Combining Texts

All the ideas for 'General Draft', 'On Formally Undecidable Propositions' and 'Causality and Determinism'

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26 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
22026 Philosophy is homesickness - the urge to be at home everywhere [Novalis]
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]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
19591 Desire for perfection is an illness, if it turns against what is imperfect [Novalis]
16. Persons / F. Free Will / 3. Constraints on the will
8353 Freedom involves acting according to an idea [Anscombe]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
8352 To believe in determinism, one must believe in a system which determines events [Anscombe]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
3192 Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
26. Natural Theory / C. Causation / 5. Direction of causation
8351 With diseases we easily trace a cause from an effect, but we cannot predict effects [Anscombe]
26. Natural Theory / C. Causation / 6. Causation as primitive
4777 The word 'cause' is an abstraction from a group of causal terms in a language (scrape, push..) [Anscombe]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
10363 Causation is relative to how we describe the primary relata [Anscombe, by Schaffer,J]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
8350 Since Mill causation has usually been explained by necessary and sufficient conditions [Anscombe]