38 ideas
| 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] |
| 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] |
| 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] |
| 4913 | Brain lesions can erase whole categories of perception, suggesting they are hard-wired [Carter,R] |
| 16674 | The quantity is just the matter, in that it has extended parts and is diffuse [Charleton] |
| 4910 | Sense organs don't discriminate; they reduce various inputs to the same electrical pulses [Carter,R] |
| 4911 | The recognition sequence is: classify, name, locate, associate, feel [Carter,R, by PG] |
| 4919 | There seems to be no dividing line between a memory and a thought [Carter,R] |
| 4908 | No one knows if animals are conscious [Carter,R] |
| 4902 | Pain doesn't have one brain location, but is linked to attention and emotion [Carter,R] |
| 4904 | Proper brains appear at seven weeks, and neonates have as many neurons as adults do [Carter,R] |
| 4915 | In primates, brain size correlates closely with size of social group [Carter,R] |
| 4917 | Consciousness involves awareness, perception, self-awareness, attention and reflection [Carter,R] |
| 4916 | There is enormous evidence that consciousness arises in the frontal lobes of the brain [Carter,R] |
| 4905 | Normal babies seem to have overlapping sense experiences [Carter,R] |
| 4918 | In blindsight V1 (normal vision) is inactive, but V5 (movement) lights up [Carter,R] |
| 4912 | Out-of-body experiences may be due to temporary loss of proprioception [Carter,R] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 4903 | Scans of brains doing similar tasks produce very similar patterns of activation [Carter,R] |
| 4920 | Thinking takes place on the upper side of the prefrontal cortex [Carter,R] |
| 4906 | Babies show highly emotional brain events, but may well be unaware of them [Carter,R] |
| 4909 | The only way we can control our emotions is by manipulating the outside world that influences them [Carter,R] |
| 4914 | A frog will starve to death surrounded by dead flies [Carter,R] |
| 4907 | The 'locus coeruleus' is one of several candidates for the brain's 'pleasure centre' [Carter,R] |