55 ideas
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| Full Idea: If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence. | |
| From: David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind' | |
| A reaction: If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later. |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists. | |
| From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4 | |
| A reaction: [p.476 in Van Heijenoort] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
| From: David Hilbert (On the Infinite [1925], p.200) | |
| A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
| From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
| A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
| From: David Hilbert (On the Infinite [1925], p.195) | |
| A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| Full Idea: Operating with the infinite can be made certain only by the finitary. | |
| From: David Hilbert (On the Infinite [1925], p.201) | |
| A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
| From: David Hilbert (On the Infinite [1925], p.186) | |
| A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
| 22886 | The modern idea of 'limit' allows infinite quantities to have a finite sum [Bardon] |
| Full Idea: The concept of a 'limit' allows for an infinite number of finite quantities to add up to a finite sum. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 1 'Aristotle's') | |
| A reaction: This is only if the terms 'converge' on some end point. Limits are convenient fictions. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence. | |
| From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist' | |
| A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!). |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
| From: David Hilbert (On the Infinite [1925], p.192) | |
| A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
| From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
| 22914 | An equally good question would be why there was nothing instead of something [Bardon] |
| Full Idea: If there were nothing, then wouldn't it be just as good a question to ask why there is nothing rather than something? There are many ways for there to be something, but only one way for there to be nothing. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 8 'Confronting') | |
| A reaction: [He credits Nozick with the question] I'm not sure whether there being nothing counts as a 'way' of being. If something exists it seems to need a cause, but no cause seems required for the absence of things. Nice, though. |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
| 22902 | Why does an effect require a prior event if the prior event isn't a cause? [Bardon] |
| Full Idea: To say that a reaction requires the earlier presence of an action just raises anew the question of why it is 'required' if it isn't bring about the reaction. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 4 'Pervasive') | |
| A reaction: This is another example of my demand that empiricists don't just describe and report conjunctions and patterns, but make some effort to explain them. |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |
| 22905 | Becoming disordered is much easier for a system than becoming ordered [Bardon] |
| Full Idea: Systems move to a higher state of entropy …because there are very many more ways for a system to be disordered than for it to be ordered. …We can also say that they tend to move from a non-equilibrium state to an equilibrium state. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 5 'Thermodynamic') | |
| A reaction: Is it actually about order, or is it just that energy radiates, and thus disperses? |
| 22913 | The universe expands, so space-time is enlarging [Bardon] |
| Full Idea: More and more space-time is literally being created from nothing all the time as the universe expands. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 8 'Realism') | |
| A reaction: [He cites Paul Davies for this] Is the universe acquiring more space, or is the given space being stretched? Acquiring more time makes no sense, so what is more space-time? |
| 22889 | We should treat time as adverbial, so we don't experience time, we experience things temporally [Bardon, by Bardon] |
| Full Idea: Kant says that instead of focusing on the nouns 'time' and 'space', it would be more on target to focus on the adverbial applications of the concepts - that we don't experience things in time and space so much as experience them temporally and spatially. | |
| From: report of Adrian Bardon (Brief History of the Philosophy of Time [2013]) by Adrian Bardon - Brief History of the Philosophy of Time 2 'Kantian' | |
| A reaction: Put like that, Kant's approach has some plausibility, given that we don't actually experience space and time as entities. To jump from that to idealism seems daft. Does every adverb imply idealism about what it specifies? |
| 22900 | How can we question the passage of time, if the question takes time to ask? [Bardon] |
| Full Idea: Even questioning the passage of time may be self-defeating: can any question be meaningfully asked or understood without presuming the passage of time from the inception of the question to its conclusion? | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 4 'Pervasive') | |
| A reaction: [He cites P.J. Zwart for this] We can at least, in B-series style, specify the starting and finishing times of the question, without talk of its passage. Nice point, though. |
| 22898 | What is time's passage relative to, and how fast does it pass? [Bardon] |
| Full Idea: If time is passing, then relative to what? How could time pass with respect to itself? Further, if time passes, at what rate does it pass? | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 4 'Pervasive') | |
| A reaction: I remember some writer grasping the nettle, and saying that time passes at one second per second. Compare travelling at one metre per metre. |
| 22897 | The A-series says a past event is becoming more past, but how can it do that? [Bardon] |
| Full Idea: In the dynamic theory of time the Battle of Waterloo is become more past. If we insist on the A-series properties, this seems inevitable. But how can a past event be changing now? | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 4 'Reasons') | |
| A reaction: [He cites Ulrich Meyer for this] We don't worry about an object changing its position when it is swept down a river. The location of the Battle of Waterloo relative to 'now' is not a property of the battle. That is a 'Cambridge' property. |
| 22901 | The B-series needs a revised view of causes, laws and explanations [Bardon] |
| Full Idea: If we accept the static (B-series) view, we have to reevaluate how we think about causation, natural laws, and scientific explanation. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 4 'Pervasive') | |
| A reaction: Any scientific account which refers to events seems to imply a dynamic view of time. Lots of scientists and philosophers endorse the static view of time, but then fail to pursue its implications. |
| 22896 | The B-series is realist about time, but idealist about its passage [Bardon] |
| Full Idea: The B-series theorist is a realist about time but an idealist about the passage of time. This is the Static Theory of time. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 4 'Reasons') | |
| A reaction: Note the both A and B are realists about time, and thus deny both the relationist and the idealist view. |
| 22903 | The B-series adds directionality when it accepts 'earlier' and 'later' [Bardon] |
| Full Idea: The static (B-series) theory, by embracing the relational temporal properties 'earlier' and 'later', adds a directional ordering to the block of events. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 5 'Time's') | |
| A reaction: I'm not clear whether this addition to the B-series picture is optional or obligatory. It is important that it seems to be a bolt-on feature, not immediately implied by the timeless series. What would Einstein say? |
| 22910 | To define time's arrow by causation, we need a timeless definition of causation [Bardon] |
| Full Idea: The problem for the causal analysis of temporal asymmetry is to come up with a definition of causation that does not itself rely on the concept of temporal asymmetry. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 5 'Causal') | |
| A reaction: This is the point at which my soul cries out 'time is a primitive concept!' Leibniz want to use dependency to define time's arrow, but how do you specify dependency if you don't know which one came first? |
| 22909 | We judge memories to be of the past because the events cause the memories [Bardon] |
| Full Idea: On the causal view of time's arrow, memories pertain to the 'past' just because they are caused by the events of which they are memories. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 5 'Causal') | |
| A reaction: How am I able to distinguish imagining the future from remembering the past? How do I tell which mental events have external causes, and which are generated by me? |
| 22904 | The psychological arrow of time is the direction from our memories to our anticipations [Bardon] |
| Full Idea: The psychological arrow of time refers to the familiar fact that that we remember (and never anticipate) the past, and anticipate (but never remember) the future. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 5 'Psychological') | |
| A reaction: Bardon rejects this on the grounds that the psychology is obviously the result of the actual order of events. Otherwise time's arrow would just result from the luck of how we individually experience things. |
| 22906 | The direction of entropy is probabilistic, not necessary, so cannot be identical to time's arrow [Bardon] |
| Full Idea: The coincidence of thermodynamic direction and the direction of time is striking, but they can't be one and the same because the thermodynamic law is merely probabilistic. Orderliness could increase, but it is highly improbable | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 5 'Thermodynamic') | |
| A reaction: This seems to be persuasive grounds for rejecting thermodynamics as the explanation of time's arrow. |
| 22907 | It is arbitrary to reverse time in a more orderly universe, but not in a sub-system of it [Bardon] |
| Full Idea: It would seem arbitrary to say that the direction of time is reversed if the whole universe becomes more orderly, but it isn't reversed for any particular sub-system that becomes more orderly. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 5 'Thermodynamic') | |
| A reaction: The thought is that if time's arrow depends on entropy, then the arrow must reverse if entropy were to reverse (however unlikely). |
| 22883 | It seems hard to understand change without understanding time first [Bardon] |
| Full Idea: It is very tough to see how we could understand what change is without understanding what time is. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], Intro) | |
| A reaction: This thought is aimed at those who are hoping to define time in terms of change. My working assumption is that time must be a primitive concept in any metaphysics. |
| 22890 | We experience static states (while walking round a house) and observe change (ship leaving dock) [Bardon] |
| Full Idea: We make a fundamental distinction between perceptions of static states and dynamic processes, …such as walking around a house, and watching a ship leave dock. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 2 'Kantian') | |
| A reaction: This seems to be a fundamental aspect of our mind, rather than of the raw experience (slightly supporting Kant). In both cases we experience a changing sequence, but we have two different interpretations of them. |
| 22884 | The motion of a thing should be a fact in the present moment [Bardon] |
| Full Idea: Whether or not something is in motion should be a fact about that thing now, not a fact about the thing in its past or in its future. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 1 'Arrow') | |
| A reaction: This is one of the present moment, in which nothing can occur if its magnitude is infinitely small. I have no solution to this problem. |
| 22892 | Experiences of motion may be overlapping, thus stretching out the experience [Bardon] |
| Full Idea: Experience itself may be constituted by overlapping, very brief, but temporally extended, acts of awareness, each of which encompassesa temporally extended streeeeetch of perceived events. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 2 'Realism') | |
| A reaction: [cites Barry Dainton 2000] I think this sounds better than Russell's suggestion, though along the same lines. I take all brain events to be a sort of memory, briefly retaining their experience. Very fast events blur because of overload. |
| 22911 | At least eternal time gives time travellers a possible destination [Bardon] |
| Full Idea: If all past, present and future events timelessly coexist, then at least there is a potential destination for the time traveller. …The Presentist treats past and future events as nonexistent, so there is no place for the time traveller to go. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 6 'Fictional') | |
| A reaction: Not a good reason to believe in the eternal block of time, of course. The growing block has a past which can be visited, but no future. |
| 22912 | Time travel is not a paradox if we include it in the eternal continuum of events [Bardon] |
| Full Idea: As long as we understand any time travel events to be timelessly included in the history of the world, and thus as part of the fixed continuum of events, time travel need not give rise to paradox. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], 6 'Time travel') | |
| A reaction: This would presumably block going back and killing your own grandparent. |
| 22882 | We use calendars for the order of events, and clocks for their passing [Bardon] |
| Full Idea: Roughly speaking, we use calendars to track the order of events in time, and clocks to track changes and the passing of events. | |
| From: Adrian Bardon (Brief History of the Philosophy of Time [2013], Intro) | |
| A reaction: So calendars cover the B-Series and clocks the A-Series, showing that this distinction is deeply embedded, and wasn't invented by McTaggart. |