Combining Texts

All the ideas for 'works', 'True in Theory, but not in Practice' and 'Model Theory'

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23 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
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]
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]