Combining Texts

All the ideas for 'Set Theory and related topics (2nd ed)', 'Eudemian Ethics' and 'Principia Mathematica'

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86 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy must abstract from the senses [Newton]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Contrary statements can both be reasonable, if they are meant in two different ways [Aristotle]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
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 / l. Limits
Quantities and ratios which continually converge will eventually become equal [Newton]
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]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
The thesis of the Form of the Good (or of anything else) is verbal and vacuous [Aristotle]
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]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
The two right angles of a triangle necessitate that a quadrilateral has four [Aristotle]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Knowing is having knowledge; understanding is using knowledge [Aristotle]
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]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Courage from spirit is natural and unconquerable, as seen in the young [Aristotle]
Whether the mind has parts is irrelevant, since it obviously has distinct capacities [Aristotle]
16. Persons / F. Free Will / 3. Constraints on the will
A man is the cause of what is within his power, and what he causes is in his power [Aristotle]
16. Persons / F. Free Will / 4. For Free Will
Only a human being can be a starting point for an action [Aristotle]
18. Thought / A. Modes of Thought / 3. Emotions / d. Emotional feeling
Some emotional states are too strong for human nature [Aristotle]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Nearly all the good and bad states of character are concerned with feelings [Aristotle]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Akrasia is the clash of two feelings - goodness and pleasure [Aristotle]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
Choice results when deliberation brings together an opinion with an inclination [Aristotle]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
Unlike in inanimate things, in animate things actions have more than one starting point [Aristotle]
The deliberative part of the soul discerns explanatory causes [Aristotle]
20. Action / C. Motives for Action / 4. Responsibility for Actions
An action is voluntary when it is accompanied by thought of some kind [Aristotle]
We are responsible if our actions reflect our motivation [Aristotle, by Frede,M]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Acts are voluntary if done knowingly, by the agent, and in his power to avoid it [Aristotle]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
What is natural for us is either there at birth, or appears by normal processes [Aristotle]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
No one would choose life just for activities not done for their own sake [Aristotle]
22. Metaethics / B. Value / 2. Values / b. Successful function
Wearing a shoe is its intrinsic use, and selling it (as a shoe) is its coincidental use [Aristotle]
22. Metaethics / B. Value / 2. Values / d. Health
Everything seeks, not a single good, but its own separate good [Aristotle]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
We judge people from their deeds because we cannot see their choices (which matter more) [Aristotle]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Horses, birds and fish are not happy, lacking a divine aspect to their natures [Aristotle]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Happiness involves three things, of which the greatest is either wisdom, virtue, or pleasure [Aristotle]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Virtue is different from continence [Aristotle]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Excellence is the best state of anything (like a cloak) which has an employment or function [Aristotle]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
Character (éthos) is developed from habit (ethos) [Aristotle]
Character virtues (such as courage) are of the non-rational part, which follows the rational part [Aristotle]
Character is shown by what is or is not enjoyed, and virtue chooses the mean among them [Aristotle]
We judge character not by their actions, but by their reasons for actions [Aristotle]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
People sometimes exhibit both extremes together, but the mean is contrary to both of them [Aristotle]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
Possessors of a virtue tend to despise what reason shows to be its opposite [Aristotle]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
Greatness of soul produces all the virtues - and vice versa [Aristotle]
23. Ethics / C. Virtue Theory / 3. Virtues / b. Temperance
If someone just looks at or listens to beautiful things, they would not be thought intemperate [Aristotle]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Courage follows reason, which tells us to choose what is noble [Aristotle]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
Honour depends on what it is for, and whether it is bestowed by worthy people [Aristotle]
23. Ethics / C. Virtue Theory / 4. External Goods / a. External goods
Goods in the soul are more worthy than those outside it, as everybody wants them [Aristotle]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Decent people can be friends with base people [Aristotle]
Friendship cannot be immediate; it takes time, and needs testing [Aristotle]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The main function of politics is to produce friendship [Aristotle]
25. Social Practice / D. Justice / 1. Basis of justice
The best cure for mutual injustice is friendship [Aristotle]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
It is folly not to order one's life around some end [Aristotle]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
Eyes could be used for a natural purpose, or for unnatural seeing, or for a non-seeing activity [Aristotle]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Each thing's function is its end [Aristotle]
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]
3: All actions of bodies have an equal and opposite reaction [Newton]
Newton's Third Law implies the conservation of momentum [Newton, by Papineau]
2: Change of motion is proportional to the force [Newton]
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]