96 ideas
| 22733 | Epicurus accepted God in his popular works, but not in his writings on nature [Epicurus, by Sext.Empiricus] |
| Full Idea: Epicurus in his popular exposition allows the existence of God, but in expounding the real nature of things he does not allow it. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Sextus Empiricus - Against the Physicists (two books) I.58 | |
| A reaction: Plato and Aristotle also distinguished their esoteric from their exoteric writings, but this is an indication that thei popular works may always have presented safer doctrines. |
| 13291 | Slavery to philosophy brings true freedom [Epicurus] |
| Full Idea: To win true freedom you must be a slave to philosophy. | |
| From: Epicurus (fragments/reports [c.289 BCE]), quoted by Seneca the Younger - Letters from a Stoic 008 | |
| A reaction: A lovely idea. It is one thing to free the body, or to free one's social situation, but the challenge to 'free your mind' is either romantic nonsense or totally baffling, apart from the suggestion offered here. Reason is freedom. Very Kantian. |
| 22758 | Philosophy aims at a happy life, through argument and discussion [Epicurus] |
| Full Idea: Philosophy is an activity which secures the happy life by arguments and discussions. | |
| From: Epicurus (fragments/reports [c.289 BCE]), quoted by Sextus Empiricus - Against the Ethicists (one book) VI.169 | |
| A reaction: Presumably this aims at the happiness of the participant. Universal happiness would need to be much more political. If this is your aim then you can't just follow the winds of the argument, but must channel it towards happiness. No nasty truths? |
| 14523 | We should come to philosophy free from any taint of culture [Epicurus] |
| Full Idea: I congratulate you, sir, because you have come to philosophy free of any taint of culture. | |
| From: Epicurus (fragments/reports [c.289 BCE]) | |
| A reaction: [source: Athenaeus, 'Deipnosophists' 13 588b] No one nowadays thinks such an aspiration remotely possible, not least because the culture is embedded in your native language, but I find the idea very appealing. |
| 22240 | The aim of medicine is removal of sickness, and philosophy similarly removes our affections [Epicurus] |
| Full Idea: Just as there is no benefit to medicine if it does not heal the sicknesses [nosos] of bodies, so too there is none to philosophy unless it expels that affections of the soul. | |
| From: Epicurus (fragments/reports [c.289 BCE], fr 221), quoted by James Allen - Soul's Virtue and the Health of the Body p.78 | |
| A reaction: This sounds rather Buddhist, if the only route to happiness is to suppress the emotions. Epicurus probably refers to the more extreme desires, which only lead to harm. Galen quotes Chrysippus as endorsing this idea (see footnote 5). |
| 1484 | We should say nothing of the whole if our contact is with the parts [Epicurus, by Plutarch] |
| Full Idea: We should make no assertion about the whole when our contact is with the parts. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Plutarch - 74: Reply to Colotes 1109e |
| 2670 | Epicurus despises and laughs at the whole of dialectic [Epicurus, by Cicero] |
| Full Idea: Epicurus despises and laughs at the whole of dialectic. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - Academica II.30.97 |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| Full Idea: Poincaré suggested that what is wrong with an impredicative definition is that it allows the set defined to alter its composition as more sets are added to the theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| Full Idea: None of the classical ways of defining one logical constant in terms of others is available in intuitionist logic (and this includes the two quantifiers). | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| Full Idea: There is so far no agreed set of axioms for set theory which is categorical, i.e. which does pick just one structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: This contrasts with Peano Arithmetic, which is categorical in its second-order version. |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| Full Idea: A 'proper class' cannot be a member of anything, neither of a set nor of another proper class. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| Full Idea: We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: Bostock says most mathematicians reject the first option, and are undecided about the second option. |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| Full Idea: The usual accounts of ZF are not restricted to subsets that we can describe, and that is what justifies the axiom of choice. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4 n36) | |
| A reaction: This contrasts interestingly with predicativism, which says we can only discuss things which we can describe or define. Something like verificationism hovers in the background. |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| Full Idea: The Axiom of Replacement (or the Axiom of Subsets, 'Aussonderung', Fraenkel 1922) in effect enforces the idea that 'limitation of size' is a crucial factor when deciding whether a proposed set or does not not exist. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| Full Idea: First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936). | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| Full Idea: From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) | |
| A reaction: The point is that the completeness requires finite proofs. |
| 21668 | Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero] |
| Full Idea: Epicurus said that not every proposition is either true or false. ...Epicurus was afraid that if he admits that every proposition is true or false he will also have to admit that all events are caused by fate (if they are so from all eternity). | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 10.21 | |
| A reaction: Epicurus proposed his 'swerve' in the movements of atoms to avoid this fatalism. Epicurus is agreeing with Aristotle, who did not accept excluded middle for a future contingent sea-fight. |
| 21676 | Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero] |
| Full Idea: Epicureans make the impudent assertion that disjunctions consisting of contrary propositions are true, but that the statements contained in the propositions are neither of them true. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 16.36 | |
| A reaction: Is that 'it is definitely one or the other, but we haven't a clue which one'? Seems to fit speculations about Goldbach's Conjecture. It doesn't sound terribly impudent to me. Or is it the crazy 'It's definitely one of them, but it's neither of them'? |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| Full Idea: Substitutional quantification and quantification understood in the usual 'ontological' way will coincide when every object in the (ontological) domain has a name. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.3 n23) |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| Full Idea: The Deduction Theorem is what licenses a system of 'natural deduction' in the first place. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| Full Idea: Berry's Paradox can be put in this form, by considering the alleged name 'The least number not named by this name'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| Full Idea: If you add to the ordinals you produce many different ordinals, each measuring the length of the sequence of ordinals less than it. They each have cardinality aleph-0. The cardinality eventually increases, but we can't say where this break comes. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| Full Idea: If we add ω onto the end of 0,1,2,3,4..., it then has a different length, of ω+1. It has a different ordinal (since it can't be matched with its first part), but the same cardinal (since adding 1 makes no difference). | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: [compressed] The ordinals and cardinals coincide up to ω, but this is the point at which they come apart. |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| Full Idea: It is the usual procedure these days to identify a cardinal number with the earliest ordinal number that has that number of predecessors. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: This sounds circular, since you need to know the cardinal in order to decide which ordinal is the one you want, but, hey, what do I know? |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| Full Idea: The cardinal aleph-1 is identified with the first ordinal to have more than aleph-0 members, and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) | |
| A reaction: That is, the succeeding infinite ordinals all have the same cardinal number of members (aleph-0), until the new total is triggered (at the number of the reals). This is Continuum Hypothesis territory. |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| Full Idea: In addition to cuts, or converging series, Cantor suggests we can simply lay down a set of axioms for the real numbers, and this can be done without any explicit mention of the rational numbers [note: the axioms are those for a complete ordered field]. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: It is interesting when axioms are best, and when not. Set theory depends entirely on axioms. Horsten and Halbach are now exploring treating truth as axiomatic. You don't give the 'nature' of the thing - just rules for its operation. |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| Full Idea: It is not difficult to show that the number of the real numbers is the same as the number of all the subsets of the natural numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: The Continuum Hypothesis is that this is the next infinite number after the number of natural numbers. Why can't there be a number which is 'most' of the subsets of the natural numbers? |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| Full Idea: As Eudoxus claimed, two distinct real numbers cannot both make the same cut in the rationals, for any two real numbers must be separated by a rational number. He did not say, though, that for every such cut there is a real number that makes it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: This is in Bostock's discussion of Dedekind's cuts. It seems that every cut is guaranteed to produce a real. Fine challenges the later assumption. |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| Full Idea: Non-standard natural numbers will yield non-standard rational and real numbers. These will include reciprocals which will be closer to 0 than any standard real number. These are like 'infinitesimals', so that notion is not actually a contradiction. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| Full Idea: A modern axiomatisation of geometry, such as Hilbert's (1899), does not need to claim the existence of real numbers anywhere in its axioms. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.ii) | |
| A reaction: This is despite the fact that geometry is reduced to algebra, and the real numbers are the equivalent of continuous lines. Bostock votes for a Greek theory of proportion in this role. |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| Full Idea: The Peano Axioms are categorical, meaning that they describe a unique structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4 n20) | |
| A reaction: So if you think there is nothing more to the natural numbers than their structure, then the Peano Axioms give the essence of arithmetic. If you think that 'objects' must exist to generate a structure, there must be more to the numbers. |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| Full Idea: Hume's Principle will not do as an implicit definition because it makes a positive claim about the size of the universe (which no mere definition can do), and because it does not by itself explain what the numbers are. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| Full Idea: Hume's Principle gives a criterion of identity for numbers, but it is obvious that many other things satisfy that criterion. The simplest example is probably the numerals (in any notation, decimal, binary etc.), giving many different interpretations. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| Full Idea: There is not just one way of giving a criterion of identity for numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| Full Idea: The Julius Caesar problem was one reason that led Frege to give an explicit definition of numbers as special sets. He does not appear to notice that the same problem affects his Axiom V for introducing sets (whether Caesar is or is not a set). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: The Julius Caesar problem is a sceptical acid that eats into everything in philosophy of mathematics. You give all sorts of wonderful accounts of numbers, but at what point do you know that you now have a number, and not something else? |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| Full Idea: There is no ground for saying that a number IS a position, if the truth is that there is nothing to determine which number is which position. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: If numbers lose touch with the empirical ability to count physical objects, they drift off into a mad world where they crumble away. |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| Full Idea: Structuralism begins from a false premise, namely that numbers have no properties other than their relations to other numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.5) | |
| A reaction: Well said. Describing anything purely relationally strikes me as doomed, because you have to say why those things relate in those ways. |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| Full Idea: Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9) |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| Full Idea: The style of nominalism which aims to reduce statements about numbers to statements about their applications does not work for the natural numbers, because they have many applications, and it is arbitrary to choose just one of them. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.iii) |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| Full Idea: We all know that in practice no physical measurement can be 100 per cent accurate, and so it cannot require the existence of a genuinely irrational number, rather than some of the rational numbers close to it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.3) |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| Full Idea: The basic use of the ordinal numbers is their use as ordinal adjectives, in phrases such as 'the first', 'the second' and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: That is because ordinals seem to attach to particulars, whereas cardinals seem to attach to groups. Then you say 'three is greater than four', it is not clear which type you are talking about. |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| Full Idea: The simple theory of types distinguishes sets into different 'levels', but this is quite different from the distinction into 'orders' which is imposed by the ramified theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) | |
| A reaction: The ramified theory has both levels and orders (p.235). Russell's terminology is, apparently, inconsistent. |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| Full Idea: The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: So the big difference between Frege and neo-logicists is the Julius Caesar problem. |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| Full Idea: The response of neo-logicists to the Julius Caesar problem is to strengthen Hume's Principle in the hope of ensuring that only numbers will satisfy it. They say the criterion of identity provided by HP is essential to number, and not to anything else. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| Full Idea: If Hume's Principle is all we are given, by way of explanation of what the numbers are, the only conclusion to draw would seem to be the structuralists' conclusion, ...studying all systems that satisfy that principle. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: Any approach that implies a set of matching interpretations will always imply structuralism. To avoid it, you need to pin the target down uniquely. |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| Full Idea: Many of the crucial definitions in the logicist programme are in fact impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| Full Idea: If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| Full Idea: In its higher reaches, which posit sets of huge cardinalities, set theory is just a fairy story. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: You can't say the higher reaches are fairy stories but the lower reaches aren't, if the higher is directly derived from the lower. The empty set and the singleton are fairy stories too. Bostock says the axiom of infinity triggers the fairy stories. |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| Full Idea: A common view is that although a fairy tale may provide very useful predictions, it cannot provide explanations for why things happen as they do. In order to do that a theory must also be true (or, at least, an approximation to the truth). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5) | |
| A reaction: Of course, fictionalism offers an explanation of mathematics as a whole, but not of the details (except as the implications of the initial fictional assumptions). |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| Full Idea: In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted. |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| Full Idea: Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: [compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?). |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| Full Idea: If an abstract object exists only when there is some suitable way of expressing it, then there are at most denumerably many abstract objects. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) | |
| A reaction: Fine by me. What an odd view, to think there are uncountably many abstract objects in existence, only a countable portion of which will ever be expressed! [ah! most people agree with me, p.243-4] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| Full Idea: Classical mathematicians say predicative mathematics omits areas of great interest, all concerning non-denumerable real numbers, such as claims about huge cardinals. There cannot be a predicative version of this theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I'm not sure that anyone will really miss huge cardinals if they are prohibited, though cryptography seems to flirt with such things. Are we ever allowed to say that some entity conjured up by mathematicians is actually impossible? |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| Full Idea: It has been claimed that only predicative mathematics has a justification through its usefulness to science (an empiricist approach). | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [compressed. Quine is the obvious candidate] I suppose predicativism gives your theory roots, whereas impredicativism is playing an abstract game. |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| Full Idea: If we accept the initial idea that we can think only of what we ourselves can describe, then something like the theory of predicativism quite naturally results | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I hate the idea that we can only talk of what falls under a sortal, but 'what we can describe' is much more plausible. Whether or not you agree with this approach (I'm pondering it), this makes predicativism important. |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| Full Idea: The predicative approach cannot accept either the usual definition of identity or the usual definition of the natural numbers, for both of these definitions are impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [Bostock 237-8 gives details] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| Full Idea: It is with the real numbers that the restrictions imposed by predicativity begin to make a real difference. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 1823 | We can't seek for things if we have no idea of them [Epicurus, by Diog. Laertius] |
| Full Idea: We could not seek for anything if we had not some notion of it. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.21 |
| 1824 | To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius] |
| Full Idea: We could not give names to things, if we had not a preliminary notion of what the things were. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.21 |
| 5949 | Epicurus says colours are relative to the eye, not intrinsic to bodies [Epicurus, by Plutarch] |
| Full Idea: Epicurus says that colours are not intrinsic to bodies but a result of certain arrangements and positions relative to the eye, which implies that body is no more colourless than coloured. | |
| From: report of Epicurus (fragments/reports [c.289 BCE], Fr 30) by Plutarch - 74: Reply to Colotes §1110 | |
| A reaction: This seems to me such a self-evident truth that I am puzzled as to why anyone would claim that colours are real features of bodies. Epicurus points out that entering a dark room we see no colour, but then colour appears after a while. |
| 1821 | Sensations cannot be judged, because similar sensations have equal value, and different ones have nothing in common [Epicurus, by Diog. Laertius] |
| Full Idea: Sensation is out of reach of control, because one sensation cannot judge another which resembles itself, as they have equal value, and different sensations have different objects. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20 | |
| A reaction: Scepticism about the possibility of purely empirical knowledge; an interesting comment on the question of whether perceptions contain any intrinsic knowledge. |
| 1820 | The criteria of truth are senses, preconceptions and passions [Epicurus, by Diog. Laertius] |
| Full Idea: The criteria of truth are the senses, the preconceptions, and the passions. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20 |
| 1822 | Reason can't judge senses, as it is based on them [Epicurus, by Diog. Laertius] |
| Full Idea: Reason cannot judge the senses, because it is based on them. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20 |
| 4549 | Epicurus denied knowledge in order to retain morality or hedonism as the highest values [Nietzsche on Epicurus] |
| Full Idea: Epicurus denied the possibility of knowledge in order to retain moral (or hedonistic) values as the highest values. | |
| From: comment on Epicurus (fragments/reports [c.289 BCE]) by Friedrich Nietzsche - The Will to Power (notebooks) §578 | |
| A reaction: The history of philosophy suggests that this dichotomy is unnecessary. Dogmatist place a high value on multitudes of things. |
| 2668 | Epicurus says if one of a man's senses ever lies, none of his senses should ever be believed [Epicurus, by Cicero] |
| Full Idea: Epicurus says that if one sense has told a lie once in a man's life, no sense must ever be believed. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - Academica II.25.79 |
| 1482 | If two people disagree over taste, who is right? [Epicurus, by Plutarch] |
| Full Idea: If one person says the wine is dry and the other that it is sweet, and neither errs in his sensation, how is the wine any more dry than sweet? | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Plutarch - 74: Reply to Colotes 1109b |
| 1483 | Bath water is too hot for some, too cold for others [Epicurus, by Plutarch] |
| Full Idea: In the very same bath some treat the water as too hot, others as too cold. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Plutarch - 74: Reply to Colotes 1109b |
| 1487 | When entering a dark room it is colourless, but colour gradually appears [Epicurus] |
| Full Idea: On entering a dark room we see no colour, but do so after waiting a short time. | |
| From: Epicurus (fragments/reports [c.289 BCE]), quoted by Plutarch - 74: Reply to Colotes 1110d |
| 14526 | The rational soul is in the chest, and the non-rational soul is spread through the body [Epicurus] |
| Full Idea: Democritus and Epicurus say the soul has two parts, one which is rational and is situated in the chest area, and the other which is non-rational and is spread throughout the entire compound of the body | |
| From: Epicurus (fragments/reports [c.289 BCE]) | |
| A reaction: [source Aetius 4.4.6] |
| 6035 | Soul is made of four stuffs, giving warmth, rest, motion and perception [Epicurus, by Aetius] |
| Full Idea: Epicurus says the soul is a blend of fiery stuff (for bodily warmth), airy stuff (rest), breath (motion), and a nameless stuff (sense-perception). | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Aetius - fragments/reports 4.3.11 | |
| A reaction: Obviously Epicurus thought the four stuffs were different combinations of atoms, rather than being elements. Is there no stuff which gives reason? Reason must reduce to motion, presumably. |
| 6018 | Epicurus was the first to see the free will problem, and he was a libertarian [Epicurus, by Long/Sedley] |
| Full Idea: By posing the problem of determinism, Epicurus became arguably the first philosopher to recognise the philosophical centrality of what we call the Free Will Question. His strongly libertarian approach is strongly contrasted with Stoic determinism. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by AA Long / DN Sedley - Hellenic Philosophers commentary | |
| A reaction: Epicurus introduced the rather dubious 'swerve' of the atoms to make room for free will. It seems to me more consistent to stick with the determinism of Democritus. Zeno became a determinist in reaction to Epicurus. |
| 20922 | Epicurus showed that the swerve can give free motion in the atoms [Epicurus, by Diogenes of Oen.] |
| Full Idea: There is a free motion in the atoms, which Democritus did not discover, but which Epicurus brought to light, and which consists in a swerve, as he demonstrated on the basis of what is seen to be the case? | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes (Oen) - Wall inscription 54.II-III | |
| A reaction: I presume the last bit means that we see that we have freedom of choice, and infer the swerve in the atoms as the only possible explanation. The worry for libertarians is, of course, who is in charge of the swerve. |
| 14516 | There is no necessity to live with necessity [Epicurus] |
| Full Idea: Necessity is a bad thing, but there is no necessity to live with necessity. | |
| From: Epicurus (fragments/reports [c.289 BCE], 9) |
| 1909 | How can pleasure or judgement occur in a heap of atoms? [Sext.Empiricus on Epicurus] |
| Full Idea: If Epicurus makes the end consist in pleasure and asserts that the soul, like all else, is composed of atoms, it is impossible to explain how in a heap of atoms there can come about pleasure, or judgement of the good. | |
| From: comment on Epicurus (fragments/reports [c.289 BCE]) by Sextus Empiricus - Outlines of Pyrrhonism III.187 | |
| A reaction: This is a nice statement of the mind-body problem. Ontologically, physics still seems to present reality as a 'heap of particles', which gives no basis for the emergence of anything as strange as consciousness. But then magnetism is pretty strange. |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| Full Idea: In Modus Ponens where the first premise is 'P' and the second 'P→Q', in the first premise P is asserted but in the second it is not. Yet it must mean the same in both premises, or it would be guilty of the fallacy of equivocation. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) | |
| A reaction: This is Geach's thought (leading to an objection to expressivism in ethics, that P means the same even if it is not expressed). |
| 7814 | It was Epicurus who made the question of the will's freedom central to ethics [Epicurus, by Grayling] |
| Full Idea: Epicurus was responsible for the innovatory recognition that the question of the will's freedom is central to ethics. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: Compare Ideas 7672 and 6018. Obviously ethical action needs freedom, but the idea of a 'free will' is quite different. It is a fiction, created to give some sort of arrogant ultimate responsibility to our actions, like God. |
| 3562 | Fine things are worthless if they give no pleasure [Epicurus] |
| Full Idea: I spit on the fine and those who emptily admire it, when it doesn't make any pleasure. | |
| From: Epicurus (fragments/reports [c.289 BCE]), quoted by Julia Annas - The Morality of Happiness Ch.16 | |
| A reaction: in Athenaeus |
| 1840 | Pleasure is the chief good because it is the most natural, especially for animals [Epicurus, by Diog. Laertius] |
| Full Idea: Pleasure is the chief good, because all animals from the moment of their birth are delighted with pleasure and offended by pain by their natural instinct, without the employment of reason. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.29 | |
| A reaction: The highest pleasure of predators is likely to be the killing of weaker animals. What all animals do isn't much of a criterion for the natural chief good. They also breathe. |
| 1839 | Pains of the soul are worse than pains of the body, because it feels the past and future [Epicurus, by Diog. Laertius] |
| Full Idea: The pains of the soul are worst, for the flesh is only sensible of present affliction, but the soul feels the past, present and future. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.29 | |
| A reaction: I don't think feeling extended across time is very relevant. What matters is that pains of the soul usually endure far longer than physical suffering. |
| 1842 | Pleasures only differ in their duration and the part of the body affected [Epicurus] |
| Full Idea: If every pleasure lasted long, and affected the whole body, then there would be no difference between one pleasure and another | |
| From: Epicurus (fragments/reports [c.289 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.31.08 | |
| A reaction: This seems to miss out on intensity, which is of great importance to most pleasure seekers. Also it is a pleasure to be alive, which is lifelong, but we barely notice it. |
| 3557 | The end for Epicurus is static pleasure [Epicurus, by Annas] |
| Full Idea: Epicurus identifies our final end with what he calls tranquillity or 'ataraxia', which is static pleasure. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Julia Annas - The Morality of Happiness Ch.7 | |
| A reaction: I don't recall any Greek ever spotting that boredom is a problem. But then they didn't have privacy, so other people always hold their attention. Maybe this is a dream of privacy. |
| 1845 | Justice has no independent existence, but arises entirely from keeping contracts [Epicurus] |
| Full Idea: Justice has no independent existence; it results from mutual contracts, and establishes itself wherever there is a mutual engagement to guard against doing or sustaining mutual injury. | |
| From: Epicurus (fragments/reports [c.289 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.31.35 |
| 1841 | We choose virtue because of pleasure, not for its own sake [Epicurus, by Diog. Laertius] |
| Full Idea: We choose the virtues for the sake of pleasure, and not on their own account. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.30 |
| 1829 | A wise man would be happy even under torture [Epicurus, by Diog. Laertius] |
| Full Idea: Even if the wise man were put to the torture, he would still be happy. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.26 |
| 1843 | Friendship is by far the most important ingredient of a complete and happy life [Epicurus] |
| Full Idea: Of all the things which wisdom provides for the happiness of the whole life, by far the most important is the acquisition of friendship. | |
| From: Epicurus (fragments/reports [c.289 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.31.28 |
| 1831 | Wise men should partake of life even if they go blind [Epicurus, by Diog. Laertius] |
| Full Idea: Even though he lose his eyes, a wise man should still partake of life. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.26 |
| 12044 | Only Epicurus denied purpose in nature, for the whole world, or for its parts [Epicurus, by Annas] |
| Full Idea: Epicurus alone among the ancient schools denies that in nature we find any teleological explanations. Nothing in nature is for anything, neither the world as a whole nor anything in it. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Julia Annas - Ancient Philosophy: very short introduction | |
| A reaction: This may explain the controversial position that epicureanism held in the seventeenth century, as well as its incipient atheism. |
| 20907 | Democritus says atoms have size and shape, and Epicurus added weight [Epicurus, by Ps-Plutarch] |
| Full Idea: Democritus said that the properties of the atoms are in number two, magnitude and shape, but Epicurus added to these a third one, weight. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by Pseudo-Plutarch - On the Doctrine of the Philosophers 1.3.18 | |
| A reaction: The addition of Epicurus seems very sensible, and an odd omission by Democritus. He seems to think that atoms have a uniform density, so that volume indicates weight. |
| 21669 | Atoms don't swerve by being struck, because they move in parallel, so the swerve is uncaused [Cicero on Epicurus] |
| Full Idea: The swerve of Epicurus takes place without a cause; it does not take place in consequence of being struck by another atom, since how can that take place if they are indivisible bodies travelling perpendicularly in straight lines by the force of gravity? | |
| From: comment on Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 10.22 | |
| A reaction: The swerve is the most ad hoc proposal in the history of theoretical physics. This is interesting for spelling out that the travel in vertical parallels. What's that all about, then? |
| 21680 | What causes atomic swerves? Do they draw lots? What decides the size or number of swerves? [Cicero on Epicurus] |
| Full Idea: What fresh cause exists in nature to make the atom swerve (or do the atoms cast lots among them which is to swerve and which not?), or to serve as the reason for making a very small swerve and not a large one, or one swerve, and not two or three swerves? | |
| From: comment on Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 20.46 | |
| A reaction: This is an appeal to the Principle of Sufficient Reason, which seems to be the main ground for rejecting the swerve. The only reason to accept the swerve is reluctance to accept determinism or fatalism. |
| 14525 | Stoics say time is incorporeal and self-sufficient; Epicurus says it is a property of properties of things [Epicurus] |
| Full Idea: Stoics posited that time is an incorporeal which is conceived of all by itself, while Epicurus thinks that it is an accident of certain things, ...and he called in a property of properties. | |
| From: Epicurus (fragments/reports [c.289 BCE]) | |
| A reaction: [Source Sextus 'Adversus Mathematicos' 10.219-227] |
| 5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |
| Full Idea: The four major disputes in classical cosmology were whether the cosmos is 'open' or 'closed', whether it is explained mechanistically or teleologically, whether it is alive or mere matter, and whether or not it has a beginning. | |
| From: report of T.M. Robinson (Classical Cosmology (frags) [1997]) by PG - Db (ideas) | |
| A reaction: A nice summary. The standard modern view is closed, mechanistic, inanimate and non-eternal. But philosophers can ask deeper questions than physicists, and I say we are entitled to speculate when the evidence runs out. |
| 2637 | For Epicureans gods are made of atoms, and are not eternal [Epicurus, by Cicero] |
| Full Idea: For Epicureans the gods are made of atoms, so in that case they are not eternal. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.68 |
| 2633 | Epicurus saw that gods must exist, because nature has imprinted them on human minds [Epicurus, by Cicero] |
| Full Idea: Epicurus alone saw that gods must exist because nature herself has imprinted an idea of them in the minds of all mankind. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.43 |
| 2639 | Some say Epicurus only pretended to believe in the gods, so as not to offend Athenians [Epicurus, by Cicero] |
| Full Idea: Some believe that Epicurus gave lip-service only to the gods, so as not to offend the Athenians, but in fact did not believe in them. | |
| From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.84 |
| 14527 | If god answered prayers we would be destroyed, because we pray for others to suffer [Epicurus] |
| Full Idea: If god acted in accordance with the prayers of men, all men would rather quickly be destroyed, since they constantly pray for many sufferings to befall each other. | |
| From: Epicurus (fragments/reports [c.289 BCE]) | |
| A reaction: [source Maximus the Abbott 'Gnom.' 14] |