Combining Texts

All the ideas for 'A Puzzle about Belief', 'Euthydemus' and 'On the Infinite'

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17 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
I aim to establish certainty for mathematical methods [Hilbert]
We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
Beautiful things must be different from beauty itself, but beauty itself must be present in each of them [Plato]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowing how to achieve immortality is pointless without the knowledge how to use immortality [Plato]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Say how many teeth the other has, then count them. If you are right, we will trust your other claims [Plato]
18. Thought / B. Mechanics of Thought / 5. Mental Files
Puzzled Pierre has two mental files about the same object [Recanati on Kripke]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
What knowledge is required to live well? [Plato]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
Only knowledge of some sort is good [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
Something which lies midway between two evils is better than either of them [Plato]