49 ideas
6118 | Philosophy is logical analysis, followed by synthesis [Russell] |
6116 | A logical language would show up the fallacy of inferring reality from ordinary language [Russell] |
6117 | Philosophy should be built on science, to reduce error [Russell] |
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] |
6110 | Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell] |
6107 | It is logic, not metaphysics, that is fundamental to philosophy [Russell] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
6115 | Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell] |
6109 | Some axioms may only become accepted when they lead to obvious conclusions [Russell] |
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] |
6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
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] |
10968 | Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read] |
6113 | To mean facts we assert them; to mean simples we name them [Russell] |
6114 | 'Simples' are not experienced, but are inferred at the limits of analysis [Russell] |
21722 | Better to construct from what is known, than to infer what is unknown [Russell] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
6111 | As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell] |
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] |
6112 | Meaning takes many different forms, depending on different logical types [Russell] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |