67 ideas
| 8605 | In addition to analysis of a concept, one can deny it, or accept it as primitive [Lewis] |
| 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] |
| 8607 | Supervenience is reduction without existence denials, ontological priorities, or translatability [Lewis] |
| 8606 | A supervenience thesis is a denial of independent variation [Lewis] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 8580 | Materialism is (roughly) that two worlds cannot differ without differing physically [Lewis] |
| 8571 | Universals are wholly present in their instances, whereas properties are spread around [Lewis] |
| 10717 | Natural properties figure in the analysis of similarity in intrinsic respects [Lewis, by Oliver] |
| 16217 | Lewisian natural properties fix reference of predicates, through a principle of charity [Lewis, by Hawley] |
| 8613 | Objects are demarcated by density and chemistry, and natural properties belong in what is well demarcated [Lewis] |
| 8585 | Reference partly concerns thought and language, partly eligibility of referent by natural properties [Lewis] |
| 8586 | Natural properties tend to belong to well-demarcated things, typically loci of causal chains [Lewis] |
| 8589 | For us, a property being natural is just an aspect of its featuring in the contents of our attitudes [Lewis] |
| 15460 | All perfectly natural properties are intrinsic [Lewis, by Lewis] |
| 15726 | Natural properties fix resemblance and powers, and are picked out by universals [Lewis] |
| 7031 | Lewis says properties are sets of actual and possible objects [Lewis, by Heil] |
| 8572 | Any class of things is a property, no matter how whimsical or irrelevant [Lewis] |
| 18433 | There are far more properties than any brain could ever encodify [Lewis] |
| 8604 | We need properties as semantic values for linguistic expressions [Lewis] |
| 14499 | Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki] |
| 15120 | Lewisian properties have powers because of their relationships to other properties [Lewis, by Hawthorne] |
| 8573 | Most properties are causally irrelevant, and we can't spot the relevant ones. [Lewis] |
| 8569 | I suspend judgements about universals, but their work must be done [Lewis] |
| 21961 | Physics aims to discover which universals actually exist [Lewis, by Moore,AW] |
| 8576 | The One over Many problem (in predication terms) deserves to be neglected (by ostriches) [Lewis] |
| 8570 | To have a property is to be a member of a class, usually a class of things [Lewis] |
| 8574 | Class Nominalism and Resemblance Nominalism are pretty much the same [Lewis] |
| 8579 | Psychophysical identity implies the possibility of idealism or panpsychism [Lewis] |
| 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] |
| 8614 | A sophisticated principle of charity sometimes imputes error as well as truth [Lewis] |
| 8615 | We need natural properties in order to motivate the principle of charity [Lewis] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 8608 | Counterfactuals 'backtrack' if a different present implies a different past [Lewis] |
| 8584 | Causal counterfactuals must avoid backtracking, to avoid epiphenomena and preemption [Lewis] |
| 8581 | Physics discovers laws and causal explanations, and also the natural properties required [Lewis] |
| 15727 | Physics aims for a list of natural properties [Lewis] |
| 8611 | A law of nature is any regularity that earns inclusion in the ideal system [Lewis] |