110 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] |
| 5300 | Philosophers have interpreted the world, but the point is to change it [Marx] |
| 5297 | Whether human thinking can be 'true' must be decided in practice, not theory [Marx] |
| 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] |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| 20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13711 | System B introduces iterated modalities [Sider] |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| 13714 | We can treat modal worlds as different times [Sider] |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 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] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 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] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| 16652 | Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 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] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| 1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
| 22598 | The authentic self exists at the level of class, rather than the individual [Marx, by Dunt] |
| 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] |
| 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] |
| 5298 | The human essence is not found in individuals but in social relations [Marx] |
| 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] |
| 3042 | Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius] |
| 5965 | The source of all justice is Zeus and the universal nature [Chrysippus] |
| 1782 | Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius] |
| 5299 | Religious feeling is social in origin [Marx] |
| 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] |