102 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. |
| 23277 | Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak] |
| Full Idea: One of the pillars of the new pragmatism is the thought that the standards of objectivity come into being and evolve over time, but that being historically situated in this way does not detract from their objectivity. | |
| From: Cheryl Misak (Introduction to 'New Pragmatists' [2007], p.2) | |
| A reaction: This looks to me like pragmatism finally coming to its senses. I would say that being any sort of 'social construct' (beloved of cultural relativists) in no way detracts from its capacity for objectivity and truth. |
| 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'. |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| Full Idea: An 'impredicative' definition is one that uses the terms being defined in order to give the definition; in some way the definition is then circular. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], Glossary) | |
| A reaction: There has been a big controversy in the philosophy of mathematics over these. Shapiro gives the definition of 'village idiot' (which probably mentions 'village') as an example. |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| Full Idea: In classical logic definitions are thought of as revealing our attempts to refer to objects, ...but for intuitionist or constructivist logics, if our definitions do not uniquely characterize an object, we are not entitled to discuss the object. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.4) | |
| A reaction: In defining a chess piece we are obviously creating. In defining a 'tree' we are trying to respond to fact, but the borderlines are vague. Philosophical life would be easier if we were allowed a mixture of creation and fact - so let's have that. |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| Full Idea: Reductio ad absurdum arguments are ones that start by denying what one wants to prove. We then prove a contradiction from this 'denied' idea and more reasonable ideas in one's theory, showing that we were wrong in denying what we wanted to prove. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is a mathematical definition, which rests on logical contradiction, but in ordinary life (and philosophy) it would be enough to show that denial led to absurdity, rather than actual contradiction. |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| Full Idea: For the anti-realist, truth belongs to us, it is our servant, and as such, it must be 'epistemically constrained'. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: Put as clearly as this, it strikes me as being utterly and spectacularly wrong, a complete failure to grasp the elementary meaning of a concept etc. etc. If we aren't the servants of truth then we jolly we ought to be. Truth is above us. |
| 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. |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| Full Idea: In the classical or realist view of logic the meaning of abstract symbols for logical connectives is given by the truth-tables for the symbol. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007]) | |
| A reaction: Presumably this is realist because it connects them to 'truth', but only if that involves a fairly 'realist' view of truth. You could, of course, translate 'true' and 'false' in the table to empty (formalist) symbols such a 0 and 1. Logic is electronics. |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| Full Idea: In intuitionist logic, if we do not know that we do not know A, it does not follow that we know A, so the inference (and, in general, double negation elimination) is not intuitionistically valid. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: That inference had better not be valid in any logic! I am unaware of not knowing the birthday of someone I have never heard of. Propositional attitudes such as 'know' are notoriously difficult to explain in formal logic. |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| Full Idea: Free logic is especially designed to help regiment our reasoning about fictional objects, or nonexistent objects of some sort. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.7) | |
| A reaction: This makes it sound marginal, but I wonder whether existential commitment shouldn't be eliminated from all logic. Why do fictional objects need a different logic? What logic should we use for Robin Hood, if we aren't sure whether or not he is real? |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| Full Idea: A 'subset' of A is a set containing only members of A, and a 'proper subset' is one that does not contain all the members of A. Note that the empty set is a subset of every set, but it is not a member of every set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Is it the same empty set in each case? 'No pens' is a subset of 'pens', but is it a subset of 'paper'? Idea 8219 should be borne in mind when discussing such things, though I am not saying I agree with it. |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| Full Idea: The 'powerset' of a set is a set made up of all the subsets of a set. For example, the powerset of {3,7,9} is {null, {3}, {7}, {9}, {3,7}, {3,9}, {7,9}, {3,7,9}}. Taking the powerset of an infinite set gets us from one infinite cardinality to the next. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Note that the null (empty) set occurs once, but not in the combinations. I begin to have queasy sympathies with the constructivist view of mathematics at this point, since no one has the time, space or energy to 'take' an infinite powerset. |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| Full Idea: As a realist choice of what is basic in mathematics, set theory is rather clever, because it only makes a very simple ontological claim: that, independent of us, there exists the empty set. The whole hierarchy of finite and infinite sets then follows. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Even so, for non-logicians the existence of the empty set is rather counterintuitive. "There was nobody on the road, so I overtook him". See Ideas 7035 and 8322. You might work back to the empty set, but how do you start from it? |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| Full Idea: Two sets are the same size if they can be placed in one-to-one correspondence. But even numbers have one-to-one correspondence with the natural numbers. So a set is infinite if it has one-one correspondence with a proper subset. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Dedekind's definition. We can match 1 with 2, 2 with 4, 3 with 6, 4 with 8, etc. Logicians seem happy to give as a definition anything which fixes the target uniquely, even if it doesn't give the essence. See Frege on 0 and 1, Ideas 8653/4. |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| Full Idea: Zermelo-Fraenkel and Gödel-Bernays set theory differ over the notions of ordinal construction and over the notion of class, among other things. Then there are optional axioms which can be attached, such as the axiom of choice and the axiom of infinity. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.6) | |
| A reaction: This summarises the reasons why we cannot just talk about 'set theory' as if it was a single concept. The philosophical interest I would take to be found in disentangling the ontological commitments of each version. |
| 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. |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| Full Idea: The law of excluded middle is purely syntactic: it says for any well-formed formula A, either A or not-A. It is not a semantic law; it does not say that either A is true or A is false. The semantic version (true or false) is the law of bivalence. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: No wonder these two are confusing, sufficiently so for a lot of professional philosophers to blur the distinction. Presumably the 'or' is exclusive. So A-and-not-A is a contradiction; but how do you explain a contradiction without mentioning truth? |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| Full Idea: In the intuitionist version of quantification, the universal quantifier (normally read as "all") is understood as "we have a procedure for checking every" or "we have checked every". | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.5) | |
| A reaction: It seems better to describe this as 'verificationist' (or, as Dummett prefers, 'justificationist'). Intuition suggests an ability to 'see' beyond the evidence. It strikes me as bizarre to say that you can't discuss things you can't check. |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| Full Idea: The realist meets the Burali-Forti paradox by saying that all the ordinals are a 'class', not a set. A proper class is what we discuss when we say "all" the so-and-sos when they cannot be reached by normal set-construction. Grammar is their only limit. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This strategy would be useful for Class Nominalism, which tries to define properties in terms of classes, but gets tangled in paradoxes. But why bother with strict sets if easy-going classes will do just as well? Descartes's Dream: everything is rational. |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| Full Idea: The Burali-Forti paradox says that if ordinals are defined by 'gathering' all their predecessors with the empty set, then is the set of all ordinals an ordinal? It is created the same way, so it should be a further member of this 'complete' set! | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is an example (along with Russell's more famous paradox) of the problems that began to appear in set theory in the early twentieth century. See Idea 8675 for a modern solution. |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| Full Idea: The set of 'integers' is all of the negative natural numbers, and zero, together with the positive natural numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Zero always looks like a misfit at this party. Credit and debit explain positive and negative nicely, but what is the difference between having no money, and money being irrelevant? I can be 'broke', but can the North Pole be broke? |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| Full Idea: The 'rational' numbers are all those that can be represented in the form m/n (i.e. as fractions), where m and n are natural numbers different from zero. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Pythagoreans needed numbers to stop there, in order to represent the whole of reality numerically. See irrational numbers for the ensuing disaster. How can a universe with a finite number of particles contain numbers that are not 'rational'? |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| Full Idea: A number is 'irrational' just in case it cannot be represented as a fraction. An irrational number has an infinite non-repeating decimal expansion. Famous examples are pi and e. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: There must be an infinite number of irrational numbers. You could, for example, take the expansion of pi, and change just one digit to produce a new irrational number, and pi has an infinity of digits to tinker with. |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| Full Idea: The natural numbers are quite primitive, and are what we first learn about. The order of objects (the 'ordinals') is one level of abstraction up from the natural numbers: we impose an order on objects. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: Note the talk of 'levels of abstraction'. So is there a first level of abstraction? Dedekind disagrees with Friend (Idea 7524). I would say that natural numbers are abstracted from something, but I'm not sure what. See Structuralism in maths. |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| Full Idea: The 'cardinal' numbers answer the question 'How many?'; the order of presentation of the objects being counted as immaterial. Def: the cardinality of a set is the number of members of the set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: If one asks whether cardinals or ordinals are logically prior (see Ideas 7524 and 8661), I am inclined to answer 'neither'. Presenting them as answers to the questions 'how many?' and 'which comes first?' is illuminating. |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| Full Idea: The set of 'real' numbers, which consists of the rational numbers and the irrational numbers together, represents "the continuum", since it is like a smooth line which has no gaps (unlike the rational numbers, which have the irrationals missing). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: The Continuum is the perfect abstract object, because a series of abstractions has arrived at a vast limit in its nature. It still has dizzying infinities contained within it, and at either end of the line. It makes you feel humble. |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| Full Idea: After the multiples of omega, we can successively raise omega to powers of omega, and after that is done an infinite number of times we arrive at a new limit ordinal, which is called 'epsilon'. We have an infinite number of infinite ordinals. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: When most people are dumbstruck by the idea of a single infinity, Cantor unleashes an infinity of infinities, which must be the highest into the stratosphere of abstract thought that any human being has ever gone. |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| Full Idea: The first 'limit ordinal' is called 'omega', which is ordinal because it is greater than other numbers, but it has no immediate predecessor. But it has successors, and after all of those we come to twice-omega, which is the next limit ordinal. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: This is the gateway to Cantor's paradise of infinities, which Hilbert loved and defended. Who could resist the pleasure of being totally boggled (like Aristotle) by a concept such as infinity, only to have someone draw a map of it? See 8663 for sequel. |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| Full Idea: Since between any two rational numbers there is an infinite number of rational numbers, we could consider that we have infinity in three dimensions: positive numbers, negative numbers, and the 'depth' of infinite numbers between any rational numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: This is before we even reach Cantor's staggering infinities (Ideas 8662 and 8663), which presumably reside at the outer reaches of all three of these dimensions of infinity. The 'deep' infinities come from fractions with huge denominators. |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| Full Idea: Successful competing founding disciplines in mathematics include: the various set theories, type theory, category theory, model theory and topology. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Or none of the above? Set theories are very popular. Type theory is, apparently, discredited. Shapiro has a version of structuralism based on model theory (which sound promising). Topology is the one that intrigues me... |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| Full Idea: Most of mathematics can be faithfully redescribed by classical (realist) set theory. More precisely, we can translate other mathematical theories - such as group theory, analysis, calculus, arithmetic, geometry and so on - into the language of set theory. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is why most mathematicians seem to regard set theory as foundational. We could also translate football matches into the language of atomic physics. |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| Full Idea: There is no interest for the mathematician in studying the number 8 in isolation from the other numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This is a crucial and simple point (arising during a discussion of Shapiro's structuralism). Most things are interesting in themselves, as well as for their relationships, but mathematical 'objects' just are relationships. |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| Full Idea: Structuralists give a historical account of why the 'same' number occupies different structures. Numbers are equivalent rather than identical. 8 is the immediate predecessor of 9 in the whole numbers, but in the rationals 9 has no predecessor. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: I don't become a different person if I move from a detached house to a terraced house. This suggests that 8 can't be entirely defined by its relations, and yet it is hard to see what its intrinsic nature could be, apart from the units which compose it. |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| Full Idea: Structuralists disagree over whether objects in structures are 'ante rem' (before reality, existing independently of whether the objects exist) or 'in re' (in reality, grounded in the real world, usually in our theories of physics). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: Shapiro holds the first view, Hellman and Resnik the second. The first view sounds too platonist and ontologically extravagant; the second sounds too contingent and limited. The correct account is somewhere in abstractions from the real. |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| Full Idea: According to the structuralist, mathematicians study the concepts (objects of study) such as variable, greater, real, add, similar, infinite set, which are one level of abstraction up from prima facie base objects such as numbers, shapes and lines. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: This still seems to imply an ontology in which numbers, shapes and lines exist. I would have thought you could eliminate the 'base objects', and just say that the concepts are one level of abstraction up from the physical world. |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| Full Idea: Structuralism says we study whole structures: objects together with their predicates, relations that bear between them, and functions that take us from one domain of objects to a range of other objects. The objects can even be eliminated. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: The unity of object and predicate is a Quinean idea. The idea that objects are inessential is the dramatic move. To me the proposal has very strong intuitive appeal. 'Eight' is meaningless out of context. Ordinality precedes cardinality? Ideas 7524/8661. |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| Full Idea: In the 'in re' version of mathematical structuralism, pattern-spotting is the process of abstraction. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This might work for non-mathematical abstraction as well, if we are allowed to spot patterns within sensual experience, and patterns within abstractions. Properties are causal patterns in the world? No - properties cause patterns. |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| Full Idea: The main philosophical problem with the position of platonism or realism is the epistemic problem: of explaining what perception or intuition consists in; how it is possible that we should accurately detect whatever it is we are realists about. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.5) | |
| A reaction: The best bet, I suppose, is that the mind directly perceives concepts just as eyes perceive the physical (see Idea 8679), but it strikes me as implausible. If we have to come up with a special mental faculty for an area of knowledge, we are in trouble. |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| Full Idea: Central to naturalism about mathematics are 'indispensability arguments', to the effect that some part of mathematics is indispensable to our best physical theory, and therefore we ought to take that part of mathematics to be true. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.1) | |
| A reaction: Quine and Putnam hold this view; Field challenges it. It has the odd consequence that the dispensable parts (if they can be identified!) do not need to be treated as true (even though they might follow logically from the dispensable parts!). Wrong! |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| Full Idea: There are not enough constraints in the Formalist view of mathematics, so there is no way to select a direction for trying to develop mathematics. There is no part of mathematics that is more important than another. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.6) | |
| A reaction: One might reply that an area of maths could be 'important' if lots of other areas depended on it, and big developments would ripple big changes through the interior of the subject. Formalism does, though, seem to reduce maths to a game. |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| Full Idea: Too much of mathematics is rejected by the constructivist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: This was Hilbert's view. This seems to be generally true of verificationism. My favourite example is that legitimate speculations can be labelled as meaningless. |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| Full Idea: An intuitionist typically retains bivalence, but rejects the law of excluded middle. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: The idea would be to say that only T and F are available as truth-values, but failing to be T does not ensure being F, but merely not-T. 'Unproven' is not-T, but may not be F. |
| 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 |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| Full Idea: What the mathematician labels an 'object' in her discipline, is called 'a place in a structure' by the structuralist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.5) | |
| A reaction: This is a strategy for dispersing the idea of an object in the world of thought, parallel to attempts to eliminate them from physical ontology (e.g. Idea 614). |
| 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? |
| 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? |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| Full Idea: In the hierarchy of reduction, when we investigate questions in biology, we have to assume the laws of chemistry but not of economics. We could never find a law of biology that contradicted something in physics or in chemistry. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.1) | |
| A reaction: This spells out the idea that there is a direction of dependence between aspects of the world, though we should be cautious of talking about 'levels' (see Idea 7003). We cannot choose the direction in which reduction must go. |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| Full Idea: The extensional presentation of a concept is just a list of the objects falling under the concept. In contrast, an intensional presentation of a concept gives a characterization of the concept, which allows us to pick out which objects fall under it. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.4) | |
| A reaction: Logicians seem to favour the extensional view, because (in the standard view) sets are defined simply by their members, so concepts can be explained using sets. I take this to be a mistake. The intensional view seems obviously prior. |
| 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. |
| 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. |