119 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] |
5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
15957 | Essential definitions show the differences that discriminate things, and make them what they are [Boyle] |
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
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] |
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] |
18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
18114 | There is no single agreed structure for set theory [Bostock] |
18107 | A 'proper class' cannot be a member of anything [Bostock] |
18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
18097 | The Peano Axioms describe a unique structure [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
18140 | The best version of conceptualism is predicativism [Bostock] |
18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
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] |
15965 | Boyle attacked a contemporary belief that powers were occult things [Boyle, by Alexander,P] |
16735 | In the 17th century, 'disposition' usually just means the spatial arrangement of parts [Boyle, by Pasnau] |
16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
16034 | Form is not a separate substance, but just the manner, modification or 'stamp' of matter [Boyle] |
15953 | To cite a substantial form tells us what produced the effect, but not how it did it [Boyle] |
16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
15962 | Boyle's term 'texture' is not something you feel, but is unobservable structures of particles [Boyle, by Alexander,P] |
15964 | Boyle's secondary qualities are not illusory, or 'in the mind' [Boyle, by Alexander,P] |
15960 | Explanation is deducing a phenomenon from some nature better known to us [Boyle] |
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] |
20808 | Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius] |
20835 | Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus] |
20836 | The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero] |
20837 | Fate is an eternal and fixed chain of causal events [Chrysippus] |
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] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
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] |
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] |
15952 | The corpuscles just have shape, size and motion, which explains things without 'sympathies' or 'forces' [Boyle, by Alexander,P] |
15972 | The corpuscular theory allows motion, but does not include forces between the particles [Boyle, by Alexander,P] |
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] |