X-Message-Number: 21743
From: 
Date: Sun, 11 May 2003 10:39:11 EDT
Subject: non-swan

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The non-swan "paradox" is slightly related to cryonics in that it is another 
spectacular example of the incredible obtuseness of the philosophical 
community, over a period of at least 60 years. It is absurdly easy to deflate 
and yet remains, to this very day, an unsettled problem among philosophers 
generally.

The non-swan "paradox" has also been called the paradox of the crow, or of 
the raven, and the Paradox of Confirmation. 

 Here's how it goes. Consider the following two propositions:

1. "All swans are white."

2. "All non-white things are non-swans."

The two propositions are logically equivalent. If you don't believe this at 
first, play with it a little and convince yourself.

Then we consider the Principle of Confirmation in statistical analysis. Any 
observation that tends to confirm your hypothesis is a "confirming instance" 
and increases your confidence that the hypothesis is correct. If we keep 
looking at swans, and keep finding them white, we gain increasing evidence 
that all swans are white--even though the evidence will not be conclusive 
until we have examined every swan. (And in fact there are some black swans.)

But now consider "confirming instances" of the second proposition. I look at 
a cow-plop, and observe that it is brown. That is a confirming instance of 
proposition 2, is it not? And since 1 and 2 are equivalent, it must also tend 
to confirm proposition 1, must it not?

Common sense shrieks, "Whoa! You can examine cow-plops until the cows come 
home, but that will not tell you anything about swans!" 

Right. But how do we explain the apparent paradox? Must we give up the 
Principle of Confirmation? Or must we reject the logical equivalence of the 
two propositions?

No, we needn't give up either principle. The answer is simple; the 
philosophers have misunderstood the meaning of "confirming instance." A 
confirming instance is an item of NEW information tending to support the 
hypothesis, not just any item.

If I see a brown cow-plop, I have added to my knowledge of the location and 
number of cow-plops, but I HAVE LEARNED NOTHING NEW that is relevant.  I 
already knew that cow-plops are not swans, and more generally that non-swans 
are not swans. Observation of a brown cow-plop is NOT a confirming instance 
of proposition 2. End of story.

Robert Ettinger

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