Author: Bill Vallicella

Does Zeno Affirm What He Denies?

Andrew Ushenko in a Mind article from 1946, "Zeno's Paradoxes," distinguishes five putative ways of refuting Zeno's paradoxes: logical, mathematical, mathematico-physical, physical, and philosophical. Ushenko points out that two logical refutations fail. This post examines one of them. This is of particular interest since a reader floated a similar suggestion. Ushenko states the objection and then answers it cogently:

"Zeno's statement of the conditions of the race [of Achilles and the Tortoise], for example, of the condition that A moves faster than T, is equivalent to the assumption that motion exists, and therefore contradicts his own conclusion that motion is an illusion. Hence Zeno is inconsistent with himself." The falsehood of this accusation can be easily demonstrated. Of course, we must grant that Zeno begins with the assumption that there is motion, and concludes that there is no motion. But this procedure means only that he asserts, on the basis of his "proof", that If there is motion, then there is no motion. And, of course, the underscored conditional statement is true if, and only if, there is no such thing as motion.

Ushenko's reply to the objection is correct. Propositions of the form p –> ~p (where the arrow stands for the Philonian conditional) are none of them contradictory.  They are equivalent to propositions of the form ~p v ~p which in turn are equivalent to propositions of the form ~p.  It follows that If there is motion, then there is no motion  is  equivalent to There is no motion.

Consider an analogy. Someone argues on Anselmian grounds that (1) if God exists, then God exists necessarily; but for Humean reasons (2) nothing exists necessarily; ergo (3) if God exists, then God does not exist. There is no logical contradiction here, since the arguer is not affirming the existence of God; he is reasoning from the assumption that God exists, an assumption he does not affirm. Similarly, Zeno is not affirming the existence of motion; he is reasoning from the assumption that motion exists, an assumption he does not affirm.

Morris Lazerowitz on Philosophy and Propositions

Immersed as I am these days in a metaphilosophical project, I once again pull Lazerowitz's Philosophy and Illusion (Humanities Press, 1968) from the shelf.  Morris Lazerowitz (1907-1987) may not be much read these days, but his ideas remain provocative and worth considering, despite the fact that they are now taken seriously by few, if any.  But if he is right in his metaphilosophy, then I am wrong in mine, and so intellectual honesty requires that I look into this in some detail.

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Zeno’s Regressive Dichotomy and the ‘Calculus Solution’

The Regressive Dichotomy is one of Zeno's paradoxes of motion. How can I get from point A, where I am, to point B, where I want to be? It seems I can't get started.

A_______1/8_______1/4_______________1/2_________________________________ B

To get from A to B, I must go halfway. But to travel halfway, I must first traverse half of the halfway distance, and thus 1/4 of the total distance. But to do this I must move 1/8 of the total distance. And so on. The sequence of runs I must complete in order to reach my goal has the form of an infinite regress with no first term:

. . . 1/16, 1/8, 1/4, 1/2, 1.

Since there is no first term, I can't get started.

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On ‘Male Chauvinist’ and ‘Relative Truth’

A reader comments:

I'm confused about a claim you make. You say: "Take 'male chauvinist.' As standardly used nowadays, this refers to a male who places an excessively high valuation on his sex vis-a-vis the opposite sex. So a male chauvinist is not a chauvinist, and 'male' functions as as an alienans adjective: it does not specify, but shifts, the sense of 'chauvinist.'"

I did a quick check at Merriam-Webster Online. It seems to me that when someone is called a male chauvinist, the second of the three senses of 'chauvinism' given by Webster's is meant, viz. 'undue partiality or attachment to a group or place to which one belongs or has belonged.' But if so, it seems that a male chauvinist is a chauvinist. Male chauvinism is one type of chauvinism. It is that type of 'undue partiality' shown to members of one's own sex.

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Marx and Kierkegaard and Buddha: Comparative Notes

Karl Marx in his Theses on Feuerbach protested that the philosophers have merely interpreted the world in various ways, when the point is to change it. (Die Philosophen haben die Welt verschieden interpretiert; aber es kommt darauf an, sie zu veraendern.) His century-mate, Soren Kierkegaard, at the opposite end of the political spectrum, but sharing Marx’s disdain for mere theory, might have said that the point was to change oneself, to become oneself. Both thinkers were anti-contemplative and anti-speculative, but in such wildly divergent ways! The social activist Marx denied interiority by trying to merge the individual into his species-being (Gattungswesen) while the existentialist Kierkegaard fetishized interiority: “Truth is subjectivity” (Concluding Unscientific Postscript).

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Is Socialism Rooted in Envy?

Having toyed with this idea, I have concluded that it is a cheap shot. Socialism is no more rooted in envy than capitalism is rooted in greed. What one can say is that envy is the characteristic vice of socialists, just as greed is the characteristic vice of capitalists. But there is no need that a socialist or capitalist, as such, be vicious.

Suppose Sam’s motive for becoming a socialist is envy: he cannot stand it that some have much more than him. It does not follow that there are no good reasons for socialism. What follows is merely that none of those good reasons — assuming dubiously that there are some — played a motivating role within Sam’s psychic economy. Now suppose that Carl’s motive for advocating capitalism is greed: he has an inordinate desire to pile up loot for his own enjoyment. It does not follow that there are no good reasons for capitalism. What follows is merely that none of these good reasons — assuming correctly that there are some — played a motivating role within Carl’s psychic economy.

Is Greed the Engine of Capitalism?

The Financial Times reports on a piece of silliness from the Pope:

Pope Benedict XVI on Tuesday condemned the “grave deviations and failures” of capitalism exposed by the financial crisis and issued a strong call for a “true world political authority” to oversee a return to ethics in the global economy.

One mistake the good Pontiff is making is to confuse capitalism and capitalists.  One who cannot see the difference may fallaciously conclude that the greed of some capitalists is rooted in capitalism.  Here is a post from a while back that counters the notion:

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Concision at War with Redundancy

One of my faults as a writer is that I am prolix. I almost wrote ‘excessively prolix,’ which would have illustrated the fault in question. Piling ‘excessively’ onto ‘prolix’ would not only have been unnecessary, but would also have suggested that one can be prolix in moderation. But wordiness is a vice, and vices should be extirpated, not moderated.

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Saturday Night at the Oldies: ‘Reason’ Titles

We need a list of 'Reason' titles.  Here are three: You're the Reason I'm Livin; You're the Reason (I Don't Sleep at Night); Reason to Believe.  Last week or so I've been forcing myself to listen to Michael Jackson stuff to see if maybe, just maybe, I may have missed something of merit.  But it's just robotic crap compared to tunes of human meaning like these that can give a man pleasure from 8 to 80.  I can't imagine anyone but a freak relating to Jackson's "Bad" at the age of 80 even if he could relate to it at 8 or 18.