Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Reply to Second Objections' and 'Declaration of the Rights of Man'

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15 ideas

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 / 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 / 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]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
The Cogito is not a syllogism but a self-evident intuition [Descartes]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
The law expresses the general will, and all citizens can participate [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 3. Constitutions
There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee]
25. Social Practice / A. Freedoms / 2. Freedom of belief
No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee]
25. Social Practice / A. Freedoms / 3. Free speech
Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee]
25. Social Practice / B. Equalities / 2. Political equality
All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee]
25. Social Practice / C. Rights / 4. Property rights
Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee]
25. Social Practice / E. Policies / 4. Taxation
Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee]