I went looking for a youtube video that reflected what I think is the proper attitude to take toward Zeno's "paradoxes" (I think the proper attitude is contempt without finding something suitable. However here's one where Meg Ryan illustrates the stupidity of it:
And here is one that, but giving some very good quotes from the people who came up with this, does a good job of setting the table:
Unfortunately, after setting the table by showing the quotes which make clear what kind of nonsense the Eleatics were after, it drops the ball and leaves things hanging.
Here's Joe Rogan giving a look of astonishment at the suggestions. I don't know who he's talking to but I see this as the attitude that anyone of common sense would have toward hearing this kind of thing stated: He says something like "maybe we should stop listening to these people."
After listening to the descriptions of these paradoxes I see these as very close to the ontological arguments for god. "Because in my mind I can imagine a god of infinite power, such a god must exist," IS VERY SIMILAR TO: "Because I can in my mind imagine that there are an infinite number of points between two other points, it must be impossible to count them all or walk across a room." To me this is very similar nonsense. Both should be rejected out of hand and considered nonsense on the ground that the reality perceived through the senses always trumps the allegations of "logic constructed by the mind" when that logic cannot ultimately be traced back to something that can be verified through the senses. Neither the purely mental contention that all-powerful beings exist nor the purely mental contention that all distances can be infinitely divided have any connection to the reality that we perceive through our senses, and both should be rejected as absurd without any more consideration than would be given to the person who asserts that all knowledge is impossible, or who asserts a totally deterministic view of human nature.
That's where Isaac Asimov's criticism of Socrates comes into play as well, and I think it applies to Zeno of Elea as well, of whom I feel also "sick and tired":
Quote from Isaac Asimov "The Relativity of Wrong"First, let me dispose of Socrates because I am sick and tired of this pretense that knowing you know nothing is a mark of wisdom. No one knows nothing. In a matter of days, babies learn to recognize their mothers. Socrates would agree, of course, and explain that knowledge of trivia is not what he means. He means that in the great abstractions over which human beings debate, one should start without preconceived, unexamined notions, and that he alone knew this. (What an enormously arrogant claim!) In his discussions of such matters as "What is justice?" or "What is virtue?" he took the attitude that he knew nothing and had to be instructed by others. (This is called "Socratic irony," for Socrates knew very well that he knew a great deal more than the poor souls he was picking on.) By pretending ignorance, Socrates lured others into propounding their views on such abstractions. Socrates then, by a series of ignorant-sounding questions, forced the others into such a mélange of self-contradictions that they would finally break down and admit they didn't know what they were talking about. It is the mark of the marvelous toleration of the Athenians that they let this continue for decades and that it wasn't till Socrates turned seventy that they broke down and forced him to drink poison.
But my attitude is best expressed in the quote from Seneca, where I think he's channeling Epicurus rather than his Stoic friends.
Quote from (Seneca’s Letters – Book II Letter XLVIII)And on this point, my excellent Lucilius, I should like to have those subtle dialecticians of yours advise me how I ought to help a friend, or how a fellowman, rather than tell me in how many ways the word “friend” is used, and how many meanings the word “man” possesses. Lo, Wisdom and Folly are taking opposite sides. Which shall I join? Which party would you have me follow? On that side, “man” is the equivalent of “friend”; on the other side, “friend” is not the equivalent of “man.” The one wants a friend for his own advantage; the other wants to make himself an advantage to his friend. What you have to offer me is nothing but distortion of words and splitting of syllables. It is clear that unless I can devise some very tricky premises and by false deductions tack on to them a fallacy which springs from the truth, I shall not be able to distinguish between what is desirable and what is to be avoided! I am ashamed! Old men as we are, dealing with a problem so serious, we make play of it! ‘Mouse’ is a syllable. Now a mouse eats its cheese; therefore, a syllable eats cheese.”
Suppose now that I cannot solve this problem; see what peril hangs over my head as a result of such ignorance! What a scrape I shall be in! Without doubt I must beware, or some day I shall be catching syllables in a mousetrap, or, if I grow careless, a book may devour my cheese! Unless, perhaps, the following syllogism is shrewder still: “‘Mouse’ is a syllable. Now a syllable does not eat cheese. Therefore a mouse does not eat cheese.” What childish nonsense! Do we knit our brows over this sort of problem? Do we let our beards grow long for this reason? Is this the matter which we teach with sour and pale faces?
Would you really know what philosophy offers to humanity? Philosophy offers counsel. Death calls away one man, and poverty chafes another; a third is worried either by his neighbor’s wealth or by his own. So-and-so is afraid of bad luck; another desires to get away from his own good fortune. Some are ill-treated by men, others by the gods. Why, then, do you frame for me such games as these? It is no occasion for jest; you are retained as counsel for unhappy men, sick and the needy, and those whose heads are under the poised axe. Whither are you straying? What are you doing? This friend, in whose company you are jesting, is in fear. Help him, and take the noose from about his neck. Men are stretching out imploring hands to you on all sides; lives ruined and in danger of ruin are begging for some assistance; men’s hopes, men’s resources, depend upon you. They ask that you deliver them from all their restlessness, that you reveal to them, scattered and wandering as they are, the clear light of truth. Tell them what nature has made necessary, and what superfluous; tell them how simple are the laws that she has laid down, how pleasant and unimpeded life is for those who follow these laws, but how bitter and perplexed it is for those who have put their trust in opinion rather than in nature.