55 ideas
| 14018 | Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne] |
| Full Idea: Mackie (1983) dismisses the Principle of Sufficient Reason quickly, arguing that it is self-refuting: there is no sufficient reason to accept it. However, a principle is not invalidated by not applying to itself; it can be a powerful heuristic tool. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.VI) | |
| A reaction: If God was entirely rational, and created everything, that would be a sufficient reason to accept the principle. You would never, though, get to the reason why God was entirely rational. Something will always elude the principle. |
| 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'? |
| 14008 | The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne] |
| Full Idea: The problem with the redundancy theory of truth is that it conflates the metalinguistic notion of bivalence with a theorem of the object language, namely the law of excluded middle. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr3) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
| 14010 | All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne] |
| Full Idea: If there are any genuine relations at all between spatio-temporal objects, then they are all either spatio-temporal or causal. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr4) | |
| A reaction: This sounds too easy, but I have wracked my brains for counterexamples and failed to find any. How about qualitative relations? |
| 14009 | It is a necessary condition for the existence of relations that both of the relata exist [Bourne] |
| Full Idea: It is widely held, and I think correctly so, that a necessary condition for the existence of relations is that both of the relata exist. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr4) | |
| A reaction: This is either trivial or false. Relations in the actual world self-evidently relate components of it. But I seem able to revere Sherlock Holmes, and speculate about relations between possible entities. |
| 14016 | The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne] |
| Full Idea: Special Relativity, with its definition of simultaneity, is shot through with verificationist assumptions. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.IIc) | |
| A reaction: [He credits Sklar with this] I love hearing such points made, because all my instincts have rebelled against Einstein's story, even after I have been repeatedly told how stupid I am, and how I should study more maths etc. |
| 14019 | Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne] |
| Full Idea: Special Relativity denies absolute simultaneity, and therefore requires a past and a future, as well as a present. The Presentist, however, only requires the present. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.VII) | |
| A reaction: It is nice to accuse Relativity of ontological extravagence. When it 'requires' past and future, that may not be a massive commitment, since the whole theory is fairly operationalist, according to Putnam. |
| 14013 | Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne] |
| Full Idea: There is in special relativity a notion of 'absolute past', and of 'absolute future', and of 'absolute elsewhere', and of 'absolute simultaneity' (of events occurring at their space-time conjunction). | |
| From: Craig Bourne (A Future for Presentism [2006], 5.III) | |
| A reaction: [My summary of his paragraph] I am inclined to agree with Bourne that there is enough here to build some sort of notion of 'present' that will support the doctrine of Presentism. |
| 14015 | No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne] |
| Full Idea: 'No-Futurists' believe in the real existence of the past and present but not the future, and hold that the world grows as more and more facts come into existence. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.IIb) | |
| A reaction: [He cites Broad 1923 and Tooley 1997] My sympathies are with Presentism, but there seems not denying that past events fix truths in a way that future events don't. The unchangeability of past events seems to make them factual. |
| 14007 | How can presentists talk of 'earlier than', and distinguish past from future? [Bourne] |
| Full Idea: Presentists have a difficulty with how they can help themselves to the notion of 'earlier than' without having to invoke real relata, and how presentism can distinguish the past from the future. | |
| From: Craig Bourne (A Future for Presentism [2006], 2.IV) | |
| A reaction: The obvious response is to infer the past from the present (fossils), and infer the future from the present (ticking bomb). But what is it that is being inferred, if the past and future are denied a priori? Tricky! |
| 14011 | Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne] |
| Full Idea: It seems that presentism cannot accommodate causation at all. In a true instance of 'c causes e', it seems to follow that both c and e exist, and it is widely accepted that c is earlier than e. But for presentists that means c and e can't coexist. | |
| From: Craig Bourne (A Future for Presentism [2006], 4) | |
| A reaction: A nice problem. Obviously if the flying ball smashed the window, we are left with only the effect existing - otherwise we could intercept the ball and prevent the disaster. To say this cause and this effect coexist would be even dafter than the problem. |
| 14017 | Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne] |
| Full Idea: Since for presentism there is an ontologically significant and basic sense in which events are present, we should expect a definition of simultaneity in terms of presentness, rather than the other way round. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.IV) | |
| A reaction: Love it. I don't see how you can even articulate questions about simultaneity if you don't already have a notion of presentness. What are the relata you are enquiring about? |
| 14003 | Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne] |
| Full Idea: Theories of time are in two broad categories, the tenseless and the tensed theories. In tenseless theories, all times are equally real, as are all objects located at them, and there is no passage of time from future to present to past. It's the B-series. | |
| From: Craig Bourne (A Future for Presentism [2006], Intro IIa) | |
| A reaction: It might solve a few of the problems, but is highly counterintuitive. Presumably it makes the passage of time an illusion, and gives no account of how events 'happen', or of their direction, and it leaves causation out on a limb. I'm afraid not. |
| 14005 | B-series objects relate to each other; A-series objects relate to the present [Bourne] |
| Full Idea: Objects in the B-series are earlier than, later than, or simultaneous with each other, whereas objects in the A-series are earlier than, later than or simultaneous with the present. | |
| From: Craig Bourne (A Future for Presentism [2006], Intro IIb) | |
| A reaction: Must we choose? Two past events relate to each other, but there is a further relation when 'now' falls between the events. If I must choose, I suppose I go for the A-series view. The B-series is a subsequent feat of imagination. McTaggart agreed. |
| 14006 | Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne] |
| Full Idea: We say that time 'flows', that the past is 'fixed' but the future is 'open'; we only dread the future, but not the past; we remember the past but not the future; we plan for the future but not the past. | |
| From: Craig Bourne (A Future for Presentism [2006], Intro III) | |
| A reaction: These seem pretty overwhelming reasons for accepting an asymmetry between the past and the future. If you reject that, you seem to be mired in a multitude of contradictions. Your error theory is going to be massive. |