Combining Texts

All the ideas for '01: Book of Genesis', 'On Formally Undecidable Propositions' and 'Utopia'

expand these ideas     |    start again     |     specify just one area for these texts

26 ideas

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
3198 Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey]
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]
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]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
3192 Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
7506 God made man in his own image [Anon (Tor)]
24. Political Theory / D. Ideologies / 3. Conservatism
7257 All modern social systems seem to be conspiracies of the rich [More,T]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
7254 If you try to get elected, you should be permanently barred from seeking office [More,T]
25. Social Practice / E. Policies / 1. War / a. Just wars
7255 Only Utopians fail to see glory in warfare [More,T]
25. Social Practice / F. Life Issues / 2. Euthanasia
7253 In Utopia, legal euthanasia is considered honourable [More,T]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
16782 The names of all the types of creature were given forever by Adam [Anon (Tor)]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
4013 And God saw the light, that it was good [Anon (Tor)]
28. God / C. Attitudes to God / 2. Pantheism
7256 In Utopia, the Supreme Being is identical with Nature [More,T]