Combining Texts

Ideas for 'Are there propositions?', 'On Formally Undecidable Propositions' and 'Questions on Aristotle's Posterior Analytics'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

6 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13979 Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle]
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]