1 Introduction
2 Defining the Sciences
Aristotle’s Accounts
Ptolemy’s Definitions Are Not Aristotle’s
Ptolemy’s Aristotelian Definitions
Conclusion
3 Knowledge or Conjecture
Ptolemy’s Epistemology: Neither Aristotle’s nor Plato’s
Platonic Epistemology
Ptolemy on Opinion and Knowledge
The Indisputability of Mathematical Demonstration
Mathematics’ Contribution to Physics and Theology
Conclusion
4 Mathematics and the Good Life
The Distinction between Theoretical and Practical Philosophy
Virtues
How to Order Actions
Resembling the Divine
Conclusion
5 Harmonia
Harmonia: What and Where It Is
The Beauty of Mathematical Objects
Harmonics
Harmonic Ratios in the Human Soul
Harmonic Ratios in the Heavens
Conclusion
6 Harmonics and Astronomy
Cousin Sciences
Sure and Incontrovertible Knowledge?
Different Methods, Different Claims to Truth
Consequences
7 Mathematizing the Human Soul
The Nature and Structure of the Soul in
On the Kritêrion and Hêgemonikon
The Structure of the Soul in the Harmonics:The Aristotelian Account
The Development of Ptolemy’s Scientific Method
The Structure of the Soul in the Harmonics: The Platonic and Synthetic Accounts
Conclusion
8 Astrology and Cosmology
Astrological Conjecture
Celestial Powers and Rays
Celestial Souls and Bodies
Conclusion
9 Conclusion
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