1/14/2020 0 Comments
Extending a Kantian Dichotomy to a PoincarÃ©an Trichotomy ABSTRACT: I argue for the possibility of knowledge by invention which is neither Ã¡ priori nor Ã¡ posteriori. My conception of knowledge by invention evolves from PoincarÃ©â€™s conventionalism, but unlike PoincarÃ©â€™s 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. Introduction Kant's Ã priori - Ã posteriori and analytic - synthetic distinctions inaugurated Modern 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 Ã priori, analytic Ã priori and synthetic Ã posteriori; analytic Ã posteriori being impossible. For Kant propositions like; "7+5=12," "all bodies have mass" and "every event has a cause." were synthetic and known Ã priorily. (2) Post-Kantian philosophy witnessed an attack on the possibility of synthetic Ã priori knowledge such as the rejections of analysis, geometry and arithmetic as synthetic Ã priori by Bolzano, Helmholtz and Frege respectively. (3) These were motivated by a fear that Kant's conceptualism, of the mind imposing space and time on the world, may lead to anti-realism, such as that of Husserl's 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 Ã priori to the realm of knowledge by invention. For PoincarÃ© fundamental definitions of mathematics are neither Ã priori nor Ã posteriori, but conventional. I suggest that "conventional" means "known by invention." I will argue in this paper for this unconventional interpretation of PoincarÃ©'s conventionalism.
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