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An essay on the foundations of geometry

Note 5 — Introductory material

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I shall, therefore, throughout the present Essay, use the word à priori without any psychological implication. My test of apriority will be purely logical: Would experience be impossible, if a certain axiom or postulate were denied? Or, in a more restricted sense, which gives apriority only within a particular science: Would experience as to the subject-matter of that science be impossible, without a certain axiom or postulate? My results also, therefore, will be purely logical. If Psychology declares that some things, which I have declared à priori, are not subjective, then, failing an error of detail in my proofs, the connection of the à priori and the subjective, so far as those things are concerned, must be given up. There will be no discussion, accordingly, throughout this Essay, of the relation of the à priori to the subjective—a relation which cannot determine what pieces of knowledge are à priori, but rather depends on that determination, and belongs, in any case, rather to Metaphysics than to Epistemology.

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