64 ideas
13395 | If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
13378 | It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
13402 | We only grasp a name if we know whether to apply it when the bearer changes [Jubien] |
13405 | The baptiser picks the bearer of a name, but social use decides the category [Jubien] |
13399 | Examples show that ordinary proper names are not rigid designators [Jubien] |
13398 | We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien] |
13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
13404 | To exist necessarily is to have an essence whose own essence must be instantiated [Jubien] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
13386 | If objects are just conventional, there is no ontological distinction between stuff and things [Jubien] |
13403 | The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien] |
13375 | The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien] |
13393 | Any entity has the unique property of being that specific entity [Jubien] |
13388 | It is incoherent to think that a given entity depends on its kind for its existence [Jubien] |
13384 | Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien] |
13385 | Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien] |
13383 | If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien] |
13400 | If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien] |
13401 | The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien] |
13380 | Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien] |
13376 | We should not regard essentialism as just nontrivial de re necessity [Jubien] |
13381 | Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien] |
13382 | Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien] |
13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
13394 | Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien] |
13391 | Modality concerns relations among platonic properties [Jubien] |
13374 | To analyse modality, we must give accounts of objects, properties and relations [Jubien] |
13389 | The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien] |
13390 | Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien] |
13396 | Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
13377 | First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |