69 ideas
13567 | Ontology should give insight into or an explanation of the world revealed by science [Ellis] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
13604 | Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [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] |
13606 | Humean conceptions of reality drive the adoption of extensional logic [Ellis] |
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] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [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] |
13584 | The extension of a property is a contingent fact, so cannot be the essence of the property [Ellis] |
13587 | There is no property of 'fragility', as things are each fragile in a distinctive way [Ellis] |
13577 | Typical 'categorical' properties are spatio-temporal, such as shape [Ellis] |
9436 | The property of 'being an electron' is not of anything, and only electrons could have it [Ellis] |
13582 | 'Being a methane molecule' is not a property - it is just a predicate [Ellis] |
13580 | Causal powers must necessarily act the way they do [Ellis] |
13598 | Causal powers are often directional (e.g. centripetal, centrifugal, circulatory) [Ellis] |
13568 | Basic powers may not be explained by structure, if at the bottom level there is no structure [Ellis] |
13586 | Maybe dispositions can be explained by intrinsic properties or structures [Ellis] |
13585 | The most fundamental properties of nature (mass, charge, spin ...) all seem to be dispositions [Ellis] |
13596 | A causal power is a disposition to produce forces [Ellis] |
13599 | Powers are dispositions of the essences of kinds that involve them in causation [Ellis] |
13572 | There are 'substantive' (objects of some kind), 'dynamic' (events of some kind) and 'property' universals [Ellis] |
13573 | Universals are all types of natural kind [Ellis] |
13571 | Scientific essentialism doesn't really need Kripkean individual essences [Ellis] |
13578 | The old idea that identity depends on essence and behaviour is rejected by the empiricists [Ellis] |
13576 | Necessities are distinguished by their grounds, not their different modalities [Ellis] |
13570 | Individual essences necessitate that individual; natural kind essences necessitate kind membership [Ellis] |
13607 | If events are unconnected, then induction cannot be solved [Ellis] |
13597 | Good explanations unify [Ellis] |
13601 | Explanations of particular events are not essentialist, as they don't reveal essential structures [Ellis] |
13569 | To give essentialist explanations there have to be natural kinds [Ellis] |
13600 | The point of models in theories is not to idealise, but to focus on what is essential [Ellis] |
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] |
15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
13583 | There might be uninstantiated natural kinds, such as transuranic elements which have never occurred [Ellis] |
13574 | Natural kinds are distinguished by resting on essences [Ellis] |
13575 | If there are borderline cases between natural kinds, that makes them superficial [Ellis] |
13595 | Laws don't exist in the world; they are true of the world [Ellis] |
13566 | A proton must have its causal role, because without it it wouldn't be a proton [Ellis] |
13579 | What is most distinctive of scientific essentialism is regarding processes as natural kinds [Ellis] |
13581 | Scientific essentialism is more concerned with explanation than with identity (Locke, not Kripke) [Ellis] |
13594 | The ontological fundamentals are dispositions, and also categorical (spatio-temporal and structural) properties [Ellis] |
13603 | A primary aim of science is to show the limits of the possible [Ellis] |