195 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] |
15209 | Like disastrous small errors in navigation, small misunderstandings can wreck intellectual life [Harré/Madden] |
15215 | Philosophy devises and assesses conceptual schemes in the service of worldviews [Harré/Madden] |
15212 | Analysis of concepts based neither on formalism nor psychology can arise from examining what we know [Harré/Madden] |
15210 | Humeans see analysis in terms of formal logic, because necessities are fundamentally logical relations [Harré/Madden] |
15236 | Positivism says science only refers to immediate experiences [Harré/Madden] |
5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
15227 | Logically, definitions have a subject, and a set of necessary predicates [Harré/Madden] |
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] |
15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
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] |
15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
15273 | Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden] |
15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
15274 | Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden] |
15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
15211 | There is not an exclusive dichotomy between the formal and the logical [Harré/Madden] |
5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
15261 | Humeans can only explain change with continuity as successive replacement [Harré/Madden] |
15268 | Humeans construct their objects from events, but we construct events from objects [Harré/Madden] |
15257 | The induction problem fades if you work with things, rather than with events [Harré/Madden] |
15300 | Fundamental particulars can't change [Harré/Madden] |
15319 | Hard individual blocks don't fix what 'things' are; fluids are no less material things [Harré/Madden] |
15320 | Magnetic and gravity fields can occupy the same place without merging [Harré/Madden] |
15318 | Gravitational and electrical fields are, for a materialist, distressingly empty of material [Harré/Madden] |
21673 | There are simple and complex facts; the latter depend on further facts [Chrysippus, by Cicero] |
15267 | Events are changes in states of affairs (which consist of structured particulars, with powers and relations) [Harré/Madden] |
16652 | Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau] |
15281 | Humeans see predicates as independent, but science says they are connected [Harré/Madden] |
15279 | Energy was introduced to physics to refer to the 'store of potency' of a moving ball [Harré/Madden] |
15276 | Some powers need a stimulus, but others are just released [Harré/Madden] |
15305 | Some powers are variable, others cannot change (without destroying an identity) [Harré/Madden] |
15218 | Scientists define copper almost entirely (bar atomic number) in terms of its dispositions [Harré/Madden] |
15302 | We explain powers by the natures of things, but explanations end in inexplicable powers [Harré/Madden] |
15303 | Maybe a physical field qualifies as ultimate, if its nature is identical with its powers [Harré/Madden] |
15258 | Powers are not qualities; they just point to directions of empirical investigation [Harré/Madden] |
15315 | What is a field of potentials, if it only consists of possible events? [Harré/Madden] |
15272 | The good criticism of substance by Humeans also loses them the vital concept of a thing [Harré/Madden] |
15304 | We can escape substance and its properties, if we take fields of pure powers as ultimate [Harré/Madden] |
16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
15309 | The assumption that shape and solidity are fundamental implies dubious 'substance' in bodies [Harré/Madden] |
15264 | The notorious substratum results from substance-with-qualities; individuals-with-powers solves this [Harré/Madden] |
15262 | In logic the nature of a kind, substance or individual is the essence which is inseparable from what it is [Harré/Madden] |
15297 | We can infer a new property of a thing from its other properties, via its essential nature [Harré/Madden] |
15266 | We say the essence of particles is energy, but only so we can tell a story about the nature of things [Harré/Madden] |
16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
15220 | To say something remains the same but lacks its capacities and powers seems a contradiction [Harré/Madden] |
15222 | Some individuals can gain or lose capacities or powers, without losing their identity [Harré/Madden] |
15296 | A particular might change all of its characteristics, retaining mere numerical identity [Harré/Madden] |
15275 | 'Dense' time raises doubts about continuous objects, so they need 'continuous' time [Harré/Madden] |
15271 | If things are successive instantaneous events, nothing requires those events to resemble one another [Harré/Madden] |
15256 | Humeans cannot step in the same river twice, because they cannot strictly form the concept of 'river' [Harré/Madden] |
15290 | What reduces the field of the possible is a step towards necessity [Harré/Madden] |
15291 | There is 'absolute' necessity (implied by all propositions) and 'relative' necessity (from what is given) [Harré/Madden] |
15230 | Logical necessity is grounded in the logical form of a statement [Harré/Madden] |
15214 | Natural necessity is not logical necessity or empirical contingency in disguise [Harré/Madden] |
15221 | The relation between what a thing is and what it can do or undergo relate by natural necessity [Harré/Madden] |
15224 | A necessity corresponds to the nature of the actual [Harré/Madden] |
15232 | Natural necessity is when powerful particulars must produce certain results in a situation [Harré/Madden] |
15288 | People doubt science because if it isn't logically necessary it seems to be absolutely contingent [Harré/Madden] |
15289 | Property or event relations are naturally necessary if generated by essential mechanisms [Harré/Madden] |
15231 | Transcendental necessity is conditions of a world required for a rational being to know its nature [Harré/Madden] |
15234 | There is a transcendental necessity for each logical necessity, but the transcendental extends further [Harré/Madden] |
15260 | Counterfactuals are just right for analysing statements about the powers which things have [Harré/Madden] |
15233 | If natural necessity is used to include or exclude some predicate, the predicate is conceptually necessary [Harré/Madden] |
15242 | Having a child is contingent for a 'man', necessary for a 'father'; the latter reflects a necessity of nature [Harré/Madden] |
15216 | Is conceptual necessity just conventional, or does it mirror something about nature? [Harré/Madden] |
15235 | There is a conceptual necessity when properties become a standard part of a nominal essence [Harré/Madden] |
15228 | Necessity and contingency are separate from the a priori and the a posteriori [Harré/Madden] |
15252 | If Goldbach's Conjecture is true (and logically necessary), we may be able to conceive its opposite [Harré/Madden] |
15245 | It is silly to say that direct experience must be justified, either by reason, or by more experience [Harré/Madden] |
15244 | We experience qualities as of objects, not on their own [Harré/Madden] |
15248 | Inference in perception is unconvincingly defended as non-conscious and almost instantaneous [Harré/Madden] |
15269 | Humean impressions are too instantaneous and simple to have structure or relations [Harré/Madden] |
15286 | Clavius's Paradox: purely syntactic entailment theories won't explain, because they are too profuse [Harré/Madden] |
15283 | Simplicity can sort theories out, but still leaves an infinity of possibilities [Harré/Madden] |
15316 | The powers/natures approach has been so successful (for electricity, magnetism, gravity) it may be universal [Harré/Madden] |
15298 | We prefer the theory which explains and predicts the powers and capacities of particulars [Harré/Madden] |
15225 | Science investigates the nature and constitution of things or substances [Harré/Madden] |
15255 | Conjunctions explain nothing, and so do not give a reason for confidence in inductions [Harré/Madden] |
15270 | Hume's atomic events makes properties independent, and leads to problems with induction [Harré/Madden] |
15284 | Contraposition may be equivalent in truth, but not true in nature, because of irrelevant predicates [Harré/Madden] |
15285 | The items put forward by the contraposition belong within different natural clusters [Harré/Madden] |
15287 | The possibility that all ravens are black is a law depends on a mechanism producing the blackness [Harré/Madden] |
15306 | Only changes require explanation [Harré/Madden] |
15293 | If explanation is by entailment, that lacks a causal direction, unlike natural necessity [Harré/Madden] |
15294 | Powers can explain the direction of causality, and make it a natural necessity [Harré/Madden] |
15254 | If the nature of particulars explains their powers, it also explains their relations and behaviour [Harré/Madden] |
15317 | Powers and natures lead us to hypothesise underlying mechanisms, which may be real [Harré/Madden] |
15310 | Solidity comes from the power of repulsion, and shape from the power of attraction [Harré/Madden] |
15219 | Essence explains passive capacities as well as active powers [Harré/Madden] |
1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
15301 | The very concepts of a particular power or nature imply the possibility of being generalised [Harré/Madden] |
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] |
15226 | What properties a thing must have to be a type of substance can be laid down a priori [Harré/Madden] |
20787 | A proposition is what can be asserted or denied on its own [Chrysippus] |
15229 | We say there is 'no alternative' in all sorts of contexts, and there are many different grounds for it [Harré/Madden] |
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] |
15292 | We can base the idea of a natural kind on the mechanisms that produce natural necessity [Harré/Madden] |
15299 | Species do not have enough constancy to be natural kinds [Harré/Madden] |
15253 | If the concept of a cause includes its usual effects, we call it a 'power' [Harré/Madden] |
15278 | Humean accounts of causal direction by time fail, because cause and effect can occur together [Harré/Madden] |
15246 | Active causal power is just objects at work, not something existing in itself [Harré/Madden] |
15213 | Causation always involves particular productive things [Harré/Madden] |
15217 | Efficient causes combine stimulus to individuals, absence of contraints on activity [Harré/Madden] |
15277 | The cause (or part of it) is what stimulates or releases the powerful particular thing involved [Harré/Madden] |
15237 | Originally Humeans based lawlike statements on pure qualities, without particulars [Harré/Madden] |
15238 | Being lawlike seems to resist formal analysis, because there are always counter-examples [Harré/Madden] |
15223 | Necessary effects will follow from some general theory specifying powers and structure of a world [Harré/Madden] |
15241 | Humeans say there is no necessity in causation, because denying an effect is never self-contradictory [Harré/Madden] |
15240 | In lawful universal statements (unlike accidental ones) we see why the regularity holds [Harré/Madden] |
15239 | We could call any generalisation a law, if it had reasonable support and no counter-evidence [Harré/Madden] |
15243 | We perceive motion, and not just successive occupations of different positions [Harré/Madden] |
15265 | 'Energy' is a quasi-substance invented as the bearer of change during interactions [Harré/Madden] |
15280 | 'Kinetic energy' is used to explain the effects of moving things when they are stopped [Harré/Madden] |
15321 | Space can't be an individual (in space), but it is present in all places [Harré/Madden] |
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] |
15259 | Chemical atoms have two powers: to enter certain combinations, and to emit a particular spectrum [Harré/Madden] |
15263 | Chemistry is not purely structural; CO2 is not the same as SO2 [Harré/Madden] |
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] |
15295 | Theism is supposed to make the world more intelligible - and should offer results [Harré/Madden] |
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] |