Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Investigations in the Foundations of Set Theory I' and 'Unpublished Notebooks 1884-85'

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46 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
All the major problems were formulated before Socrates [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
What matters is how humans can be developed [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Thinkers might agree some provisional truths, as methodological assumptions [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Aristotle enjoyed the sham generalities of a system, as the peak of happiness! [Nietzsche]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Thoughts are uncertain, and are just occasions for interpretation [Nietzsche]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Mathematics is just accurate inferences from definitions, and doesn't involve objects [Nietzsche]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
There is no 'being'; it is just the opposition to nothingness [Nietzsche]
7. Existence / D. Theories of Reality / 5. Naturalism
I only want thinking that is anchored in body, senses and earth [Nietzsche]
11. Knowledge Aims / A. Knowledge / 2. Understanding
We can only understand through concepts, which subsume particulars in generalities [Nietzsche]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
Strongly believed a priori is not certain; it may just be a feature of our existence [Nietzsche]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
An affirmative belief is present in every basic sense impression [Nietzsche]
13. Knowledge Criteria / E. Relativism / 1. Relativism
We now have innumerable perspectives to draw on [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Mind is a mechanism of abstraction and simplification, aimed at control [Nietzsche]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
A cognitive mechanism wanting to know itself is absurd! [Nietzsche]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
A 'person' is just one possible abstraction from a bundle of qualities [Nietzsche]
16. Persons / F. Free Will / 6. Determinism / b. Fate
I have perfected fatalism, as recurrence and denial of the will [Nietzsche]
Fate is inspiring, if you understand you are part of it [Nietzsche]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
We start with images, then words, and then concepts, to which emotions attach [Nietzsche]
20. Action / C. Motives for Action / 4. Responsibility for Actions
Judging actions by intentions - like judging painters by their thoughts! [Nietzsche]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
Values need a perspective, of preserving some aspect of life [Nietzsche]
22. Metaethics / B. Value / 2. Values / g. Love
If you love something, it is connected with everything, so all must be affirmed as good [Nietzsche]
22. Metaethics / B. Value / 2. Values / i. Self-interest
Egoism should not assume that all egos are equal [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
After Socrates virtue is misunderstood, as good for all, not for individuals [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We contain multitudes of characters, which can brought into the open [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
Who can endure the thought of eternal recurrence? [Nietzsche]
If you want one experience repeated, you must want all of them [Nietzsche]
24. Political Theory / B. Nature of a State / 4. Citizenship
Humans are determined by community, so its preservation is their most valued drive [Nietzsche]
25. Social Practice / A. Freedoms / 1. Slavery
There is always slavery, whether we like it or not [Nietzsche]
25. Social Practice / E. Policies / 5. Education / d. Study of history
After history following God, or a people, or an idea, we now see it in terms of animals [Nietzsche]
26. Natural Theory / C. Causation / 7. Eliminating causation
Cause and effect is a hypothesis, based on our supposed willing of actions [Nietzsche]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Having a sense of time presupposes absolute time [Nietzsche]