Zeno's paradoxes

[Invariance]

It reminds me of the Barber 'Paradox.'

Pretend there is a town with a single male barber, and that every man in the town dislikes beards and hence keeps himself clean shaven. They do this either by shaving themselves or by attending the barber. Hence, the barber shaves all and only those men in town who do not shave themselves. Does the barber shave himself? Well, if the barbed does not shave himself, he must abide by the rule and shave himself. If he does shave himself, according to the rule he will not shave himself.

This is the work and progression of thousands of years of philosophy! Since Rosa is a Wittgensteinian of a sort, perhaps she can address the problems with this 'paradox.'

[Rosa Lichtenstein]

Vinnie:

This is the work and progression of thousands of years of philosophy!

Well, this is a popularisation of Russell's challenge to Frege's attempt to define numbers with a naive form of set theory, so it can hardly be called "The work and progression of thousands of years of philosophy!"

Or, if it is, then as this old Greek saying surely applies:

The Mountain labor'd, groaning loud,
On which a num'rous gaping crowd
Of noodles came to see the sight,
When, lo! a mouse was brought to light! [Phaedrus, IV, XXIV.]

The mountain gave birth to a mouse!

All this after 2500 years of aimless, linguistic chicanery!

The solution is, of course, to point out that there can be no such set (defined in the way it has been), so there is no such town, and no such barber.

[Cumannach]

Surely Zeno at least deserves some credit for revealing that our intuitive conceptions of space and time and the interaction between them must be wrong?

[gilhyle]

THe point is he did not use language in odd ways, rather one must use language in odd ways to eliminate the paradox.

[Rosa Lichtenstein]

Gil, the midnight creeper:

THe point is he did not use language in odd ways, rather one must use language in odd ways to eliminate the paradox

Unfortunately for you, and for Zeno, he did.

And, as I have shown, and as Wittgenstein noted, this paradox can indeed be eliminated by returning the language Zeno used from its metaphysical to its ordinary use.

[Rosa Lichtenstein]

Cummanach:

Surely Zeno at least deserves some credit for revealing that our intuitive conceptions of space and time and the interaction between them must be wrong?

1) What 'intuitive conceptions' are these? [I doubt you can say.]

3) The bottom line is that all he 'revealed' was his own narrow use of certain words, which he employed in rather odd ways.

3) He deserves no credit at all since he was a mystic, and a confused mystic at that (rather like Hegel and Engels, in fact).

[Cumannach]

1) What 'intuitive conceptions' are these? [I doubt you can say.]

These conceptions; that to get from any place to any other place you have to travel from one to the other. That to travel from one place to the other you have to travel to every place between the two places. That to travel between any two places takes time. That you can't make an infinite number of trips and arrive at a place etc.

The bottom line is that all he 'revealed' was his own narrow use of certain words, which he employed in rather odd ways.

Well that's not a very profound criticism.

3) He deserves no credit at all since he was a mystic, and a confused mystic at that (rather like Hegel and Engels, in fact).

He deserves plenty of credit. These problems have generated quite a bit of enquiry and discovery over two and a half thousand years have they not?

[Rosa Lichtenstein]

Cummanach:

These conceptions; that to get from any place to any other place you have to travel from one to the other. That to travel from one place to the other you have to travel to every place between the two places. That to travel between any two places takes time. That you can't make an infinite number of trips and arrive at a place etc.

But this just transfers the ambiguity onto 'place', a word you have simply taken for granted, as did Zeno, Hegel and Engels.

Well that's not a very profound criticism.

That's not a very convincing answer.

He deserves plenty of credit. These problems have generated quite a bit of enquiry and discovery over two and a half thousand years have they not?

No, they haven't. I defy you to show otherwise.

What they have generated is much wasted time by armchair theorists.

[Cumannach]

But this just transfers the ambiguity onto 'place', a word you have simply taken for granted, as did Zeno, Hegel and Engels.

You asked what intuitive conceptions of time and space Zeno exposed problems with. Maybe it does transfer the ambuguity that wasn't the issue.

What they have generated is much wasted time by armchair theorists.

It is philosophy we're talking.

[Rosa Lichtenstein]

Cummanach:

You asked what intuitive conceptions of time and space Zeno exposed problems with. Maybe it does transfer the ambuguity that wasn't the issue.

Even so, I question whether these are 'intuitive conceptions', and even if they are, that they are at all representative of our use of words like 'move', 'time' and 'place'.

If a wider selection of uses are chosen, your 'intuitive conceptions' will soon appear rather restrictive/odd.

It is philosophy we're talking.

Yes, a ruling-class total waste of time, if no real interest to socialists.

[gilhyle]

And, as I have shown, and as Wittgenstein noted, this paradox can indeed be eliminated by returning the language Zeno used from its metaphysical to its ordinary use.

The true situation is self evidently exactly the opposite - Zeno follows a common usage, you refine usage in a quite unnatural way in order to create an appearance of the disappearance of the paradox (and thus to project a rationalist picture of the underlying reality).

[Rosa Lichtenstein]

Midnight-Creeper:

The true situation is self evidently exactly the opposite - Zeno follows a common usage, you refine usage in a quite unnatural way in order to create an appearance of the disappearance of the paradox (and thus to project a rationalist picture of the underlying reality).

Not so, as you would know if you had read the evidence I have amassed -- but you prefer to defend mystics and idealists, don't you?

[gilhyle]

You dont need to read a 'mass' of evidence - you need only read the texts of Zeno's paradoxes which patently conform to a common usage, there is nothing strange about his usage of terms at all, it is just that those common usages led on to an apparently bizarre concluion. Thats what a paradox is for Zeno

[Rosa Lichtenstein]

Midnight Creeper:

You dont need to read a 'mass' of evidence - you need only read the texts of Zeno's paradoxes which patently conform to a common usage, there is nothing strange about his usage of terms at all, it is just that those common usages led on to an apparently bizarre concluion. Thats what a paradox is for Zeno

But, it only works if Zeno applies language in odd ways -- for more details you will need to (shock-horror!) read my essays.

Silly me -- we all know you prefer to stay ignorant...

[gilhyle]

But that very concept of yours shifts the point - the usage is normal, the application is not, but the application is only the way the normal usages are combined to illuminate that the common usages contain some bizarre features. You charge Zeno with the error of revealing the problem beneath. Zeno's application could not occur if the potential usage did not allow it. Thats the point.

[Rosa Lichtenstein]

Midnight Creeper:

But that very concept of yours shifts the point - the usage is normal, the application is not, but the application is only the way the normal usages are combined to illuminate that the common usages contain some bizarre features. You charge Zeno with the error of revealing the problem beneath. Zeno's application could not occur if the potential usage did not allow it. Thats the point.

Usage cannot be normal if the application is wierd.

I suppose you think that if someone used 'socialist' to describe, say, Margaret Thatcher, and they meant it, you'd be Ok with that.

[mikelepore]

It reminds me of the Barber 'Paradox.'

Pretend there is a town with a single male barber, and that every man in the town dislikes beards and hence keeps himself clean shaven. They do this either by shaving themselves or by attending the barber. Hence, the barber shaves all and only those men in town who do not shave themselves. Does the barber shave himself? Well, if the barbed does not shave himself, he must abide by the rule and shave himself. If he does shave himself, according to the rule he will not shave himself.

This is the work and progression of thousands of years of philosophy! Since Rosa is a Wittgensteinian of a sort, perhaps she can address the problems with this 'paradox.'

Bertrand Russell's original form was based on the idea that some sets are subsets of themselves and some are not. The paradox occurs as soon as someone says: "the set of all sets that are not subsets of themselves." Many people use the example of a book that list the titles of books. A book entitled "A listing of all the books that do not include their own names", and trying to determine whether it should include itself, would generate the same paradox.

[Rosa Lichtenstein]

Mike:

Bertrand Russell's original form was based on the idea that some sets are subsets of themselves and some are not. The paradox occurs as soon as someone says: "the set of all sets that are not subsets of themselves." Many people use the example of a book that list the titles of books. A book entitled "A listing of all the books that do not include their own names", and trying to determine whether it should include itself, would generate the same paradox.

But only with a naive view of a set.

The last part I think you have wrong. The alleged paradox concerns bibliographies. There are bibliographies which list bibliographies that list themselves as bibliographies and there are bibliographies which list bibliographies that do not list themselves as bibliographies.

But, does the latter sort list itself? If it does then it shouldn't; if it doesn't then it should.

However, this shows that there can be no such set of (the latter sort of) bibliographies, so there is no paradox.

[Rascolnikova]

http://en.wikipedia.org/wiki/Infinitesimal

I think infinitesimals are the most intuitive way to deal with these problems. I do think it's a mathematical question, not sloppy language, but I'm not interested in arguing it.

[Rosa Lichtenstein]

Rascolnikova:

I do think it's a mathematical question, not sloppy language, but I'm not interested in arguing it.

It certainly can be made into a mathematical problem, but only if we are dealing with a mathematical space -- something Zeno had no comprehension of. Hence, he was constrained by his confusion of physical space, and notions of place, motion and time, with mathematical versions of the same words. The two languages are not at all the same, as we now know; so the original 'paradox' arose because of this early confusion.

This was compounded by Zeno and later mathematicians/philosophers' failure to consider a wider use of ordinary words we have for space, time, place and movement -- or, rather, they ran these together with no little lack of sensitivity.

Hence, this is no paradox, even if it presents us wth interesting mathematical puzzles (which have largely been solved).