50 ideas
12667 | Metaphysics aims at the simplest explanation, without regard to testability [Ellis] |
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] |
12666 | We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis] |
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] |
12688 | Mathematics is the formal study of the categorical dimensions of things [Ellis] |
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] |
12683 | Objects and substances are a subcategory of the natural kinds of processes [Ellis] |
12670 | A physical event is any change of distribution of energy [Ellis] |
12673 | Physical properties are those relevant to how a physical system might act [Ellis] |
12665 | I support categorical properties, although most people only want causal powers [Ellis] |
12682 | Essentialism needs categorical properties (spatiotemporal and numerical relations) and dispositions [Ellis] |
12684 | Spatial, temporal and numerical relations have causal roles, without being causal [Ellis] |
12672 | Properties and relations are discovered, so they can't be mere sets of individuals [Ellis] |
12676 | Causal powers can't rest on things which lack causal power [Ellis] |
23781 | Categoricals exist to influence powers. Such as structures, orientations and magnitudes [Ellis, by Williams,NE] |
12686 | Causal powers are a proper subset of the dispositional properties [Ellis] |
12685 | Categorical properties depend only on the structures they represent [Ellis] |
12679 | A real essence is a kind's distinctive properties [Ellis] |
12668 | Metaphysical necessity holds between things in the world and things they make true [Ellis] |
12687 | Metaphysical necessities are those depending on the essential nature of things [Ellis] |
12669 | Science aims to explain things, not just describe them [Ellis] |
21833 | Research suggest that we overrate conscious experience [Flanagan] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
21834 | Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan] |
21837 | Morality is normative because it identifies best practices among the normal practices [Flanagan] |
21830 | For Darwinians, altruism is either contracts or genetics [Flanagan] |
21835 | We need Eudaimonics - the empirical study of how we should flourish [Flanagan] |
21831 | Alienation is not finding what one wants, or being unable to achieve it [Flanagan] |
12681 | There are natural kinds of processes [Ellis] |
12680 | Natural kind structures go right down to the bottom level [Ellis] |
12675 | Laws of nature are just descriptions of how things are disposed to behave [Ellis] |
12671 | I deny forces as entities that intervene in causation, but are not themselves causal [Ellis] |
12674 | Energy is the key multi-valued property, vital to scientific realism [Ellis] |
12689 | Simultaneity can be temporal equidistance from the Big Bang [Ellis] |
12690 | The present is the collapse of the light wavefront from the Big Bang [Ellis] |
21832 | Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan] |