Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Investigations in the Foundations of Set Theory I' and 'Introduction to the Philosophy of Religion'

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28 ideas

2. Reason / D. Definition / 8. Impredicative Definition
15924 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
17608 We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
17607 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
10870 ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
13012 Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
17609 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
13017 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
13015 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
13020 The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
13486 Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13487 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
18178 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
13027 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
9627 Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
28. God / A. Divine Nature / 5. God and Time
20712 God is 'eternal' either by being non-temporal, or by enduring forever [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
20701 Can God be good, if he has not maximised goodness? [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
20702 The goodness of God may be a higher form than the goodness of moral agents [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
20703 How could God have obligations? What law could possibly impose them? [Davies,B]
28. God / B. Proving God / 1. Proof of God
20694 'Natural theology' aims to prove God to anyone (not just believers) by reason or argument [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
20706 A distinct cause of the universe can't be material (which would be part of the universe) [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
20707 The universe exhibits design either in its sense of purpose, or in its regularity [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
20708 If God is an orderly being, he cannot be the explanation of order [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / d. Religious Experience
20710 Maybe an abnormal state of mind is needed to experience God? [Davies,B]
20711 A believer can experience the world as infused with God [Davies,B]
20709 The experiences of God are inconsistent, not universal, and untestable [Davies,B]
29. Religion / D. Religious Issues / 1. Religious Commitment / b. Religious Meaning
20697 One does not need a full understanding of God in order to speak of God [Davies,B]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
20699 Paradise would not contain some virtues, such as courage [Davies,B]