Wednesday, 10 September 2008

Dretske's definition of informational content

The first time I had a go at Dretske (Knowledge and the flow of information, Blackwell 1981, CLSI publications 1991), some years back, I remember struggling with this. I'd hit it again, on re-reading Dretske, and after some grappling with it (I just couldn't parse the sentences), think I do now get it. Here it is:
Informational Content:A signal r carries the information that s is F = The conditional probability of s's being F, given r (and k), is 1 (but, given k alone, less than 1)
This is what I think he is saying.

The equals sign is saying that what comes on the right is the definition for what is on the left. That is, what is on the right is the condition under which we can say that a signal r carries the information that s is F.

This condition is a follows.

P(s=F|r and k) = 1
P(s=F|k and (r not received)) < 1

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