54 ideas
| 421 | Men who love wisdom must be inquirers into very many things indeed [Heraclitus] |
| Full Idea: Men who love wisdom must be inquirers into very many things indeed. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B035), quoted by Clement - Miscellanies 5.140.5 | |
| A reaction: …which invites the question 'Is there anything that a wisdom-seeker should NOT be interested in?' |
| 1491 | Everyone has the potential for self-knowledge and sound thinking [Heraclitus] |
| Full Idea: Everyone has the potential for self-knowledge and sound thinking. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B116), quoted by John Stobaeus - Anthology 3.05.06 | |
| A reaction: This is true. When people are labelled as incapable of philosophy (e.g. by Plato), it is just that they are slow developers. |
| 5863 | Reason is eternal, but men are foolish [Heraclitus] |
| Full Idea: Although reason exists forever, men are foolish. | |
| From: Heraclitus (fragments/reports [c.500 BCE]), quoted by Aristotle - The Art of Rhetoric 1407b | |
| A reaction: The despair of all philosophers (e.g. Plato) who think reason is the easiest thing in the world, and stares everyone in the face, and yet people seem to spurn this supreme gift from the gods. They needed the optimism of the career teacher. |
| 414 | Logos is common to all, but most people live as if they have a private understanding [Heraclitus] |
| Full Idea: Although the universal law (logos) is common to all, the majority live as if they had understanding peculiar to themselves. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B002), quoted by Sextus Empiricus - Against the Professors (six books) 7.133.4- | |
| A reaction: Heraclitus mentions 'logos' in just three fragments - this one, and Idea 15660 and Idea 424. |
| 416 | Beautiful harmony comes from things that are in opposition to one another [Heraclitus] |
| Full Idea: That which is in opposition is in concert, and from things that differ comes the beautiful harmony. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B008), quoted by Aristotle - Nicomachean Ethics 1155b04 |
| 425 | A thing can have opposing tensions but be in harmony, like a lyre [Heraclitus] |
| Full Idea: They do not understand how that which differs with itself is in agreement: harmony consists of opposing tensions, like that of the bow and the lyre. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B051), quoted by Hippolytus - Refutation of All Heresies 9.9.2 | |
| A reaction: Like squabbling couples who resent outside intervention. The remark suggests the virtues of 'dialectic', and may get to the heart of what philosophy is. |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
| Full Idea: The remark of Heraclitus that all things are and are not effectively renders all assertions true, and that of Anaxagoras that there is an intermediary between assertion and negation makes all assertions false. | |
| From: comment on Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Metaphysics 1012a | |
| A reaction: Compare Idea 416. Heraclitus is discussing truth-value 'gluts', as in paraconsistent logic, and Anaxagoras is discussing truth-value 'gaps', as in three-valued Kleene logic. |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 15658 | The hidden harmony is stronger than the visible [Heraclitus] |
| Full Idea: The hidden harmony is stronger (or 'better') than the visible. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B055), quoted by Hippolytus - Refutation of All Heresies 9.9.5 | |
| A reaction: 'An unapparent connection [harmonia] is stronger than an apparent one' is Curd's translation. I'm taking this for essentialism. It is the basic idea of the essentialising child (see Gelman). The hidden explains the apparent. |
| 13782 | Everything gives way, and nothing stands fast [Heraclitus] |
| Full Idea: Everything gives way, and nothing stands fast. | |
| From: Heraclitus (fragments/reports [c.500 BCE]), quoted by Plato - Cratylus 402a | |
| A reaction: This is as good a summary of the Heraclitus view of things as any, and Plato appears to present it as a verbatim quotation. |
| 11853 | A mixed drink separates if it is not stirred [Heraclitus] |
| Full Idea: The mixed drink, of wine, cheese and barley, separates if it is not stirred. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B125) | |
| A reaction: Wiggins quotes this, because it seems to be Heraclitus struggling to decide what sortal his drink falls under. I take it to be a problem of vagueness, since separation and mixing occur along a continuum, like a sorites. |
| 427 | It is not possible to step twice into the same river [Heraclitus] |
| Full Idea: It is not possible to step twice into the same river. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B091), quoted by Plutarch - 24: The E at Delphi 392b10- |
| 11091 | You can bathe in the same river twice, but not in the same river stage [Quine on Heraclitus] |
| Full Idea: You can bathe in the same river twice, but not in the same river stage. | |
| From: comment on Heraclitus (fragments/reports [c.500 BCE]) by Willard Quine - Identity, Ostension, and Hypostasis 1 | |
| A reaction: This seems to make Quine a 'perdurantist', committed to time-slices of objects, rather than whole objects enduring through change. |
| 2064 | If flux is continuous, then lack of change can't be a property, so everything changes in every possible way [Plato on Heraclitus] |
| Full Idea: According to Heracliteans, since things must be changing, and since lack of change can't be a property of anything, then everything is always undergoing change of every kind. | |
| From: comment on Heraclitus (fragments/reports [c.500 BCE], B030) by Plato - Theaetetus 182a |
| 430 | Senses are no use if the soul is corrupt [Heraclitus] |
| Full Idea: The eyes and ears are bad witnesses for men if they have barbarian souls. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B107), quoted by Sextus Empiricus - Against the Mathematicians 7.126 |
| 1500 | When we sleep, reason closes down as the senses do [Heraclitus, by Sext.Empiricus] |
| Full Idea: Since when we sleep the senses are closed, mind is separated from its surroundings and loses the power of memory. When we wake the mind re-contacts the world, and regains the power of reason. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE], A16) by Sextus Empiricus - Against the Professors (six books) 7.130 |
| 417 | Donkeys prefer chaff to gold [Heraclitus] |
| Full Idea: Donkeys prefer chaff to gold. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B009), quoted by Aristotle - Nicomachean Ethics 1176a07 |
| 426 | Sea water is life-giving for fish, but not for people [Heraclitus] |
| Full Idea: Sea-water is the purest and the most polluted: for fish it is drinkable and life-giving; for men, not drinkable and destructive. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B061), quoted by Hippolytus - Refutation of All Heresies 9.10.5 |
| 431 | Health, feeding and rest are only made good by disease, hunger and weariness [Heraclitus] |
| Full Idea: Disease makes health pleasant and good, hunger makes satisfaction good, weariness makes rest good. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B111), quoted by John Stobaeus - Anthology 3.1.178 |
| 429 | To God (though not to humans) all things are beautiful and good and just [Heraclitus] |
| Full Idea: To God, all things are beautiful, good and just; but men have assumed some things to be unjust, others just. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B102), quoted by Porphyry - Notes on Homer Il.4.4 | |
| A reaction: The idea that all things are actually 'just' strikes me as nonsense. I also don't think I can get my head round the idea that everything is actually good and beautiful. Must try harder. |
| 12294 | Good and evil are the same thing [Heraclitus, by Aristotle] |
| Full Idea: Heraclitus said that good and evil are the same thing. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE], 58/102) by Aristotle - Topics 159b32 | |
| A reaction: Heaven knows what he meant by this, though it sounds suspiciously like moral nihilism. Maybe Heraclitus was not a very nice man. Or is the thought a more sophisticated one, in line with Nietzsche's remarks about cultural morality? |
| 419 | If one does not hope, one will not find the unhoped-for, since nothing leads to it [Heraclitus] |
| Full Idea: If one does not hope, one will not find the unhoped-for, since there is no trail leading to it and no path. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B018), quoted by Clement - Miscellanies 2.17.4 | |
| A reaction: The best remark about hope I have ever encountered. Usually they are empty platitudes. |
| 5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
| Full Idea: Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'. | |
| From: Xenophon (Symposium [c.391 BCE], 3.5) | |
| A reaction: This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue |
| 415 | If happiness is bodily pleasure, then oxen are happy when they have vetch to eat [Heraclitus] |
| Full Idea: If happiness lay in bodily pleasures, we would call oxen happy when they find vetch to eat. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B004), quoted by Albertus Magnus - On Vegetables 6.401 | |
| A reaction: But surely oxen are happy when they find some good vetch? Presumably, though, they are not 'eudaimon'. What is the complete fulfilment of life for an ox? |
| 5155 | It is hard to fight against emotion, but harder still to fight against pleasure [Heraclitus] |
| Full Idea: It is hard to fight against emotion, but harder still to fight against pleasure. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B085), quoted by Aristotle - Nicomachean Ethics 1105a08 | |
| A reaction: 'Emotion' is the Greek word 'thumos'. "The only way to get rid of a temptation is to yield to it", said Oscar Wilde. Heraclitus underestimates how very good many modern people are at dieting. |
| 433 | For man character is destiny [Heraclitus] |
| Full Idea: For man character is destiny. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B119), quoted by John Stobaeus - Anthology 4.40.23 | |
| A reaction: This is the extreme opposite of Sartre's existentialist claim that we can entirely change ourselves. Personally I am with Heraclitus, though I don't see why our destined character shouldn't be modified (e.g. by education). |
| 422 | The people should fight for the law as if for their city-wall [Heraclitus] |
| Full Idea: The people should fight for the law as if for their city-wall. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B044), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.2 | |
| A reaction: This may be the first recorded assertion of the rule of law, and hence of the separation of powers. We still have plenty of people who reject this principle. |
| 5833 | Education is the greatest of human goods [Xenophon] |
| Full Idea: Education is the greatest of human goods. | |
| From: Xenophon (Apology of Socrates [c.392 BCE], 22) | |
| A reaction: Of course, one might ask what education is for, and arrive at a greater good. If you ask what is the greatest good which a society can provide for you, or which you can give to your children, this seems to me a good answer. |
| 614 | Heraclitus said sometimes everything becomes fire [Heraclitus, by Aristotle] |
| Full Idea: Heraclitus claimed that from time to time everything becomes fire. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Metaphysics 1067a |
| 424 | Reason tells us that all things are one [Heraclitus] |
| Full Idea: When you have listened, not to me but to the law (logos), it is wise to agree that all things are one. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B050), quoted by Hippolytus - Refutation of All Heresies 9.9.1 |
| 5096 | Heraclitus says that at some time everything becomes fire [Heraclitus, by Aristotle] |
| Full Idea: Heraclitus says that at some time everything becomes fire. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Physics 204b37 | |
| A reaction: Modern cosmology says that Heraclitus was right (pretty much). If we say 'energy' instead of 'fire' (which may be what he meant), then he is absolutely spot-on. |
| 17539 | The sayings of Heraclitus are still correct, if we replace 'fire' with 'energy' [Heraclitus, by Heisenberg] |
| Full Idea: If we replace Heraclitus's word 'fire' by the word 'energy' we can almost repeat his statements word for word from our modern point of view. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Werner Heisenberg - Physics and Philosophy 04 | |
| A reaction: My problem has always been that I have no idea what 'energy' is, so I'm none the wiser. |
| 3054 | Heraclitus said fire could be transformed to create the other lower elements [Heraclitus, by Diog. Laertius] |
| Full Idea: Heraclitus taught that fire when densified becomes liquid, and becoming concrete, becomes also water; again, that the water when concrete is turned to earth, and this is the road down. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.1.6 |
| 15660 | Logos is the source of everything, and my theories separate and explain each nature [Heraclitus] |
| Full Idea: All things come into being according to this Law ('logos'), ...and I expound theories (words) and processes (actions) separating each thing according to its nature and explaining how it is made. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B001), quoted by Sextus Empiricus - Against the Mathematicians 7.133 | |
| A reaction: I like the fact that things are separated according to their natures (particulars!), and not that natures are somehow bestowed on individuals. |
| 12269 | All things are in a state of motion [Heraclitus, by Aristotle] |
| Full Idea: All things are in a state of motion. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Topics 104b22 | |
| A reaction: This seems right, I would say. It seems to make a 'process' the fundamental category of ontology, rather than an 'object'. |
| 420 | The cosmos is eternal not created, and is an ever-living and changing fire [Heraclitus] |
| Full Idea: This cosmos, which is the same for all, was not created by any one of the gods or of mankind, but it was ever and is and shall be ever-living fire, kindled and quenched in measure. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B030), quoted by Clement - Miscellanies 5.1.103 |
| 1499 | Heraclitus says intelligence draws on divine reason [Heraclitus, by Sext.Empiricus] |
| Full Idea: According to Heraclitus we become intelligent by drawing on divine reason. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE], A16) by Sextus Empiricus - Against the Professors (six books) 7.129 |
| 15659 | Purifying yourself with blood is as crazy as using mud to wash off mud [Heraclitus] |
| Full Idea: They purify themselves by staining themselves with other blood, as if one were to step into mud to wash off mud. But a man would be thought mad if any of his fellow-men should perceive him acting thus. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B005), quoted by Origen - Against Celsus 7.62 |
| 1501 | In their ignorance people pray to statues, which is like talking to a house [Heraclitus] |
| Full Idea: In their ignorance of the true nature of gods and heroes people pray to these statues, which is like someone holding a conversation with a house. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B005), quoted by Anon (Pyth) - Theosophia Tubigensis 68 |