59 ideas
23770 | Reductive analysis makes a concept clearer, by giving an alternative simpler set [Williams,NE] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
23769 | Promoting an ontology by its implied good metaphysic is an 'argument-by-display' [Williams,NE] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [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] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [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] |
18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
23783 | Change exists, it is causal, and it needs an explanation [Williams,NE] |
23784 | Processes don't begin or end; they just change direction unexpectedly [Williams,NE] |
23790 | Processes are either strings of short unchanging states, or continuous and unreducible events [Williams,NE] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
23786 | The status quo is part of what exists, and so needs metaphysical explanation [Williams,NE] |
23768 | A metaphysic is a set of wider explanations derived from a basic ontology [Williams,NE] |
23773 | Humeans say properties are passive, possibility is vast, laws are descriptions, causation is weak [Williams,NE] |
23779 | We shouldn't posit the existence of anything we have a word for [Williams,NE] |
23775 | Powers are 'multi-track' if they can produce a variety of manifestations [Williams,NE] |
23780 | Every possible state of affairs is written into its originating powers [Williams,NE] |
23789 | Naming powers is unwise, because that it usually done by a single manifestation [Williams,NE] |
23771 | Fundamental physics describes everything in terms of powers [Williams,NE] |
23776 | Rather than pure powers or pure categoricals, I favour basics which are both at once [Williams,NE] |
23777 | Powers are more complicated than properties which are always on display [Williams,NE] |
23774 | There are basic powers, which underlie dispositions, potentialities, capacities etc [Williams,NE] |
23791 | Dispositions are just useful descriptions, which are explained by underlying powers [Williams,NE] |
23772 | If objects are property bundles, the properties need combining powers [Williams,NE] |
23788 | Four-Dimensional is Perdurantism (temporal parts), plus Eternalism [Williams,NE] |
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] |
9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
23782 | Causation is the exercise of powers [Williams,NE] |
23785 | Causation needs to explain stasis, as well as change [Williams,NE] |
23787 | If causes and effects overlap, that makes changes impossible [Williams,NE] |
23778 | Powers contain lawlike features, pointing to possible future states [Williams,NE] |