100 ideas
| 4194 | Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe] |
| 4214 | Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe] |
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
| 4222 | If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe] |
| 4217 | It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe] |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| 8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
| 14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
| 14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
| 14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
| 14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
| 14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
| 14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
| 14443 | The British parliament has one representative selected from each constituency [Russell] |
| 14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
| 14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
| 14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
| 14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
| 14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
| 8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
| 8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
| 14452 | All the propositions of logic are completely general [Russell] |
| 14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
| 10057 | Logic can only assert hypothetical existence [Russell] |
| 12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
| 14464 | Logic can be known a priori, without study of the actual world [Russell] |
| 14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
| 10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
| 14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
| 7311 | The only genuine proper names are 'this' and 'that' [Russell] |
| 14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
| 4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
| 4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
| 14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
| 14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
| 13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
| 14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
| 14439 | A complex number is simply an ordered couple of real numbers [Russell] |
| 14421 | Discovering that 1 is a number was difficult [Russell] |
| 14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| 14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
| 14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
| 14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
| 14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
| 14425 | A number is something which characterises collections of the same size [Russell] |
| 14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
| 4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
| 14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
| 13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
| 14449 | There is always something psychological about inference [Russell] |
| 14463 | Existence can only be asserted of something described, not of something named [Russell] |
| 4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
| 4202 | Change can be of composition (the component parts), or quality (properties), or substance [Lowe] |
| 4201 | Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG] |
| 4219 | Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe] |
| 4221 | Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe] |
| 4220 | Maybe an event is the exemplification of a property at a time [Lowe] |
| 4225 | Events are changes in the properties of or relations between things [Lowe] |
| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| 4196 | The main categories of existence are either universal and particular, or abstract and concrete [Lowe] |
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| 4234 | Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe] |
| 4235 | Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe] |
| 4236 | Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe] |
| 4197 | The category of universals can be sub-divided into properties and relations [Lowe] |
| 4232 | Nominalists believe that only particulars exist [Lowe] |
| 4205 | 'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe] |
| 4233 | If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe] |
| 4206 | Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe] |
| 4204 | Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe] |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| 4200 | If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe] |
| 4198 | If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe] |
| 4199 | A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe] |
| 4203 | Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe] |
| 4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
| 12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
| 14450 | All forms of implication are expressible as truth-functions [Russell] |
| 4207 | We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe] |
| 14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| 4223 | Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 4193 | The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe] |
| 4238 | The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe] |
| 4237 | Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 4210 | If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe] |
| 4215 | It seems proper to say that only substances (rather than events) have causal powers [Lowe] |
| 4209 | The theories of fact causation and event causation are both worth serious consideration [Lowe] |
| 4211 | Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe] |
| 4213 | Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe] |
| 4212 | Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe] |
| 14581 | The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum] |
| 4208 | 'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe] |
| 4224 | If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe] |
| 4227 | Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe] |
| 4228 | If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe] |