Paradoxes: Their Roots, Range, and Resolution [Paperback]

Nicholas Rescher (Author)

Book Description

Publication Date: April 19, 2001

A paradox (from the Greek word meaning "contrary to expectation") is a statement that seems self-contradictory but may be true. Exploring the distinction between truth and plausibility, the author presents a standardized, straightforward approach for deciphering paradoxes -- one that can be applied to all their forms, whether clever wordplay or more complex issues.

Product Details

• Paperback: 320 pages
• Publisher: Open Court (April 19, 2001)
• Language: English
• ISBN-10: 0812694376
• ISBN-13: 978-0812694376
• Product Dimensions: 9 x 6 x 0.7 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #323,521 in Books (See Top 100 in Books)

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44 of 45 people found the following review helpful:

5.0 out of 5 stars The first sentence of this review is true, December 11, 2002

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John S. Ryan "Scott Ryan" (Cuyahoga Falls, OH) - See all my reviews
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This review is from: Paradoxes: Their Roots, Range, and Resolution (Paperback)

The title of this review is false.

I love paradoxes. A good paradox is something like an incongruity in the structure of the Matrix, an indication that there's something not quite right about our take on reality. Jorge Luis Borges even took paradoxes as evidence of monistic absolute idealism -- proof that the "undivided divinity operating within us" had "dreamt the world" but left in a few "crevices of unreason" so that we could tell we were dreaming. ("Avatars of the Tortoise," in _Labyrinths_.)

I also love Nicholas Rescher's books, of which he's written many. This one is very, very good.

Every time Rescher writes a book, it seems, he founds (or at least names) a new discipline. This time it's "aporetics," the study of paradoxes and their resolution. (An "apory," Rescher says, is a "group of acceptable-seeming propositions that are collectively inconsistent" [p. 7].)

Rescher studies a _lot_ of paradoxes in this volume. Even if you're interested in it only as a sort of bestiary of paradoxes, you'll be impressed by the sheer number of the things he's managed to include. He's combed the philosophical literature from the present day on back through the European Middle Ages clear to ancient Greece. And I'm willing to bet that he didn't miss any of importance.

But what's actually supposed to be new here is Rescher's method for dealing with paradoxes. So let's chat about that.

First of all, Rescher spends some time discussing the difference between truth and plausibility. His point here is that paradoxes become resoluble if we break them out into propositions, each of which is under consideration as a _candidate_ for truth, but which we can decide to reject if we like. In an aporetic analysis, the propositions in an "aporetic cluster" may have a _presumption_ of acceptability (if they're plausible, which they probably are or we wouldn't have a paradox) but we don't just assume indefeasibly that they're all true.

Now, when we get down to cases, what we do is this: when we encounter a paradox/apory, we break it down into a set of propositions that give rise to the paradox. Then we sort the propositions according to their degrees of plausibility. Then, based on the resulting "retention prioritization," we decide which one(s) to reject. There are some complications here but that's the skinny of it.

How far does this take us? Well, frankly, what it's doing is giving us a useful and organized way to _think_ about paradoxes (which of course is no small thing), but not necessarily a method for actually resolving them.

First, as Rescher himself acknowledges, different people may have different "retention prioritizations" (as in the "Paradox of Evil," p. 31, about which, Rescher says, religious believers and committed atheists would presumably disagree). This fact alone means that in lots of controversial cases, Rescher's method will generate different results for different people.

Second, and arguably more seriously, it's not altogether clear that different people will break a paradox out into exactly the _same_ set of propositions. On the contrary, I would have thought that actually _finding_ this set of propositions would have been a major subdiscipline of aporetics. But Rescher essentially hands us these on a silver platter and tends to presume that there's no question about how to arrive at them.

Third, and probably _most_ seriously, even when we're through with our aporetic analysis, we still may not have satisfactorily resolved our paradox! I'll illustrate with the "Liar Paradox," which Rescher discusses in his tenth chapter.

The "Liar Paradox" arises, of course, from the statement "This statement is false" -- which seems to be true if it's false and false if it's true. Rescher resolves it by breaking it out into a set of propositions that includes this one: "S [the Liar statement] is a semantically meaningful statement -- that is, it is either true or false and not both." His "retention prioritization" concludes that this is the one to reject; the Liar statement must be dismissed as "semantically meaningless" [p. 202].

This is all well and good; at the very least, that proposition is almost undoubtedly the place at which to concentrate one's philosophical fire in an analysis of the Liar Paradox. But does Rescher's analysis really _resolve_ the paradox?

I think it does not. Not all readers would agree (I don't) that "semantically meaningful" is identical in meaning to "either true or false and not both"; indeed, if Rescher had broken _this_ proposition out separately, I might have regarded _it_ as the one to reject.

Which means that the paradox hasn't really gone away. Indeed, the engine that drives it seems to be our very sense that a statement _can_ be semantically meaningful and yet fail to be decisively true or false. For surely the heart of the paradox is precisely that we _can_ tell what the Liar statement means well enough to recognize that it is self-referring and self-undermining (or, in Rescher's marvellous coinage, "self-counterexemplifying" [p. 194]). We may very well have to dismiss it as semantically meaningless after all -- but the paradox hasn't been resolved until we know _why_. Rescher's method, even if fully sound, would tell us only _that_ we should do so.

This isn't a fatal flaw, so long as we don't expect to use Rescher's aporetic analysis for more than it can do. As a method of organizing our thoughts when we sit down to think through a paradox, it's very, very good. It's just not complete (and probably isn't supposed to be) as a method for actually figuring out what makes a paradox tick and what we should do about it.

If you enjoy paradoxes even a tenth as much as I do, you'll like this book.

If you're just starting to investigate the subject, I recommend William Poundstone's _Labyrinths of Reason_ and Mark Sainsbury's _Paradoxes_ as introductory volumes. Eventually you'll also want to get around to Barwise and Etchemendy's book on the Liar Paradox, Raymond Smullyan's books, Douglas Hofstadter's _Goedel, Escher, Bach_, and Rudy Rucker's _Infinity and the Mind_, and a host of others.