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 / 2. Geometry
Newton developed a kinematic approach to geometry [Kitcher]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Quantities and ratios which continually converge will eventually become equal
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 [Heisenberg]
14. Science / C. Induction / 1. Induction
Science deduces propositions from phenomena, and generalises them by induction
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
We should admit only enough causes to explain a phenomenon, and no more
Natural effects of the same kind should be assumed to have the same causes
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
From the phenomena, I can't deduce the reason for the properties of gravity
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Newton's four fundamentals are: space, time, matter and force [Russell]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
Mass is central to matter [Hart,WD]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
An attraction of a body is the sum of the forces of their particles
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
You have discovered that elliptical orbits result just from gravitation and planetary movement [Leibniz]
We have given up substantial forms, and now aim for mathematical laws
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. Classical Physics / 1. Mechanics / a. Explaining movement
Newton reclassified vertical motion as violent, and unconstrained horizontal motion as natural [Harré]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
Newton's Third Law implies the conservation of momentum [Papineau]
Inertia rejects the Aristotelian idea of things having natural states, to which they return [Alexander,P]
1: Bodies rest, or move in straight lines, unless acted on by forces
2: Change of motion is proportional to the force
3: All actions of bodies have an equal and opposite reaction
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Newton's idea of force acting over a long distance was very strange
Newton introduced forces other than by contact [Papineau]
Newton's laws cover the effects of forces, but not their causes [Papineau]
Newton's forces were accused of being the scholastics' real qualities [Pasnau]
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
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
Newton showed that falling to earth and orbiting the sun are essentially the same [Ellis]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
Early Newtonians could not formulate conservation of energy, having no concept of potential energy [Papineau]
27. Natural Reality / C. Space-Time / 1. Space / d. Substantival space
Absolute space is independent, homogeneous and immovable
27. Natural Reality / C. Space-Time / 2. Time / a. Time
If there is no uniform motion, we cannot exactly measure time
27. Natural Reality / C. Space-Time / 2. Time / c. Tenseless (B) time
Absolute time, from its own nature, flows equably, without relation to anything external
27. Natural Reality / C. Space-Time / 2. Time / e. Existence of time
Time exists independently, and flows uniformly
28. God / A. Divine Nature / 3. Divine Perfections
If a perfect being does not rule the cosmos, it is not God
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The elegance of the solar system requires a powerful intellect as designer