30 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. |
| 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) |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 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. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4 | |
| A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817). |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
| A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness. |
| 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. |