41 ideas
| 12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
| 12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
| 12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
| 12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
| 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] |
| 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] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 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] |
| 12121 | We don't assume there is no land, because we can only see sea [Bacon] |
| 12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
| 12127 | Many different theories will fit the observed facts [Bacon] |
| 12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 3926 | The human heart has a natural concern for public good [Hume] |
| 3929 | No moral theory is of any use if it doesn't serve the interests of the individual concerned [Hume] |
| 3925 | Personal Merit is the possession of useful or agreeable mental qualities [Hume] |
| 3922 | Justice only exists to support society [Hume] |
| 23560 | If we all naturally had everything we could ever desire, the virtue of justice would be irrelevant [Hume] |
| 3918 | Moral philosophy aims to show us our duty [Hume] |
| 3919 | Conclusions of reason do not affect our emotions or decisions to act [Hume] |
| 3928 | Virtue just requires careful calculation and a preference for the greater happiness [Hume] |
| 3923 | No one would cause pain to a complete stranger who happened to be passing [Hume] |
| 3924 | Nature makes private affections come first, because public concerns are spread too thinly [Hume] |
| 3921 | The safety of the people is the supreme law [Hume] |
| 3927 | Society prefers helpful lies to harmful truth [Hume] |
| 3920 | If you equalise possessions, people's talents will make them unequal again [Hume] |
| 12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
| 12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |