62 ideas
6123 | Empirical investigation can't discover if holes exist, or if two things share a colour [Merricks] |
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] |
6143 | Prolonged events don't seem to endure or exist at any particular time [Merricks] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
6135 | A crumbling statue can't become vague, because vagueness is incoherent [Merricks] |
6145 | Intrinsic properties are those an object still has even if only that object exists [Merricks] |
6124 | I say that most of the objects of folk ontology do not exist [Merricks] |
6134 | Is swimming pool water an object, composed of its mass or parts? [Merricks] |
6125 | We can eliminate objects without a commitment to simples [Merricks] |
14229 | Merricks agrees that there are no composite objects, but offers a different semantics [Merricks, by Liggins] |
6142 | The 'folk' way of carving up the world is not intrinsically better than quite arbitrary ways [Merricks] |
14472 | If atoms 'arranged baseballwise' break a window, that analytically entails that a baseball did it [Merricks, by Thomasson] |
14469 | Overdetermination: the atoms do all the causing, so the baseball causes no breakage [Merricks] |
6137 | Clay does not 'constitute' a statue, as they have different persistence conditions (flaking, squashing) [Merricks] |
6127 | 'Unrestricted composition' says any two things can make up a third thing [Merricks] |
6131 | Composition as identity is false, as identity is never between a single thing and many things [Merricks] |
6132 | Composition as identity is false, as it implies that things never change their parts [Merricks] |
6141 | There is no visible difference between statues, and atoms arranged statuewise [Merricks] |
6130 | 'Composition' says things are their parts; 'constitution' says a whole substance is an object [Merricks] |
6138 | It seems wrong that constitution entails that two objects are wholly co-located [Merricks] |
6128 | Objects decompose (it seems) into non-overlapping parts that fill its whole region [Merricks] |
6136 | Eliminativism about objects gives the best understanding of the Sorites paradox [Merricks] |
6133 | If my counterpart is happy, that is irrelevant to whether I 'could' have been happy [Merricks] |
6150 | The 'warrant' for a belief is what turns a true belief into knowledge [Merricks] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
6144 | You hold a child in your arms, so it is not mental substance, or mental state, or software [Merricks] |
6140 | Maybe the word 'I' can only refer to persons [Merricks] |
6149 | Free will and determinism are incompatible, since determinism destroys human choice [Merricks] |
6148 | Human organisms can exercise downward causation [Merricks] |
6146 | Before Creation it is assumed that God still had many many mental properties [Merricks] |
6147 | The hypothesis of solipsism doesn't seem to be made incoherent by the nature of mental properties [Merricks] |
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] |