54 ideas
17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
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] |
17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
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] |
17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
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] |
17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [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] |
17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
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] |
17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
17732 | Success semantics explains representation in terms of success in action [Jenkins] |
17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |