I think even Zenoman must agree with you there Dave.
Sorry the word “was” should have been edited out –While I don't doubt that you're making a valid point, I cannot understand what you are saying, especially in the above. It is grammatically so poorly-formed as to be unintelligible.The point of Zeno’s arguments is he was used the logic of those that believe things do move “pluralists” to construct a paradox based on their own pluralist rules of movement that reduces to an absurd result; therefore refuting as absurd the idea that anything moves at all;
Thus supporting Zeno’s monism (what today we would call “Absolute Monism”) which believe that all is just one thing within which we and everything only exist as essentially an idea with nothing real actually moving.
On the contrary; most peoples' approach to this paradox is to demonstrate that the stepThe problem is most do not approach Zeno on the terms he established for the paradox.
Nothing contrary in that demonstration at all, Zeno’s point was that using the reasoning based on motion is invalid – your agreeing with Zeno here.On the contrary; most peoples' approach to this paradox is to demonstrate that the step
With that for Zeno it was clear that there would always be a halfway point the must first be traveled before the Line could EVER be reached – and logically EVER becomes NEVER.is not justified. In particular, they take their best guess as to what Zeno might have been thinking -- usually something like "each individual subgoal takes time, and so infinitely many subgoals must take infinitely much time" -- and actively demonstrate that the reasoning is invalid.
AS the line can NEVER be reached since there will always be a halfway point that must be reached first!
But that is exactly what Zeno was hoping for – to show that when he uses the logic and rules of motion to build and argument, only a flawed absurd result is obtained – additional points about that flaw are points in Zeno’s favor – he appreciates the help. [/QUOTE] Since (to the best of my knowledge) Zeno does not actually state his rationale for this step, we cannot be sure what he really thinking here. [/QUOTE] Again, it is not his rational – it is our rational in believing in the rules for motion that he is applying against us! The modern knowledge of Zeno’s thinking is known - how he logically argues this point is included in advance modern philosophical logic, but is still based on the basic principles of logic (reducing to the absurd & begging the question) taught in Logic 101. Often scientist don’t included the more advanced training of Formal Logic in their training and knowledge. That is why many miss the point that Zeno wants his argument to be shown as absurd, because it is a argument based on motion – and that in the end was his objective – a logical debate demonstrate our ideas of motion were simply absurd.(To reject Zeno's argument, it is of course sufficient to simply point out the lack of justification for this step. But it seems to be the popular practice to go beyond simply pointing out the omission and attempt to actually demonstrate the flaw)
And there it it is - the statement Zeno was waiting for as you debate him on the marble steps in Athens.However, what Zeno really meant is a mostly irrelevant question, since we have the more practical matter of considering what people today are thinking when they consider this argument.
You seem to have completely misinterpreted me. Hopefully, the following is clear:Zeno’s point was that using the reasoning based on motion is invalid – your agreeing with Zeno here.
I’m not aware of the sophism of Zeno have every haven been seriously “resurrected” - I’d need to see some credible reference for that. AFAIK that has been dead for centuries displaced by the accepted assumption that things do move.pallidin said:Zeno appears to have been resurrected more times than Lazarus.
These assumptions here stated as facts directly contradict the claims made in the Wiki links about what real experts in formal logic say about them. If there is evidence for these claims then the Wiki information should be corrected.…. the following is clear:Zeno's argument is invalid.In fact, assuming the consistency of Peano arithmetic, Zeno's argument doesn't merely contain a gap: it is provably a non sequitur. …
I interpret "space" to mean Q³.Just show us the proof,
what is so hard about that?Just for fun...
ithat there would always be a halfway point the must first be traveled before the Line could EVER be reached – and logically EVER becomes NEVER.would you care to take a stab at justifying this passage?
I'm surprised you put such faith in Wikipedia.Otherwise just because I agree with the science of motion is no reason to accept your logic or assumptions like "instantaneous velocity" over Wikipedia information that real experts say these paradoxes have not been formally rejected.
That is not a valid argument. Instead of using a chain of deductive reasoning to justify your conclusion, you are appealing to your ignorance about how the conclusion could fail.what is so hard about that?
Zeno uses our logic of motion and space to define a halfway point that will always be between our object and the finish line – if there is always something between it and the finish how can the finish ever be reached. As Zeno says this shows it cannot and will never be reached – he uses our rules of space and motion to produces absurd results, his paradox still stands.
An "obvious" point Zeno would raise isThese forums expect a statement like “Zeno's argument is an invalid argument” to be supported by more than a “Straw man” debate - you have an obligation to present obvious points Zeno would raise not just pretend he would stand mute.
That is impossible – I was clear that Zeno was presenting a argument based on the a priori assumption of motion to build an absurd result. You cannot possible be so dense as to miss that point.Since your argument is informal, it can never be truly refuted, because you can always surprise us at the last minute and say "Haha, this whole time I was really making the a priori assumption that motion is impossible, I just never bothered to explicitly state it!" (of course, at this point we'd all dismiss your argument as vacuous) But I can (and have) refuted the particular argument you have put forth.
Randall, you place relatively too much confidence in your authorities, and relatively too little confidence in your own ability to reason.That is impossible – I was clear that Zeno was presenting a argument based on the a priori assumption of motion to build an absurd result. You cannot possible be so dense as to miss that point.
If you seriously think that all philosophers agree with you, then site an authority in the field and have them see to that that Wikipedia is revised based on that authority to remove the statement:
However, some philosophers insist that the deeper metaphysical questions, as raised by Zeno's paradoxes, are not addressed by the calculus. That is, while calculus tells us where and when Achilles will overtake the Tortoise, philosophers do not see how calculus takes anything away from Zeno's reasoning that concludes that this event cannot take place in the first place. Most importantly, many philosophers do not see where, according to the calculus, Zeno's reasoning goes wrong …
Absent that I’ll only be able to logically assume you are not really serious.
Your illogical logic resorting to insults disqualify you as useful as a mentor on this topic – so see you in another thread on another subject someday, but you and I are done in this one.
If you believe I have insulted you, then you should use the 'report post' feature to make the other mentors (and the administration) aware of my behavior. Assuming you're serious, I'm not really sure what prompted your opinion -- was it the phrase 'appeal to ignorance'? That wasn't an insult: I am using it in its technical meaning describing a class of formal fallacies resembling that of justifying a position on the basis that one is unaware of evidence to the contrary.Your illogical logic resorting to insults
He only demonstrates such a halfway point exists when the object is not yet at the finish line.Zeno uses our logic of motion and space to define a halfway point that will always be between our object and the finish line
Zenoman,The segments that the line is divided into. If we have a line of length D and we divide it into an infinite amount of sections then each section would be the width of D/(infinite)