57 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] |
13258 | The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki] |
13288 | Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki] |
14506 | 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki] |
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] |
14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
13289 | Structures have positions, constituent types and number, and some invariable parts [Koslicki] |
14501 | 'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki] |
14495 | I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki] |
13264 | If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki] |
14497 | The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki] |
13280 | Statue and clay differ in modal and temporal properties, and in constitution [Koslicki] |
14496 | Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki] |
13279 | There are at least six versions of constitution being identity [Koslicki] |
14498 | For three-dimensionalist parthood must be a three-place relation, including times [Koslicki] |
13283 | The parts may be the same type as the whole, like a building made of buildings [Koslicki] |
13266 | Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki] |
14500 | Wholes are entities distinct from their parts, and have different properties [Koslicki] |
13281 | Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki] |
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] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
14504 | The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki] |
13285 | Natural kinds support inductive inferences, from previous samples to the next one [Koslicki] |
13287 | Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki] |
13284 | Should vernacular classifications ever be counted as natural kind terms? [Koslicki] |
13286 | There are apparently no scientific laws concerning biological species [Koslicki] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |