Southern Journal of Philosophy 54 (3):312-332 (2016)

Authors
Zvi Biener
University of Cincinnati
Abstract
Accounts of Hobbes’s ‘system’ of sciences oscillate between two extremes. On one extreme, the system is portrayed as wholly axiomtic-deductive, with statecraft being deduced in an unbroken chain from the principles of logic and first philosophy. On the other, it is portrayed as rife with conceptual cracks and fissures, with Hobbes’s statements about its deductive structure amounting to mere window-dressing. This paper argues that a middle way is found by conceiving of Hobbes’s _Elements of Philosophy_ on the model of a mixed-mathematical science, not the model provided by Euclid’s _Elements of Geometry_. I suggest that Hobbes is a test case for understanding early-modern system-construction more generally, as inspired by the structure of the applied mathematical sciences. This approach has the additional virtue of bolstering, in a novel way, the thesis that the transformation of philosophy in the long seventeenth century was heavily indebted to mathematics, a thesis that has increasingly come under attack in recent years.
Keywords Hobbes  Philosophy of Science  Mixed-Mathematics  Subalternation  Deduction  Mathematization  Geometry  Optics
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Reprint years 2016
DOI 10.1111/sjp.12175
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Spinoza on Extension.Alison Peterman - 2015 - Philosophers' Imprint 15.
Aristotle on Meaning and Essence.Travis Butler - 2002 - Philosophical Review 111 (2):302.

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Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics.Marcus P. Adams - 2016 - Studies in History and Philosophy of Science Part A 56:43-51.

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