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    (Original post by HearTheThunder)
    But the arrow cannot move within this length it occupies. It would need extra space in which to move, and it of course has none. So at every point in its flight, the arrow is at rest. And if then it follows that it is at rest during the entire flight.
    It's nonsense because an arrow is not fixed in length. It is composed of atoms which are moving continually. Of course, Zeno couldn't know that, but he ought to have known the obvious solution: the space which an arrow occupies is not fixed in some absolute medium. It doesn't exist as an object.

    Anyway, I thought the paradox was based on the asymptote - that an arrow has to travel half the distance, then half the next distance etc. ad infinitum. So it never actually arrives.
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    (Original post by grumballcake)
    It's nonsense because an arrow is not fixed in length. It is composed of atoms which are moving continually. Of course, Zeno couldn't know that, but he ought to have known the obvious solution: the space which an arrow occupies is not fixed in some absolute medium. It doesn't exist as an object.

    Anyway, I thought the paradox was based on the asymptote - that an arrow has to travel half the distance, then half the next distance etc. ad infinitum. So it never actually arrives.
    Oh yeah I know that, but you have to admit it is an interesting notion of logical fallacies :p: And yeah that's another one of his paradoxes, that has also been disproven in modern times. I want a good argument against Descartes' Cogito myself :cool:
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    (Original post by HearTheThunder)
    I want a good argument against Descartes' Cogito myself :cool:
    They're not hard to come by

    How about: if doubting everything, he should have also doubted the reliability of memory. If doubting the reliability of memory, all he could be sure of was any current sensations/perceptions, and not a chain of them such as would be sufficient to posit the existence of some single, continuous thinking "thing" behind it all. Ie. he would only ever be sure of one single fleeting immediate perception and then would have to doubt that it had happened the very next minute - so where's this "self"? Is a single fleeting act of doubting enough to establish one?

    Meh, I dunno. Tbh I've forgotten them all but that springs to mind and I don't think I've recalled it too inaccurately for it to make sense...:s

    ZarathustraX

    EDIT: You wouldn't be getting us to do your homework for you by any chance, would you? :rolleyes:
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    (Original post by Zarathustra)
    They're not hard to come by

    How about: if doubting everything, he should have also doubted the reliability of memory. If doubting the reliability of memory, all he could be sure of was any current sensations/perceptions, and not a chain of them such as would be sufficient to posit the existence of some single, continuous thinking "thing" behind it all. Ie. he would only ever be sure of one single fleeting immediate perception and then would have to doubt that it had happened the very next minute - so where's this "self"? Is a single fleeting act of doubting enough to establish one?

    Meh, I dunno. Tbh I've forgotten them all but that springs to mind and I don't think I've recalled it too inaccurately for it to make sense...:s

    ZarathustraX

    EDIT: You wouldn't be getting us to do your homework for you by any chance, would you? :rolleyes:
    Hmmm. Following that argument (which I pretty much agree with) it becomes pretty much impossible to establish more than 'something exists'.

    As for Xeno, there were three famous paradoxes - HTT's one, grumballcakes one, and another one that I can't remember. The 'atoms' answer doens't really wash because the paradoxes aren't really about objects (they can just as easily be applied to point particles) but about whether space and time are continuous or discrete (they're supposed to disprove both). I'd say that if you allow an 'instant' of time, something which is kind of dubious anyway, an object in motion is distinguished from one at rest by the fact that it possesses momentum.
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    (Original post by wanderer)
    Hmmm. Following that argument (which I pretty much agree with) it becomes pretty much impossible to establish more than 'something exists'.
    Only if you insist on Cartesian doubt as a starting point

    ZarathustraX
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    (Original post by Zarathustra)
    Only if you insist on Cartesian doubt as a starting point

    ZarathustraX
    Give me a better one then! :p:
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    Two points: Zeno One how is momentum to exist if time is fixed? Surely momentum is only a measurement of some kind of effect in time? We say something has momentum if it does this in Time x. How can it have momentum if time is fixed at an instant?

    My confusion is this idea that something cannot move in its own space. I'll accept it can't but I don't see how that stops it moving. After all arguably movement is movement through spaces, not in spaces.


    As for arguments against Descartes. Well he's probably right... if you want to call knowledge "that of which we can be certain". But why do you want to call it that? Call that Knowledge1. That's certainly not all the word means. I might say "look, I know your angry but..." I don't mean i'm certain you're angry, I just mean I'm aware of it. Call that Knowledge2. I'm sure there are lots of other ways we can understand "knowledge". Descarte ignores all uses of the word knowledge but his own special use, so it's harldy surprising his argument is so counter intuitive.
    But then if you accept his use as a special case, its hardly surprising he proves what he does. After all, I can say no people exist if I define 'person' rigorously enough.

    That being said, even if we accept Descartes point. How can he be certain he's considered every possibility? Maybe he's being unimaginative in thinking he cannot doubt his own existence. Just because he can't think of how its possible now doesn't mean its impossible. So how can he really be certain of anything? There is always the chance he hasn't considered every logical possibility.
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    (Original post by Calvin)
    Two points: Zeno One how is momentum to exist if time is fixed? Surely momentum is only a measurement of some kind of effect in time? We say something has momentum if it does this in Time x. How can it have momentum if time is fixed at an instant?

    My confusion is this idea that something cannot move in its own space. I'll accept it can't but I don't see how that stops it moving. After all arguably movement is movement through spaces, not in spaces.
    It has momentum because it possesses kinetic energy. You may argue that the only way you can show it has kinetic energy is by letting time flow - but that doesn't mean that in a single instant it doesn't have it. You need time to make any kind of observation anyway.

    (Original post by Calvin)
    As for arguments against Descartes. Well he's probably right... if you want to call knowledge "that of which we can be certain". But why do you want to call it that? Call that Knowledge1. That's certainly not all the word means. I might say "look, I know your angry but..." I don't mean i'm certain you're angry, I just mean I'm aware of it. Call that Knowledge2. I'm sure there are lots of other ways we can understand "knowledge". Descarte ignores all uses of the word knowledge but his own special use, so it's harldy surprising his argument is so counter intuitive.
    But then if you accept his use as a special case, its hardly surprising he proves what he does. After all, I can say no people exist if I define 'person' rigorously enough.

    That being said, even if we accept Descartes point. How can he be certain he's considered every possibility? Maybe he's being unimaginative in thinking he cannot doubt his own existence. Just because he can't think of how its possible now doesn't mean its impossible. So how can he really be certain of anything? There is always the chance he hasn't considered every logical possibility.
    The conclusion that we can't be certain of anything much comes up again. Saying that knowledge is more than certainty kind of misses out on the fairly massive repurcussions of that statement.
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    (Original post by Calvin)
    Surely momentum is only a measurement of some kind of effect in time? We say something has momentum if it does this in Time x. How can it have momentum if time is fixed at an instant?
    Momentum = mass x velocity. So momentum is related to time by velocity - if there is velocity, then there is momentum. Time is not a thing, but a dimension. If an object has length, that's simply an extension in one dimension, but it also extends in time. You cannot separate out time from space - since Einstein, we've known that the two are inseperable. If an object exists in space, it also exists in time.

    The "moving in space" bit is nonsense. It's just misunderstanding how things work. An object does not move by moving in its space - it moves relative to other objects. As it moves, it also experiences relative time shift, so it's not on the same time as any other object wither. What we see is the relationship between objects, but that's not an object in itself. There's a famous paradox when you close a pair of scissors. If you look at the point where the two blades interect, it moves forward as the blades close. This point can actually move faster than light as you snap them shut. It can do so, because it doesn't exist as such, so isn't contrained like a physical object would be.
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    (Original post by wanderer)
    The conclusion that we can't be certain of anything much comes up again. Saying that knowledge is more than certainty kind of misses out on the fairly massive repurcussions of that statement.

    I'm not entirely sure what you mean here. I'm saying that Descartes point applies to everything and as such if we follow through his reasoning then we cannot be sure of anything at all, including his cogito and all the more fundamental things people have invented since "something exists" etc.

    As for saying that knowledge is more than certainty... what are the massive reprocussions you're talking about?


    (Original post by Grumballcake)
    Momentum = mass x velocity. So momentum is related to time by velocity - if there is velocity, then there is momentum. Time is not a thing, but a dimension. If an object has length, that's simply an extension in one dimension, but it also extends in time. You cannot separate out time from space - since Einstein, we've known that the two are inseperable. If an object exists in space, it also exists in time.
    Good point, I'm not too hot on Einstein but surely if Time is a dimension then it can at least be conceptually seperated from the other three space dimensions; if Time is a dimension then it would suggest the two things (space and time) are interrelated, but not logically dependent. No?

    I guess what I was trying to say is that momentum can only be understood dispositionally. After all, we invent things like energy in order to explain what happens. Thus momentum and energy, as they are dispositional concepts, require time to be meaningful.
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    (Original post by Calvin)
    if Time is a dimension then it can at least be conceptually seperated from the other three space dimensions; if Time is a dimension then it would suggest the two things (space and time) are interrelated, but not logically dependent. No?
    Not quite. There aren't two things: space and time, there's just one - spacetime. We conceptually divide it into four dimensions, three of which we can move in freely and the fourth in which we can only move (at present) in one. However, if you move in space, relative to something else, the speed at which you move will affect the time which you experience while moving. Your mass and size will also change - the faster you move, the more massive (but the smaller) you will become.
    I guess what I was trying to say is that momentum can only be understood dispositionally.
    I'm not sure what you mean by this. Are you arguing that we've experienced it in a particular way, so we explain it in that context?
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    (Original post by grumballcake)
    Not quite. There aren't two things: space and time, there's just one - spacetime. We conceptually divide it into four dimensions, three of which we can move in freely and the fourth in which we can only move (at present) in one. However, if you move in space, relative to something else, the speed at which you move will affect the time which you experience while moving. Your mass and size will also change - the faster you move, the more massive (but the smaller) you will become.
    Gotcha
    (Original post by grumballcake)
    I'm not sure what you mean by this. Are you arguing that we've experienced it in a particular way, so we explain it in that context?
    I'm saying that we use the idea of energy as a model to explain what we see. It isn't that things have energy, we interpret them as having energy as part of our model of the universe. Without time, to say something has momentum makes no sense because the idea of momentum is based on modelling what happens. If there is no time, nothing is happening. If we are ignoring time nothing is happening and 'energy' is essentially meaningless.
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    (Original post by Calvin)
    I'm not entirely sure what you mean here. I'm saying that Descartes point applies to everything and as such if we follow through his reasoning then we cannot be sure of anything at all, including his cogito and all the more fundamental things people have invented since "something exists" etc.

    As for saying that knowledge is more than certainty... what are the massive reprocussions you're talking about?
    You just stated them. Philosophers have a tendency to be a bit blasé about the idea that we can't be certain of anything - it comes as a shock to most lay people, and it's certainly pretty alien to the way we normally think of things. And aren't you saying that knowledge is less than certainty, rather than the other way around?

    P.S

    I do actually agree with you, btw.
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    (Original post by wanderer)
    You just stated them. Philosophers have a tendency to be a bit blasé about the idea that we can't be certain of anything - it comes as a shock to most lay people, and it's certainly pretty alien to the way we normally think of things. And aren't you saying that knowledge is less than certainty, rather than the other way around?

    P.S

    I do actually agree with you, btw.
    But even certainty. I'm certain there is a lamp in front of me. I'd normally say that. But if you start raising doubts like "well what if you're really asleep and dreaming" then I might agree I'm not certain. The more crazy examples you give the wider I make my understanding of certainty. Arguably it isn't that I'm not certain of anything but rather that I always have the possibility of retracting my statement of certainty given more and more outlandish suggestions. Again, you can always raise points I've never considered. Perhaps thus making the same point I made earlier- we are limited beings!

    (not sure about this post, it's meant to be a tentative suggestion)
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    (Original post by Calvin)
    But even certainty. I'm certain there is a lamp in front of me. I'd normally say that. But if you start raising doubts like "well what if you're really asleep and dreaming" then I might agree I'm not certain. The more crazy examples you give the wider I make my understanding of certainty. Arguably it isn't that I'm not certain of anything but rather that I always have the possibility of retracting my statement of certainty given more and more outlandish suggestions. Again, you can always raise points I've never considered. Perhaps thus making the same point I made earlier- we are limited beings!

    (not sure about this post, it's meant to be a tentative suggestion)
    Hmm. Just thinking that it seems a bit odd, language wise, to talk about 'not being certain of anything'. After all, I'm certain of a lot of things - perhaps its more accurate to say that certainty is generally unfounded. I think what your recasting points at is the idea that certainty has to be construed within given limits or assumptions. Which is still quite hard to deal with coming from a basic 'there is a lamp in front of me and that is absolute truth' viewpoint.
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    Not that certainty has to be construed within limits in natural language. But that any attempt to use it in philosophy will ultimately require precise definition and so precise limits. Perhaps in that definition, in that attempt to clarfy we miss the natural language aspect, we miss the thing we were so interested in in the first place. Admittedly we need need to be clear in philosophy if we want to make progress, but perhaps our progress is always going to be restricted by the formalising of language and the destruction of the murky, imprecise natural language aspect of the word.

    I propose the Calvin-Heisenburg Uncertainty principle for Philosophy: "the more precisely you say what a word means the further you get from understanding the nature of the word in language."

    hehe
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    (Original post by Calvin)
    Not that certainty has to be construed within limits in natural language. But that any attempt to use it in philosophy will ultimately require precise definition and so precise limits. Perhaps in that definition, in that attempt to clarfy we miss the natural language aspect, we miss the thing we were so interested in in the first place. Admittedly we need need to be clear in philosophy if we want to make progress, but perhaps our progress is always going to be restricted by the formalising of language and the destruction of the murky, imprecise natural language aspect of the word.

    I propose the Calvin-Heisenburg Uncertainty principle for Philosophy: "the more precisely you say what a word means the further you get from understanding the nature of the word in language."

    hehe
    Hmm, I think this has got quite interesting. My brother is hassling me of the PC, butI will return with thoughts on this and its implications later.
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    OK. This leads back to you wanting there to be no such thing as meaning, doesn't it? I think the problem runs deeper than this anyway. Even within precise definitions of things, too much is arbitrary, axiomatic, self-referential, assumed.
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    (Original post by Calvin)
    I propose the Calvin-Heisenburg Uncertainty principle for Philosophy: "the more precisely you say what a word means the further you get from understanding the nature of the word in language."
    You're a bit late, I'm afraid. Wittgenstein was saying that 30 years ago.
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    hehe, well ok then The :juggle: Calvin :juggle:-Heisenburg-Wittgenstein Uncertainty Principle for Philosophy
 
 
 
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