43 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 18767 | Free logics has terms that do not designate real things, and even empty domains [Anderson,CA] |
| 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] |
| 17699 | Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel] |
| 18763 | Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA] |
| 18771 | Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA] |
| 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] |
| 18769 | Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 18770 | We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA] |
| 18768 | We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA] |
| 18766 | 's is non-existent' cannot be said if 's' does not designate [Anderson,CA] |
| 18765 | Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA] |
| 18764 | The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA] |
| 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] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |