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  1.  53 DLs
    Andrei Rodin (2011). Categories Without Structures. Philosophia Mathematica 19 (1):20-46.
    The popular view according to which category theory provides a support for mathematical structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies ‘invariant form’ (Awodey) categorical mathematics studies covariant and contravariant transformations which, generally, have no invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics.
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  2.  35 DLs
    Andrei Rodin (2010). How Mathematical Concepts Get Their Bodies. Topoi 29 (1):53-60.
    When the traditional distinction between a mathematical concept and a mathematical intuition is tested against examples taken from the real history of mathematics one can observe the following interesting phenomena. First, there are multiple examples where concepts and intuitions do not well fit together; some of these examples can be described as “poorly conceptualised intuitions” while some others can be described as “poorly intuited concepts”. Second, the historical development of mathematics involves two kinds of corresponding processes: poorly conceptualised intuitions are (...)
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  3.  16 DLs
    Andrei Rodin (2008). Category Theory and Mathematical Structuralism. Proceedings of the Xxii World Congress of Philosophy 41:37-40.
    Category theory doesn't support Mathematical Structuralism but suggests a new philosophical view on mathematics, which differs both from Structuralism and from traditional Substantialism about mathematical objects. While Structuralism implies thinking of mathematical objects up to isomorphism the new categorical view implies thinking up to general morphism.
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  4.  14 DLs
    Andrei Rodin (2004). The Vessels and the Glue: Space, Time, and Causation. Behavioral and Brain Sciences 27 (5):633-634.
    In addition to the “universal glue,” which is the local mechanical causation, the standard explanatory scheme of classical science presumes two “universal vessels,” which are global space and time. I call this outdated metaphysical setting “black-and-white” because it allows for only two principal scales. A prospective metaphysics able to bind existing sciences together needs to be “colored,” that is, allow for scale relativity and diversification by domain.
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  5.  12 DLs
    Valeria de Paiva & Andrei Rodin (2013). Elements of Categorical Logic: Fifty Years Later. [REVIEW] Logica Universalis 7 (3):265-273.
  6.  7 DLs
    Juha Räikkä & Andrei Rodin (2015). Environmental Security and Just Causes for War. Almanac: Discourses of Ethics 10 (1):47-54.
    This article asks whether a country that suffers from serious environmental problems caused by another country could have a just cause for a defensive war? Danish philosopher Kasper Lippert-Rasmussen has argued that under certain conditions extreme poverty may give a just cause for a country to defensive war, if that poverty is caused by other countries. This raises the question whether the victims of environmental damages could also have a similar right to self-defense. Although the article concerns justice of war, (...)
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  7.  6 DLs
    Andrei Rodin (2007). Identity and Categorification. Philosophia Scientiae 11 (2):27-65.
    In this paper I consider the standard approach to identity in mathematics originating from Frege’s and Russell’s works and contrast it with alternative approaches due to Plato and Geach. Then I put the problem in a category-theoretic setting and show that the notion of identity cannot be “internalized” with usual categorical means. Finally I present two more specific mathematical approaches to the identity problem: one based on a categorical fibration and the other involving weak higher categories.RésuméDans cet article je présente (...)
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