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Tag Archives: Arithmetic
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
Posted in Philosophy of Mathematics
Tagged After Aristotle, Alfred North Whitehead’s Process and Reality, Aristotelianism in the Philosophy of Mathematics, Arithmetic, Geometry, Number, Number and Reality, Ontology, Philosophy of Mathematics, Platonism in the Philosophy of Mathematics, Realism in the Philosophy of Mathematics, Richard Hennessey, Stewart Shapiro’s Thinking about Mathematics
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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
Posted in Philosophy of Mathematics
Tagged After Aristotle, Arithmetic, Definition of What It Is to Be Four Existents, Definition of What It Is to Be One Existent, Definition of What It Is to Be Three Existents, Definition of What It Is to Be Two Existents, Ontological Arithmetic, Ontology, Philosophy of Mathematics, Proof That Any Existent Is One Existent, Proof That One Existent Plus One Existent Are Two Existents, Proof That Two Existents Plus One Existent Are Three Existents, Proof That Two Existents Plus Two Existents Are Four Existents, Richard. E. Hennessey
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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
Posted in Philosophy of Mathematics
Tagged After Aristotle, Apodicticism in Philosophy of Mathematics, Arithmetic, Definition of What It Is to Be Four Existents, Definition of What It Is to Be One Existent, Definition of What It Is to Be Three Existents, Definition of What It Is to Be Two Existents, Identity, Ontological Arithmetic, Philosophy of Mathematics, Reflexivity of Identity, Richard Hennessey, Symmetry of Identity, Transitivity of Identity
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Introduction
The aim of After Aristotle is that of promoting and engaging in serious philosophical discussion from the point of view of a Neo-Aristotelian philosophical perspective. This philosophical perspective is one that, as suggested by the blog title, is in some central theses … Continue reading
After Aristotle 
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 →