Xeno's Paradoxes

[Hirsap]

I do apologise I didn't realise how many times i posted this thread! first 2 times i reset the thing because i thought it wasn't working.

Hope this is the right thread .

But anyway I'm sure most have heard of them, at least in essence.

That is , to get to point A to point B, you must first go past the half way point. But to reach that half way point, you must reach the half-way point of this half way point, etc etc, ad infinitum. But since an infinite number of points cannot be traversed, the final point cannot be reached, when in observation it can be.

Therefore if one were to accept this theory, he/she would also have to accept that motion itself is an illusion. Obviously this is untenable on the point of natural observation, not to mention the Catholic faith (i would say) which emphasises the capacity for human beings to observe and know correctly the basic things of nature (from our natural reason).

But what does everybody else think? Moreover, how is this resolved?

Edited January 13, 2007 by Hirsap

[Paddington]

Hirsap,

Xeno's paradox is false. There is the idea that things can keep being broken down and down and down without ending. I don't know how much merit there is to that. I guess that could be true. But also if you go from point A to point B.....each step you take would then be infinite. Each step can be broken down and down and down and down. I guess that explains how our "infinite steps" are capable of crossing "infinite space."
Since we take "infinite steps," I guess that it just looks like we're walking slow. We're really cruising faster than the speed of light. But, of course we are not.

Also, take the number 1.

add .1
add.01
add.001
add.0001

Keep adding and you will never reach the number 2 as a sum. Not even close actually. If you don't get to the number 2 this way, then you certainly won't get to infinity. That second illustration might not even be relevant, idunno.

Peace,
Paddington

[Guest JeffCR07]

Hirsap, the "paradoxes" that Zeno invented were created for the purpose of proving the Eleatic thesis that change is impossible, and that the only thing that exists is one, eternal, unchanging, homogeneous whole "What Is." In many respects, we can consider Platonic and Aristotelian philosophy to be an attempt at refuting Parmenides (the founder of the Eleatic school, of which Zeno was a part).

Personally, I find Aristotelian philosophy significantly more persuasive than Platonic thought, and the distinction between potency and anct, and the motion from the former to the latter, provides the solution to such "paradoxes." Most contemporary philosophies, however, do not even treat the problem.

[Laudate_Dominum]

Haha, sweet!

There are numerous "solutions" to Zeno's paradoxes but in my opinion they are still up for discussion and quite interesting. How one answers the paradoxes often says much about the general philosophical assumptions of the answerer.

Perhaps the paradox in question is simply a reification of number? Perhaps it is a misunderstanding of dimension and continuum? In abstract terms a dimension (either spatial or temporal) is continuous and unbroken; perhaps the paradox assumes that the "space" between two points constitutes an actual series of dimensionless "points", which is not a conceptually sound assumption.
Some might like to say that this abstract space is "potentially" infinite, but apart from the demarcation of actual existents in relationality or some external act of division the space is simply continuous and unbroken, thus saying that there is an "actual" infinity of some kind is nonsense.

I suppose there are more naturalistic approaches which would attempt to "solve" the paradoxes via calculus / geometric series, but again this approach, in my opinion, articulates more the philosophical assumptions of the answerer than it does an actual "solution". The grossest supposed solution, which is no doubt out of fashion these days, would be to invoke aspects of quantum mechanics (quantum leap, etc) and in broad terms suggest the actual impossibility of an infinite reduction of dimensional quantities.

I suppose a Kantian could assert an antimony of reason. Anyway, there are, I believe, endless ways to approach the paradoxes.

:-)

[Laudate_Dominum]

Btw, I'm just trying to instigate discussion because I think this thread is phat.

In fact, I believe that these sort of paradoxes rest upon faulty assumptions regarding dimensionality, possibility, necessity and the metaphysical status of mathematical abstraction.
In simplest terms these paradoxes conceive of being, which is seamlessly dynamic, in radically static terms; hence my first posed question: 'is this a reification of number?’ would seem to be close to my own take on the matter.

In spite of my own view I do not assert that these paradoxes have a clear cut answer. Every answer that I've encountered brings with it its own set of questions and assumptions.

What do all you philosophy buffs think?

[Guest JeffCR07]

At first I thought that your arguments about the reification of numbers was right, but I just can't seem to square that with Eleatic philosophy in general. Parmenides would have denied any number at all, so I can't see Zeno, his student, making the mistake of hypostatizing them vis-a-vis Pythagoras. Then again, maybe Zeno just got in wrong on both accounts.

[Laudate_Dominum]

[quote name='JeffCR07' post='1167295' date='Jan 16 2007, 07:29 PM']
At first I thought that your arguments about the reification of numbers was right, but I just can't seem to square that with Eleatic philosophy in general. Parmenides would have denied any number at all, so I can't see Zeno, his student, making the mistake of hypostatizing them vis-a-vis Pythagoras. Then again, maybe Zeno just got in wrong on both accounts.
[/quote]
I suppose since the paradoxes were intended as [i]reductio ad absurdum[/i] there is no need to square the inner logic with Eleatic philosophy in such a way. Number, multiplicity, quantity was the assumption of his opponents so he was sort of playing on their turf.

[Guest JeffCR07]

oh thats definately true, I was just thinking that he already had enough assumptions (two physical entities at physical distance) to get his reductio going without reifying number, so I just dont see what doing it would gain him, especially since it is not in line with his thought.

[Laudate_Dominum]

[quote name='JeffCR07' post='1167400' date='Jan 16 2007, 09:06 PM']
oh thats definately true, I was just thinking that he already had enough assumptions (two physical entities at physical distance) to get his reductio going without reifying number, so I just dont see what doing it would gain him, especially since it is not in line with his thought.


[/quote]
I suppose to my thinking such a reification is already implied in general Eleatic thought and would be most natural.

The main current of Eleatic philosophy being that sense perception is deceptive and that only "pure reason" can afford a true understanding of being. This extreme is directly articulated by Parmenides when he says such things as "thought and being are the same".

In many respects Eleatic philosophy would seem to be characterized by a radical reification of static abstractions. I would say that it is through [i]logos[/i], precisely in dualites, antinomies and infinities, that one transcends perception to the realization of [i]aletheia[/i].

Thus it seems perfectly natural to me that arguments based on the properties of numbers would be employed as a means of indicating [i]aletheia[/i].

[Guest JeffCR07]

That's what I was thinking at first too, but the problem is we have to ask ourselves [i]what[/i] the eliatics were reifying, and the answer to that is "What Is" - pure Being considered as One, Eternal, Unchanging, Homogeneous, and Whole. As such, any reification that we talk about concerning the Parmenidean system must be understood in this context, and this context does not make room for any numbers, any individuation, any distinction, or any change.

If Parmenides was reifying anything at all, it was Being - and beyond pointing out his conflation of contingent and necessary being, I don't really know how we can argue that he "reified" Being.

It seems to me that part of the problem is in approach. Our critiques thus far (and now I am speaking of Eleatic philosophy as a whole) have been taking their starting place with qualified things - time, space, number, etc - and yet these are exactly what Parmenides was denying. If we really want to point out where his philosophy goes wrong, we have to start where he starts and stop him when he makes a mistake.

To this end, I think we can agree with him that both the Way of [i]Is Not[/i] (the assertion of being that it simply is not) and the Way of [i]is and is not[/i] (that being both is and is not) are false. Thus, he moves on to the Way of [i]Is[/i]. Now it is at this point that I would argue that he makes a mistake, for whenever a thing is asserted to be, I can question whether it is contingent or necessary. Now Parmenides would certainly try to reject this distinction, for he says of the Way of [i]Is[/i] that "It is...and cannot not be." However, in stating this, he has implicitly accepted the distinction which I introduced: namely, he has admitted that when he speaks of "It Is" he is speaking of [i]necessary[/i] being. Thus, his claims concerning "What Is" are claims that apply only to necessary being, and not to contingent being. It follows, then, that any attempt on his parts to force conclusions that he draws concerning necessary being upon contingent being will result in a category mistake and render the argument fallacious.

In this way, we see Parmenides making, really, the first ontological argument for God (his descriptions of "It Is" - eternal, unchanging, one, whole - are eerily similar to the Divine Attributes). His error was in thinking that such an argument logically entailed that nothing else [i]but[/i] God could possibly exist.

[phatcatholic]

what does "reification" mean? what does it mean to "reify"? Thanks

[Guest JeffCR07]

it is substantially the same as "to hypostatize" - it just means assigning a certain degree of being to a thing. So, for example, Arians denied the hypostatization of the Son when they denied that he was one in being with the Father. Similarly, Aristotle denied Plato's hypostatization of the Forms when he argued that the Forms are not realities in existing in themselves seperately from things in the world.

The question we are discussing now is the role of reification or hypostatization in Eleatic philosophy (aka, Parmenides and his lackies) :

[Laudate_Dominum]

Shoot. I don't want this thread to die..

[quote name='JeffCR07' post='1168056' date='Jan 17 2007, 09:32 AM']
That's what I was thinking at first too, but the problem is we have to ask ourselves [i]what[/i] the eliatics were reifying, and the answer to that is "What Is" - pure Being considered as One, Eternal, Unchanging, Homogeneous, and Whole. As such, any reification that we talk about concerning the Parmenidean system must be understood in this context, and this context does not make room for any numbers, any individuation, any distinction, or any change.

If Parmenides was reifying anything at all, it was Being - and beyond pointing out his conflation of contingent and necessary being, I don't really know how we can argue that he "reified" Being.

It seems to me that part of the problem is in approach. Our critiques thus far (and now I am speaking of Eleatic philosophy as a whole) have been taking their starting place with qualified things - time, space, number, etc - and yet these are exactly what Parmenides was denying. If we really want to point out where his philosophy goes wrong, we have to start where he starts and stop him when he makes a mistake.

To this end, I think we can agree with him that both the Way of [i]Is Not[/i] (the assertion of being that it simply is not) and the Way of [i]is and is not[/i] (that being both is and is not) are false. Thus, he moves on to the Way of [i]Is[/i]. Now it is at this point that I would argue that he makes a mistake, for whenever a thing is asserted to be, I can question whether it is contingent or necessary. Now Parmenides would certainly try to reject this distinction, for he says of the Way of [i]Is[/i] that "It is...and cannot not be." However, in stating this, he has implicitly accepted the distinction which I introduced: namely, he has admitted that when he speaks of "It Is" he is speaking of [i]necessary[/i] being. Thus, his claims concerning "What Is" are claims that apply only to necessary being, and not to contingent being. It follows, then, that any attempt on his parts to force conclusions that he draws concerning necessary being upon contingent being will result in a category mistake and render the argument fallacious.

In this way, we see Parmenides making, really, the first ontological argument for God (his descriptions of "It Is" - eternal, unchanging, one, whole - are eerily similar to the Divine Attributes). His error was in thinking that such an argument logically entailed that nothing else [i]but[/i] God could possibly exist.
[/quote]
Jeff,

I appreciate your criticisms but I do believe that I can squirm out of the problem by simply clarifying my position a bit.

The clear sense we get from Plato's [i]Parmenides[/i] coupled with statements in Aristotle's [i]Physics[/i] and other source (Proclus for example) is that Zeno's paradoxes were not positive arguments for the views of Parmenides but were intended as elucidations of the flaws inherent to the Pythagorean view. Thus we don't have to talk about an Eleatic reification of number since my position really accuses the Pythagoreans of reifying number (which is borderline self-evident in my opinion).

Pythagorean thought (as far as I can tell) in essence takes the realm of [i]the science of the accident of quantity[/i] to be reality as such.

I would like to fully enunciate my analysis of the issues at hand but I must go to bed.

Peace.

[Guest JeffCR07]

ah, I see the problem. We are not actually disagreeing - I should have been more clear. I agree that the specific paradoxes that Zeno brings up regarding space and motion constitute simply his attempt to engage in a [i]reductio[/i] on the pythagorean (and more) notion that there exist a multiplicity of things. A Pythagorean would have accepted his premises and, perhaps, may have been persuaded by his conclusions.

My point was that it is not necessary to deal with the particulars of the specific examples of paradoxes that Zeno brings up (which, as you correctly pointed out [i]do[/i] engage in the reification of number). Rather, my point was that a truly sufficient response to Zeno will not simply deal with rejecting the paradoxes that he raises against now-questionably-relevant opponents, but rather, the sufficient answer will have to attack the problematic outlook [i]behind[/i] those paradozes - that is, the Parmenidean philosophy itself. It is in doing [i]this[/i] that I think it is unnecessary to address the reification of number, since the implicit stance behind the paradoxes denies such a reification.

In a sense, what I am saying is "yes, if someone is a pythagorean (or a Platonist) that person will have to grapple with error of the reification of number, but if someone is agrees that number ought not be reified (a position I have up until now assumed implicitly - so sorry about that) the best path of rebuttle is to attack the Eleatic philosophy at its core, rather then at the level of a [i]reductio[/i] aimed at someone else.

I hope that makes what I have been saying more clear

Your Brother In Christ,

Jeff

[phatcatholic]

[quote name='JeffCR07' post='1168926' date='Jan 18 2007, 10:25 AM']
The question we are discussing now is the role of reification or hypostatization in Eleatic philosophy (aka, Parmenides and his lackies) :
[/quote]
thank you

next question: what is Eleatic philosophy?