54 ideas
| 6259 | Why can't a wise man doubt everything? [Montaigne] |
| Full Idea: Why cannot a wise man dare to doubt anything and everything? | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0562) | |
| A reaction: This question seems to be the start of the Enlightenment Project, of attempting to prove everything. MacIntyre warns of the dangers of this in ethical theory. The story of modern philosophy is the discovery of its impossibility. E.g. Davidson on truth. |
| 6263 | No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne] |
| Full Idea: Take a beam wide enough to walk along: suspend it between two towers: there is no philosophical wisdom, however firm, which could make us walk along it just as we would if we were on the ground. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0672) | |
| A reaction: This proposes great scepticism about the practical application of philosophical wisdom, but if we talk in terms of the wise assessment of risk in any undertaking, our caution on the raised beam makes perfectly good sense. |
| 23122 | Montaigne was the founding father of liberalism [Montaigne, by Gopnik] |
| Full Idea: The first liberal, the founding father if we have one, is the great sixteenth century French essayist Michel de Montaigne. | |
| From: report of Michel de Montaigne (On Cruelty [1580]) by Adam Gopnik - A Thousand Small Sanities 1 | |
| A reaction: He says this not on the basis of his politicies or achievements, but his general attitudes and values. It may be another hundred years before we can identify another obvious liberal (Locke?). |
| 9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
| Full Idea: Priest says there is room for contradictions. He gives the example of someone in a doorway; is he in or out of the room. Given that in and out are mutually exclusive and exhaustive, and neither is the default, he seems to be both in and not in. | |
| From: report of Graham Priest (What is so bad about Contradictions? [1998]) by Roy Sorensen - Vagueness and Contradiction 4.3 | |
| A reaction: Priest is a clever lad, but I don't think I can go with this. It just seems to be an equivocation on the word 'in' when applied to rooms. First tell me the criteria for being 'in' a room. What is the proposition expressed in 'he is in the room'? |
| 6258 | Virtue is the distinctive mark of truth, and its greatest product [Montaigne] |
| Full Idea: The distinctive mark of the Truth we hold ought to be virtue, which is the most exacting mark of Truth, the closest one to heaven and the most worthy thing that Truth produces. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0493) | |
| A reaction: A long way from Tarski and minimalist theories of truth! But not so far from pragmatism. Personally I think Montaigne is making an important claim, which virtue theorists should be attempting to incorporate into their theory. Aristotle would sympathise. |
| 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
| Full Idea: Priest and Routley have developed paraconsistent relevant logic. 'Relevant' logics insist on there being some sort of connection between the premises and the conclusion of an argument. 'Paraconsistent' logics allow contradictions. | |
| From: report of Graham Priest (works [1998]) by Michčle Friend - Introducing the Philosophy of Mathematics 6.8 | |
| A reaction: Relevance blocks the move of saying that a falsehood implies everything, which sounds good. The offer of paraconsistency is very wicked indeed, and they are very naughty boys for even suggesting it. |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| Full Idea: Free logic is an unusual example of a non-classical logic which is first-order. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], Pref) |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| Full Idea: X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets, the set of all the n-tuples with its first member in X1, its second in X2, and so on. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.0) |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| Full Idea: <a,b> is a set whose members occur in the order shown; <x1,x2,x3, ..xn> is an 'n-tuple' ordered set. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| Full Idea: a ∈ X means that a is a member of the set X, that is, a is one of the objects in X. a ∉ X indicates that a is not in X. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| Full Idea: {x; A(x)} indicates a set of objects which satisfy the condition A(x). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| Full Idea: {a1, a2, ...an} indicates that the set comprises of just those objects. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| Full Idea: Φ indicates the empty set, which has no members | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| Full Idea: {a} is the 'singleton' set of a, not to be confused with the object a itself. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| Full Idea: X⊂Y means set X is a 'proper subset' of set Y (if and only if all of its members are members of Y, but some things in Y are not in X) | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| Full Idea: X⊆Y means set X is a 'subset' of set Y (if and only if all of its members are members of Y). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| Full Idea: X = Y means the set X equals the set Y, which means they have the same members (i.e. X⊆Y and Y⊆X). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| Full Idea: X ∩ Y indicates the 'intersection' of sets X and Y, which is a set containing just those things that are in both X and Y. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| Full Idea: X ∪ Y indicates the 'union' of sets X and Y, which is a set containing just those things that are in X or Y (or both). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| Full Idea: Y - X indicates the 'relative complement' of X with respect to Y, that is, all the things in Y that are not in X. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| Full Idea: The 'relative complement' of one set with respect to another is the things in the second set that aren't in the first. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| Full Idea: The 'intersection' of two sets is a set containing the things that are in both sets. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| Full Idea: The 'union' of two sets is a set containing all the things in either of the sets | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8) |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| Full Idea: The 'induction clause' says that whenever one constructs more complex formulas out of formulas that have the property P, the resulting formulas will also have that property. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.2) |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| Full Idea: An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| Full Idea: A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10) |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| Full Idea: A 'set' is a collection of objects. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| Full Idea: The 'empty set' or 'null set' is a set with no members. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| Full Idea: A set is a 'subset' of another set if all of its members are in that set. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| Full Idea: A set is a 'proper subset' of another set if some things in the large set are not in the smaller set | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| Full Idea: A 'singleton' is a set with only one member. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4) |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| Full Idea: A 'member' of a set is one of the objects in the set. | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2) |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| Full Idea: The empty set Φ is a subset of every set (including itself). | |
| From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6) |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976). |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| Full Idea: A natural principle is the same kind of paradox will have the same kind of solution. Standardly Ramsey's first group are solved by denying the existence of some totality, and the second group are less clear. But denial of the groups sink both. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §5) | |
| A reaction: [compressed] This sums up the argument of Priest's paper, which is that it is Ramsey's division into two kinds (see Idea 13334) which is preventing us from getting to grips with the paradoxes. Priest, notoriously, just lives with them. |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| Full Idea: König: there are indefinable ordinals, and the least indefinable ordinal has just been defined in that very phrase. (Recall that something is definable iff there is a (non-indexical) noun-phrase that refers to it). | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: Priest makes great subsequent use of this one, but it feels like a card trick. 'Everything indefinable has now been defined' (by the subject of this sentence)? König, of course, does manage to pick out one particular object. |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| Full Idea: Berry: if we take 'x is a natural number definable in less than 19 words', we can generate a number which is and is not one of these numbers. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [not enough space to spell this one out in full] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| Full Idea: Richard: φ(x) is 'x is a definable real number between 0 and 1' and ψ(x) is 'x is definable'. We can define a real by diagonalization so that it is not in x. It is and isn't in the set of reals. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [this isn't fully clear here because it is compressed] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| Full Idea: Burali-Forti: φ(x) is 'x is an ordinal', and so w is the set of all ordinals, On; δ(x) is the least ordinal greater than every member of x (abbreviation: log(x)). The contradiction is that log(On)∈On and log(On)∉On. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| Full Idea: Mirimanoff: φ(x) is 'x is well founded', so that w is the cumulative hierarchy of sets, V; &delta(x) is just the power set of x, P(x). If x⊆V, then V∈V and V∉V, since δ(V) is just V itself. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| Full Idea: In the family of the Liar is the Knower Paradox, where φ(x) is 'x is known to be true', and there is a set of known things, Kn. By knowing a sentence is not in the known sentences, you know its truth. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [mostly my wording] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| Full Idea: There are liar chains which fit the pattern of Transcendence and Closure, as can be seen with the simplest case of the Liar Pair. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [Priest gives full details] Priest's idea is that Closure is when a set is announced as complete, and Transcendence is when the set is forced to expand. He claims that the two keep coming into conflict. |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types. |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213). |
| 6262 | We lack some sense or other, and hence objects may have hidden features [Montaigne] |
| Full Idea: We may all lack some sense or other; because of that defect, most of the features of objects may be concealed from us. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0666) | |
| A reaction: This strikes me as simple, straightforward common sense, and right. I cannot make sense of the claim that reality really is just the way it appears. We do not have a built-in neutrino detector, for example. |
| 6260 | Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne] |
| Full Idea: Pyrrhonians say that truth and falsehood exist; within us we have means of looking for them, but not of making any lasting judgements: we have no touchstone. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0564) | |
| A reaction: This states the key difference between sceptics and relativists. The latter are more extreme as they say there is no such thing as truth. The former concede truth, and their scepticism is about the abilities of human beings. I am an anti-relativist. |
| 6261 | The soul is in the brain, as shown by head injuries [Montaigne] |
| Full Idea: The seat of the powers of the soul is in the brain, as is clearly shown by the fact that wounds and accidents affecting the head immediately harm the faculties of the soul. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0614) | |
| A reaction: At last someone has finally got the facts clear. It seems surprising that the Greeks never clearly grasped this piece of irrefutable evidence - even those Greeks who speculated that the brain was the key. Here we have a fixed fact of philosophy of mind. |
| 7496 | Rules and duties are based on the will, as that is all we control [Montaigne] |
| Full Idea: Since actions and performances are not wholly in our power and since nothing is really in our power but our will - it is on the will that all the rules and duties of Man are based and established. | |
| From: Michel de Montaigne (I.7 Our deeds are judged by intention [1580], p.0028) | |
| A reaction: This is almost Kant's claim that the only truly good thing is a good will (e.g. Idea 3711). Aristotle disagrees, because a virtuous person should also have good desires. We may will to have good desires, but virtue requires actually having them. |
| 7495 | Apart from the fear, dying is an easy duty [Montaigne] |
| Full Idea: If our fears did not lend it weight, dying would be one of our lighter duties. | |
| From: Michel de Montaigne (III.12 On physiognomy [1580], p.1191) | |
| A reaction: An Epicurean thought. 'Duties' is nice - presumably death qualifies as a duty, because Nature requires it of us (we each of us 'owe nature a death'). The remark appears to me to be true. |
| 22269 | We must fight fiercely to hang on to the few pleasures which survive into old age [Montaigne] |
| Full Idea: I am training and sharpening my appetite for those pleasures that are left. ...We must cling tooth and claw to the use of the pleasures of this life which the advancing years, one after another, rip from our grasp. | |
| From: Michel de Montaigne (I.39 On Solitude [1580], p.276) | |
| A reaction: That may be one of the most inspiring ideas I have read about pleasure. |
| 20482 | Virtue inspires Stoics, but I want a good temperament [Montaigne] |
| Full Idea: What Stoics did from virtue I teach myself to do from temperament. | |
| From: Michel de Montaigne (III.10 On Restraining your Will [1580], p.1153) | |
| A reaction: I take this to be an Aristotelian criticism of Stoicism. They venerate virtue above everything, but Aristotle says you must integrate virtue into your very being, so that right actions flow from you, with very little need for premeditation. |
| 20480 | There is not much point in only becoming good near the end of your life [Montaigne] |
| Full Idea: It is almost better never to become a good man at all than to do so tardily, understanding how to live when you have no life left. | |
| From: Michel de Montaigne (III.10 On Restraining your Will [1580], p.1142) | |
| A reaction: A very nice perspective, which I don't recall Aristotle mentioning. It does, though, reinforce Aristotle's belief that early training is essential. |
| 20481 | Nothing we say can be worse than unsaying it in the face of authority [Montaigne] |
| Full Idea: Nothing which a gentleman says can seem worse than the shame of his unsaying it under duress from authority. | |
| From: Michel de Montaigne (III.10 On Restraining your Will [1580], p.1153) | |
| A reaction: The point is that you have to fight every day for free speech, because no matter what the law says, there are always people in power who want to shut you up. |
| 20479 | People at home care far more than soldiers risking death about the outcome of wars [Montaigne] |
| Full Idea: How many soldiers put themselves at risk every day in wars which they care little about, rushing into danger in battles the loss of which will not make them lose a night's sleep. Meanwhile a man at home is more passionate about the war than the soldier. | |
| From: Michel de Montaigne (III.10 On Restraining your Will [1580], p.1139) | |
| A reaction: It depends whether you are a mercenary (which the majority probably were in 1680), and what are the implications of defeat. |