53 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] |
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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
22427 | To explain object qualities, primary qualities must be more than mere sources of experience [McGinn] |
22413 | Being red simply consists in looking red [McGinn] |
22415 | Relativity means differing secondary perceptions are not real disagreements [McGinn] |
22416 | Phenomenalism is correct for secondary qualities, so scepticism is there impossible [McGinn] |
22422 | Maybe all possible sense experience must involve both secondary and primary qualities [McGinn] |
22428 | You understood being red if you know the experience involved; not so with thngs being square [McGinn] |
22414 | You don't need to know how a square thing looks or feels to understand squareness [McGinn] |
22423 | Touch doesn't provide direct experience of primary qualities, because touch feels temperature [McGinn] |
22426 | We can perceive objectively, because primary qualities are not mind-created [McGinn] |
22412 | Lockean secondary qualities (unlike primaries) produce particular sensory experiences [McGinn] |
22421 | Could there be a mind which lacked secondary quality perception? [McGinn] |
22424 | Secondary qualities contain information; their variety would be superfluous otherwise [McGinn] |
22425 | The utility theory says secondary qualities give information useful to human beings [McGinn] |
7629 | We see objects 'directly' by representing them [McGinn] |
18410 | Indexical thought is in relation to my self-consciousness [McGinn] |
22417 | Indexicals do not figure in theories of physics, because they are not explanatory causes [McGinn] |
22420 | The indexical perspective is subjective, incorrigible and constant [McGinn] |
18402 | Indexical concepts are indispensable, as we need them for the power to act [McGinn] |
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] |
22418 | I can know indexical truths a priori, unlike their non-indexical paraphrases [McGinn] |
15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |