Combining Texts

All the ideas for 'works', 'Phil of Mathematics: why nothing works' and 'Number Determiners, Numbers, Arithmetic'

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41 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 / C. Styles of Reason / 1. Dialectic
Two contradictories force us to find a relation which will correlate them [Plato, by Weil]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
An adjective contributes semantically to a noun phrase [Hofweber]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
'2 + 2 = 4' can be read as either singular or plural [Hofweber]
What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
How can you contemplate Platonic entities without causal transactions with them? [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
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]
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]
Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas]
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 / 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 / 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]
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]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
Our minds are at their best when reasoning about objects [Hofweber]
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]
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 / 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
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 / F. Existentialism / 4. Boredom
Plato is boring [Nietzsche on Plato]
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]