118 ideas
| 9199 | Wisdom for one instant is as good as wisdom for eternity [Chrysippus] |
| Full Idea: If a person has wisdom for one instant, he is no less happy than he who possesses it for eternity. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Pierre Hadot - Philosophy as a way of life 8 | |
| A reaction: [Hadot quotes Plutarch 'On Common Conceptions' 8,1062a] This makes it sound awfully like some sort of Buddhist 'enlightenment', which strikes like lightning. He does wisdom recognise itself - by a warm glow, or by the cautious thought that got you there? |
| 20853 | Wise men should try to participate in politics, since they are a good influence [Chrysippus, by Diog. Laertius] |
| Full Idea: The wise man will participate in politics unless something prevents him, for he will restrain vice and promote virtue. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.121 | |
| A reaction: [from lost On Ways of Life Bk 1] We have made modern politics so hostile for its participants, thanks to cruel media pressure, that the best people now run a mile from it. Disastrous. |
| 20772 | Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus] |
| Full Idea: There are three kinds of philosophical theorems, logical, ethical, and physical; of these the logic should be placed first, ethics second, and physics third (and theology is the final topic in physics). | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Plutarch - 70: Stoic Self-contradictions 1035a | |
| A reaction: [in his lost 'On Lives' Bk 4] 'Theology is the final topic in physics'! That should create a stir in theology departments. Is this an order of study, or of importance? You come to theology right at the end of your studies. |
| 5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
| Full Idea: Chrysippus said that the uncaused is altogether non-existent. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - 70: Stoic Self-contradictions 1045c | |
| A reaction: The difficulty is to see what empirical basis there can be for such a claim, or what argument of any kind other than an intuition. Induction is the obvious answer, but Hume teaches us scepticism about any claim that 'there can be no exceptions'. |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| Full Idea: Poincaré suggested that what is wrong with an impredicative definition is that it allows the set defined to alter its composition as more sets are added to the theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 21388 | The causes of future true events must exist now, so they will happen because of destiny [Chrysippus, by Cicero] |
| Full Idea: True future events cannot be such as do not possess causes on account of which they will happen; therefore that which is true must possess causes: and so, when the [true future events] happen they will have happened as a result of destiny. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 9.23-8 | |
| A reaction: [exact ref unclear] Presumably the current causes are the truthmakers for the future events, and so the past is the truthmaker of the future, if you are a determinist. |
| 20780 | Graspable presentations are criteria of facts, and are molded according to their objects [Chrysippus, by Diog. Laertius] |
| Full Idea: Of presentations, some are graspable, some non-graspable. The graspable presentation, which they say is the criterion of facts [pragmata], is that which comes from an existing object and is stamped and molded in accordance wth the existing object itself. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.46 | |
| A reaction: [in lost Physics Bk 2] The big modern anguish over truth-as-correspondence is how you are supposed to verify the 'accordance'. This idea seems to blur the ideas of truth and justification (the 'criterion'), and you can't have both as accordance. |
| 20793 | How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus] |
| Full Idea: One cannot say that the soul grasps the externally existing objects by means of the states of the senses on the basis of the similarity of these states to the externally existing objects. For on what basis will it know the similarity? | |
| From: comment on Chrysippus (fragments/reports [c.240 BCE]) by Sextus Empiricus - Outlines of Pyrrhonism 2.74 | |
| A reaction: This exactly the main modern reason for rejecting the correspondence theory of truth. You are welcome to affirm a robust view of truth, but supporting it by claiming a correspondence or resemblance is dubious. |
| 8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
| Full Idea: In Stoic logic propositions are treated the way atoms are treated in present-day chemistry, where the focus is on the way atoms fit together to form molecules, rather than on the internal structure of the atoms. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
| A reaction: A nice analogy to explain the nature of Propositional Logic, which was invented by the Stoics (N.B. after Aristotle had invented predicate logic). |
| 20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
| Full Idea: Chrysippus has five indemonstrables that do not need demonstration:1) If 1st the 2nd, but 1st, so 2nd; 2) If 1st the 2nd, but not 2nd, so not 1st; 3) Not 1st and 2nd, the 1st, so not 2nd; 4) 1st or 2nd, the 1st, so not 2nd; 5) 1st or 2nd, not 2nd, so 1st. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.80-81 | |
| A reaction: [from his lost text 'Dialectics'; squashed to fit into one quote] 1) is Modus Ponens, 2) is Modus Tollens. 4) and 5) are Disjunctive Syllogisms. 3) seems a bit complex to be an indemonstrable. |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| Full Idea: None of the classical ways of defining one logical constant in terms of others is available in intuitionist logic (and this includes the two quantifiers). | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| Full Idea: There is so far no agreed set of axioms for set theory which is categorical, i.e. which does pick just one structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: This contrasts with Peano Arithmetic, which is categorical in its second-order version. |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| Full Idea: A 'proper class' cannot be a member of anything, neither of a set nor of another proper class. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| Full Idea: We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: Bostock says most mathematicians reject the first option, and are undecided about the second option. |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| Full Idea: The usual accounts of ZF are not restricted to subsets that we can describe, and that is what justifies the axiom of choice. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4 n36) | |
| A reaction: This contrasts interestingly with predicativism, which says we can only discuss things which we can describe or define. Something like verificationism hovers in the background. |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| Full Idea: The Axiom of Replacement (or the Axiom of Subsets, 'Aussonderung', Fraenkel 1922) in effect enforces the idea that 'limitation of size' is a crucial factor when deciding whether a proposed set or does not not exist. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| Full Idea: First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936). | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| Full Idea: From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) | |
| A reaction: The point is that the completeness requires finite proofs. |
| 8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
| Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
| A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true. |
| 6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
| Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38 | |
| A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc. |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| Full Idea: Substitutional quantification and quantification understood in the usual 'ontological' way will coincide when every object in the (ontological) domain has a name. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.3 n23) |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| Full Idea: The Deduction Theorem is what licenses a system of 'natural deduction' in the first place. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| Full Idea: Berry's Paradox can be put in this form, by considering the alleged name 'The least number not named by this name'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| Full Idea: If you add to the ordinals you produce many different ordinals, each measuring the length of the sequence of ordinals less than it. They each have cardinality aleph-0. The cardinality eventually increases, but we can't say where this break comes. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| Full Idea: If we add ω onto the end of 0,1,2,3,4..., it then has a different length, of ω+1. It has a different ordinal (since it can't be matched with its first part), but the same cardinal (since adding 1 makes no difference). | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: [compressed] The ordinals and cardinals coincide up to ω, but this is the point at which they come apart. |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| Full Idea: It is the usual procedure these days to identify a cardinal number with the earliest ordinal number that has that number of predecessors. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: This sounds circular, since you need to know the cardinal in order to decide which ordinal is the one you want, but, hey, what do I know? |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| Full Idea: The cardinal aleph-1 is identified with the first ordinal to have more than aleph-0 members, and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) | |
| A reaction: That is, the succeeding infinite ordinals all have the same cardinal number of members (aleph-0), until the new total is triggered (at the number of the reals). This is Continuum Hypothesis territory. |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| Full Idea: In addition to cuts, or converging series, Cantor suggests we can simply lay down a set of axioms for the real numbers, and this can be done without any explicit mention of the rational numbers [note: the axioms are those for a complete ordered field]. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: It is interesting when axioms are best, and when not. Set theory depends entirely on axioms. Horsten and Halbach are now exploring treating truth as axiomatic. You don't give the 'nature' of the thing - just rules for its operation. |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| Full Idea: It is not difficult to show that the number of the real numbers is the same as the number of all the subsets of the natural numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: The Continuum Hypothesis is that this is the next infinite number after the number of natural numbers. Why can't there be a number which is 'most' of the subsets of the natural numbers? |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| Full Idea: As Eudoxus claimed, two distinct real numbers cannot both make the same cut in the rationals, for any two real numbers must be separated by a rational number. He did not say, though, that for every such cut there is a real number that makes it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: This is in Bostock's discussion of Dedekind's cuts. It seems that every cut is guaranteed to produce a real. Fine challenges the later assumption. |
| 16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
| Full Idea: 'Numerical identity' implies the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical. | |
| From: Harold Noonan (Identity [2009], §1) | |
| A reaction: Noonan cites Geach, presumably to remind us of relative identity, where two things may be one or two, depending on what they are relative to. The one 'guard on the gate' may actually be two men. |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| Full Idea: Non-standard natural numbers will yield non-standard rational and real numbers. These will include reciprocals which will be closer to 0 than any standard real number. These are like 'infinitesimals', so that notion is not actually a contradiction. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| Full Idea: A modern axiomatisation of geometry, such as Hilbert's (1899), does not need to claim the existence of real numbers anywhere in its axioms. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.ii) | |
| A reaction: This is despite the fact that geometry is reduced to algebra, and the real numbers are the equivalent of continuous lines. Bostock votes for a Greek theory of proportion in this role. |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| Full Idea: The Peano Axioms are categorical, meaning that they describe a unique structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4 n20) | |
| A reaction: So if you think there is nothing more to the natural numbers than their structure, then the Peano Axioms give the essence of arithmetic. If you think that 'objects' must exist to generate a structure, there must be more to the numbers. |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| Full Idea: Hume's Principle will not do as an implicit definition because it makes a positive claim about the size of the universe (which no mere definition can do), and because it does not by itself explain what the numbers are. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| Full Idea: Hume's Principle gives a criterion of identity for numbers, but it is obvious that many other things satisfy that criterion. The simplest example is probably the numerals (in any notation, decimal, binary etc.), giving many different interpretations. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| Full Idea: There is not just one way of giving a criterion of identity for numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| Full Idea: The Julius Caesar problem was one reason that led Frege to give an explicit definition of numbers as special sets. He does not appear to notice that the same problem affects his Axiom V for introducing sets (whether Caesar is or is not a set). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: The Julius Caesar problem is a sceptical acid that eats into everything in philosophy of mathematics. You give all sorts of wonderful accounts of numbers, but at what point do you know that you now have a number, and not something else? |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| Full Idea: There is no ground for saying that a number IS a position, if the truth is that there is nothing to determine which number is which position. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: If numbers lose touch with the empirical ability to count physical objects, they drift off into a mad world where they crumble away. |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| Full Idea: Structuralism begins from a false premise, namely that numbers have no properties other than their relations to other numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.5) | |
| A reaction: Well said. Describing anything purely relationally strikes me as doomed, because you have to say why those things relate in those ways. |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| Full Idea: Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9) |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| Full Idea: The style of nominalism which aims to reduce statements about numbers to statements about their applications does not work for the natural numbers, because they have many applications, and it is arbitrary to choose just one of them. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.iii) |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| Full Idea: We all know that in practice no physical measurement can be 100 per cent accurate, and so it cannot require the existence of a genuinely irrational number, rather than some of the rational numbers close to it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.3) |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| Full Idea: The basic use of the ordinal numbers is their use as ordinal adjectives, in phrases such as 'the first', 'the second' and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: That is because ordinals seem to attach to particulars, whereas cardinals seem to attach to groups. Then you say 'three is greater than four', it is not clear which type you are talking about. |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| Full Idea: The simple theory of types distinguishes sets into different 'levels', but this is quite different from the distinction into 'orders' which is imposed by the ramified theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) | |
| A reaction: The ramified theory has both levels and orders (p.235). Russell's terminology is, apparently, inconsistent. |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| Full Idea: The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: So the big difference between Frege and neo-logicists is the Julius Caesar problem. |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| Full Idea: The response of neo-logicists to the Julius Caesar problem is to strengthen Hume's Principle in the hope of ensuring that only numbers will satisfy it. They say the criterion of identity provided by HP is essential to number, and not to anything else. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| Full Idea: If Hume's Principle is all we are given, by way of explanation of what the numbers are, the only conclusion to draw would seem to be the structuralists' conclusion, ...studying all systems that satisfy that principle. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: Any approach that implies a set of matching interpretations will always imply structuralism. To avoid it, you need to pin the target down uniquely. |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| Full Idea: Many of the crucial definitions in the logicist programme are in fact impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| Full Idea: If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| Full Idea: In its higher reaches, which posit sets of huge cardinalities, set theory is just a fairy story. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: You can't say the higher reaches are fairy stories but the lower reaches aren't, if the higher is directly derived from the lower. The empty set and the singleton are fairy stories too. Bostock says the axiom of infinity triggers the fairy stories. |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| Full Idea: A common view is that although a fairy tale may provide very useful predictions, it cannot provide explanations for why things happen as they do. In order to do that a theory must also be true (or, at least, an approximation to the truth). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5) | |
| A reaction: Of course, fictionalism offers an explanation of mathematics as a whole, but not of the details (except as the implications of the initial fictional assumptions). |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| Full Idea: In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted. |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| Full Idea: Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: [compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?). |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| Full Idea: If an abstract object exists only when there is some suitable way of expressing it, then there are at most denumerably many abstract objects. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) | |
| A reaction: Fine by me. What an odd view, to think there are uncountably many abstract objects in existence, only a countable portion of which will ever be expressed! [ah! most people agree with me, p.243-4] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| Full Idea: Classical mathematicians say predicative mathematics omits areas of great interest, all concerning non-denumerable real numbers, such as claims about huge cardinals. There cannot be a predicative version of this theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I'm not sure that anyone will really miss huge cardinals if they are prohibited, though cryptography seems to flirt with such things. Are we ever allowed to say that some entity conjured up by mathematicians is actually impossible? |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| Full Idea: It has been claimed that only predicative mathematics has a justification through its usefulness to science (an empiricist approach). | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [compressed. Quine is the obvious candidate] I suppose predicativism gives your theory roots, whereas impredicativism is playing an abstract game. |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| Full Idea: If we accept the initial idea that we can think only of what we ourselves can describe, then something like the theory of predicativism quite naturally results | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I hate the idea that we can only talk of what falls under a sortal, but 'what we can describe' is much more plausible. Whether or not you agree with this approach (I'm pondering it), this makes predicativism important. |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| Full Idea: The predicative approach cannot accept either the usual definition of identity or the usual definition of the natural numbers, for both of these definitions are impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [Bostock 237-8 gives details] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| Full Idea: It is with the real numbers that the restrictions imposed by predicativity begin to make a real difference. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
| Full Idea: Chrysippus regarded power to act and be acted upon as the criterion for existence or being - a test satisfied by bodies alone. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Teun L. Tieleman - Chrysippus | |
| A reaction: This defines existence in terms of causation. Is he ruling out a priori a particle (say) which exists, but never interacts with anything? If so, he is inclining towards anti-realism. |
| 21673 | There are simple and complex facts; the latter depend on further facts [Chrysippus, by Cicero] |
| Full Idea: Chrysippus says there are two classes of facts, simple and complex. An instance of a simple fact is 'Socrates will die at a given date', ...but 'Milo will wrestle at Olympia' is a complex statement, because there can be no wrestling without an opponent. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 13.30 | |
| A reaction: We might say that there are atomic and complex facts, but our atomic facts tend to be much simpler, usually just saying some object has some property. |
| 16652 | Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau] |
| Full Idea: The Stoics proposed a rather modest categorisation of Substrate, Quality, Disposition, and Relation. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Robert Pasnau - Metaphysical Themes 1274-1671 12.1 |
| 16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
| Full Idea: If two individuals occupied one substance let one individual (Dion) be thought of as whole-limbed, the other (Theon) as minus one foot. Then let one of Dion's feet be amputated. Theon is the stronger candidate to have perished. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Philo (Alex) - On the Eternity of the World 48 | |
| A reaction: [SVF 2.397 - from Chrysippus's lost 'On the Growing Argument'] This is the original of Tibbles the Cat. Dion must persist to change, and then ousts Theon (it seems). Philo protests at Theon ceasing to exist when nothing has happened to him. |
| 16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
| Full Idea: The Growing Argument said any change of matter is a change of identity. Chrysippus presents it with a case (Dion and Theon) where material diminution is the necessary condition of enduring identity, since the diminished footless Dion survives. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by AA Long / DN Sedley - Hellenic Philosophers commentary 28:175 | |
| A reaction: [The example, in Idea 16058, is the original of Tibbles the Cat] This is a lovely bold idea which I haven't met in the modern discussions - that identity actually requires change. The concept of identity is meaningless without change? |
| 16024 | I could have died at five, but the summation of my adult stages could not [Noonan] |
| Full Idea: Persons have different modal properties from the summations of person-stages. I might have died when I was five. But the maximal summation of person-stages which perdurantists say is me could not have had a temporal extent of a mere five years. | |
| From: Harold Noonan (Identity [2009], §5) | |
| A reaction: Thus the summation of stages seems to fail Leibniz's Law, since truths about a part are not true of the whole. But my foot might be amputated without me being amputated. The objection is the fallacy of composition? |
| 16023 | Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan] |
| Full Idea: Stage theorists, accepting the ontology of perdurance, modify the semantics to secure the result that fatness is a property of a cat. Every temporal part of a cat (such as Tabby-on-Monday) is a cat. (but they pay a price over the counting of cats). | |
| From: Harold Noonan (Identity [2009], §5) | |
| A reaction: [Noonan cites Hawley and Sider for this view. The final parenthesis compresses Noonan] I would take the difficulty over counting cats to be fatal to the view. It produces too many cats, or too few, or denies counting altogether. |
| 16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
| Full Idea: If identity is problematic, it is difficult to see how the problem could be resolved, since it is difficult to see how a thinker could have the conceptual resources with which to explain the concept of identity whilst lacking that concept itself. | |
| From: Harold Noonan (Identity [2009], §1) | |
| A reaction: I don't think I accept this. We can comprehend the idea of a mind that didn't think in terms of identities (at least for objects). I suppose any relation of a mind to the world has to distinguish things in some way. Does the Parmenidean One have identity? |
| 16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
| Full Idea: Numerical identity is usually defined as the equivalence relation (or: the reflexive relation) satisfying Leibniz's Law, the indiscernibility of identicals, where everything true of x is true of y. | |
| From: Harold Noonan (Identity [2009], §2) | |
| A reaction: Noonan says this must include 'is identical to x' among the truths, and so is circular |
| 16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
| Full Idea: Identity can be circularly defined, as 'the relation everything has to itself and to nothing else', or as 'the smallest equivalence relation'. | |
| From: Harold Noonan (Identity [2009], §2) | |
| A reaction: The first one is circular because 'nothing else' implies identity. The second is circular because it has to quantify over all equivalence relations. (So says Noonan). |
| 16020 | Identity can only be characterised in a second-order language [Noonan] |
| Full Idea: There is no condition in a first-order language for a predicate to express identity, rather than indiscernibility within the resources of the language. Leibniz's Law is statable in a second-order language, so identity can be uniquely characterised. | |
| From: Harold Noonan (Identity [2009], §2) | |
| A reaction: The point is that first-order languages only refer to all objects, but you need to refer to all properties to include Leibniz's Law. Quine's 'Identity, Ostension and Hypostasis' is the source of this idea. |
| 16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
| Full Idea: Leibniz's Law (the indiscernibility of identicals) appears to be crucial to our understanding of identity, and, more particularly, to our understanding of distinctness. | |
| From: Harold Noonan (Identity [2009], §2) | |
| A reaction: True, but indiscernibility concerns the epistemology, and identity concerns the ontology. |
| 16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
| Full Idea: Leibniz's Law must be clearly distinguished from the substitutivity principle, that if 'a' and 'b' are codesignators they are substitutable salva veritate. | |
| From: Harold Noonan (Identity [2009], §2) | |
| A reaction: He gives a bunch of well-known problem cases for substitutivity. The Morning Star, Giorgione, and the number of planets won't work. Belief contexts, or facts about spelling, may not be substitutable. |
| 1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
| Full Idea: A dog makes use of the fifth complex indemonstrable syllogism when, arriving at a spot where three ways meet, after smelling at two roads by which the quarry did not pass, he rushes off at once by the third without pausing to smell. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Sextus Empiricus - Outlines of Pyrrhonism I.69 | |
| A reaction: As we might say: either A or B or C; not A; not B; therefore C. I wouldn't want to trust this observation without a lot of analysis of slow-motion photography of dogs as crossroads. Even so, it is a nice challenge to Descartes' view of animals. |
| 20834 | Chrysippus allows evil to say it is fated, or even that it is rational and natural [Plutarch on Chrysippus] |
| Full Idea: Chrysippus gives vice blatant freedom to say not only that it is necessary and according to fate, but even that it occurs according to god's reason and the best nature. | |
| From: comment on Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - 70: Stoic Self-contradictions 1050c | |
| A reaction: This is Plutarch's criticism of stoic determinism or fatalism. Zeno replied that the punishment for vice may also be fated. It seems that Chysippus did believe that punishments were too harsh, given that vices are fated [p.109]. |
| 20833 | A swerve in the atoms would be unnatural, like scales settling differently for no reason [Chrysippus, by Plutarch] |
| Full Idea: Chrysippus argues against the 'swerve' of the Epicureans, on the grounds that they are doing violence to nature by positing something which is uncaused, and cites dice or scales, which can't settle differently without some cause or difference. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - 70: Stoic Self-contradictions 1045c | |
| A reaction: That is, the principle of sufficient reason (or of everything having a cause) is derived from observation, not a priori understanding. Pace Leibniz. As in modern discussion, free will or the swerve only occur in our minds, and not elsewhere. |
| 20835 | Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus] |
| Full Idea: Chrysippus's accounts of possibility and fate are in conflict. If he is right that 'everything that permits of occurring even if it is not going to occur is possible', then many things are possible which are not according to fate. | |
| From: comment on Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - 70: Stoic Self-contradictions 1055e | |
| A reaction: A palpable hit, I think. Plutarch refers to Chrysippus's rejection of Diodorus Cronus's Master Argument. Fatalism seems to entail that the only future possibilities are the ones that actually occur. |
| 20808 | Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius] |
| Full Idea: Chrysippus says (in his 'On Fate') that everything happens by fate. Fate is a continuous string of causes of things which exist or a rational principle according to which the cosmos is managed. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.148 |
| 20837 | Fate is an eternal and fixed chain of causal events [Chrysippus] |
| Full Idea: Fate is a sempiternal and unchangeable series and chain of things, rolling and unravelling itself through eternal sequences of cause and effect, of which it is composed and compounded. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Aulus Gellius - Noctes Atticae 7.2.01 | |
| A reaction: It seems that Chrysippus (called by Aulus Gellius 'the chief Stoic philosopher') had a rather grandly rhetorical prose style. |
| 20836 | The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero] |
| Full Idea: Chrysippus responded to the Lazy Argument (that the outcome of an illness is fated, so there is no point in calling the doctor) by saying 'calling the doctor is fated just as much as recovering', which he calls 'co-fated'. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 28-30 | |
| A reaction: From a pragmatic point of view, this idea also nullifies fatalism, since you can plausibly fight against your fate to your last breath. No evidence could ever be offered in support of fatalism, not even the most unlikely events. |
| 21679 | When we say events are fated by antecedent causes, do we mean principal or auxiliary causes? [Chrysippus] |
| Full Idea: Some causes are perfect and principal, others auxiliary and proximate. Hence when we say that everything takes place by fate owing to antecedent causes, what we wish to be understood is not perfect and principal causes but auxiliary and proximate causes. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by M. Tullius Cicero - On Fate ('De fato') 18.41 | |
| A reaction: This move is described by Cicero as enabling Chrysippus to 'escape necessity and to retain fate'. |
| 5971 | Destiny is only a predisposing cause, not a sufficient cause [Chrysippus, by Plutarch] |
| Full Idea: Chrysippus considered destiny to be not a cause sufficient of itself but only a predisposing cause. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE], fr 997) by Plutarch - 70: Stoic Self-contradictions 1056b | |
| A reaction: This appears to be a rejection of determinism, and is the equivalent of Epicurus' introduction of the 'swerve' in atoms. They had suddenly become bothered about the free will problem in about 305 BCE. There must be other non-destiny causes? |
| 20787 | A proposition is what can be asserted or denied on its own [Chrysippus] |
| Full Idea: A proposition is what can be asserted or denied on its own, for example, 'It is day' or 'Dion is walking'. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 07.65 | |
| A reaction: Note the phrase 'on its own'. If you say 'it is day and Dion is walking', that can't be denied on its own, because first the two halves must each be evaluated, so presumably that doesn't count as a stoic proposition. |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| Full Idea: In Modus Ponens where the first premise is 'P' and the second 'P→Q', in the first premise P is asserted but in the second it is not. Yet it must mean the same in both premises, or it would be guilty of the fallacy of equivocation. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) | |
| A reaction: This is Geach's thought (leading to an objection to expressivism in ethics, that P means the same even if it is not expressed). |
| 20850 | Passions are judgements; greed thinks money is honorable, and likewise drinking and lust [Chrysippus, by Diog. Laertius] |
| Full Idea: Chrysippus says (in his On Passions) that the passions are judgements; for greed is a supposition that money is honorable, and similarly for drunkennes and wantonness and others. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.111 | |
| A reaction: This is an endorsement of Socrates's intellectualist reading of weakness of will, as against Aristotle's assigning it to overpowering passions. |
| 20869 | The highest degree of morality performs all that is appropriate, omitting nothing [Chrysippus] |
| Full Idea: He who makes moral progress to the highest degree performs all the appropriate actions in all circumstances, and omits none. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Sophocles - Sophocles' Electra 4.39.22 | |
| A reaction: Hence concerns about omission as well as commission in the practice of ethics can be seen in the light of character and virtue. The world is fully of nice people who act well, but don't do so well on omissions. Car drivers, for example. |
| 3044 | Stoics say that beauty and goodness are equivalent and linked [Chrysippus, by Diog. Laertius] |
| Full Idea: Stoics say the beautiful is the only good. Good is an equivalent term to the beautiful; since a thing is good, it is beautiful; and it is beautiful, therefore it is good. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.1.59 |
| 20838 | Fate initiates general causes, but individual wills and characters dictate what we do [Chrysippus] |
| Full Idea: The order and reason of fate set in motion the general types and starting points of the causes, but each person's own will [or decisions] and the character of his mind govern the impulses of our thoughts and minds and our very actions. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Aulus Gellius - Noctes Atticae 7.2.11 | |
| A reaction: So if you try and fail it was fate, but if you try and succeed it was you? |
| 20813 | Human purpose is to contemplate and imitate the cosmos [Chrysippus] |
| Full Idea: The human being was born for the sake of contemplating and imitating the cosmos. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') 2.37 | |
| A reaction: [This seems to be an idea of Chrysippus] Remind me how to imitate the cosmos. Presumably this is living according to nature, but that becomes more obscure when express like this. |
| 3045 | Stoics say justice is a part of nature, not just an invented principle [Chrysippus, by Diog. Laertius] |
| Full Idea: Stoics say that justice exists by nature, and not because of any definition or principle. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.1.66 | |
| A reaction: cf Idea 3024. Stoics thought that nature is intrinsically rational, and therein lies its justice. 'King Lear' enacts this drama about whether nature is just. |
| 20774 | Only nature is available to guide action and virtue [Chrysippus] |
| Full Idea: What am I to take as the principle of appropriate action and raw material for virtue if I give up nature and what is according to nature? | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Plutarch - On Common Conceptions 1069e | |
| A reaction: 'Nature' is awfully vague as a guideline, even when we are told nature is rational. I can only make sense of it as 'human nature', which is more Aristotelian than stoic. 'Go with the flow' and 'lay the cards you are dealt' might capture it. |
| 20864 | Live in agreement, according to experience of natural events [Chrysippus] |
| Full Idea: The goal of life is to live in agreement, which is according to experience of the things which happen by nature. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by John Stobaeus - Anthology 2.06a | |
| A reaction: Cleanthes added 'with nature' to Zeno's slogan, and Chyrisppus added this variation. At least it gives you some idea of what the consistent rational principle should be. You still have to assess which aspects of nature should influence us. |
| 5972 | Living happily is nothing but living virtuously [Chrysippus, by Plutarch] |
| Full Idea: According to Chrysippus, living happily consists solely in living virtuously. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE], fr139) by Plutarch - 72: Against Stoics on common Conceptions 1060d | |
| A reaction: This, along with 'live according to nature', is the essential doctrine of stoicism. This is 'eudaimonia', not the modern idea of feeling nice. Is it possible to admire another person for anything other than virtue? (Yes! Looks, brains, strength, wealth). |
| 1777 | Pleasure is not the good, because there are disgraceful pleasures [Chrysippus, by Diog. Laertius] |
| Full Idea: Pleasure is not the good, because there are disgraceful pleasures, and nothing disgraceful is good. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.60 | |
| A reaction: I certainly approve of the idea that not all pleasure is intrinsically good. Indeed, I think good has probably got nothing to do with pleasure. 'Disgraceful' is hardly objective though. |
| 5973 | Justice can be preserved if pleasure is a good, but not if it is the goal [Chrysippus, by Plutarch] |
| Full Idea: Chrysippus thinks that, while justice could not be preserved if one should set up pleasure as the goal, it could be if one should take pleasure to be not a goal but simply a good. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE], fr 23) by Plutarch - 72: Against Stoics on common Conceptions 1070d | |
| A reaction: This is an interesting and original contribution to the ancient debate about pleasure. It shows Aristotle's moderate criticism of pleasure (e.g. Idea 84), but attempts to pinpoint where the danger is. Aristotle says it thwarts achievement of the mean. |
| 20845 | There are shameful pleasures, and nothing shameful is good, so pleasure is not a good [Chrysippus, by Diog. Laertius] |
| Full Idea: Chrysippus (in his On Pleasure) denies even of pleasure that it is a good; for there are also shameful pleasures, and nothing shameful is good. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.103 | |
| A reaction: Socrates seems to have started this line of the thought, to argue that pleasure is not The Good. Stoics are more puritanical. Nothing counts as good if it is capable of being bad. Thus good pleasures are not good, which sounds odd. |
| 5967 | People need nothing except corn and water [Chrysippus, by Plutarch] |
| Full Idea: Chrysippus praises ad nauseam the lines "For what need mortals save two things alone,/ Demeter's grain and draughts of water clear". | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - 70: Stoic Self-contradictions 1043e | |
| A reaction: "Oh, reason not the need!" says King Lear. The remark shows the close affinity of stoicism and cynicism, as the famous story of Diogenes is that he threw away his drinking cup when he realised you could drink with your hands. |
| 5966 | All virtue is good, but not always praised (as in not lusting after someone ugly) [Chrysippus] |
| Full Idea: Although deeds done in accordance with virtue are congenial, not all are cited as examples, such as courageously extending one's finger, or continently abstaining from a half-dead old woman, or not immediately agreeing that three is four. | |
| From: Chrysippus (fragments/reports [c.240 BCE], fr 211), quoted by Plutarch - 70: Stoic Self-contradictions 1038f | |
| A reaction: Presumably the point (so elegantly expressed - what a shame we have lost most of Chrysippus) is that virtue comes in degrees, even though its value is an absolute. The same has been said (by Russell and Bonjour) about self-evidence. |
| 20855 | Chrysippus says virtue can be lost (though Cleanthes says it is too secure for that) [Chrysippus, by Diog. Laertius] |
| Full Idea: Chrysippus says that virtue can be lost, owing to drunkenness and excess of black bile, whereas Cleanthes says it cannot, because it consists in secure intellectual grasps, and it is worth choosing for its own sake. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.127 | |
| A reaction: Succumbing to drunkenness looks like evidence that you were not truly virtuous. Mental illness is something else. On the whole I agree the Cleanthes. |
| 5970 | Chrysippus says nothing is blameworthy, as everything conforms with the best nature [Chrysippus, by Plutarch] |
| Full Idea: Chrysippus has often written on the theme that there is nothing reprehensible or blameworthy in the universe since all things are accomplished in conformity with the best nature. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - 70: Stoic Self-contradictions 1051b | |
| A reaction: This is Leibniz's "best of all possible worlds", but deriving the idea from the rightness of nature rather than the perfection of God. Chrysippus has a more plausible ground than Leibniz, as for him nasty things follow from conscious choice. |
| 20842 | Rational animals begin uncorrupted, but externals and companions are bad influences [Chrysippus, by Diog. Laertius] |
| Full Idea: The rational animal is corrupted, sometimes because of the persuasiveness of external activities and sometimes because of the influence of companions. For the starting points provided by nature are uncorrupted. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.89 | |
| A reaction: If companions corrupt us, what corrupted the companions? Aren't we all in this together? And where do the 'external activities' originate? |
| 20856 | Justice, the law, and right reason are natural and not conventional [Chrysippus, by Diog. Laertius] |
| Full Idea: Chrysippus says (in On the Honourable) that justice is natural and not conventional, as are the law and right reason. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.128 | |
| A reaction: How does he explain variations in the law between different states? Presumably some of them have got it wrong. What is the criterion for deciding which laws are natural? |
| 1779 | We don't have obligations to animals as they aren't like us [Chrysippus, by Diog. Laertius] |
| Full Idea: We have no obligations of justice to other animals, because they are dissimilar to us. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.66 | |
| A reaction: "Dissimilar" begs questions. Some human beings don't seem much like me. How are we going to treat visiting aliens? |
| 20857 | Justice is irrelevant to animals, because they are too unlike us [Chrysippus, by Diog. Laertius] |
| Full Idea: There is no justice between us and other animals because of the dissimilarity between us and them. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.129 | |
| A reaction: [from lost On Justice Bk 1] What would he make of modern revelations about bonobos and chimpanzees? If there is great dissimilarity between some peoples, does that invalidate justice between them? He also said animals exist for our use. |
| 20812 | Covers are for shields, and sheaths for swords; likewise, all in the cosmos is for some other thing [Chrysippus] |
| Full Idea: Just as the cover was made for the sake of the shield, and the sheath for the sword, in the same way everything else except the cosmos was made for the sake of other things. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') 2.37 | |
| A reaction: Chrysippus was wise to stop at the cosmos. Similarly, religious teleology had better not ask about the purpose of God. What does he think pebbles are for? Nature is the source of stoic value, so it needs to be purposeful. |
| 21403 | The later Stoics identified the logos with an air-fire compound, called 'pneuma' [Chrysippus, by Long] |
| Full Idea: From Chrysippus onwards, the Stoics identified the logos throughout each world-cycle not with pure fire, but with a compound of fire and air, 'pneuma'. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by A.A. Long - Hellenistic Philosophy 4.4.2 | |
| A reaction: I suspect this was because breath is so vital to the human body. |
| 20828 | Fire is a separate element, not formed with others (as was previously believed) [Chrysippus, by Stobaeus] |
| Full Idea: In his theory fire is said independently to be an element, since it is not formed together with another one, whereas according to the earlier theory fire is formed with other elements. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by John Stobaeus - Anthology 1.10.16c | |
| A reaction: The point is that fire precedes the other elements, and is superior to them. |
| 5975 | Stoics say earth, air, fire and water are the primary elements [Chrysippus, by Plutarch] |
| Full Idea: The Stoics call the four bodies - earth and water and air and fire - primary elements. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE], fr 444) by Plutarch - 72: Against Stoics on common Conceptions 1085c | |
| A reaction: Elsewhere (fr 413) Chrysippus denies that they are all 'primary'. Essentially, though, he seems to be adopting the doctrine of Empedocles and Aristotle, in specific opposition to Epicurus' atomism. |
| 20819 | The past and the future subsist, but only the present exists [Chrysippus, by Plutarch] |
| Full Idea: When he wished to be subtle, Chrysippus wrote that the past part of time and the future part do not exist but subsist, and only the present exists. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - On Common Conceptions 1081f | |
| A reaction: [from lost On Void] I think I prefer the ontology of Idea 20818. Idea 20819 does not offer an epistemology. Is the present substantial enough to be known? The word 'subsist' is an ontological evasion (even though Russell briefly relied on it). |
| 20818 | The present does not exist, so our immediate experience is actually part past and part future [Chrysippus, by Plutarch] |
| Full Idea: Stoics do not allow a minimal time to exist, and do not want to have a partless 'now'; so what one thinks one has grasped as present is in part future and in part past. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Plutarch - On Common Conceptions 1081c | |
| A reaction: [from lost On Parts Bk3-5] I agree with the ontology here, but I take our grasp of the present to be very short-term memory of the past. I ignore special relativity. Chrysippus expressed two views about this; in the other one he was a Presentist. |
| 20821 | Time is continous and infinitely divisible, so there cannot be a wholly present time [Chrysippus, by Stobaeus] |
| Full Idea: Chrysippus says most clearly that no time is wholly present; for since the divisibility of continuous things is infinite, time as a whole is also subject to infinite divisibility by this method of division. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: But what is his reason for thinking that time is a continuous thing? There is a minimum time in quantum mechanics (the Planck Time), but do these quantum intervals overlap? Compare Idea 20819. |
| 3048 | Stoics say that God the creator is the perfection of all animals [Chrysippus, by Diog. Laertius] |
| Full Idea: Stoics say that God is an animal immortal, rational, perfect, and intellectual in his happiness, unsusceptible of any kind of evil, having a foreknowledge of the world; however, he is not the figure of a man, and is the creator of the universe. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.1.72 |
| 20773 | The origin of justice can only be in Zeus, and in nature [Chrysippus] |
| Full Idea: One can find no other starting point or origin for justice except the one derived from Zeus and that derived from the common nature; for everything like this must have that starting point, if we are going to say anything at all about good and bad things. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Plutarch - 70: Stoic Self-contradictions 1035c | |
| A reaction: [in lost 'On Gods' bk 3] This appears to offer two starting points, in the mind of Zeus, and in nature, though since nature is presumed to be rational the two may run together. Is Zeus the embodiment, or the unconscious source, or the maker of decrees? |
| 5965 | The source of all justice is Zeus and the universal nature [Chrysippus] |
| Full Idea: It is not possible to discover any other beginning of justice or any source for it other than that from Zeus and from the universal nature. | |
| From: Chrysippus (fragments/reports [c.240 BCE], fr 326), quoted by Plutarch - 70: Stoic Self-contradictions 1035c | |
| A reaction: If the source is 'universal nature', that could agree with Plato, but if the source is Zeus, then stoicism is a religion rather than a philosophy. |
| 3042 | Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius] |
| Full Idea: Stoics teach that common law is identical with that right reason which pervades everything, being the same with Zeus, who is the regulator and chief manager of all existing things. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.1.53 |
| 1782 | Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius] |
| Full Idea: Stoics teach that God is unity, and that he is called Mind, and Fate, and Jupiter, and by many names besides. | |
| From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.68 |
| 20830 | Death can't separate soul from body, because incorporeal soul can't unite with body [Chrysippus] |
| Full Idea: Death is a separation of soul from body. But nothing incorporeal can be separated from a body. For neither does anything incorporeal touch a body, and the soul touches and is separated from the body. Therefore the soul is not incorporeal. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by Tertullian - The Soul as an 'Astral Body' 5.3 | |
| A reaction: This is the classic interaction difficulty for substance dualist theories of mind. |
| 21404 | There is a rationale in terrible disasters; they are useful to the whole, and make good possible [Chrysippus] |
| Full Idea: The evil which occurs in terrible disasters has a rationale [logos] peculiar to itself: for in a sense it occurs in accordance with universal reason, and is not without usefulness in relation to the whole. For without it there could be no good. | |
| From: Chrysippus (fragments/reports [c.240 BCE]), quoted by A.A. Long - Hellenistic Philosophy 4.4.5 | |
| A reaction: [a quotation from Chrysippus. Plutarch, Comm Not 1065b] A nice question about any terrible disaster is whether it is in some way 'useful', if we take a broader view of things. Almost everything has a good aspect, from that perspective. |