Combining Texts

All the ideas for 'Set Theory', 'The Artworld' and 'Tractatus Theologico-Politicus'

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45 ideas

2. Reason / A. Nature of Reason / 4. Aims of Reason
Without reason and human help, human life is misery [Spinoza]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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
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
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
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
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
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
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
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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
Constructibility: V = L (all sets are constructible) [Kunen]
16. Persons / F. Free Will / 2. Sources of Free Will
People are only free if they are guided entirely by reason [Spinoza]
21. Aesthetics / B. Nature of Art / 6. Art as Institution
A thing is only seen as art in an 'artworld', which has a theory and a history [Danto]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Peoples are created by individuals, not by nature, and only distinguished by language and law [Spinoza]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
In nature everything has an absolute right to do anything it is capable of doing [Spinoza]
Natural rights are determined by desire and power, not by reason [Spinoza]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
Society exists to extend human awareness [Spinoza, by Watson]
The state aims to allow personal development, so its main purpose is freedom [Spinoza]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
Sovereignty must include the power to make people submit to it [Spinoza]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
Kings tend to fight wars for glory, rather than for peace and liberty [Spinoza]
Monarchs are always proud, and can't back down [Spinoza]
Deposing a monarch is dangerous, because the people are used to royal authority [Spinoza]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
Every state is more frightened of its own citizens than of external enemies [Spinoza]
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
Democracy is a legitimate gathering of people who do whatever they can do [Spinoza]
24. Political Theory / D. Ideologies / 10. Theocracy
If religion is law, then piety is justice, impiety is crime, and non-believers must leave [Spinoza]
Allowing religious ministers any control of the state is bad for both parties [Spinoza]
25. Social Practice / A. Freedoms / 1. Slavery
Slavery is not just obedience, but acting only in the interests of the master [Spinoza]
25. Social Practice / A. Freedoms / 2. Freedom of belief
Government is oppressive if opinions can be crimes, because people can't give them up [Spinoza]
Without liberty of thought there is no trust in the state, and corruption follows [Spinoza]
25. Social Practice / A. Freedoms / 3. Free speech
Treason may be committed as much by words as by deeds [Spinoza]
25. Social Practice / A. Freedoms / 6. Political freedom
The freest state is a rational one, where people can submit themselves to reason [Spinoza]
25. Social Practice / C. Rights / 1. Basis of Rights
Spinoza wanted democracy based on individual rights, and is thus the first modern political philosopher [Stewart,M on Spinoza]
The sovereignty has absolute power over citizens [Spinoza]
25. Social Practice / C. Rights / 3. Alienating rights
Forming a society meant following reason, and giving up dangerous appetites and mutual harm [Spinoza]
People only give up their rights, and keep promises, if they hope for some greater good [Spinoza]
Once you have given up your rights, there is no going back [Spinoza]
In democracy we don't abandon our rights, but transfer them to the majority of us [Spinoza]
No one, in giving up their power and right, ceases to be a human being [Spinoza]
Everyone who gives up their rights must fear the recipients of them [Spinoza]
The early Hebrews, following Moses, gave up their rights to God alone [Spinoza]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
The order of nature does not prohibit anything, and allows whatever appetite produces [Spinoza]
25. Social Practice / E. Policies / 2. Religion in Society
State and religious law can clash, so the state must make decisions about religion [Spinoza]
29. Religion / B. Monotheistic Religion / 2. Judaism
Hebrews were very hostile to other states, who had not given up their rights to God [Spinoza]
29. Religion / B. Monotheistic Religion / 5. Bible
The Bible has nothing in common with reasoning and philosophy [Spinoza]