80 ideas
1798 | He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius] |
4194 | Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe] |
4214 | Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe] |
4222 | If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe] |
1800 | Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius] |
4217 | It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe] |
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] |
4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
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] |
4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
4202 | Change can be of composition (the component parts), or quality (properties), or substance [Lowe] |
4201 | Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG] |
4219 | Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe] |
4221 | Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe] |
4220 | Maybe an event is the exemplification of a property at a time [Lowe] |
4225 | Events are changes in the properties of or relations between things [Lowe] |
4196 | The main categories of existence are either universal and particular, or abstract and concrete [Lowe] |
4234 | Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe] |
4235 | Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe] |
4236 | Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe] |
4197 | The category of universals can be sub-divided into properties and relations [Lowe] |
4232 | Nominalists believe that only particulars exist [Lowe] |
4205 | 'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe] |
4233 | If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe] |
4206 | Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe] |
4204 | Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe] |
4200 | If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe] |
4198 | If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe] |
4199 | A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe] |
4203 | Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe] |
4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
4207 | We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe] |
6595 | If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin] |
6593 | The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin] |
6592 | Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin] |
1805 | Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius] |
1803 | Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius] |
1807 | Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius] |
1810 | Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius] |
1802 | Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius] |
1801 | Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius] |
1804 | Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius] |
1808 | Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius] |
1806 | Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius] |
1809 | Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius] |
4223 | Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe] |
4193 | The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
4238 | The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe] |
4237 | Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe] |
4210 | If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe] |
3062 | There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius] |
4209 | The theories of fact causation and event causation are both worth serious consideration [Lowe] |
4215 | It seems proper to say that only substances (rather than events) have causal powers [Lowe] |
4211 | Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe] |
4213 | Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe] |
4212 | Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe] |
14581 | The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum] |
4208 | 'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe] |
3063 | Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius] |
4224 | If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe] |
4227 | Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe] |
4228 | If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe] |