183 ideas
9199 | Wisdom for one instant is as good as wisdom for eternity [Chrysippus] |
20853 | Wise men should try to participate in politics, since they are a good influence [Chrysippus, by Diog. Laertius] |
20772 | Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus] |
12865 | Analytic philosophers may prefer formal systems because natural language is such mess [Simons] |
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
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] |
21388 | The causes of future true events must exist now, so they will happen because of destiny [Chrysippus, by Cicero] |
20780 | Graspable presentations are criteria of facts, and are molded according to their objects [Chrysippus, by Diog. Laertius] |
20793 | How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus] |
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] |
8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
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] |
12815 | Classical mereology doesn't apply well to the objects around us [Simons] |
12832 | Complement: the rest of the Universe apart from some individual, written x-bar [Simons] |
12834 | Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons] |
12819 | A 'part' has different meanings for individuals, classes, and masses [Simons] |
12822 | Proper or improper part: x < y, 'x is (a) part of y' [Simons] |
12824 | Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons] |
12827 | Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons] |
12823 | Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons] |
12825 | Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons] |
12826 | Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons] |
12828 | General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons] |
12829 | General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons] |
12830 | Universe: the mereological sum of all objects whatever, written 'U' [Simons] |
12831 | Atom: an individual with no proper parts, written 'At x' [Simons] |
12844 | Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons] |
12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
12846 | A 'group' is a collection with a condition which constitutes their being united [Simons] |
12848 | The same members may form two groups [Simons] |
12861 | 'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons] |
14452 | All the propositions of logic are completely general [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
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] |
6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
12876 | Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons] |
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] |
12845 | Some natural languages don't distinguish between singular and plural [Simons] |
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] |
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] |
5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
12838 | Four-dimensional ontology has no change, since that needs an object, and time to pass [Simons] |
12842 | There are real relational changes, as well as bogus 'Cambridge changes' [Simons] |
12841 | I don't believe in processes [Simons] |
12836 | Fans of process ontology cheat, since river-stages refer to 'rivers' [Simons] |
12880 | Moments are things like smiles or skids, which are founded on other things [Simons] |
12883 | Moving disturbances are are moments which continuously change their basis [Simons] |
12881 | A smiling is an event with causes, but the smile is a continuant without causes [Simons] |
12882 | A wave is maintained by a process, but it isn't a process [Simons] |
12840 | I do not think there is a general identity condition for events [Simons] |
12839 | Relativity has an ontology of things and events, not on space-time diagrams [Simons] |
12879 | Independent objects can exist apart, and maybe even entirely alone [Simons] |
12847 | Mass nouns admit 'much' and 'a little', and resist 'many' and 'few'. [Simons] |
12863 | Mass terms (unlike plurals) are used with indifference to whether they can exist in units [Simons] |
12862 | Gold is not its atoms, because the atoms must be all gold, but gold contains neutrons [Simons] |
12858 | Mixtures disappear if nearly all of the mixture is one ingredient [Simons] |
12859 | A mixture can have different qualities from its ingredients. [Simons] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
21673 | There are simple and complex facts; the latter depend on further facts [Chrysippus, by Cicero] |
16652 | Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau] |
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] |
12850 | To individuate something we must pick it out, but also know its limits of variation [Simons] |
12860 | Sortal nouns for continuants tell you their continuance- and cessation-conditions [Simons] |
12886 | A whole requires some unique relation which binds together all of the parts [Simons] |
12857 | Tibbles isn't Tib-plus-tail, because Tibbles can survive its loss, but the sum can't [Simons] |
16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
12835 | Does Tibbles remain the same cat when it loses its tail? [Simons] |
12820 | Without extensional mereology two objects can occupy the same position [Simons] |
12866 | Composition is asymmetric and transitive [Simons] |
12867 | A hand constitutes a fist (when clenched), but a fist is not composed of an augmented hand [Simons] |
12864 | We say 'b is part of a', 'b is a part of a', 'b are a part of a', or 'b are parts of a'. [Simons] |
12814 | Classical mereology says there are 'sums', for whose existence there is no other evidence [Simons] |
12817 | 'Mereological extensionality' says objects with the same parts are identical [Simons] |
12833 | If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals [Simons] |
12849 | Sums are more plausible for pluralities and masses than they are for individuals [Simons] |
12877 | Sums of things in different categories are found within philosophy. [Simons] |
12888 | The wholeness of a melody seems conventional, but of an explosion it seems natural [Simons] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
12871 | Objects have their essential properties because of the kind of objects they are [Simons] |
12870 | We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence [Simons] |
12873 | Original parts are the best candidates for being essential to artefacts [Simons] |
12874 | An essential part of an essential part is an essential part of the whole [Simons] |
16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
12837 | Four dimensional-objects are stranger than most people think [Simons] |
12856 | Intermittent objects would be respectable if they occurred in nature, as well as in artefacts [Simons] |
12885 | Objects like chess games, with gaps in them, are thereby less unified [Simons] |
12854 | An entrepreneur and a museum curator would each be happy with their ship at the end [Simons] |
12855 | The 'best candidate' theories mistakenly assume there is one answer to 'Which is the real ship?' [Simons] |
12872 | The zygote is an essential initial part, for a sexually reproduced organism [Simons] |
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] |
12889 | The limits of change for an individual depend on the kind of individual [Simons] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
20834 | Chrysippus allows evil to say it is fated, or even that it is rational and natural [Plutarch on Chrysippus] |
20833 | A swerve in the atoms would be unnatural, like scales settling differently for no reason [Chrysippus, by Plutarch] |
20835 | Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus] |
20808 | Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius] |
20837 | Fate is an eternal and fixed chain of causal events [Chrysippus] |
20836 | The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero] |
21679 | When we say events are fated by antecedent causes, do we mean principal or auxiliary causes? [Chrysippus] |
5971 | Destiny is only a predisposing cause, not a sufficient cause [Chrysippus, by Plutarch] |
20787 | A proposition is what can be asserted or denied on its own [Chrysippus] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
12843 | With activities if you are doing it you've done it, with performances you must finish to have done it [Simons] |
20850 | Passions are judgements; greed thinks money is honorable, and likewise drinking and lust [Chrysippus, by Diog. Laertius] |
20869 | The highest degree of morality performs all that is appropriate, omitting nothing [Chrysippus] |
12875 | One false note doesn't make it a performance of a different work [Simons] |
3044 | Stoics say that beauty and goodness are equivalent and linked [Chrysippus, by Diog. Laertius] |
20838 | Fate initiates general causes, but individual wills and characters dictate what we do [Chrysippus] |
20813 | Human purpose is to contemplate and imitate the cosmos [Chrysippus] |
3045 | Stoics say justice is a part of nature, not just an invented principle [Chrysippus, by Diog. Laertius] |
20774 | Only nature is available to guide action and virtue [Chrysippus] |
20864 | Live in agreement, according to experience of natural events [Chrysippus] |
5972 | Living happily is nothing but living virtuously [Chrysippus, by Plutarch] |
1777 | Pleasure is not the good, because there are disgraceful pleasures [Chrysippus, by Diog. Laertius] |
5973 | Justice can be preserved if pleasure is a good, but not if it is the goal [Chrysippus, by Plutarch] |
20845 | There are shameful pleasures, and nothing shameful is good, so pleasure is not a good [Chrysippus, by Diog. Laertius] |
5967 | People need nothing except corn and water [Chrysippus, by Plutarch] |
5966 | All virtue is good, but not always praised (as in not lusting after someone ugly) [Chrysippus] |
20855 | Chrysippus says virtue can be lost (though Cleanthes says it is too secure for that) [Chrysippus, by Diog. Laertius] |
5970 | Chrysippus says nothing is blameworthy, as everything conforms with the best nature [Chrysippus, by Plutarch] |
20842 | Rational animals begin uncorrupted, but externals and companions are bad influences [Chrysippus, by Diog. Laertius] |
20856 | Justice, the law, and right reason are natural and not conventional [Chrysippus, by Diog. Laertius] |
1779 | We don't have obligations to animals as they aren't like us [Chrysippus, by Diog. Laertius] |
20857 | Justice is irrelevant to animals, because they are too unlike us [Chrysippus, by Diog. Laertius] |
20812 | Covers are for shields, and sheaths for swords; likewise, all in the cosmos is for some other thing [Chrysippus] |
21403 | The later Stoics identified the logos with an air-fire compound, called 'pneuma' [Chrysippus, by Long] |
20828 | Fire is a separate element, not formed with others (as was previously believed) [Chrysippus, by Stobaeus] |
5975 | Stoics say earth, air, fire and water are the primary elements [Chrysippus, by Plutarch] |
20819 | The past and the future subsist, but only the present exists [Chrysippus, by Plutarch] |
20818 | The present does not exist, so our immediate experience is actually part past and part future [Chrysippus, by Plutarch] |
20821 | Time is continous and infinitely divisible, so there cannot be a wholly present time [Chrysippus, by Stobaeus] |
3048 | Stoics say that God the creator is the perfection of all animals [Chrysippus, by Diog. Laertius] |
20773 | The origin of justice can only be in Zeus, and in nature [Chrysippus] |
5965 | The source of all justice is Zeus and the universal nature [Chrysippus] |
3042 | Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius] |
1782 | Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius] |
20830 | Death can't separate soul from body, because incorporeal soul can't unite with body [Chrysippus] |
21404 | There is a rationale in terrible disasters; they are useful to the whole, and make good possible [Chrysippus] |