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It is commonly claimed that Kant's critical philosophy aims to limit reason's speculative use and its metaphysical pretensions. This paper argues that such claims should be amended in light of a technical distinction between negative limits and positive boundaries that Kant held throughout his career. Kant's only extended discussion of this distinction appears in §§57–60 of the Prolegomena, a division entitled "On pure reason's boundary‐determination". I examine these sections in detail in order to elucidate the account of the limits and boundaries of the activity of different cognitive faculties in the Critique of Pure Reason. I argue that once we understand a key ambition of the Critique to be the positive determination of the boundary between objects of experience and things in themselves, we gain insight into the essential contribution that Kant's theory of the positive utility of ideas of reason makes to the critical philosophy. [ABSTRACT FROM AUTHOR]

Abstract: Salomon Maimon argued forcefully for the indispensability of what he called “the method of fictions” in mathematics and physics, but also in philosophy. This last claim provoked critical responses from G. E. Brastberger, G. E. Schultze, and K. L. Reinhold. This paper offers a brief exposition of Maimon's “method of fictions” and an analysis of his response to critics of his claims concerning the employment of this method within philosophy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, I argue that in spite of suggestions to the contrary, Merleau‐Ponty defends a positive account of the kind of abstract thought involved in mathematics and natural science. More specifically, drawing on both the Phenomenology of Perception and his later writings, I show that, for Merleau‐Ponty, abstract thought and perception stand in the two‐way relation of “foundation,” according to which abstract thought makes what we perceive explicit and determinate, and what we perceive is made to appear by abstract thought. I claim that, on Merleau‐Ponty's view, although this process can sometimes lead to falsification, it can also be carried out in such a manner that allows mathematics and natural science to articulate what we perceive in a way that is non‐distortive and in keeping with the demands of perception itself. [ABSTRACT FROM AUTHOR]