164 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] |
| 17240 | Definitions are the first step in philosophy [Hobbes] |
| 10237 | Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro] |
| 5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
| 17237 | Definitions of things that are caused must express their manner of generation [Hobbes] |
| 17239 | Definition is resolution of names into successive genera, and finally the difference [Hobbes] |
| 10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
| 17241 | A defined name should not appear in the definition [Hobbes] |
| 17242 | 'Petitio principii' is reusing the idea to be defined, in disguised words [Hobbes] |
| 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] |
| 10206 | Modal operators are usually treated as quantifiers [Shapiro] |
| 10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
| 10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
| 10207 | Anti-realists reject set theory [Shapiro] |
| 17245 | A part of a part is a part of a whole [Hobbes] |
| 10259 | The two standard explanations of consequence are semantic (in models) and deductive [Shapiro] |
| 8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
| 10257 | Intuitionism only sanctions modus ponens if all three components are proved [Shapiro] |
| 10253 | Either logic determines objects, or objects determine logic, or they are separate [Shapiro] |
| 10251 | The law of excluded middle might be seen as a principle of omniscience [Shapiro] |
| 6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
| 10212 | Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 10268 | Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro] |
| 10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
| 10240 | Model theory deals with relations, reference and extensions [Shapiro] |
| 10239 | The central notion of model theory is the relation of 'satisfaction' [Shapiro] |
| 10214 | Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro] |
| 10238 | The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro] |
| 10234 | Any theory with an infinite model has a model of every infinite cardinality [Shapiro] |
| 10201 | Virtually all of mathematics can be modeled in set theory [Shapiro] |
| 17258 | If we just say one, one, one, one, we don't know where we have got to [Hobbes] |
| 10213 | Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro] |
| 18243 | Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro] |
| 18245 | Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro] |
| 10236 | There is no grounding for mathematics that is more secure than mathematics [Shapiro] |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| 10202 | Natural numbers just need an initial object, successors, and an induction principle [Shapiro] |
| 10205 | Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic) [Shapiro] |
| 10222 | Mathematical foundations may not be sets; categories are a popular rival [Shapiro] |
| 10218 | Baseball positions and chess pieces depend entirely on context [Shapiro] |
| 10224 | The even numbers have the natural-number structure, with 6 playing the role of 3 [Shapiro] |
| 10228 | Could infinite structures be apprehended by pattern recognition? [Shapiro] |
| 10230 | The 4-pattern is the structure common to all collections of four objects [Shapiro] |
| 10249 | The main mathematical structures are algebraic, ordered, and topological [Shapiro] |
| 10273 | Some structures are exemplified by both abstract and concrete [Shapiro] |
| 10276 | Mathematical structures are defined by axioms, or in set theory [Shapiro] |
| 10270 | The main versions of structuralism are all definitionally equivalent [Shapiro] |
| 10221 | Is there is no more to structures than the systems that exemplify them? [Shapiro] |
| 10248 | Number statements are generalizations about number sequences, and are bound variables [Shapiro] |
| 10220 | Because one structure exemplifies several systems, a structure is a one-over-many [Shapiro] |
| 10223 | There is no 'structure of all structures', just as there is no set of all sets [Shapiro] |
| 8703 | Shapiro's structuralism says model theory (comparing structures) is the essence of mathematics [Shapiro, by Friend] |
| 10274 | Does someone using small numbers really need to know the infinite structure of arithmetic? [Shapiro] |
| 10200 | We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro] |
| 10210 | If mathematical objects are accepted, then a number of standard principles will follow [Shapiro] |
| 10215 | Platonists claim we can state the essence of a number without reference to the others [Shapiro] |
| 10233 | Platonism must accept that the Peano Axioms could all be false [Shapiro] |
| 10244 | Intuition is an outright hindrance to five-dimensional geometry [Shapiro] |
| 10280 | A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro] |
| 10254 | Can the ideal constructor also destroy objects? [Shapiro] |
| 10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
| 10279 | Can we discover whether a deck is fifty-two cards, or a person is time-slices or molecules? [Shapiro] |
| 5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
| 17253 | Change is nothing but movement [Hobbes] |
| 10227 | The abstract/concrete boundary now seems blurred, and would need a defence [Shapiro] |
| 10226 | Mathematicians regard arithmetic as concrete, and group theory as abstract [Shapiro] |
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| 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] |
| 16670 | Accidents are just modes of thinking about bodies [Hobbes] |
| 16621 | Accidents are not parts of bodies (like blood in a cloth); they have accidents as things have a size [Hobbes] |
| 16734 | The complete power of an event is just the aggregate of the qualities that produced it [Hobbes] |
| 17247 | The only generalities or universals are names or signs [Hobbes] |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| 14960 | Bodies are independent of thought, and coincide with part of space [Hobbes] |
| 17250 | If you separate the two places of one thing, you will also separate the thing [Hobbes] |
| 17249 | If you separated two things in the same place, you would also separate the places [Hobbes] |
| 17248 | If a whole body is moved, its parts must move with it [Hobbes] |
| 16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
| 10275 | A blurry border is still a border [Shapiro] |
| 16790 | A body is always the same, whether the parts are together or dispersed [Hobbes] |
| 17244 | To make a whole, parts needn't be put together, but can be united in the mind [Hobbes] |
| 17233 | Particulars contain universal things [Hobbes] |
| 17246 | Some accidental features are permanent, unless the object perishes [Hobbes] |
| 17251 | The feature which picks out or names a thing is usually called its 'essence' [Hobbes] |
| 16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
| 17257 | It is the same river if it has the same source, no matter what flows in it [Hobbes] |
| 12853 | Some individuate the ship by unity of matter, and others by unity of form [Hobbes] |
| 17256 | If a new ship were made of the discarded planks, would two ships be numerically the same? [Hobbes] |
| 16794 | As an infant, Socrates was not the same body, but he was the same human being [Hobbes] |
| 17255 | Two bodies differ when (at some time) you can say something of one you can't say of the other [Hobbes] |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| 16582 | We can imagine a point swelling and contracting - but not how this could be done [Hobbes] |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| 17238 | Science aims to show causes and generation of things [Hobbes] |
| 1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
| 17260 | Imagination is just weakened sensation [Hobbes] |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| 19373 | A 'conatus' is an initial motion, experienced by us as desire or aversion [Hobbes, by Arthur,R] |
| 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] |
| 2948 | Sensation is merely internal motion of the sentient being [Hobbes] |
| 17261 | Apart from pleasure and pain, the only emotions are appetite and aversion [Hobbes] |
| 17236 | Words are not for communication, but as marks for remembering what we have learned [Hobbes] |
| 10229 | Simple types can be apprehended through their tokens, via abstraction [Shapiro] |
| 10217 | We can apprehend structures by focusing on or ignoring features of patterns [Shapiro] |
| 9554 | We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro] |
| 10231 | Abstract objects might come by abstraction over an equivalence class of base entities [Shapiro] |
| 20787 | A proposition is what can be asserted or denied on its own [Chrysippus] |
| 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] |
| 16600 | Prime matter is body considered with mere size and extension, and potential [Hobbes] |
| 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] |
| 17252 | Acting on a body is either creating or destroying a property in it [Hobbes] |
| 17254 | An effect needs a sufficient and necessary cause [Hobbes] |
| 17235 | A cause is the complete sum of the features which necessitate the effect [Hobbes] |
| 17234 | Motion is losing one place and acquiring another [Hobbes] |
| 17259 | 'Force' is the quantity of movement imposed on something [Hobbes] |
| 20819 | The past and the future subsist, but only the present exists [Chrysippus, by Plutarch] |
| 17243 | Past times can't exist anywhere, apart from in our memories [Hobbes] |
| 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] |