Hartshorne & Lovejoy
on combinatorics & philosophical significance

As I have emphasized exhaustiveness in searching the possible answers philosophical question, he stresses the exhaustiveness of pertinent considerations. Perhaps both maxims come to much the same, I am not yet sure of this. How does one find the pertinent or relevant considerations to a philosophical question or issue? How does one know that one’s list is exhaustive? My answer is, by the mathematics of combinations of concepts, either ignoring permutations, or definitely including them. Otherwise I see no way. Lovejoy barely mentions mathematics in the article (Hartshorne 1990, p. 390).

Minor points by great philosophers are dealt with, often with loving care, but major points by minor philosophers are missed. One reason for this is that the historians have not sufficiently considered beforehand what the important ideas might be. In doing general history good common sense, shrewdness, and broad culture enable the historian to know what the important possibilities for human action are, but in doing history of philosophy more than this is required. One must have in mind some carefully worked-out system of possible positions on various problems in order to decide what in intellectual history is most worth knowing. Here position matrices, made exhaustive by formal logical means, are valuable. With such schemes in mind the historian can ask himself, who has held position (1) out of a set of, say, three possible positions arising from a given matrix, and who has held positions (2) or (3)? It may then turn out that all the major philosophers missed one position, while some minor philosophers did not. This in my view has actually happened (Hartshorne 1970, pp. 86-87.


Campbell, James. “Arthur Lovejoy and the Progress of PhilosophyTransactions of the Charles S. Peirce Society, vol. 39, no. 4, Fall, 2003, pp. 617-643.

Dombrowski, Daniel. “Lovejoy, Hartshorne, and Progress in PhilosophyMetaphilosophy, vol. 25, no. 4, October 1994, pp. 335-347. [Source of above quotes.]

Hartshorne, Charles. Creative Synthesis and Philosophic Method. LaSalle, IL: Open Court, 1970.

________________. The Darkness and the Light. Albany: State University of New York Press, 1990.

Lovejoy, Arthur O. “On Some Conditions of Progress in Philosophical Inquiry,” The Philosophical Review, vol. 26, no. 2, March 1917, pp. 123-163.

Is philosophical creativity combinatorial? by Henri Lefebvre

Why Isn’t There More Progress in Philosophy (theses or arguments?)
by David J. Chalmers

Adorno on Progress in Philosophy

Is Systematic Philosophy Possible Today?” (1975 / 1977) by Mihailo Marković

Mihailo Marković on systematic philosophy in 1975 by R. Dumain

Problems of the History of Philosophy by Theodore Oizerman, review
by Ralph Dumain

Principles of the Theory of Historical Process in Philosophy by T.I Oizerman & A.S. Bogomolov, review
by R. Dumain

Leibniz & Ideology: Selected Bibliography

Philosophical and Universal Languages, 1600-1800, and Related Themes: Selected Bibliography

Ars Combinatoria Study Guide

Philosophy of History of Philosophy & Historiography of Philosophy:
Selected Bibliography


Ars Combinatoria @ Ĝirafo (blog)

ars combinatoria @ Studies in a Dying Culture

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