Category Archives: Philosophy of Mathematics

Number and Reality 2. Towards a Philosophy of Mathematics Bibliography

[This post is an exact replacement for the now deleted “Number and Reality 3.” One should not, I think we can all agree, have “Number and Reality 3” immediately succeed “Number and Reality 1” in a series devoted to number … Continue reading

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Number and Reality 1. Some Initial Questions and the Initial Question

1. In the immediately previous post, I observed that I now find myself enjoying the leisure that will allow me “to engage in some serious thinking in the philosophy of mathematics.” More specifically, I announced my intention “to begin the … Continue reading

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Number and Reality 0. An Introduction to a Project in the Philosophy of Mathematics

1. At long last I find myself enjoying a set of circumstances that will allow me to engage in some serious thinking in the philosophy of mathematics; the two September posts, “Ontological Arithmetic. One Realistic Foot in the Door of … Continue reading

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Ontological Arithmetic. The Second Foot in the Door

Greetings. In the immediately previous post, the “Ontological Arithmetic. One Realistic Foot in the Door of the Philosophy of Mathematics” of September 24, 2020, I said that in the present post I would “spell out how one can prove, demonstrate, … Continue reading

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Ontological Arithmetic. One Realistic Foot in the Door of the Philosophy of Mathematics

The aim of the present post is three-fold. I wish first to draw attention to the ontological theory of identity, i.e., of existents as identical with existents, and three quite basic principles of the theory. I then wish to then … Continue reading

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Thomas Aquinas: Beyond Aristotle’s Aristotelian Conception of the Numerical

1. In the first lecture of his Commentary on Aristotle’s Physics* and in the course of an effort at distinguishing the science of physics from those of mathematics and metaphysics, Thomas Aquinas presents the well-known (at least within Aristotelian circles) … Continue reading

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The Beginnings of a Neo-Aristotelian Critique of the Aristotelian Philosophy of Mathematics

0. The purpose of the present post is to take a first step in spelling out the “neo-Aristotelian,” as its tagline characterizes it, point of view motivating this blog. First, the “Aristotelian” of the “neo-Aristotelian” remains apt, despite the “neo.” … Continue reading

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