83 ideas
| 23350 | A wise philosophers uses reason to cautiously judge each aspect of living [Epictetus] |
| Full Idea: The sinews of a philosopher are desire that never fails in its achievement; aversion that never meets with what it would avoid; appropriate impulse; carefully considered purpose; and assent that is never precipitate. | |
| From: Epictetus (The Discourses [c.56], 2.08.29) | |
| A reaction: This is a very individual view of wisdom and the philosopher, whereas wisdom is often thought to have a social role. Is it not important for a philosopher to at least offer advice? |
| 23355 | The task of philosophy is to establish standards, as occurs with weights and measures [Epictetus] |
| Full Idea: Things are judged and weighed, when we have the standards ready. This is the task of philosophy: to examine and establish the standards. | |
| From: Epictetus (The Discourses [c.56], 2.11.24) | |
| A reaction: It is interesting that this gives philosophers a very specific social role, and also that it seems to identify epistemology as First Philosophy. Other disciplines, of course, establish their own standards without reference to philosophy. |
| 21394 | Philosophy is knowing each logos, how they fit together, and what follows from them [Epictetus] |
| Full Idea: [Philosophical speculation] consists in knowing the elements of 'logos', what each of them is like, how they fit together, and what follows from them. | |
| From: Epictetus (The Discourses [c.56], 4.08.14), quoted by A.A. Long - Hellenistic Philosophy 4.1 | |
| A reaction: [Said to echo Zeno] If you substitute understanding for 'logos' (plausibly), I think this is exactly the view of philosophy I would subscribe to. We want to understand each aspect of life, and we want those understandings to cohere with one another. |
| 20876 | Philosophy investigates the causes of disagreements, and seeks a standard for settling them [Epictetus] |
| Full Idea: The start of philosophy is perception of the mutual conflict among people, and a search for its cause, plus the rejection and distrust of mere opinion, an investigation to see if opinion is right, and the discovery of some canon, like scales for weighing. | |
| From: Epictetus (The Discourses [c.56], 2.11.13) | |
| A reaction: So the number one aim of philosophy is epistemological, to find the criterion for true opinion. But it starts in real life, and would cease to trade if people would just agree. I think we should set the bar higher than that. |
| 23344 | Reason itself must be compounded from some of our impressions [Epictetus] |
| Full Idea: What is reason itself? Something compounded from impressions of a certain kind. | |
| From: Epictetus (The Discourses [c.56], 1.20.05) | |
| A reaction: This seems to be the only escape from the dead end attempts to rationally justify reason. Making reason a primitive absolute is crazy metaphysics. |
| 23343 | Because reason performs all analysis, we should analyse reason - but how? [Epictetus] |
| Full Idea: Since it is reason that analyses and completes all other things, reason itself should not be left unanalysed. But by what shall it be analysed? ..That is why philosophers put logic first, just as when measuring grain we first examine the measure. | |
| From: Epictetus (The Discourses [c.56], 1.17.01) | |
| A reaction: The problem of the definitive metre rule in Paris. I say we have to test reason against the physical world, and the measure of reason is truth. Something has to be primitive, but reason is too vague for that role. Idea 23344 agrees with me! |
| 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. |
| 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. |
| 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. |
| 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). |
| 23359 | We can't believe apparent falsehoods, or deny apparent truths [Epictetus] |
| Full Idea: It is impossible to assent to an apparent falsehood, or to deny an apparent truth. | |
| From: Epictetus (The Discourses [c.56], 3.07.15) | |
| A reaction: The way some philosophers write you would think that most beliefs just result from private whims or social fashion. That happens, of course, but most beliefs result from direct contact with reality. |
| 23356 | Self-evidence is most obvious when people who deny a proposition still have to use it [Epictetus] |
| Full Idea: It is about the strongest proof one could offer of a proposition being evident, that even he who contradicts it finds himself having to make use of it. | |
| From: Epictetus (The Discourses [c.56], 2.20.01) | |
| A reaction: Philosophers sometimes make fools of themselves by trying, by the use of elaborate sophistry, to demolish propositions which are self-evidently true. Don't be one of these philosophers! |
| 23329 | We make progress when we improve and naturalise our choices, asserting their freedom [Epictetus] |
| Full Idea: Progress is when any of you turns to his own faculty of choice, working at it and perfecting it, so as to bring it fully into harmony with nature; elevated, free, unrestrained, unhindered, faithful, self-respecting. | |
| From: Epictetus (The Discourses [c.56], 1.04.18) | |
| A reaction: [See also Disc.3.5.7] Rationality is the stoic concept of being in 'harmony with nature'. It appears (from reading Frede) that this may be the FIRST EVER reference to free will. Note the very rhetorical way in which it is presented. |
| 23342 | Freedom is acting by choice, with no constraint possible [Epictetus] |
| Full Idea: He is free for whom all things happen in accordance with his choice, and whom no one can constrain. | |
| From: Epictetus (The Discourses [c.56], 1.12.09) | |
| A reaction: Presumable this means that constraint is absolutely impossible, even by Zeus, and not just contingent possibility, when no one sees me raid the fridge. |
| 23330 | Freedom is making all things happen by choice, without constraint [Epictetus] |
| Full Idea: He is free for whom all things happen in accordance with his choice, and whom no one can constrain. | |
| From: Epictetus (The Discourses [c.56], 1.12.09) | |
| A reaction: The idea of 'free' will seems to have resulted from a wide extension of the idea of constraint, with global determinism lurking in the background. |
| 23332 | Zeus gave me a nature which is free (like himself) from all compulsion [Epictetus] |
| Full Idea: Zeus placed my good nature in my own power, and gave it to me as he has it himself, free from all hindrance, compulsion and restraint. | |
| From: Epictetus (The Discourses [c.56], 3.03.10) | |
| A reaction: Although Frede traces the origin of free will to the centrality of choice in moral life (and hence to the elevation of its importance), this remark shows that there is a religious aspect to it. Zeus is supreme, and obviously has free will. |
| 23331 | Not even Zeus can control what I choose [Epictetus] |
| Full Idea: You can fetter my leg, but not even Zeus himself can get the better of my choice. | |
| From: Epictetus (The Discourses [c.56], 1.01.23) | |
| A reaction: This is the beginnings of the idea of free will. It is based on the accurate observation that the intrinsic privacy of a mind means that no external force can be assured of controlling its actions. Epictetus failed to think of internal forces. |
| 23338 | You can fetter my leg, but not even Zeus can control my power of choice [Epictetus] |
| Full Idea: What are you saying, man? Fetter me? You will fetter my leg; but not even Zeus himself can get the better of my choice. | |
| From: Epictetus (The Discourses [c.56], 1.01.23) | |
| A reaction: This seems to be the beginning of the idea of 'absolute' freedom, which is conjured up to preserve perfect inegrity and complete responsibility. Obviously you can be prevented from doing what you choose, so this is not compatibilism. |
| 20875 | If we could foresee the future, we should collaborate with disease and death [Epictetus] |
| Full Idea: The philosophers are right to say that if the honorable and good person knew what was going to happen, he would even collaborate with disease, death and lameness. | |
| From: Epictetus (The Discourses [c.56], 2.10.05) | |
| A reaction: The 'philosophers' must be the earlier stoics, founders of his school. |
| 23347 | If I know I am fated to be ill, I should want to be ill [Epictetus] |
| Full Idea: If I really knew that it was ordained for me to be ill at this moment, I would aspire to be so. | |
| From: Epictetus (The Discourses [c.56], 2.06.10) | |
| A reaction: The rub, of course, is that it is presumably impossible to know what is fated. Book 2.7 is on divination. I don't see any good in a mortally ill person desiring, for that reason alone, to die. Rage against the dying of the light, I say. |
| 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. |
| 23325 | Epictetus developed a notion of will as the source of our responsibility [Epictetus, by Frede,M] |
| Full Idea: The notion of will in Epictetus is clearly developed to pinpoint the source of our responsibility for our actions and to identify precisely what it is that makes them our own doings. | |
| From: report of Epictetus (The Discourses [c.56]) by Michael Frede - A Free Will 3 | |
| A reaction: So the key move is that responsibility needs a 'source', rather than being a generalisation about how our actions arise. The next step is demand an 'ultimate' source, and this leads to the idea that this new will is 'free'. This will can be good or bad. |
| 20873 | Tragedies are versified sufferings of people impressed by externals [Epictetus] |
| Full Idea: Tragedies are nothing but the sufferings of people who are impressed by externals, performed in the right sort of meter. | |
| From: Epictetus (The Discourses [c.56], 1.04.26) | |
| A reaction: The externals are things like honour, position and wealth. Wonderfully dismissive! |
| 23364 | Homer wrote to show that the most blessed men can be ruined by poor judgement [Epictetus] |
| Full Idea: Did not Homer write to show us that the noblest, the strongest, the richest, the handsomest of men may nevertheless be the most unfortunate and wretched, if they do not hold the judgements that they ought to hold? | |
| From: Epictetus (The Discourses [c.56], 4.10.36) | |
| A reaction: This seems to be right. He clearly wrote about the greatest and most memorable events of recent times, but not just to record triumphs, because almost every hero (in the Iliad, at least) ends in disaster. |
| 23340 | We consist of animal bodies and god-like reason [Epictetus] |
| Full Idea: We have these two elements mingled within us, a body in common with the animals, and reason and intelligence in common with the gods. | |
| From: Epictetus (The Discourses [c.56], 1.03.03) | |
| A reaction: This is what I call Human Exceptionalism, but note that it doesn't invoke a Christian soul or spiritual aspect. This separation of reason goes back at least to Plato. High time we stopped thinking this way. Animals behave very sensibly. |
| 23358 | Every species produces exceptional beings, and we must just accept their nature [Epictetus] |
| Full Idea: In every species nature produces some exceptional being, in oxen, in dogs, in bees, in horses. We do not say to them 'Who are you?' It will tell you 'I am like the purple in the robe. Do not expect me to be like the rest, or find fault with my nature'. | |
| From: Epictetus (The Discourses [c.56], 3.01.23) | |
| A reaction: This idea began with Aristotle's 'great soul', and presumably culminates in Nietzsche, who fills in more detail. In the modern world such people are mostly nothing but trouble. |
| 23339 | I will die as becomes a person returning what he does not own [Epictetus] |
| Full Idea: When the time comes, then I will die - as becomes a person who gives back what is not his own. | |
| From: Epictetus (The Discourses [c.56], 1.01.32) | |
| A reaction: There is a tension between his demand that he have full control of his choices, and this humility that says his actual life is not his own. The things which can't be controlled, though, are 'indifferents' so life and death are indifferent. |
| 23345 | Don't be frightened of pain or death; only be frightened of fearing them [Epictetus] |
| Full Idea: It is not pain or death that is to be feared, but the fear of pain or death. | |
| From: Epictetus (The Discourses [c.56], 2.01.13) | |
| A reaction: These two cases are quite different, I would say. I'm much more frightened of pain than I am of the fear of pain, and the opposite view seems absurd. About death, though, I think this is right. Mostly I'm with Spinoza: think about life, not death. |
| 23357 | Knowledge of what is good leads to love; only the wise, who distinguish good from evil, can love [Epictetus] |
| Full Idea: Whoever has knowledge of good things would know how to love them; and how could he who cannot distinguish good things from evil still have to power to love? It follows that the wise man alone has the power to love. | |
| From: Epictetus (The Discourses [c.56], 2.22.03) | |
| A reaction: A rather heartwarming remark, but hard to assess for its truth. Evil people are unable to love? Not even love a cat, or their favourite car? We would never call someone wise if they lacked love. |
| 23363 | The evil for everything is what is contrary to its nature [Epictetus] |
| Full Idea: Where is the paradox if we say that what is evil for everything is what is contrary to its nature? | |
| From: Epictetus (The Discourses [c.56], 4.01.125) | |
| A reaction: A very Greek view. For humans, it must rely on the belief that human nature is essentially good. If I am sometimes grumpy and annoying, why is that not part of my nature? |
| 23328 | The essences of good and evil are in dispositions to choose [Epictetus] |
| Full Idea: The essence of the good is a certain disposition of our choice, and essence of evil likewise. | |
| From: Epictetus (The Discourses [c.56], 1.29.01) | |
| A reaction: This is the origin of Kant's famous view, that the only true good is a good will. This is the alternative to good character or good states of affairs as the good. It points towards the modern more legalistic view of morality, as concerning actions. |
| 23362 | All human ills result from failure to apply preconceptions to particular cases [Epictetus] |
| Full Idea: The cause of all human ills is that people are incapable of applying their general preconceptions to particular cases. | |
| From: Epictetus (The Discourses [c.56], 4.01.42) | |
| A reaction: I'm not sure whether 'preconceptions' is meant pejoratively (as unthinking, and opposed to true principles). This sounds like modern particularism (e.g. Jonathan Dancy) to the letter. |
| 23353 | We have a natural sense of honour [Epictetus] |
| Full Idea: What faculty do you mean? - Have we not a natural sense of honour? - We have. | |
| From: Epictetus (The Discourses [c.56], 2.10.22) | |
| A reaction: This seems unlikely, given the lower status that honour now has with us, compared to two hundred years ago. But there may be a natural sense of status, and of humiliation and shame. |
| 23354 | If someone harms themselves in harming me, then I harm myself by returning the harm [Epictetus] |
| Full Idea: Since he has harmed himself by wronging me, shall not I harm myself by harming him? | |
| From: Epictetus (The Discourses [c.56], 2.10.26) | |
| A reaction: I am very keen on this idea. See Hamlet's remarks to Polonius about 'honour and dignity'. The best strategy for achieving moral excellence is to focus on our own characters, rather than how to act, and to respond to others. |
| 23324 | In the Discourses choice [prohairesis] defines our character and behaviour [Epictetus, by Frede,M] |
| Full Idea: In Epictetus's 'Discourses' the notion of choice [prohairesis] plays perhaps the central role. It is our prohairesis which defines us a person, as the sort of person we are; it is our prohairesis which determines how we behave. | |
| From: report of Epictetus (The Discourses [c.56]) by Michael Frede - A Free Will 3 | |
| A reaction: Frede is charting the gradual move in Greek philosophy from action by desire, reason and habit to action by the will (which then turns out to be 'free'). Character started as dispositions and ended as choices. |
| 23361 | Health is only a good when it is used well [Epictetus] |
| Full Idea: Is health a good and sickness an evil? No. Health is good when used well, and bad when used ill. | |
| From: Epictetus (The Discourses [c.56], 3.20.04) | |
| A reaction: Although I like the idea that health is a natural value, which bridges the gap from facts to values (as a successful function), there is no denying that the health of very evil people is not something the rest of us hope for. |
| 23346 | A person is as naturally a part of a city as a foot is part of the body [Epictetus] |
| Full Idea: Just as the foot in detachment is no longer a foot, so you in detachment are not longer a man. For what is a man? A part of a city, first. | |
| From: Epictetus (The Discourses [c.56], 2.05.26) | |
| A reaction: It is, of course, not true that a detached foot ceases to be a foot (and an isolated human is still a human). This an extreme version of the Aristotelian idea that we are essentially social. It is, though, the sort of view favoured by totalitarianism. |
| 23351 | We are citizens of the universe, and principal parts of it [Epictetus] |
| Full Idea: You are a citizen of the universe, and a part of it; and no subservient, but a principal part of it. | |
| From: Epictetus (The Discourses [c.56], 2.10.03) | |
| A reaction: He got this view from Diogenes of Sinope, one of his heroes. What community you are a part of seems to be a choice as much as a fact. Am I British or a European? |
| 20874 | A citizen is committed to ignore private advantage, and seek communal good [Epictetus] |
| Full Idea: The commitment of the citizen is to have no private advantage, not to deliberate about anything as though one were a separate part. | |
| From: Epictetus (The Discourses [c.56], 2.10.04) | |
| A reaction: This is the modern problem of whether democratic voters are choosing for themselves or for the community. I think we should make an active effort at every election to persuade voters to aim for the communal good. Cf Rawls. |
| 23352 | A citizen should only consider what is good for the whole society [Epictetus] |
| Full Idea: The calling of a citizen is to consider nothing in terms of personal advantage, never to deliberate on anything as though detached from the whole, but be like our hand or foot. | |
| From: Epictetus (The Discourses [c.56], 2.10.04) | |
| A reaction: Fat chance of that in an aggressively capitalist society. I've always voted for what I thought was the common good, and was shocked to gradually realise that many people only vote for what promotes their own interests. Heigh ho. |
| 22604 | Punishing a criminal for moral ignorance is the same as punishing someone for being blind [Epictetus] |
| Full Idea: You should ask 'Ought not this man to be put to death, who is deceived in things of the greatest importance, and is blinded in distinguishing good from evil?' …You then see how inhuman it is, and the same as 'Ought not this blind man to be put to death?' | |
| From: Epictetus (The Discourses [c.56], 1.18.6-7) | |
| A reaction: This is the doctrine of Socrates, that evil is ignorance (and weakness of will [akrasia] is impossible). Epictetus wants us to reason with the man, but what should be do if reasoning fails and he persists in his crimes? |
| 23349 | Asses are born to carry human burdens, not as ends in themselves [Epictetus] |
| Full Idea: An ass is surely not born as an end in itself? No, but because we had need of a back that is able to carry burdens. | |
| From: Epictetus (The Discourses [c.56], 2.08.07) | |
| A reaction: This is the absurd human exceptionalism which plagues our thinking. It would be somewhat true of animals which are specifically bred for human work, such as large cart horses. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 23341 | God created humans as spectators and interpreters of God's works [Epictetus] |
| Full Idea: God has introduced man into the world as a spectator of himself and of his works: and not only as a spectator of them, but an interpreter of them as well. | |
| From: Epictetus (The Discourses [c.56], 1.06.19) | |
| A reaction: This idea (which strikes me as bizarre) was picked up directly by the Christians. I can't imagine every Johnson wanting to creating their own Boswell. If you think we are divinely created, you have to propose some motive for it, I suppose. |
| 23348 | Both god and the good bring benefits, so their true nature seems to be the same [Epictetus] |
| Full Idea: God brings benefits; but the good also brings benefit. It would seem, then, that where the true nature of god is, there too is the true nature of good. | |
| From: Epictetus (The Discourses [c.56], 2.08.01) | |
| A reaction: An enthymeme, missing the premise that there can only be one source of benefit (which sounds unlikely). Does god bring anything other than benefits? And does the good? I think this is an idea from later platonism. |
| 23360 | Each of the four elements in you is entirely scattered after death [Epictetus] |
| Full Idea: Whatever was in you of fire, departs into fire; what was of earth, into earth; what of air, into air; what of water, into water. There is no Hades, nor Acheron. | |
| From: Epictetus (The Discourses [c.56], 3.13.15) | |
| A reaction: This sort of remark may explain why so few of the great Stoic texts (such as those of Chrysippus) survived the Christian era. |