Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Justice: What's the right thing to do?' and 'Principia Mathematica'

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66 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy must abstract from the senses [Newton]
3. Truth / A. Truth Problems / 3. Value of Truth
Speak truth only to those who deserve the truth [Sandel]
Careful evasions of truth at least show respect for it [Sandel]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Newton developed a kinematic approach to geometry [Newton, by Kitcher]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Quantities and ratios which continually converge will eventually become equal [Newton]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
I suspect that each particle of bodies has attractive or repelling forces [Newton]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Particles mutually attract, and cohere at short distances [Newton]
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 [Newton]
14. Science / B. Scientific Theories / 6. Theory Holism
If you changed one of Newton's concepts you would destroy his whole system [Heisenberg on Newton]
14. Science / C. Induction / 1. Induction
Science deduces propositions from phenomena, and generalises them by induction [Newton]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
We should admit only enough causes to explain a phenomenon, and no more [Newton]
Natural effects of the same kind should be assumed to have the same causes [Newton]
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 [Newton]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Does consent create the obligation, or must there be some benefit? [Sandel]
Moral contracts involve both consent and reciprocity; making the deal, and keeping it [Sandel]
Not all deals are fair deals [Sandel]
23. Ethics / B. Contract Ethics / 2. Golden Rule
The categorical imperative is not the Golden Rule, which concerns contingent desires [Sandel]
23. Ethics / D. Deontological Ethics / 5. Persons as Ends
Man cannot dispose of himself, because he is not a thing to be owned [Sandel]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Just visiting (and using roads) is hardly ratifying the Constitution [Sandel]
24. Political Theory / B. Nature of a State / 3. Constitutions
A ratified constitution may not be a just constitution [Sandel]
A just constitution harmonises the different freedoms [Sandel]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Liberal freedom was a response to assigned destinies like caste and class [Sandel]
25. Social Practice / B. Equalities / 4. Economic equality
Libertarians just want formal equality in a free market; the meritocratic view wants fair equality [Sandel]
25. Social Practice / D. Justice / 1. Basis of justice
We can approach justice through welfare, or freedom, or virtue [Sandel]
Justice concerns how a society distributes what it prizes - wealth, rights, power and honours [Sandel]
Should we redress wrongs done by a previous generation? [Sandel]
Distributive justice concern deserts, as well as who gets what [Sandel]
Justice is about how we value things, and not just about distributions [Sandel]
Work is not fair if it is negotiated, even in a fair situation, but if it suits the nature of the worker [Sandel]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
Teleological thinking is essential for social and political issues [Sandel]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Newton's four fundamentals are: space, time, matter and force [Newton, by Russell]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
Mass is central to matter [Newton, by 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 [Newton]
26. Natural Theory / C. Causation / 1. Causation
Newtonian causation is changes of motion resulting from collisions [Newton, by Baron/Miller]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
You have discovered that elliptical orbits result just from gravitation and planetary movement [Newton, by Leibniz]
We have given up substantial forms, and now aim for mathematical laws [Newton]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
I am not saying gravity is essential to bodies [Newton]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Newton reclassified vertical motion as violent, and unconstrained horizontal motion as natural [Newton, by Harré]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
Inertia rejects the Aristotelian idea of things having natural states, to which they return [Newton, by Alexander,P]
1: Bodies rest, or move in straight lines, unless acted on by forces [Newton]
2: Change of motion is proportional to the force [Newton]
3: All actions of bodies have an equal and opposite reaction [Newton]
Newton's Third Law implies the conservation of momentum [Newton, by Papineau]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Newton's idea of force acting over a long distance was very strange [Heisenberg on Newton]
Newton introduced forces other than by contact [Newton, by Papineau]
Newton's laws cover the effects of forces, but not their causes [Newton, by Papineau]
Newton's forces were accused of being the scholastics' real qualities [Pasnau on Newton]
I am studying the quantities and mathematics of forces, not their species or qualities [Newton]
The aim is to discover forces from motions, and use forces to demonstrate other phenomena [Newton]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
Newton showed that falling to earth and orbiting the sun are essentially the same [Newton, by 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 [Newton, by Papineau]
27. Natural Reality / C. Space / 4. Substantival Space
Absolute space is independent, homogeneous and immovable [Newton]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Newton needs intervals of time, to define velocity and acceleration [Newton, by Le Poidevin]
Newton thought his laws of motion needed absolute time [Newton, by Bardon]
Time exists independently, and flows uniformly [Newton]
Absolute time, from its own nature, flows equably, without relation to anything external [Newton]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
Newtonian mechanics does not distinguish negative from positive values of time [Newton, by Coveney/Highfield]
27. Natural Reality / D. Time / 3. Parts of Time / d. Measuring time
If there is no uniform motion, we cannot exactly measure time [Newton]
28. God / A. Divine Nature / 3. Divine Perfections
If a perfect being does not rule the cosmos, it is not God [Newton]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The elegance of the solar system requires a powerful intellect as designer [Newton]