Combining Texts

All the ideas for 'fragments/reports', 'reports' and 'On Formally Undecidable Propositions'

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30 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
1765 Diogenes said avoidance of philosophy is the lack of a desire to live properly [Diogenes of Sin., by Diog. Laertius]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
21752 Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17835 Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17886 The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner]
5. Theory of Logic / K. Features of Logics / 2. Consistency
10071 Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]
5. Theory of Logic / K. Features of Logics / 3. Soundness
19123 If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10621 Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel]
17888 The undecidable sentence can be decided at a 'higher' level in the system [Gödel]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10132 There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10072 First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P]
9590 Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman]
3198 Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey]
11069 Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna]
10118 First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman]
10122 Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman]
10611 There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P]
10867 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8747 Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
18933 Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
1762 When someone denied motion, Diogenes got up and walked away [Diogenes of Sin., by Diog. Laertius]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
3192 Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
19. Language / F. Communication / 1. Rhetoric
9866 Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
5864 Destroy seriousness with laughter, and laughter with seriousness [Gorgias]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
7813 Cynicism was open to anyone, and needed neither education nor sophistication [Diogenes of Sin., by Grayling]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
1763 Diogenes said a plucked chicken fits Plato's definition of man [Diogenes of Sin., by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
5071 The Cynics rejected what is conventional as irrational, and aimed to live by nature [Taylor,R on Diogenes of Sin.]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
7812 For peace of mind, you need self-government, indifference and independence [Diogenes of Sin.]
24. Political Theory / B. Nature of a State / 4. Citizenship
1764 Diogenes said he was a citizen of the world [Diogenes of Sin., by Diog. Laertius]
24. Political Theory / D. Ideologies / 2. Anarchism
5968 Diogenes masturbated in public, wishing he could get rid of hunger so easily [Diogenes of Sin., by Plutarch]
25. Social Practice / A. Freedoms / 3. Free speech
1766 Diogenes said that the most excellent thing among men was freedom of speech [Diogenes of Sin., by Diog. Laertius]