Ideas from 'Principia Mathematica' by Isaac Newton [1687], by Theme Structure

[found in 'Philosophical Writings' by Newton,Isaac [CUP 2004,0-521-53848-3]].

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1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy must abstract from the senses
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / m. Limits
Quantities and ratios which continually converge will eventually become equal
6. Mathematics / A. Nature of Mathematics / 5. Geometry
Newton developed a kinematic approach to geometry
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
I suspect that each particle of bodies has attractive or repelling forces
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Particles mutually attract, and cohere at short distances
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
The place of a thing is the sum of the places of its parts
14. Science / B. Scientific Theories / 6. Theory Holism
If you changed one of Newton's concepts you would destroy his whole system
14. Science / C. Induction / 1. Induction
Science deduces propositions from phenomena, and generalises them by induction
14. Science / D. Explanation / 2. Types of Explanation / f. Causal explanations
Natural effects of the same kind should be assumed to have the same causes
We should admit only enough causes to explain a phenomenon, and no more
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by essence
From the phenomena, I can't deduce the reason for the properties of gravity
26. Natural Theory / B. Concepts of Nature / 1. Basis of Nature
Newton's four fundamentals are: space, time, matter and force
26. Natural Theory / B. Concepts of Nature / 3. Space / c. Substantival space
Absolute space is independent, homogeneous and immovable
26. Natural Theory / B. Concepts of Nature / 4. Time / a. Time
If there is no uniform motion, we cannot exactly measure time
26. Natural Theory / B. Concepts of Nature / 4. Time / c. Tenseless (B) time
Absolute time, from its own nature, flows equably, without relation to anything external
26. Natural Theory / B. Concepts of Nature / 4. Time / e. Existence of time
Time exists independently, and flow uniformly
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
We have given up substantial forms, and now aim for mathematical laws
You have discovered that elliptical orbits result just from gravitation and planetary movement
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
I am not saying gravity is essential to bodies
27. Natural Reality / A. Physics / 1. Matter / f. Corpuscles
An attraction of a body is the sum of the forces of their particles
27. Natural Reality / A. Physics / 1. Matter / i. Modern matter
Mass is central to matter
27. Natural Reality / A. Physics / 2. Movement
2: Change of motion is proportional to the force
3: All actions of bodies have an equal and opposite reaction
Newton reclassified vertical motion as violent, and unconstrained horizontal motion as natural
Inertia rejects the Aristotelian idea of things having natural states, to which they return
1: Bodies rest, or move in straight lines, unless acted on by forces
27. Natural Reality / A. Physics / 3. Force
Newton's forces were accused of being the scholastics' real qualities
Newton showed that falling to earth and orbiting the sun are essentially the same
I am studying the quantities and mathematics of forces, not their species or qualities
The aim is to discover forces from motions, and use forces to demonstrate other phenomena
Newton's idea of force acting over a long distance was very strange
28. God / A. Divine Nature / 3. Divine Perfections
If a perfect being does not rule the cosmos, it is not God
28. God / D. Proofs of Evidence / 2. Teleological Proof
The elegance of the solar system requires a powerful intellect as designer