116 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] |
4588 | There is no such thing as 'science'; there are just many different sciences [Heil] |
5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
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] |
13520 | A 'tautology' must include connectives [Wolf,RS] |
13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
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] |
13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
4616 | A higher level is 'supervenient' if it is determined by lower levels, but has its own natural laws [Heil] |
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] |
4603 | Functionalists in Fodor's camp usually say that a genuine property is one that figures in some causal laws [Heil] |
4617 | A stone does not possess the property of being a stone; its other properties make it a stone [Heil] |
4615 | Complex properties are not new properties, they are merely new combinations of properties [Heil] |
4612 | Complex properties are just arrangements of simple properties; they do not "emerge" as separate [Heil] |
4587 | From the property predicates P and Q, we can get 'P or Q', but it doesn't have to designate another property [Heil] |
4611 | The supporters of 'tropes' treat objects as bundles of tropes, when I think objects 'possess' properties [Heil] |
16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
4592 | If you can have the boat without its current planks, and the planks with no boat, the planks aren't the boat [Heil] |
4586 | You can't embrace the formal apparatus of possible worlds, but reject the ontology [Heil] |
4591 | Idealism explains appearances by identifying appearances with reality [Heil] |
4610 | Different generations focus on either the quality of mind, or its scientific standing, or the content of thought [Heil] |
4618 | If minds are realised materially, it looks as if the material laws will pre-empt any causal role for mind [Heil] |
1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
4621 | Whatever exists has qualities, so it is no surprise that states of minds have qualities [Heil] |
4623 | Propositional attitudes are not the only intentional states; there is also mental imagery [Heil] |
4626 | The widespread externalist view says intentionality has content because of causal links of agent to world [Heil] |
4622 | Error must be possible in introspection, because error is possible in all judgements [Heil] |
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] |
4590 | If causation is just regularities in events, the interaction of mind and body is not a special problem [Heil] |
4614 | Disposition is a fundamental feature of reality, since basic particles are capable of endless possible interactions [Heil] |
4595 | No mental state entails inevitable behaviour, because other beliefs or desires may intervene [Heil] |
4599 | Hearts are material, but functionalism says the property of being a heart is not a material property [Heil] |
4624 | If you are a functionalist, there appears to be no room for qualia [Heil] |
4601 | Higher-level sciences cannot be reduced, because their concepts mark boundaries invisible at lower levels [Heil] |
4602 | Higher-level sciences designate real properties of objects, which are not reducible to lower levels [Heil] |
4593 | 'Property dualism' says mind and body are not substances, but distinct families of properties [Heil] |
4597 | Early identity theory talked of mind and brain 'processes', but now the focus is properties [Heil] |
4609 | It seems contradictory to be asked to believe that we can be eliminativist about beliefs [Heil] |
4596 | The appeal of the identity theory is its simplicity, and its solution to the mental causation problem [Heil] |
4598 | Functionalists emphasise that mental processes are not to be reduced to what realises them [Heil] |
4619 | 'Multiple realisability' needs to clearly distinguish low-level realisers from what is realised [Heil] |
4620 | Multiple realisability is not a relation among properties, but an application of predicates to resembling things [Heil] |
4594 | A scientist could know everything about the physiology of headaches, but never have had one [Heil] |
4625 | Is mental imagery pictorial, or is it propositional? [Heil] |
4607 | Folk psychology and neuroscience are no more competitors than cartography and geology are [Heil] |
4605 | Truth-conditions correspond to the idea of 'literal meaning' [Heil] |
4606 | To understand 'birds warble' and 'tigers growl', you must also understand 'tigers warble' [Heil] |
20787 | A proposition is what can be asserted or denied on its own [Chrysippus] |
4604 | If propositions are abstract entities, how do human beings interact with them? [Heil] |
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] |
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] |