49 ideas
| 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] |
| 4986 | A weaker kind of reductionism than direct translation is the use of 'bridge laws' [Kirk,R] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| 5001 | Maybe we should see intentionality and consciousness as a single problem, not two [Kirk,R] |
| 4993 | If a bird captures a worm, we could say its behaviour is 'about' the worm [Kirk,R] |
| 5000 | Behaviourism says intentionality is an external relation; language of thought says it's internal [Kirk,R] |
| 4982 | Dualism implies some brain events with no physical cause, and others with no physical effect [Kirk,R] |
| 4991 | Behaviourism seems a good theory for intentional states, but bad for phenomenal ones [Kirk,R] |
| 4994 | Behaviourism offers a good alternative to simplistic unitary accounts of mental relationships [Kirk,R] |
| 4992 | In 'holistic' behaviourism we say a mental state is a complex of many dispositions [Kirk,R] |
| 4990 | The inverted spectrum idea is often regarded as an objection to behaviourism [Kirk,R] |
| 4984 | All meaningful psychological statements can be translated into physics [Kirk,R] |
| 4998 | Instead of representation by sentences, it can be by a distribution of connectionist strengths [Kirk,R] |
| 4985 | If mental states are multiply realisable, they could not be translated into physical terms [Kirk,R] |
| 4997 | It seems unlikely that most concepts are innate, if a theory must be understood to grasp them [Kirk,R] |
| 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] |
| 4999 | For behaviourists language is just a special kind of behaviour [Kirk,R] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 4995 | Behaviourists doubt whether reference is a single type of relation [Kirk,R] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |