Combining Texts

All the ideas for 'Set Theory', 'The History of the Jews' and 'The Reality of Numbers'

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28 ideas

3. Truth / B. Truthmakers / 1. For Truthmakers
18344 Truth and falsehood must track what does or doesn't exist [Bigelow]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
24. Political Theory / D. Ideologies / 10. Theocracy
7337 In Mosaic legal theory, crimes are sins and sins are crimes [Johnson,P]
7339 Because human life is what is sacred, Mosaic law has no death penalty for property violations [Johnson,P]
25. Social Practice / A. Freedoms / 1. Slavery
7353 The Pharisees undermined slavery, by giving slaves responsibility and status in law courts [Johnson,P]
25. Social Practice / B. Equalities / 3. Legal equality
7340 Mosaic law was the first to embody the rule of law, and equality before the law [Johnson,P]
25. Social Practice / F. Life Issues / 1. Causing Death
7338 Man's life is sacred, because it is made in God's image [Johnson,P]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
7348 The Jews sharply distinguish human and divine, but the Greeks pull them closer together [Johnson,P]
29. Religion / B. Monotheistic Religion / 2. Judaism
7336 A key moment is the idea of a single moral God, who imposes his morality on humanity [Johnson,P]
7341 Sampson illustrates the idea that religious heroes often begin as outlaws and semi-criminals [Johnson,P]
7342 Isaiah moved Israelite religion away from the local, onto a more universal plane [Johnson,P]
7355 The Torah pre-existed creation, and was its blueprint [Johnson,P]
7344 Judaism involves circumcision, Sabbath, Passover, Pentecost, Tabernacles, New Year, and Atonement [Johnson,P]
7345 In exile the Jews became a nomocracy [Johnson,P]
29. Religion / B. Monotheistic Religion / 3. Zoroastrianism
7347 Zoroastrians believed in one eternal beneficent being, Creator through the holy spirit [Johnson,P]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
7349 Immortality based on judgement of merit was developed by the Egyptians (not the Jews) [Johnson,P]
7354 The main doctrine of the Pharisees was belief in resurrection and the afterlife [Johnson,P]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
7356 Pious Jews saw heaven as a vast library [Johnson,P]