Online research in philosophy

In the chapter “The Geometry of Visibles” in his ‘Inquiry into the Human Mind’, Thomas Reid constructs a special space, develops a special geometry for that space, and offers a natural model for this geometry. In doing so, Reid “discovers” non-Euclidean Geometry sixty years before the mathematicians. This paper examines this “discovery” and the philosophical motivations underlying it. By reviewing Reid’s ideas on visible space and confronting him with Kant and Berkeley, I hope, moreover, to resolve an alleged impasse in Reid’s philosophy concerning the contradictory characteristics of Reid’s tangible and visible space.

In this paper, I reconstruct Edmund Husserl's view on the relationship between formal inquiry and the life-world, using the example of formal geometry. I first outline Husserl's account of geometry and then argue that he believed that the applicability of formal geometry to intuitive space (the space of everyday-experience) guarantees the conceptual continuity between different notions of space.

The standard mathematical account of the sub-metrical geometry of a space employs topology, whose foundational concept is the open set. This proves to be an unhappy choice for discrete spaces, and offers no insight into the physical origin of geometrical structure. I outline an alternative, the Theory of Linear Structures, whose foundational concept is the line. Application to Relativistic space-time reveals that the whole geometry of space-time derives from temporal structure. In this sense, instead of spatializing time, Relativity temporalizes space.

I elaborate and defend an interpretation of Leibniz on which he is committed to a stronger space-time structure than so-called Leibnizian space-time, with absolute speeds grounded in his concept of force rather than in substantival space and time. I argue that this interpretation is well-motivated by Leibniz's mature writings, that it renders his views on space, time, motion, and force consistent with his metaphysics, and that it makes better sense of his replies to Clarke than does the standard interpretation. Further, it illuminates the way in which Leibniz took his physics to be grounded in his metaphysics.

Earman and Norton argue that manifold realism leads to inequivalence of Leibniz-shifted space-time models, with undesirable consequences such as indeterminism. I respond that intrinsic axiomatization of space-time geometry shows the variant models to be isomorphic with respect to the physically meaningful geometric predicates, and therefore certainly physically equivalent because no theory can characterize its models more closely than this. The contrary philosophical arguments involve confusions about identity and representation of space-time points, fostered by extrinsic coordinate formulations and irrelevant modal metaphysics. I conclude that neither the revived Einstein hole argument nor the original Leibniz indiscernibility argument have any force against manifold realism.

Anthony Savile clearly identifies the intellectual assumptions that underlie Leibniz's thought and locates the text within Leibniz's larger philosophical ...

Two of Leibniz's most studied and often quoted works appear in this volume. Published in 1686, the Discourse on Metaphysics consists of the philosopher's explanation of individual perception as an expression of the rest of the universe from a unique perspective. The whole world--the best of all possible worlds, as he famously remarks--is thus contained in each individual substance. The Monadology, written in 1714, offers a concise synopsis of Leibniz's philosophy, establishing the laws of final causes, which underlie God's free choice to create the best possible world--a world that serves as dynamic and perfectly ordered evidence of the wisdom of its creator. Translated by George R. Montgomery.

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