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A good account on genesis of the modern view of definitions (as opposed to the definitions-first Aristotelian one) is Fontanella, Axioms as Definitions: Revisiting Poincaré and Hilbert. Perhaps the clearest expression of it from Poincare comes from his response to Russell Sur les principes de la géométrie: réponse à M. Russell, Revue de Métaphysique et de ...

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