‘Could a rule be given from without, poetry would cease to be poetry, and sink into a mechanical art. It would be μóρφωσις, not ποίησις. The rules of the IMAGINATION are themselves the very powers of growth and production. The words to which they are reducible, present only the outlines and external appearance of the fruit. A deceptive counterfeit of the superficial form and colours may be elaborated; but the marble peach feels cold and heavy, and children only put it to their mouths.’ [Coleridge, Biographia ch. 18]

‘ποίησις’ (poiēsis) means ‘a making, a creation, a production’ and is used of poetry in Aristotle and Plato. ‘μóρφωσις’ (morphōsis) in essence means the same thing: ‘a shaping, a bringing into shape.’ But Coleridge has in mind the New Testament use of the word as ‘semblance’ or ‘outward appearance’, which the KJV translates as ‘form’: ‘An instructor of the foolish, a teacher of babes, which hast the form [μóρφωσις] of knowledge and of the truth in the law’ [Romans 2:20]; ‘Having a form [μóρφωσις] of godliness, but denying the power thereof: from such turn away’ [2 Timothy 3:5]. I trust that's clear.

There is much more on Coleridge at my other, Coleridgean blog.

Saturday, 18 March 2017

The Conjunction Problem


A minor philosophical niggle, this. ‘The Conjunction Problem’ is what Daniel Kahneman, in his Thinking, Fast and Slow (2011), calls a particular problem in probabilistic thinking. It goes like this:
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable?

a) Linda is a bank teller.

b) Linda is a bank teller and is active in the feminist movement.
Kahneman says people will choose (b) as more probable, because they are wrongheaded wrongy wrong-wrongs, the berks. Phil Edwards (in a post discussing something else) summarises: ‘The correct answer is—logically has to be—(a); “A and also B” cannot be more probable than “A with or without B”, whatever A and B are. But we’re not hard-wired to be good at probability; we seem to read the question as an invitation to fill in the blank in the way that gives the most satisfying story, in this case option (b).’

Something about this smells fishy to me. I take the force of Kahneman's point, of course; and we can make it clearer by rephrasing the original question.
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable?

a) Linda is a bank teller and either is or is not active in the feminist movement

b) Linda is a bank teller and is active in the feminist movement.
Put like that, (a) certainly looks more probable. But there seem to me two problems with it. One has to do with the vagueness with which the question is framed, a haziness that devolves upon being asked to compare a simple with a compound probability. The other has to do with the different valences of probability itself. ‘Given this information about a person, what do you consider plausible extrapolations as to the person's life or work?’ is a different kind of question to ‘this tossed coin has come up heads ten times in a row, what are the odds of an eleventh head?’

It may be, as Edwards suggests, that people plump for (b) because they prefer its implied story, rather than for reasons of pure probabilistic estimation. But then again, that might have nothing to do with it. Conceivably people choose (b) because they simply consider it more probable, irrespective of narrative. Reframe the question another way:
Here's quite a lot of information about Linda, designed to give you a sense of the kind of person she is, so as to feel confident making informed guesses as to the sorts of things she likes and what she does. Which is more probable?

a) Linda is doing something you consider unlikely.

b) Linda is doing something you consider unlikely. Linda is also doing something you consider she'd be likely to do.
The ‘likelihood’ angle is there in the original formulation as, if you like, Kahneman's sleight of hand, to try and nudge people to the ‘wrong’ answer. But it seems to me, when you frame it this way, it's reasonable to select (b). The thinking would be: (a) is, by definition, unlikely, so it doesn't make much sense to choose it. Of course (b) also includes that unlikely thing, but it also includes something much more likely, so if I select it I'll at least get 50%, instead of the all-or-nothing, weighted heavily towards nothing, unlikeliness of (a). The fuzziness is in the question not specifying whether we are selecting for the likelihood of the statement, or the likelihood of that statement plus literally everything else that might or might not be the case. And when you put it like that (a) becomes not so much unlikely as impossible with regard to anything save the Supreme Being. Quite apart from anything else, that's simply not how we assess statements for likelihood. Is it?

It puts me in mind of a version of the celebrated twins-at-the-fork-in-the-road logic puzzle, I think by Raymond Smullyan. You know the original puzzle. You have to get to Blogtown, urgently. But you've come to a fork in the road and don't know the way. Happily there are two people right there, identical twins, who do know the way. Unhappily, for obscure reasons (perhaps to do with their religion) one of them always tells the truth and the other always lies; and, moreover, they will only answer one question from you. What do you ask? The standard answer is: you pick one at random and ask ‘if I asked your brother which road to follow, what would he say?’ and then proceed up the other road than the one indicated. Fair enough. But the Smullyan solution, which seems to me to have a bearing on the Kahneman dilemma, is: ‘pick one brother and ask him the way to Blogtown. If you have chosen the truth-telling twin, he will point you in the right direction. If you have chosen the liar, he will point along the wrong fork in the road and also, with his other hand,  point down the road along which you have just come.’ That's bonkers in similar ways to the manner of Kahneman's bonkers explanation. Isn't it?

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