Combining Texts

All the ideas for 'fragments/reports', 'What are Sets and What are they For?' and 'True in Theory, but not in Practice'

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25 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
21059 General rules of action also need a judgement about when to apply them [Kant]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
21061 Duty does not aim at an end, but gives rise to universal happiness as aim of the will [Kant]
23. Ethics / D. Deontological Ethics / 2. Duty
21060 It can't be a duty to strive after the impossible [Kant]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
21062 The will's motive is the absolute law itself, and moral feeling is receptivity to law [Kant]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
21071 There can be no restraints on freedom if reason does not reveal some basic rights [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
21063 Personal contracts are for some end, but a civil state contract involves a duty to share [Kant]
21068 There must be a unanimous contract that citizens accept majority decisions [Kant]
21069 A contract is theoretical, but it can guide rulers to make laws which the whole people will accept [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
21070 A law is unjust if the whole people could not possibly agree to it [Kant]
24. Political Theory / B. Nature of a State / 4. Citizenship
21067 A citizen must control his own life, and possess property or an important skill [Kant]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
21064 A lawful civil state must embody freedom, equality and independence for its members [Kant]
25. Social Practice / B. Equalities / 4. Economic equality
21066 Citizens can rise to any rank that talent, effort and luck can achieve [Kant]
25. Social Practice / C. Rights / 3. Alienating rights
21065 You can't make a contract renouncing your right to make contracts! [Kant]
25. Social Practice / E. Policies / 1. War / a. Just wars
21072 The people (who have to fight) and not the head of state should declare a war [Kant]