Extending a Kantian Dichotomy to a Poincaréan Trichotomy :: Philosophy Philosophical Papers

Extending a Kantian Dichotomy to a Poincaran TrichotomyABSTRACT I argue for the possibility of experience by innovation which is neither priori nor posteriori. My caprice of companionship by invention evolves from Poincars conventionalism, but unlike Poincars conventions, propositions known by invention have a truth value. An individuating criteria for this type of knowledge is conjectured. The proposition known through invention is gounded historically in the discipline to which it belongs a result of the careful, sincere and objective quest and effort of the knower chosen freely by the inventer or knower and, private in its invention but public once invented. I extend knowledge by invention to include the knowledge of the invented proposition by those who do not invent it but accept it as a convention for good reasons. Finally, knowledge by invention combined with a revisionist, Platonist definition of knowledge as actively justified true belief provides a pedagogical model reviving the proactive spirit of the Socratic method with an emphasis on invention and activity and a de-emphasis on information gathering and passivity.I. IntroductionKants priori - posteriori and analytic - synthetic distinctions inaugurated mod epistemology and provided the architecture for knowledge in mathematics, science and metaphysics. (1) The product of the two distinctions yields three kinds of knowledge synthetic priori, analytic priori and synthetic posteriori analytic posteriori being impossible. For Kant propositions like 7+5=12, all bodies have mass and every event has a cause. were synthetic and known priorily. (2) Post-Kantian philosophy witnessed an attack on the possibility of synthetic priori knowledge such as the rejections of analysis, geometry and arithmetic as synthetic priori by Bolzano, Helmholtz and Frege respectively. (3) These were motivated by a fear that Kants conceptualism, of the mind imposing space and time on the world, may lead to anti-r ealism, such as that of Husserls bracketing the existence of the world based on his extensions of Descartes and Kant. (4) Nominalism and idealism are anti-realist but conceptualism and conventionalism need not be. I extend the typology of knowledge by adding knowledge by invention. Many fundamental propositions of mathematics, science and metaphysics hence shift from the realm of synthetic priori to the realm of knowledge by invention. For Poincar fundamental definitions of mathematics are neither priori nor posteriori, but conventional. I suggest that conventional means known by invention. I will argue in this paper for this unconventional interpretation of Poincars conventionalism.