40 ideas
| 9136 | The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen] |
| 9131 | Two long understandable sentences can have an unintelligible conjunction [Sorensen] |
| 9139 | If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen] |
| 9140 | Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 9119 | No attempt to deny bivalence has ever been accepted [Sorensen] |
| 9135 | We now see that generalizations use variables rather than abstract entities [Sorensen] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 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] |
| 9125 | Denying problems, or being romantically defeated by them, won't make them go away [Sorensen] |
| 9137 | Banning self-reference would outlaw 'This very sentence is in English' [Sorensen] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 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] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 9116 | Vague words have hidden boundaries [Sorensen] |
| 9132 | An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen] |
| 9128 | It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen] |
| 9130 | Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen] |
| 9118 | The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen] |
| 9124 | We are unable to perceive a nose (on the back of a mask) as concave [Sorensen] |
| 9126 | Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen] |
| 9121 | Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 9134 | The negation of a meaningful sentence must itself be meaningful [Sorensen] |
| 9133 | Propositions are what settle problems of ambiguity in sentences [Sorensen] |
| 9129 | I can buy any litre of water, but not every litre of water [Sorensen] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 9122 | God cannot experience unwanted pain, so God cannot understand human beings [Sorensen] |