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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
Posted in Philosophy of Mathematics
Tagged After Aristotle, Peter Smith, Peter Smith's An Introduction to Formal Logic, Philosophy of Mathematics, Richard. E. Hennessey, Stewart Shapiro, Stewart Shapiro's The Oxford Handbook of Philosophy of Mathematics and Logic, Stewart Shapiro’s Thinking about Mathematics
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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
Posted in Philosophy of Mathematics
Tagged After Aristotle, Anti-realism in the Ontology of Mathematical Objects, Anti-realism in the Ontology of Numbers, Complex Questions, Numbers, Philosophy of Mathematics, Realism in the Ontology of Mathematical Objects, Realism in the Ontology of Numbers, Realism in the Philosophy of Mathematics, Richard. E. Hennessey, Sets, Stewart Shapiro’s Thinking about Mathematics
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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
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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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 →