of Arithmetic. According to this view, which analyzes numbers in terms of properties and not in terms of extensions, numbers are properties of concepts vs. properties of objects. The latter view is held by Mill and is famously criticized in the Foundations. I argue that on the property account numbers cannot only be properties of concepts but they also have to be properties of objects. My (...)
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  • John Stuart mill.Fred Wilson - 2008 - Stanford Encyclopedia of Philosophy.
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  • Frege on Number Properties.Andrew D. Irvine - 2010 - Studia Logica 96 (2):239-260.
    In the Grundlagen , Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive.
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