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All the ideas for '', 'What is Cantor's Continuum Problem?' and 'Ideas'

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31 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 / 4. Axioms for Sets / a. Axioms for sets
We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Mesopotamian numbers applied to specific things, and then became abstract [Watson]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
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]