Skip to main content

Thoughts on Induction


Continuing the thoughts on induction I began last week, re: David Stove. If we know that there are 100 swans in the world, and we have seen each swan, recording each as white, then the conclusion "all swans are white" is a matter no longer of induction but of deduction. I'm not sure how it would go formally, but I'm pretty sure you get to that conclusion from those premises. [Even there, one might wonder -- is the first swan that I checked still white? Maybe they can go black as they molt, or something? But let's ignore the impact of the passage of time on swans.] I've seen all swans, all the swans I've seen are white, therefore all swans are white. That's a deduction, so nobody likely objects to calling it a proof. 

If so, then let's relax the assumption of completeness: the gradual addition of swans to my data base, the movement from 20 to 30, swans, thus from 20% to 30% of the universe, remains induction, remains something less than proof, BUT is important. For if we're on the same page so far, we may agree that induction is a process that approaches deduction at the limit. It approaches proof-ishness as it proceeds. This takes some of the mystery out of the question, does it not? 

But, you will object, we don't know how many swans there are, so the presumption is unrealistic. Well, that hardly makes it unique among philosophical thought-experiments, but perhaps we can relax that too. Simply assume that however many swans there are in the world, their number is finite, and (if it is growing, as given a food supply and a lack of predators it may well be) we can reasonably assume that humans add to a data sample more rapidly than the universe of swans itself increases. In this less demanding situation, it will still be the case that our sample is moving in the direction of universality. Is that enough to make our increasing confidence rational?

Comments

Popular posts from this blog

A Story About Coleridge

This is a quote from a memoir by Dorothy Wordsworth, reflecting on a trip she took with two famous poets, her brother, William Wordsworth, and their similarly gifted companion, Samuel Taylor Coleridge.   We sat upon a bench, placed for the sake of one of these views, whence we looked down upon the waterfall, and over the open country ... A lady and gentleman, more expeditious tourists than ourselves, came to the spot; they left us at the seat, and we found them again at another station above the Falls. Coleridge, who is always good-natured enough to enter into conversation with anybody whom he meets in his way, began to talk with the gentleman, who observed that it was a majestic waterfall. Coleridge was delighted with the accuracy of the epithet, particularly as he had been settling in his own mind the precise meaning of the words grand, majestic, sublime, etc., and had discussed the subject with William at some length the day before. “Yes, sir,” says Coleridge, “it is a maj...

The Lyrics of "Live Like You Were Dying"

Back in 2004 Tim McGraw recorded the song "Live Like You were Dying." As a way of marking the one-decade anniversary of this song, I'd like to admit that a couple of the lines have confused me for years. I could use your help understanding them. In the first couple of verses, the song seems easy to follow. Two men are talking, and one tells the other about his diagnosis. The doctors have (recently? or a long time ago and mistakenly? that isn't clear) given him the news that he would die soon. "I spent most of the next days/Looking at the X-rays." Then we get a couple of lines about a man crossing items off of his bucket list. "I went sky diving, I went rocky mountain climbing, I went two point seven seconds on a bull named Fu Man Chu." Then the speaker -- presumably still the old man -- shifts to the more characterological consequences of the news. As he was doing those things, he found he was loving deeper and speaking sweeter, and givin...

Searle: The Chinese Room

John Searle has become the object of accusations of improper conduct. These accusations even have some people in the world of academic philosophy saying that instructors in that world should try to avoid teaching Searle's views. That is an odd contention, and has given rise to heated exchanges in certain corners of the blogosphere.  At Leiter Reports, I encountered a comment from someone describing himself as "grad student drop out." GSDO said: " This is a side question (and not at all an attempt to answer the question BL posed): How important is John Searle's work? Are people still working on speech act theory or is that just another dead end in the history of 20th century philosophy? My impression is that his reputation is somewhat inflated from all of his speaking engagements and NYRoB reviews. The Chinese room argument is a classic, but is there much more to his work than that?" I took it upon myself to answer that on LR. But here I'll tak...