56 ideas
| 8558 | One system has properties, powers, events, similarity and substance [Shoemaker] |
| 8559 | Analysis aims at internal relationships, not reduction [Shoemaker] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 15092 | Formerly I said properties are individuated by essential causal powers and causing instantiation [Shoemaker, by Shoemaker] |
| 8543 | Genuine properties are closely related to genuine changes [Shoemaker] |
| 8551 | Properties must be essentially causal if we can know and speak about them [Shoemaker] |
| 8557 | To ascertain genuine properties, examine the object directly [Shoemaker] |
| 15761 | We should abandon the idea that properties are the meanings of predicate expressions [Shoemaker] |
| 15756 | Some truths are not because of a thing's properties, but because of the properties of related things [Shoemaker] |
| 15758 | Things have powers in virtue of (which are entailed by) their properties [Shoemaker] |
| 8547 | One power can come from different properties; a thing's powers come from its properties [Shoemaker] |
| 8549 | Properties are functions producing powers, and powers are functions producing effects [Shoemaker] |
| 12678 | Shoemaker says all genuine properties are dispositional [Shoemaker, by Ellis] |
| 8545 | A causal theory of properties focuses on change, not (say) on abstract properties of numbers [Shoemaker] |
| 15757 | 'Square', 'round' and 'made of copper' show that not all properties are dispositional [Shoemaker] |
| 15759 | The identity of a property concerns its causal powers [Shoemaker] |
| 15760 | Properties are clusters of conditional powers [Shoemaker] |
| 15762 | Could properties change without the powers changing, or powers change without the properties changing? [Shoemaker] |
| 8552 | If properties are separated from causal powers, this invites total elimination [Shoemaker] |
| 4040 | The notions of property and of causal power are parts of a single system of related concepts [Shoemaker] |
| 15765 | Actually, properties are individuated by causes as well as effects [Shoemaker] |
| 8548 | Dispositional predicates ascribe powers, and the rest ascribe properties [Shoemaker] |
| 9485 | Universals concern how things are, and how they could be [Shoemaker, by Bird] |
| 8550 | Triangular and trilateral are coextensive, but different concepts; but powers and properties are the same [Shoemaker] |
| 8555 | There is no subset of properties which guarantee a thing's identity [Shoemaker] |
| 8554 | Possible difference across worlds depends on difference across time in the actual world [Shoemaker] |
| 15764 | 'Conceivable' is either not-provably-false, or compatible with what we know? [Shoemaker] |
| 8562 | It is possible to conceive what is not possible [Shoemaker] |
| 8556 | Grueness is not, unlike green and blue, associated with causal potential [Shoemaker] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 8542 | If causality is between events, there must be reference to the properties involved [Shoemaker] |
| 8560 | If causal laws describe causal potentialities, the same laws govern properties in all possible worlds [Shoemaker] |
| 15763 | If properties are causal, then causal necessity is a species of logical necessity [Shoemaker] |
| 8561 | If a world has different causal laws, it must have different properties [Shoemaker] |
| 8553 | It looks as if the immutability of the powers of a property imply essentiality [Shoemaker] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |