On the theory of the infinite in modern thought

by Eleanor F. Jourdain

[6] So Galileo, Newton, Huygens were philosophers in science. Descartes, Pascal, Leibniz were mathematicians as well as philosophers.

[7] See S. Augustine, De Civitate Dei, Book XII. ch. xix.: “Ita vero suis quisque numerus proprietatibus terminatur, ut nullus eorum par esse cuicumque alteri possit. Ergo et dispares inter se atque diversi sunt, et singuli quique finiti sunt, et omnes infiniti sunt.”

[8] See R. Dedekind, Was sind und was sollen die Zahlen? 1893.

[9] Two transfinite aggregates can have an ordinal correspondence with one another.

[10] See G. Cantor, Zur Lehre vom Transfiniten. 1890.

[11] e.g. Mr. P. Jourdain, Philosophical Magazine. 1904.

[12] The same result is hinted at by Mr. Taylor. Taylor, “Elements of Metaphysics,” p. 22.

[13] Linear order, 1, 2, 3, &c. Circular. A CD B, A CD B.… The latter, it is true, involves the idea of separation. But this idea can be developed from those of inclusion and exclusion, which belong to the fundamental laws of thought.

[14] The Absolute, according to a recent metaphysical thinker, is “a conscious life which embraces the totality of existence, all at once, and in a perfect systematic unity, as the content of its experience.”—Taylor, “Elements of Metaphysics,” p. 60.