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All the ideas for 'works', 'Travels in Four Dimensions' and 'Structures and Structuralism in Phil of Maths'

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50 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
     Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
     Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do?
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
     Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
     Full Idea: 'Analysis' is the theory of the real numbers.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
     Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
     Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'!
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
     Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
     Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
     Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight?
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
     Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6)
     A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start.
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
     Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7)
     A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds..
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
     Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9)
     A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind?
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
     Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3)
     A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations.
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
     Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
     Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator.
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
     Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
     Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity.
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
A thing which makes no difference seems unlikely to exist [Le Poidevin]
     Full Idea: It is a powerful argument for something's non-existence that it would make absolutely no difference.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 02 'Everything')
     A reaction: Powerful, but not conclusive. Neutrinos don't seem to do much, so it isn't far from there to get a particle which does nothing.
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
     Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity.
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
In addition to causal explanations, they can also be inferential, or definitional, or purposive [Le Poidevin]
     Full Idea: Not all explanations are causal. We can explain some things by showing what follows logically from what, or what is required by the definition of a term, or in terms of purpose.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'Limits')
     A reaction: Would these fully qualify as 'explanations'? You don't explain the sea by saying that 'wet' is part of its definition.
19. Language / C. Assigning Meanings / 9. Indexical Semantics
We don't just describe a time as 'now' from a private viewpoint, but as a fact about the world [Le Poidevin]
     Full Idea: In describing a time as 'now' one is not merely describing the world from one's own point of view, but describing the world as it is.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Mystery')
     A reaction: If we accept this view (which implies absolute time, and the A-series view), then 'now' is not an indexical, in the way that 'I' and 'here' are indexicals.
26. Natural Theory / C. Causation / 1. Causation
The logical properties of causation are asymmetry, transitivity and irreflexivity [Le Poidevin]
     Full Idea: The usual logical properties of the causal relation are asymmetry (one-way), transitivity and irreflexivity (no self-causing).
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'Great')
     A reaction: If two balls rebound off each other, that is only asymmetric if we split the action into two parts, which may be a fiction. Does a bomb cause its own destruction?
27. Natural Reality / C. Space / 3. Points in Space
We can identify unoccupied points in space, so they must exist [Le Poidevin]
     Full Idea: If the midpoint on a line between the chair and the window is five feet from the end of the bookcase. This can be true, but if no object occupies that midpoint, then unoccupied points exist
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Lessons')
     A reaction: We can also locate perfect circles (running through fairy rings, or the rings of Saturn), so they must also exist. But then we can also locate the Loch Ness monster. Hm.
If spatial points exist, then they must be stationary, by definition [Le Poidevin]
     Full Idea: If there are such things as points in space, independently of any other object, then these points are by definition stationary (since to be stationary is to stay in the same place, and a point is a place).
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Search')
     A reaction: So what happens if the whole universe moves ten metres to the left? Is the universe defined by the objects in it (which vary), or by the space that contains them? Why can't a location move, even if that is by definition undetectable?
27. Natural Reality / C. Space / 4. Substantival Space
Absolute space explains actual and potential positions, and geometrical truths [Le Poidevin]
     Full Idea: Absolutists say space plays a number of roles. It is what we refer to when we talk of positions. It makes other things possible (by moving into unoccupied positions). And it explains geometrical truths.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Redundancy')
     A reaction: I am persuaded by these, and am happy to treat space (and time) as a primitive of metaphysics.
27. Natural Reality / C. Space / 5. Relational Space
For relationists moving an object beyond the edge of space creates new space [Le Poidevin]
     Full Idea: For the relationist, if Archytas goes to the edge of space and extends his arm, he is creating a new spatial relation between objects, and thus extending space, which is, after all, just the collection of thos relations.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'beyond')
     A reaction: The obvious point is what are you moving your arm into? And how can some movements be in space, while others create new space? It's a bad theory.
27. Natural Reality / C. Space / 6. Space-Time
We distinguish time from space, because it passes, and it has a unique present moment [Le Poidevin]
     Full Idea: The most characteristic features of time, which distinguish it from space, are the fact that time passes, and the fact that the present is in some sense unique
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Mystery')
     A reaction: The B-series view tries to avoid passing time and present moments. I suspect that modern proponents of the B-series mainly want to unifying their view of time with Einstein's, to give us a scientific space-time.
27. Natural Reality / D. Time / 1. Nature of Time / e. Eventless time
Since nothing occurs in a temporal vacuum, there is no way to measure its length [Le Poidevin]
     Full Idea: Since, by definition, nothing happens in a temporal vacuum, there is no possible means of determining its length.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 02 'without change')
     A reaction: This is offered a part of a dubious proof that a temporal vacuum is impossible. I like Shoemaker's three worlds thought experiment, which tests this idea to the limit.
Temporal vacuums would be unexperienced, unmeasured, and unending [Le Poidevin]
     Full Idea: Three arguments that a temporal vacuum is impossible: we can't experience it, we can't measure it, and it would have no reason to ever terminate.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Lessons')
     A reaction: [summarised] The first two reasons are unimpressive. The interiors of black holes are off limits for us. The arrival of time into a timeless situation may actually have occurred, but be beyond our understanding.
27. Natural Reality / D. Time / 2. Passage of Time / b. Rate of time
Time can't speed up or slow down, so it doesn't seem to be a 'process' [Le Poidevin]
     Full Idea: Processes can speed up or slow down, but surely the passage of time is not something that can speed up or slow down?
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Mystery')
     A reaction: If something is a process we can ask 'process of what?', but the only answer seems to be that it's a process of processing. So it is that which makes processes possible (and so, as I keep saying) it is best viewed as a primitive.
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
The B-series doesn't seem to allow change [Le Poidevin]
     Full Idea: How can anything change in a B-universe?
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Second')
     A reaction: It seems that change needs time to move on. A timeless series of varying states doesn't seem to be the same thing as change. B-seriesers must be tempted to deny change, and yet nothing seems more obvious to us than change.
To say that the past causes the present needs them both to be equally real [Le Poidevin]
     Full Idea: The causal connection between the past and the present seems to require that the past is as real as the present.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'First')
     A reaction: Cause and effect need to conjoin in space, but their subsequent separation doesn't seem to be a problem. The idea that causes and their effects must be eternally compresent is an absurdity.
If the B-universe is eternal, why am I trapped in a changing moment of it? [Le Poidevin]
     Full Idea: What in the B-universe determines my temporal perspective? I can move around in space at will, but I have no choice over where I am in time. What time I am is something that changes, and again I have no control over that
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Second')
     A reaction: The B-series always has to be asserted from the point of view of eternity (e.g. by Einstein). Yet an omniscient mind would still see each of us trapped in our transient moments, so that is part of eternal reality.
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
Time's arrow is not causal if there is no temporal gap between cause and effect [Le Poidevin]
     Full Idea: If there is no temporal gap between cause and effect, then the causal analysis of time's arrow is doomed.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'simultaneous')
     A reaction: A number of recent commentators have rejected the sharp distinction between cause and effect, seeing it as a unified process (which takes time to occur).
An ordered series can be undirected, but time favours moving from earlier to later [Le Poidevin]
     Full Idea: A series can be ordered without being directed (such as the series of integers), …but the passage of time indicates a preferred direction, moving from earlier to later events, and never the other way around.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Hidden')
     A reaction: I wonder what 'preferred' means here? It is not just memory versus anticipation. The saddest words in the English language are 'Too late!'. It is absurd to say that being too late is an illusion.
If time's arrow is causal, how can there be non-simultaneous events that are causally unconnected? [Le Poidevin]
     Full Idea: An objection to the Causal analysis of time's arrow is that it is surely possible for non-simultaneous events to be causally unconnected.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Seeds')
     A reaction: I suppose the events could be linked causally by intermediaries. If reality is a vast causal nexus, everything leads to everything else, in some remote way. It's still a good objections, though.
If time's arrow is psychological then different minds can impose different orders on events [Le Poidevin]
     Full Idea: If the Psychological account of time's arrow is correct …then there is nothing to prevent different minds from imposing different orders on the world.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'The mind's')
     A reaction: All we need is for two people to disagree about the order of some past events. The idea that we are psychologically creating time's arrow when everyone feels they are its victims strikes me as a particularly silly theory.
There are Thermodynamic, Psychological and Causal arrows of time [Le Poidevin]
     Full Idea: The three most significant arrows of time are the Thermodynamic (the direction from order to disorder), the Psychological (from perceptions of events to memories), and the Causal (from cause to effect).
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Three')
     A reaction: It would be nice if one of these explained the other two. Le Poidevin rejects the Psychological arrow, and seems to favour the Causal. Since I favour taking time as a primitive, I'm inclined to think that the arrow is included in the deal.
Presumably if time's arrow is thermodynamic then time ends when entropy is complete [Le Poidevin]
     Full Idea: One consequence of the Thermodynamic analysis of time's arrow is that a universe in which things are as disordered as they could be would exhibit no direction of time at all, because there would be no more significant changes in entropy.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Three')
     A reaction: And presumably time would gradually fizzle out, rather than ending abruptly. If entropy then went into reverse, there would be no time interval between the end and the new beginning. Entropy can vary locally, so it has to be universal.
If time is thermodynamic then entropy is necessary - but the theory says it is probable [Le Poidevin]
     Full Idea: The Second Law of Thermodynamics says it is overwhelmingly probable that entropy will increase. This leaves the door open for occasional isolated instances of decrease. But the thermodynamic arrow makes the increase a necessity.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Three')
     A reaction: Le Poidevin sees this as a clincher against the thermodynamic explanation of the arrow. I'm now sure how the Second Law can even be stated without explicit or implicit reference to time.
27. Natural Reality / D. Time / 2. Passage of Time / i. Time and motion
Instantaneous motion is an intrinsic disposition to be elsewhere [Le Poidevin]
     Full Idea: Being in motion at a particular time can be an intrinsic property of an object, as a disposition to be elsewhere than the place it is.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'in present')
     A reaction: This needs an ontology which includes unrealised dispositions. People trapped in boring meetings have a disposition to be elsewhere, but they are stuck. I think 'power' is a better word here than 'disposition'. The disposition isn't just for 'elsewhere'.
The dynamic view of motion says it is primitive, and not reducible to objects, properties and times [Le Poidevin]
     Full Idea: According to the dynamic account of motion, an object's being in motion is a primitive event, not further analysable in terms of objects, properties and times.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'Zeno')
     A reaction: [The rival view is 'static'] Physics suggests that motion may be indefinable, but acceleration can be given a reductive account. If time and space are taken as primitive (which seems sensible to me), then making motion also primitive is a bit greedy.
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
If the present could have diverse pasts, then past truths can't have present truthmakers [Le Poidevin]
     Full Idea: If any number of pasts are compatible with the present state of affairs, and it is only the present state of affairs which can make true or false statements about the past, then no statement about the past is either true or false.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'First')
     A reaction: He suggests an explosion which could have had innumerable different causes. The explosion could have had different origins, but not sure that the whole of present reality could. Presentists certainly have problems with truthmakers for the past.
27. Natural Reality / D. Time / 3. Parts of Time / a. Beginning of time
The present is the past/future boundary, so the first moment of time was not present [Le Poidevin]
     Full Idea: The present is the boundary between past and future, therefore if there was a first moment of time, it could not have been present - because there can be no past at the beginning of time.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'Limits')
     A reaction: How about at the start of a race the athletes cannot be running. How about 'all moments of time have preceding moments - apart from the first moment'?
27. Natural Reality / D. Time / 3. Parts of Time / c. Intervals
The primitive parts of time are intervals, not instants [Le Poidevin]
     Full Idea: Intervals of time can be viewed as primitive, and not decomposable into a series of instants.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'in present')
     A reaction: Given that instants are nothing, and intervals are something, the latter are clearly the better candidates to be the parts of time. Is there a smallest interval?
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
If time is infinitely divisible, then the present must be infinitely short [Le Poidevin]
     Full Idea: Assuming time to be infinitely divisible, the present can have no duration at all, for if it did, we could divide it into parts, and some parts would be earlier than others.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'in present')
     A reaction: I quite like Aristotle's view that things only have parts when you actually divide them. In modern physics fields don't seem to be infinitely divisible. It's a puzzle, though, innit?
27. Natural Reality / E. Cosmology / 10. Multiverse
The multiverse is distinct time-series, as well as spaces [Le Poidevin]
     Full Idea: The multiverse is not just a collection of distinct spaces, it is also a collection of distinct time-series.
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 11 'Objections')
     A reaction: This boggles the imagination even more than distinct spatial universes.
28. God / A. Divine Nature / 5. God and Time
How could a timeless God know what time it is? So could God be both timeless and omniscient? [Le Poidevin]
     Full Idea: Could a timeless being now know what the time was? If so, does this show that there must be something wrong with the idea of God as both timeless and omniscient?
     From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'Questions')
     A reaction: This is a potential contradiction between the perfections of a supreme God which I had not noticed before. Leibniz tried to refute such objections, but not very successfully, I think.
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
     Full Idea: Philosophers are the forefathers of heretics.
     From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]
     Full Idea: I believe because it is absurd ('Credo quia absurdum est').
     From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
     A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.