Central topic: Nature of space(time).
A. Metaphysics: What kind of thing is space?
Space is an absolute substance existing
independently of physical objects. If
you take all physical objects out of th
15. Einstein and Minkowski Spacetime
Light Postulate of Special Relativity entails:
The speed of light c is
the same in all inertial
c for O
c for O'
O' is moving at consta
14. Poincar and the Conventionality of Geometry
Sum of angles = 180
Sum of angles > 180
Sum of angles < 180
All are logically consistent (all describe
13. Kant and Geometry
What is the ontological status of space?
New topic: How is knowledge of space possible?
Knowledge originates in reason.
Knowledge originates in experience.
Classical Empiricist View:
12. Kant and Handedness
"Concerning the Ultimate Foundation of the Differentiation of
Regions of Space" (1768).
Claim: Absolute space is necessary to explain the existence
of incongruent counterparts.
[An incongruent counterpart
1. Types of Spacetimes
A spacetime is a 4-dim collection of points with additional structure.
Typically, one or more metrics = a specification of
the spatial and temporal distances between points.
10. Berkeley and Mach
1. Berkeley On Absolute Space and Absolute Motion:
"[Absolute space] seems therefore to be mere nothing. The only
slight difficulty arising is that it is extended, and extension is a
positive quality. But
09. The Leibniz-Clarke Correspondence
Series of letters written in 1715-1716.
Defends absolutism (absolute space exists).
Critic of Newton.
Defends relationism (relational theory of space
08. Newton (1643-1727)
De Gravitatione et Aequipondio Fluidorum
(On the Gravity and Equilibrium of Fluids) (~1670)
Mathematical Principles of Natural Philosophy
(Philosophia Naturalis Principia Mathematica) (1687).
space = "pure" matter
07. Descartes (1596-1650)
I. Cartesian Metaphysics
Principia Philosophiae (The Principles of Philosophy)
Three things exist:
minds = thinking substance
bodies = extended substance
God = infinite substance
Complete separation of mind from bod
06. The Aristotelian Tradition
1. John Philoponus (~490-570 A.D.)
Two problems for Aristotle's Theory of Motion:
(1) Problem of Rotation.
The place of an object is the
innermost motionless surface
of the object that contains it.
So: The place of the terr
05. Aristotle (4th century B.C.)
1. The Cosmos
A series of concentric spheres divided into two realms:
The Terestrial Realm
Composed of the elements fire,
air, water, earth.
The Celestial Realm
Composed of the element aether.
The spheres of the sun
03. Euclid's Elements (~300 B.C.)
Earliest existing copy
First English translation
III. Common Notions
more complex claims
02. Plato (427-~348 B.C.)
A. The Theory of Forms
(Phaedo, Republic, Timaeus)
1. Metaphysical Aspects. Two levels to reality:
World of Forms
- World of Being
- true reality
World of sensible objects
16. Einstein and General Relativistic Spacetimes
Problem: Special relativity does not account for the gravitational force.
To include gravity.
Geometricize it! Make it a
feature of spacetime geometry.
(1) New theory ("general relativity