150 ideas
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
5082 | Reason grasps generalities, while the senses grasp particulars [Aristotle] |
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] |
14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [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] |
13270 | Are a part and whole one or many? Either way, what is the cause? [Aristotle] |
14452 | All the propositions of logic are completely general [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
14464 | Logic can be known a priori, without study of the actual world [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] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [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] |
9790 | Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle] |
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] |
22962 | Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle] |
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] |
18090 | Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle] |
14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
22929 | Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin] |
22930 | Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin] |
18833 | A continuous line cannot be composed of indivisible points [Aristotle] |
14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
14422 | Any founded, non-repeating series all reachable in steps will satisfy 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] |
9974 | Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle] |
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] |
5105 | The incommensurability of the diagonal always exists, and so it is not in time [Aristotle] |
22960 | The sophists thought a man in the Lyceum is different from that man in the marketplace [Aristotle] |
16115 | Change is the implied actuality of that which exists potentially [Aristotle] |
17262 | Aristotle's formal and material 'becauses' [aitiai] arguably involve grounding [Aristotle, by Correia/Schnieder] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
16656 | The separation from here to there is not the same as the separation from there to here [Aristotle] |
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] |
16644 | The features of a thing (whether quality or quantity) are inseparable from their subjects [Aristotle] |
5117 | Heavy and light are defined by their tendency to move down or up [Aristotle] |
17041 | Natural objects include animals and their parts, plants, and the simple elements [Aristotle] |
16172 | Substance is not predicated of anything - but it still has something underlying it, that originates it [Aristotle] |
16623 | We only infer underlying natures by analogy, observing bronze of a statue, or wood of a bed [Aristotle] |
16174 | A nature is related to a substance as shapeless matter is to something which has a shape [Aristotle] |
17043 | Form, not matter, is a thing's nature, because it is actual, rather than potential [Aristotle] |
16970 | A thing's form and purpose are often the same, and form can be the initiator of change too [Aristotle] |
16104 | Unity of the form is just unity of the definition [Aristotle] |
11255 | In feature-generation the matter (such as bronze) endures, but in generation it doesn't [Aristotle, by Politis] |
16791 | There is no whole except for the parts [Aristotle] |
9071 | We first sense whole entities, and then move to particular parts of it [Aristotle] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
16972 | The four explanations are the main aspects of a thing's nature [Aristotle, by Moravcsik] |
5084 | A thing's nature is what causes its changes and stability [Aristotle] |
16173 | Coming to be is by shape-change, addition, subtraction, composition or alteration [Aristotle] |
17042 | Natural things are their own source of stability through change [Aristotle] |
16691 | A day, or the games, has one thing after another, actually and potentially occurring [Aristotle] |
16574 | Coming-to-be may be from nothing in a qualified way, as arising from an absence [Aristotle] |
11254 | Matter is potentiality [Aristotle, by Politis] |
13110 | Intrinsic cause is prior to coincidence, so nature and intelligence are primary causes, chance secondary [Aristotle] |
13106 | Maybe there is no pure chance; a man's choices cause his chance meetings [Aristotle] |
13108 | Chance is a coincidental cause among events involving purpose and choice [Aristotle] |
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] |
14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
8331 | To know something we need understanding, which is grasp of the primary cause [Aristotle] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
5080 | We know a thing if we grasp its first causes, principles and basic elements [Aristotle] |
7082 | Nature requires causal explanations, but society requires clarification by reasons and motives [Weber, by Critchley] |
11250 | Four Explanations: the essence and form; the matter; the source; and the end [Aristotle, by Politis] |
12045 | Aristotle's four 'causes' are four items which figure in basic explanations of nature [Aristotle, by Annas] |
16968 | There are as many causes/explanations as there are different types of why-question [Aristotle] |
16969 | Science refers the question Why? to four causes/explanations: matter, form, source, purpose [Aristotle] |
13109 | Chance is inexplicable, because we can only explain what happens always or usually [Aristotle] |
9789 | You can't abstract natural properties to make Forms - objects and attributes are defined together [Aristotle] |
9788 | Mathematicians study what is conceptually separable, and doesn't lead to error [Aristotle] |
5107 | Predicates are substance, quality, place, relation, quantity and action or affection [Aristotle] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
20042 | We assign the cause of someone's walking when we say why they are doing it [Aristotle] |
22155 | We are disenchanted because we rely on science, which ignores values [Weber, by Boulter] |
5110 | Goodness is when a thing (such as a circle) is complete, and conforms with its nature [Aristotle] |
5111 | All moral virtue is concerned with bodily pleasure and pain [Aristotle] |
5092 | Nature is a principle of change, so we must understand change first [Aristotle] |
5113 | Nothing natural is disorderly, because nature is responsible for all order [Aristotle] |
5085 | 'Nature' refers to two things - form and matter [Aristotle] |
5089 | Nature has purpose, and aims at what is better. Is it coincidence that crops grow when it rains? [Aristotle] |
5086 | The nature of a thing is its end and purpose [Aristotle] |
5087 | A thing's purpose is ambiguous, and from one point of view we ourselves are ends [Aristotle] |
5091 | Teeth and crops are predictable, so they cannot be mere chance, but must have a purpose [Aristotle] |
5108 | Is ceasing-to-be unnatural if it happens by force, and natural otherwise? [Aristotle] |
5093 | Continuity depends on infinity, because the continuous is infinitely divisible [Aristotle] |
5095 | The heavens seem to be infinite, because we cannot imagine their end [Aristotle] |
16762 | Matter desires form, as female desires male, and ugliness desires beauty [Aristotle] |
17464 | When Aristotle's elements compound they are stable, so why would they ever separate? [Weisberg/Needham/Hendry on Aristotle] |
11252 | The 'form' of a thing explains why the matter constitutes that particular thing [Aristotle, by Politis] |
11253 | A 'material' cause/explanation is the form of whatever is the source [Aristotle, by Politis] |
13107 | Causes produce a few things in their own right, and innumerable things coincidentally [Aristotle] |
8332 | The four causes are the material, the form, the source, and the end [Aristotle] |
9787 | Scientists must know the essential attributes of the things they study [Aristotle] |
20063 | Motion fulfils potentiality [Aristotle] |
5114 | If movement can arise within an animal, why can't it also arise in the universe? [Aristotle] |
5116 | When there is unnatural movement (e.g. fire going downwards) the cause is obvious [Aristotle] |
5097 | If everything has a place, this causes an infinite regress, because each place must have place [Aristotle] |
5099 | The universe as a whole is not anywhere [Aristotle] |
5098 | Place is not shape, or matter, or extension between limits; it is the limits of a body [Aristotle] |
20920 | If there were many cosmoses, each would have its own time, giving many times [Aristotle] |
5106 | Would there be time if there were no mind? [Aristotle] |
22967 | It is unclear whether time depends on the existence of soul [Aristotle] |
8590 | Time does not exist without change [Aristotle] |
5104 | Time is an aspect of change [Aristotle] |
22885 | For Aristotle time is not a process but a means for measuring processes [Aristotle, by Bardon] |
22965 | Time measures rest, as well as change [Aristotle] |
22959 | Time is not change, but the number we associate with change [Aristotle] |
22964 | Change only exists in time through its being temporally measure [Aristotle] |
22956 | How can time exist, when it is composed of what has ceased to be and is yet to be? [Aristotle] |
5102 | If all of time has either ceased to exist, or has not yet happened, maybe time does not exist [Aristotle] |
5103 | Time is not change, but requires change in our minds to be noticed [Aristotle] |
22961 | The present moment is obviously a necessary feature of time [Aristotle] |
22916 | Unlike time, change goes at different rates, and is usually localised [Aristotle, by Le Poidevin] |
16693 | Time has parts, but the now is not one of them, and time is not composed of nows [Aristotle] |
22958 | Nows can't be linked together, any more than points on a line [Aristotle] |
22968 | Circular motion is the most obvious measure of time, and especially the celestial sphere [Aristotle] |
22963 | We measure change by time, and time by change, as they are interdefined [Aristotle] |
22966 | The present moment is a link (of past to future), and also a limit (of past and of future) [Aristotle] |
22957 | We can't tell whether the changing present moment is one thing, or a succession of things [Aristotle] |
5083 | Do things come to be from what is, or from what is not? Both seem problematical. [Aristotle] |
5119 | The source of all movement must be indivisible and have no magnitude [Aristotle] |