51 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 19215 | Arguers often turn the opponent's modus ponens into their own modus tollens [Merricks] |
| 19205 | 'Snow is white' only contingently expresses the proposition that snow is white [Merricks] |
| 19209 | Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks] |
| 19208 | The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks] |
| 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] |
| 19207 | Sentence logic maps truth values; predicate logic maps objects and sets [Merricks] |
| 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] |
| 19214 | In twinning, one person has the same origin as another person [Merricks] |
| 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] |
| 19217 | I don't accept that if a proposition is directly about an entity, it has a relation to the entity [Merricks] |
| 19203 | A sentence's truth conditions depend on context [Merricks] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 19200 | Propositions are standardly treated as possible worlds, or as structured [Merricks] |
| 19206 | 'Cicero is an orator' represents the same situation as 'Tully is an orator', so they are one proposition [Merricks] |
| 19202 | Propositions are necessary existents which essentially (but inexplicably) represent things [Merricks] |
| 19204 | True propositions existed prior to their being thought, and might never be thought [Merricks] |
| 19210 | The standard view of propositions says they never change their truth-value [Merricks] |
| 19201 | Propositions can be 'about' an entity, but that doesn't make the entity a constituent of it [Merricks] |
| 19211 | Early Russell says a proposition is identical with its truthmaking state of affairs [Merricks] |
| 19212 | Unity of the proposition questions: what unites them? can the same constituents make different ones? [Merricks] |
| 19213 | We want to explain not just what unites the constituents, but what unites them into a proposition [Merricks] |
| 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] |