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All the ideas for 'works', 'Philosophy of Mathematics' and 'Theaetetus'

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57 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
Hegel produced modern optimism; he failed to grasp that consciousness never progresses [Hegel, by Cioran]
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
Hegel was the last philosopher of the Book [Hegel, by Derrida]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophers are always switching direction to something more interesting [Plato]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Hegel doesn't storm the heavens like the giants, but works his way up by syllogisms [Kierkegaard on Hegel]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
For Hegel, things are incomplete, and contain external references in their own nature [Hegel, by Russell]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
On the continent it is generally believed that metaphysics died with Hegel [Benardete,JA on Hegel]
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Understanding mainly involves knowing the elements, not their combinations [Plato]
Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato]
2. Reason / A. Nature of Reason / 6. Coherence
A rational account is essentially a weaving together of things with names [Plato]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux]
2. Reason / C. Styles of Reason / 1. Dialectic
Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie]
2. Reason / C. Styles of Reason / 3. Eristic
Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato]
2. Reason / D. Definition / 4. Real Definition
A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We master arithmetic by knowing all the numbers in our soul [Plato]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
The dialectical opposition of being and nothing is resolved in passing to the concept of becoming [Hegel, by Scruton]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton]
7. Existence / B. Change in Existence / 1. Nature of Change
There seem to be two sorts of change: alteration and motion [Plato]
7. Existence / E. Categories / 4. Category Realism
For Hegel, categories shift their form in the course of history [Hegel, by Houlgate]
Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate]
7. Existence / E. Categories / 5. Category Anti-Realism
Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
A sum is that from which nothing is lacking, which is a whole [Plato]
The whole can't be the parts, because it would be all of the parts, which is the whole [Plato]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Things are only knowable if a rational account (logos) is possible [Plato]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Expertise is knowledge of the whole by means of the parts [Plato]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
It is impossible to believe something which is held to be false [Plato]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
How can a belief exist if its object doesn't exist? [Plato]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H]
12. Knowledge Sources / B. Perception / 1. Perception
Perception is infallible, suggesting that it is knowledge [Plato]
Our senses could have been separate, but they converge on one mind [Plato]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato]
Thought must grasp being itself before truth becomes possible [Plato]
You might mistake eleven for twelve in your senses, but not in your mind [Plato]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
An inadequate rational account would still not justify knowledge [Plato]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Parts and wholes are either equally knowable or equally unknowable [Plato]
Without distinguishing marks, how do I know what my beliefs are about? [Plato]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato]
A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Maybe primary elements can be named, but not receive a rational account [Plato]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
A rational account of a wagon would mean knowledge of its hundred parts [Plato]
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
What evidence can be brought to show whether we are dreaming or not? [Plato]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato]
Clearly some people are superior to others when it comes to medicine [Plato]
How can a relativist form opinions about what will happen in the future? [Plato]
23. Ethics / F. Existentialism / 1. Existentialism
Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Hegel's Absolute Spirit is the union of human rational activity at a moment, and whatever that sustains [Hegel, by Eldridge]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton]
26. Natural Theory / A. Speculations on Nature / 1. Nature
When man wills the natural, it is no longer natural [Hegel]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof [Schopenhauer on Hegel]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
There must always be some force of evil ranged against good [Plato]