44 ideas
| 23247 | The need to act produces consciousness, and practical reason is the root of all reason [Fichte] |
| 23232 | Sufficient reason makes the transition from the particular to the general [Fichte] |
| 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] |
| 23227 | Each object has a precise number of properties, each to a precise degree [Fichte] |
| 23228 | The principle of activity and generation is found in a self-moving basic force [Fichte] |
| 23241 | I am myself, but not the external object; so I only sense myself, and not the object [Fichte] |
| 21966 | Self-consciousness is the basis of knowledge, and knowing something is knowing myself [Fichte] |
| 21967 | There is nothing to say about anything which is outside my consciousness [Fichte] |
| 21969 | Awareness of reality comes from the free activity of consciousness [Fichte] |
| 23231 | I immediately know myself, and anything beyond that is an inference [Fichte] |
| 23246 | Faith is not knowledge; it is a decision of the will [Fichte] |
| 23245 | Knowledge can't be its own foundation; there has to be regress of higher and higher authorities [Fichte] |
| 23242 | Consciousness has two parts, passively receiving sensation, and actively causing productions [Fichte] |
| 23240 | We can't know by sight or hearing without realising that we are doing so [Fichte] |
| 23243 | Consciousness of external things is always accompanied by an unnoticed consciousness of self [Fichte] |
| 23244 | Forming purposes is absolutely free, and produces something from nothing [Fichte] |
| 23237 | The capacity for freedom is above the laws of nature, with its own power of purpose and will [Fichte] |
| 23235 | I want independent control of the fundamental cause of my decisions [Fichte] |
| 23230 | Nature contains a fundamental force of thought [Fichte] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 23233 | The will is awareness of one of our inner natural forces [Fichte] |
| 23234 | I cannot change the nature which has been determined for me [Fichte] |
| 23239 | The self is, apart from outward behaviour, a drive in your nature [Fichte] |
| 23238 | If life lacks love it becomes destruction [Fichte] |
| 23236 | Freedom means making yourself become true to your essential nature [Fichte] |
| 23229 | Nature is wholly interconnected, and the tiniest change affects everything [Fichte] |
| 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] |