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All the ideas for 'works', 'fragments/reports' and 'The Foundations of Mathematics'

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92 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
For Plato true wisdom is supernatural [Plato, by Weil]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Everything happens necessarily, and for a reason [Democritus]
2. Reason / C. Styles of Reason / 1. Dialectic
Two contradictories force us to find a relation which will correlate them [Plato, by Weil]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / L. Paradox / 1. Paradox
Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
True Being only occurs when it is completely full, with atoms and no void [Democritus, by Aristotle]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
Being does not exist more than non-being [Democritus, by Aristotle]
The non-existent exists as much as the existent, because it has causal powers [Democritus]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
The only distinctions are Configuration (shape), Disposition (order) and Turning (position) [Democritus, by Aristotle]
7. Existence / B. Change in Existence / 1. Nature of Change
Nothing comes from non-existence, or passes into it [Democritus, by Diog. Laertius]
7. Existence / E. Categories / 5. Category Anti-Realism
It is not possible to know what sort each thing is [Democritus]
8. Modes of Existence / A. Relations / 3. Structural Relations
Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle]
Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas]
When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato]
The Forms cannot be changeless if they are in changing things [Aristotle on Plato]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki]
Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Democritus denies reality to large objects, because atomic entities can't combine to produce new ones [Benardete,JA on Democritus]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Democritus said that substances could never be mixed, so atoms are the substances [Democritus, by Aristotle]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki]
9. Objects / D. Essence of Objects / 2. Types of Essence
Only universals have essence [Plato, by Politis]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Plato and Aristotle take essence to make a thing what it is [Plato, by Politis]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
I just confront the evidence, and let it act on me [Ramsey]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / a. Qualities in perception
Sensible qualities can't be real if they appear different to different creatures [Democritus, by Theophrastus]
12. Knowledge Sources / B. Perception / 3. Representation
Man is separated from reality [Democritus]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
All evidence comes from senses, so they are indispensable to the mind [Democritus]
Obscure knowledge belongs to the five senses, and genuine knowledge is the other type [Democritus]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Democritus says there is either no truth, or it is concealed from us [Democritus, by Aristotle]
We actually know nothing, and opinions are mere flux [Democritus]
We in fact know nothing, but we each restructure our reality with beliefs [Democritus]
It is obviously impossible to understand the reality of each thing [Democritus]
We know nothing in reality; for truth lies in an abyss [Democritus]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Democritus was devoted to discovering causal explanations [Democritus, by Eusebius]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Democritus says soul consists of smooth round bodies brought together in accidental collision [Democritus, by Cicero]
Atomists say soul has a rational part in the chest, and a diffused non-rational part [Democritus, by Aetius]
The soul is the same as the mind [Democritus, by Aristotle]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Animals have a share of reason [Democritus, by Porphyry]
15. Nature of Minds / A. Nature of Mind / 8. Brain
The directive centre is located in the whole head [Democritus, by Ps-Plutarch]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Democritus said everything happens of necessity, by natural motion of atoms [Democritus, by Cicero]
Some say there is a determinate cause for every apparently spontaneous event [Democritus, by Aristotle]
Democritus said atoms only move by their natural motions, which are therefore necessary [Democritus, by Cicero]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Democritus says spherical atoms are fire, and constitute the soul [psuche] [Democritus, by Aristotle]
Democritus says the soul is the body, and thinking is thus the mixture of the body [Democritus, by Theophrastus]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Plato wanted to somehow control and purify the passions [Vlastos on Plato]
19. Language / F. Communication / 1. Rhetoric
Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato]
20. Action / C. Motives for Action / 1. Acting on Desires
Pleasure and pain guide our choices of good and bad [Democritus]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Plato never refers to examining the conscience [Plato, by Foucault]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato]
22. Metaethics / B. Value / 2. Values / d. Health
Wisdom creates a healthy passion-free soul [Democritus]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Happiness is identifying and separating the pleasures [Democritus, by Stobaeus]
Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
Contentment comes from moderation and proportion in life [Democritus, by Stobaeus]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
Democritus says wealth is a burden to the virtuous mind [Democritus, by Seneca]
23. Ethics / F. Existentialism / 4. Boredom
Plato is boring [Nietzsche on Plato]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Atoms cling together, until a stronger necessity disperses them [Democritus, by Aristotle]
Atoms are irregular, hooked, concave, convex, and many other shapes [Democritus, by Aristotle]
'Full' and 'Void' secularised Parmenides's Being and Not-being [Democritus, by Heisenberg]
Atomists say there are only three differences - in shape, arrangement and position [Democritus, by Aristotle]
Experiences are merely convention; only atoms and the void are real [Democritus]
If only atoms are real and the rest is convention, we wouldn't bother to avoid pain [Democritus, by Diogenes of Oen.]
When atoms touch, why don't they coalesce, like water drops? [Aristotle on Democritus]
Because appearance is infinitely varied, atomists assume infinitely many shapes of atom [Democritus, by Aristotle]
There could be an atom the size of the world [Democritus, by Ps-Plutarch]
There must be atoms, to avoid the absurdity of infinite division down to nothing [Democritus, by Aristotle]
The basic atoms are without qualities - which only arise from encounters between atoms [Democritus, by Galen]
If a cone is horizontally sliced the surfaces can't be equal, so it goes up in steps [Democritus]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Greeks explained regularity by intellectual design, not by laws [Democritus, by Frede,M]
27. Natural Reality / C. Space / 1. Void
Growth and movement would not exist if there were no void to receive them [Democritus]
Democritus is wrong: in a void we wouldn't see a distant ant in exact detail [Aristotle on Democritus]
Movement is impossible in a void, because nothing can decide the direction of movement [Aristotle on Democritus]
27. Natural Reality / D. Time / 3. Parts of Time / a. Beginning of time
Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle]
27. Natural Reality / E. Cosmology / 1. Cosmology
There are unlimited worlds of varying sizes, some without life or water [Democritus, by Hippolytus]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
Democritus said people imagined gods as the source of what awed or frightened them [Democritus, by Sext.Empiricus]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
The soul is destroyed with the body [Democritus, by Ps-Plutarch]