# Categories of Space and of Quantity

@inproceedings{Lawvere1992CategoriesOS, title={Categories of Space and of Quantity}, author={F. William Lawvere}, year={1992} }

0. The ancient and honorable role of philosophy as a servant to the learning, development and use of scientific knowledge, though sadly underdeveloped since Grassmann, has been re-emerging from within the particular science of mathematics due to the latter's internal need; making this relationship more explicit (as well as further investigating the reasons for the decline) will, it is hoped, help to germinate the seeds of a brighter future for philosophy as well as help to guide the much wider…

## 45 Citations

Foundations and Philosophy

- Philosophy
- 2018

This work will explore the connection between foundations and philosophy, outline what is distinctive about the logic of UF, and then describe new philosophical theses one can express in terms of this new logic.

Lautman and the Reality of Mathematics

- Philosophy
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Working in he 1930s, Albert Lautman described with extraordinary clarity the new understanding of mathematics of that time. He delighted in the multiple manifestations of a common idea in different…

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- PhysicsAppl. Categorical Struct.
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The description in engineering mechanics of continuous bodies that can undergo cracking is clarified by an example involving lattices, raising a new questions about the foundations of topology.

Taking Cognition Seriously: A generalised physics of cognition

- PhysicsArXiv
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This work shows that by considering a highly-compact cognitive system, there are fundamental physical trade-offs resulting in a utility problem, and proposes some requirements for ”cognitive categories”, before investigating the phenomenona of topological defects in gauge fields over conceptual spaces.

Grassmann’s Dialectics and Category Theory

- Mathematics
- 1996

In several key connections in his foundations of geometrical algebra, Grassmann makes significant use of the dialectical philosophy of 150 years ago. Now, after fifty years of development of category…

Towards An Approach to Hilbert's Sixth Problem: A Brief Review

- Mathematics
- 2020

In 1900 David Hilbert published his famous list of 23 problems. The sixth of them-the axiomatization of Physics-remains partially unsolved. In this work we will give a gentle introduction and a brief…

Volterra's functionals and covariant cohesion of space

- Philosophy
- 1998

Volterra’s principle of passage from finiteness to infinity is far less limited than a linearized construal of it might suggest; I outline in Section III a nonlinear version of the principle with the…

Hard, Harder, and the Hardest Problem: The Society of Cognitive Selves

- PsychologyTattva - Journal of Philosophy
- 2020

The hard problem of consciousness is explicating how moving matter becomes thinking matter. Harder yet is the problem of spelling out the mutual determinations of individual experiences and the…

Meaning and duality : from categorical logic to quantum physics

- Philosophy
- 2016

Categorical universal logic is developed on the basis of Lawvere’s hyperdoctrine and Hyland-Johnstone-Pitts’ tripos, thereby expanding the realm of (first-order/higher-order) categorical logic so as to encompass, inter alia, classical, intuitionistic, quantum, fuzzy, relevant, and linear logics.

Mathematical Lives: Protagonists of the Twentieth Century from Hilbert to Wiles

- Art
- 2010

Preface.- Hilbert's Problems. A Research Program for Future Generations: U.Bottazzini.-The Way We Were. The Protagonists of the "Italian Spring" in the First Decades of the Twentieth Century:…

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