64 ideas
6979 | Serious metaphysics cares about entailment between sentences [Jackson] |
6980 | Conceptual analysis studies whether one story is made true by another story [Jackson] |
6983 | Intuitions about possibilities are basic to conceptual analysis [Jackson] |
14707 | Conceptual analysis is needed to establish that metaphysical reductions respect original meanings [Jackson, by Schroeter] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
7005 | Something can only have a place in a preferred account of things if it is entailed by the account [Jackson] |
6994 | Truth supervenes on being [Jackson] |
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] |
10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
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] |
10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
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] |
6984 | Smooth reductions preserve high-level laws in the lower level [Jackson] |
10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
6978 | Baldness is just hair distribution, but the former is indeterminate, unlike the latter [Jackson] |
6993 | Redness is a property, but only as a presentation to normal humans [Jackson] |
6987 | We should not multiply senses of necessity beyond necessity [Jackson] |
6988 | Mathematical sentences are a problem in a possible-worlds framework [Jackson] |
6975 | Possible worlds could be concrete, abstract, universals, sentences, or properties [Jackson] |
6982 | Long arithmetic calculations show the a priori can be fallible [Jackson] |
6991 | We examine objects to determine colour; we do not introspect [Jackson] |
6976 | In physicalism, the psychological depends on the physical, not the other way around [Jackson] |
6986 | Is the dependence of the psychological on the physical a priori or a posteriori? [Jackson] |
6992 | If different states can fulfil the same role, the converse must also be possible [Jackson] |
6996 | Folk psychology covers input, internal role, and output [Jackson] |
6977 | Egocentric or de se content seems to be irreducibly so [Jackson] |
6990 | Keep distinct the essential properties of water, and application conditions for the word 'water' [Jackson] |
6985 | Analysis is finding necessary and sufficient conditions by studying possible cases [Jackson] |
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] |
6995 | Successful predication supervenes on nature [Jackson] |
6989 | I can understand "He has a beard", without identifying 'he', and hence the truth conditions [Jackson] |
6998 | Folk morality does not clearly distinguish between doing and allowing [Jackson] |
6997 | Moral functionalism says moral terms get their meaning from their role in folk morality [Jackson] |
7000 | Which are prior - thin concepts like right, good, ought; or thick concepts like kindness, equity etc.? [Jackson] |
6999 | It is hard to justify the huge difference in our judgements of abortion and infanticide [Jackson] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |