Combining Texts

All the ideas for 'The Bhagavad Gita', 'On Formally Undecidable Propositions' and 'On the Frame of Reference'

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31 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
7990 Serene wisdom is freedom from ties, and indifference to fortune [Anon (Bhag)]
2. Reason / A. Nature of Reason / 7. Status of Reason
7989 Seek salvation in the wisdom of reason [Anon (Bhag)]
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 / G. Quantification / 4. Substitutional Quantification
10009 Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin]
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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
7996 I am all the beauty and goodness of things, says Krishna [Anon (Bhag)]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
7995 In all living beings I am the light of consciousness, says Krishna [Anon (Bhag)]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
3192 Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
20. Action / A. Definition of Action / 1. Action Theory
7999 All actions come from: body, lower self, perception, means of action, or Fate [Anon (Bhag)]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
7991 Hate and lust have their roots in man's lower nature [Anon (Bhag)]
25. Social Practice / E. Policies / 1. War / a. Just wars
7988 There is no greater good for a warrior than to fight in a just war [Anon (Bhag)]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
7992 The visible forms of nature are earth, water, fire, air, ether; mind, reason, and the sense of 'I' [Anon (Bhag)]
28. God / A. Divine Nature / 1. God
7994 Everything, including the gods, comes from me, says Krishna [Anon (Bhag)]
29. Religion / A. Polytheistic Religion / 3. Hinduism
7993 Brahman is supreme, Atman his spirit in man, and Karma is the force of creation [Anon (Bhag)]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
7997 Only by love can men see me, know me, and come to me, says Krishna [Anon (Bhag)]
29. Religion / D. Religious Issues / 2. Immortality / e. Hell
7998 The three gates of hell are lust, anger and greed [Anon (Bhag)]