55 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. |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
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Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
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| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
| A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2) |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: The definition is similar for predicate logic. |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 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. |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8) |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3) | |
| A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'. |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) | |
| A reaction: The second version of semantics is model theory. |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean. |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| Full Idea: In first-order languages, logically true sentences are true in all structures. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3) |
| 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. |
| 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). |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 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. |
| 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 |