Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Notebooks' and 'Model Theory'

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29 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
8093 Seek wisdom rather than truth; it is easier [Joubert]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
8095 We must think with our entire body and soul [Joubert]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
8107 The love of certainty holds us back in metaphysics [Joubert]
2. Reason / A. Nature of Reason / 9. Limits of Reason
8099 The truths of reason instruct, but they do not illuminate [Joubert]
2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
3. Truth / A. Truth Problems / 1. Truth
8098 Truth consists of having the same idea about something that God has [Joubert]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
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]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
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]
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
8101 To know is to see inside oneself [Joubert]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
8094 The imagination has made more discoveries than the eye [Joubert]
18. Thought / A. Modes of Thought / 1. Thought
8103 A thought is as real as a cannon ball [Joubert]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
8100 Where does the bird's idea of a nest come from? [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
8096 He gives his body up to pleasure, but not his soul [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
8104 What will you think of pleasures when you no longer enjoy them? [Joubert]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
8097 Virtue is hard if we are scorned; we need support [Joubert]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
8106 In raising a child we must think of his old age [Joubert]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
8105 We can't exactly conceive virtue without the idea of God [Joubert]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
8102 We cannot speak against Christianity without anger, or speak for it without love [Joubert]