46 ideas
| 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'? |
| 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) |
| 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. |
| 20400 | Intentions either succeed or fail, so external evidence for them is always irrelevant [Wimsatt/Beardsley, by Davies,S] |
| Full Idea: Wimsatt and Beardsley claimed that either the intention succeeded, so one does not need to look outside the work for its meaning, or the intention failed, so external evidence does not help. | |
| From: report of W Wimsatt/W Beardsley (The Intentional Fallacy [1946]) by Stephen Davies - The Philosophy of Art (2nd ed) 5.3 | |
| A reaction: Actually, the external evidence may tell you much more clearly and accurately what the intention was than the work itself does. The best example may be the title of the work, which is presumably outside the work. |
| 7266 | The author's intentions are irrelevant to the judgement of a work's success [Wimsatt/Beardsley] |
| Full Idea: The design or intention of the author is neither available nor desirable as a standard for judging the success of a work of literary art. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §I) | |
| A reaction: This famous proposal may have been misunderstood. Note that it is a comment about judging the work, not about understanding it. The idea allows for a work being much more successful than the author's humble intentions (e.g. Pepys). |
| 7267 | Poetry, unlike messages, can be successful without communicating intentions [Wimsatt/Beardsley] |
| Full Idea: Poetry differs from practical messages, which are successful if and only if we correctly infer the intention. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §I) | |
| A reaction: I am not convinced by this claim. It is plausible that a work does much more than it intends (Astaire said he danced "to make a buck"), but it is rather odd to rate very highly a work of which you have missed the point. |
| 7268 | The thoughts of a poem should be imputed to the dramatic speaker, and hardly at all to the poet [Wimsatt/Beardsley] |
| Full Idea: We ought to impute the thoughts and attitudes of the poem immediately to the dramatic speaker, and if to the author at all, only by an act of biographical inference. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §I) | |
| A reaction: Wrong. If in Browning's "My Last Duchess" (say), we only inferred the mind of the speaker (and his Duchess), and took no interest in Browning's view of things, we would miss the point. We might end up respecting the Duke, which would be daft. |
| 7269 | The intentional fallacy is a romantic one [Wimsatt/Beardsley] |
| Full Idea: The intentional fallacy is a romantic one. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §II) | |
| A reaction: Wrong. Even with those most famous of anonymous artists, the architects and carvers of medieval cathedrals, without some discernment of the purpose you won't get it. The Taj Mahal is a love letter, not a potential ice cream parlour. |
| 7271 | Biography can reveal meanings and dramatic character, as well as possible intentions [Wimsatt/Beardsley] |
| Full Idea: The use of biographical evidence need not involve intentionalism, because while it may be evidence of what the author intended, it may also be evidence of the meaning of his words and the dramatic character of his utterance. | |
| From: W Wimsatt/W Beardsley (The Intentional Fallacy [1946], §IV) | |
| A reaction: I am very keen to penetrate the author's intentions, but I have always be doubtful about the use of biography as a means to achieve this. Most of the effort to infer intentions must come from a study of the work itself, not introductions, letters etc. |
| 4787 | Causation interaction is an exchange of conserved quantities, such as mass, energy or charge [Dowe, by Psillos] |
| Full Idea: Dowe argues that a 'causal process' is a world line of an object with a conserved quantity (such as mass, energy, momentum, charge), and a 'causal interaction' is an exchange between two such objects. | |
| From: report of Phil Dowe (Physical Causation [2000]) by Stathis Psillos - Causation and Explanation §4.4 | |
| A reaction: This looks very promising. Nice distinction between causal process and causal interaction. 'Conserved quantities' is better physics than just 'energy'. We can hand causation over to the scientist? |
| 14586 | Physical causation consists in transference of conserved quantities [Dowe, by Mumford/Anjum] |
| Full Idea: For Dowe physical causation consists in transference of conserved quantities. | |
| From: report of Phil Dowe (Physical Causation [2000]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 10.2 | |
| A reaction: [see Psillos 2002 on this] This is evidently a modification of the idea of physical causation as energy-transfer, but narrowing it down to exclude trivial cases. I guess. Need better physics. |
| 4788 | Dowe commends the Conserved Quantity theory as it avoids mention of counterfactuals [Dowe, by Psillos] |
| Full Idea: Dowe commends the Conserved Quantity theory because it avoids any mention of counterfactuals. | |
| From: report of Phil Dowe (Physical Causation [2000]) by Stathis Psillos - Causation and Explanation §4.4 | |
| A reaction: Clearly the truth of a counterfactual is quite a problem for an empiricist/scientist, but one needs to distinguish between reality and our grasp of it. We commit ourselves to counterfactuals, even if causation is transfer of conserved quantities. |