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The View from 1763: Kant on the Arithmetical Method before Intuition

Ofra Rechter

In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 21--46 (2006)

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Arbitrary combination and the use of signs in mathematics: Kant’s 1763 Prize Essay and its Wolffian background.Katherine Dunlop - 2014 - Canadian Journal of Philosophy 44 (5-6):658-685.details In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) Download Export citation Bookmark 6 citations
Conceptual Analysis and the Analytic Method in Kant’s Prize Essay.Gabriele Gava - 2024 - Hopos: The Journal of the International Society for the History of Philosophy of Science 14 (1):164-184.details Famously, in the essay Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality (Prize Essay), Kant attempts to distance himself from the Wolffian model of philosophical inquiry. In this respect, Kant scholars have pointed out Kant’s claim that philosophy should not imitate the method of mathematics and his appeal to Newton’s “analytic method.” In this article, I argue that there is an aspect of Kant’s critique of the Wolffian model that has been neglected. Kant presents a powerful (...) Download Export citation Bookmark
Kant on the imagination and geometrical certainty.Mary Domski - 2010 - Perspectives on Science 18 (4):409-431.details My goal in this paper is to develop our understanding of the role the imagination plays in Kant’s Critical account of geometry, and I do so by attending to how the imagination factors into the method of reasoning Kant assigns the geometer in the First Critique. Such an approach is not unto itself novel. Recent commentators, such as Friedman (1992) and Young (1992), have taken a careful look at the constructions of the productive imagination in pure intuition and highlighted the (...) Download Export citation Bookmark 1 citation
Kant's Conception of Number.Daniel Sutherland - 2017 - Philosophical Review Current Issue 126 (2):147-190.details Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets aside the role of intuition for the nonce to investigate Kant's conception of natural number. Although Kant himself doesn't distinguish between a cardinal and an ordinal conception of number, some of the properties Kant attributes to number (...) Download Export citation Bookmark 3 citations

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