Friday, July 06, 2007


Mere Probability and Warranted Assertion

On the flight back to Austin I reread a chunk of Louis Menand's The Metaphysical Club, which I really enjoyed again. I hear that for American school kids, the period around the civil war is the equivalent of the Second World War in Europe; you end up studying it countless times, almost to the exclusion of anything else. But I'm coming at it all fresh, and I haven't really had much contact with Pragmaticism, so it's all very new and very interesting to me. Plus there's great stuff on the philosophical agenda of On the Origin of Species and its reception, and, if my memory serves me correctly, there's the story of the philosophy departments at Chicago and John Hopkins to come.

Here are just a couple of quotes I liked. First of all, there's Oliver Wendell Holmes Jr. on the KK principle (p62):

"I detest a man who knows what he knows."

"The abolitionists had a stock phrase that a man was either a knave or a fool who did not act as they knew to be right. So Calvin thought of the Catholics and the Catholics of Calvin. So I don't doubt do the more convinced prohibitionists think of their opponents today. When you know that you know persecution comes easy. It is as well that some of us don't know that we know anything."

More seriously, I thought a quote from Benjamin Peirce raised a nice issue. As part of a court case, he and Charles Sanders Peirce were to figure out the likelihood that a woman had signed her name perfectly twice, once on her will, and once on a purported secret 'second page' to that will nullifying any further will that might be drawn up on that person's behalf. The person who had produced both documents stood to gain all of the money if they were accepted as genuine, so obviously the authenticity of the documents became of great importance. The Peirces calculated that the chance that the lady had produced a second signature quite so like the first, with precisely the same distribution of distinctive strokes, was 1 in 2,666,000,000,000,000,000,000, and so they urged the signature on the 'second page' must have been traced from the first page. Peirce testified that this number:

"transcends human experience. So vast an improbability is practically an impossibility. Such evanescent shadows of probability cannot belong to actual life. They are unimaginably less than those least things which the law cares not for.

The coincidence which is presented in this case cannot therefor be reasonably regarded as having occurred in the ordinary course of signing a name. Under a solemn sense of the responsibility involved in the assertion, I declare that the coincidence which has here occured must have had its origin in an intention to produce it...[I]t is utterly repugnant to sound reason to attribute this coincidence to any cause but design." (p172-3)

I thought it was interesting that Peirce makes no bones about his merely probabilistic grounds to make this assertion, but he also acknowledges that he is in a situation which make the standards for warranted assertion particularly high. There's a well known argument from Williamson in favor of the knowledge account of assertion which proceeds by pushing the intuition that you cannot flat-out assert that a lottery ticket has lost (before the outcome of the draw is known), even if the probability that it hasn't lost is utterly minuscule. The diagnosis given is that mere probabilistic grounds are enough for assertion; one needs to know. But who would resent Peirce's assertion on these grounds were he to make it?

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I've generally thought something like this about Williamson's claim. He's right that lottery cases show that there's no number less than 1 such that degree of belief that high suffices for knowledge. But unless I missed part of the argument, that doesn't mean that degree 1 is necessary for knowledge.
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