Combining Texts

All the ideas for 'The Gettier Problem', 'On Formally Undecidable Propositions' and 'Intro to Principles of Morals and Legislation'

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28 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
17888 The undecidable sentence can be decided at a 'higher' level in the system [Gödel]
10621 Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on 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]
3198 Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey]
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]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
19699 A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
3192 Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
5901 Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
5934 Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
3777 Pleasure and pain control all human desires and duties [Bentham]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
3554 Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham]
3781 The value of pleasures and pains is their force [Bentham]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
3778 The community's interest is a sum of individual interests [Bentham]
25. Social Practice / F. Life Issues / 6. Animal Rights
20280 Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham]
26. Natural Theory / A. Speculations on Nature / 1. Nature
3779 Unnatural, when it means anything, means infrequent [Bentham]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
3780 We must judge a thing morally to know if it conforms to God's will [Bentham]