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All the ideas for 'Mahaprajnaparamitashastra', 'Ideas' and 'Set Theory and Its Philosophy'

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36 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Because of Darwin, wisdom as a definite attainable state has faded [Watson]
1. Philosophy / B. History of Ideas / 1. History of Ideas
The three key ideas are the soul, Europe, and the experiment [Watson]
The big idea: imitation, the soul, experiments, God, heliocentric universe, evolution? [Watson]
2. Reason / E. Argument / 3. Analogy
Babylonian thinking used analogy, rather than deduction or induction [Watson]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
Mesopotamian numbers applied to specific things, and then became abstract [Watson]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
Priority is a modality, arising from collections and members [Potter]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
Modern democracy is actually elective oligarchy [Watson]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Greek philosophers invented the concept of 'nature' as their special subject [Watson]
27. Natural Reality / G. Biology / 3. Evolution
DNA mutation suggests humans and chimpanzees diverged 6.6 million years ago [Watson]
28. God / C. Attitudes to God / 4. God Reflects Humanity
During the rise of civilizations, the main gods changed from female to male [Watson]
29. Religion / A. Polytheistic Religion / 3. Hinduism
Hinduism has no founder, or prophet, or creed, or ecclesiastical structure [Watson]
29. Religion / B. Monotheistic Religion / 2. Judaism
Modern Judaism became stabilised in 200 CE [Watson]
The Israelites may have asserted the uniqueness of Yahweh to justify land claims [Watson]
Monotheism was a uniquely Israelite creation within the Middle East [Watson]
29. Religion / B. Monotheistic Religion / 3. Zoroastrianism
The Gathas (hymns) of Zoroastrianism date from about 1000 BCE [Watson]
Zoroaster conceived the afterlife, judgement, heaven and hell, and the devil [Watson]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Jesus never intended to start a new religion [Watson]
Paul's early writings mention few striking episodes from Jesus' life [Watson]
29. Religion / C. Spiritual Disciplines / 1. Confucianism
Confucius revered the spiritual world, but not the supernatural, or a personal god, or the afterlife [Watson]
29. Religion / C. Spiritual Disciplines / 2. Taoism
Taoism aims at freedom from the world, the body, the mind, and nature [Watson]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
The three basic ingredients of religion are: the soul, seers or priests, and ritual [Watson]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
In ancient Athens the souls of the dead are received by the 'upper air' [Watson]