69 ideas
17663 | If you know what it is, investigation is pointless. If you don't, investigation is impossible [Armstrong] |
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] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
17688 | Negative facts are supervenient on positive facts, suggesting they are positive facts [Armstrong] |
17691 | Nothing is genuinely related to itself [Armstrong] |
17679 | All instances of some property are strictly identical [Armstrong] |
12677 | Armstrong holds that all basic properties are categorical [Armstrong, by Ellis] |
17666 | Actualism means that ontology cannot contain what is merely physically possible [Armstrong] |
17667 | Dispositions exist, but their truth-makers are actual or categorical properties [Armstrong] |
17687 | If everything is powers there is a vicious regress, as powers are defined by more powers [Armstrong] |
17678 | Universals are just the repeatable features of a world [Armstrong] |
17669 | Realist regularity theories of laws need universals, to pick out the same phenomena [Armstrong] |
17677 | Past, present and future must be equally real if universals are instantiated [Armstrong] |
15442 | Universals are abstractions from their particular instances [Armstrong, by Lewis] |
17686 | Universals are abstractions from states of affairs [Armstrong] |
17668 | It is likely that particulars can be individuated by unique conjunctions of properties [Armstrong] |
17680 | The identity of a thing with itself can be ruled out as a pseudo-property [Armstrong] |
17693 | The necessary/contingent distinction may need to recognise possibilities as real [Armstrong] |
17685 | Induction aims at 'all Fs', but abduction aims at hidden or theoretical entities [Armstrong] |
17683 | Science suggests that the predicate 'grue' is not a genuine single universal [Armstrong] |
17675 | Unlike 'green', the 'grue' predicate involves a time and a change [Armstrong] |
17674 | The raven paradox has three disjuncts, confirmed by confirming any one of them [Armstrong] |
17672 | A good reason for something (the smoke) is not an explanation of it (the fire) [Armstrong] |
17684 | To explain observations by a regular law is to explain the observations by the observations [Armstrong] |
17676 | Best explanations explain the most by means of the least [Armstrong] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
17664 | Each subject has an appropriate level of abstraction [Armstrong] |
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] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
17692 | We can't deduce the phenomena from the One [Armstrong] |
17689 | Absences might be effects, but surely not causes? [Armstrong] |
17682 | A universe couldn't consist of mere laws [Armstrong] |
17662 | Science depends on laws of nature to study unobserved times and spaces [Armstrong] |
17690 | Oaken conditional laws, Iron universal laws, and Steel necessary laws [Armstrong, by PG] |
17670 | Newton's First Law refers to bodies not acted upon by a force, but there may be no such body [Armstrong] |
8582 | Regularities are lawful if a second-order universal unites two first-order universals [Armstrong, by Lewis] |
17671 | A naive regularity view says if it never occurs then it is impossible [Armstrong] |
17681 | The laws of nature link properties with properties [Armstrong] |
16246 | Rather than take necessitation between universals as primitive, just make laws primitive [Maudlin on Armstrong] |
9480 | Armstrong has an unclear notion of contingent necessitation, which can't necessitate anything [Bird on Armstrong] |