d

Probability

In induction on 15/06/2011 at 7:37 am
The inductivist chooses to solve the problem of induction by assigning probabilities to theories. They are in search of theories that are immensely probable, not improbable: their goal is to adopt theories only if they are probably true. However, they are caught in a reductio due to an unforeseen consequence: if they adopt probable theories, they ought to adopt theories with as little content as possible; one ought to adopt tautologies and historical claims of the form “I have observed …” — and nothing more.This goes against the stated aims of science and any sort of process of induction, since it shies away from making any sort of predictions. Assigning probabilities to theories is then at odds with the process of induction.
Consider the theory “all ravens are black”. This theory is equivalent to the infinite conjunction of statements which the structure “The raven R is black.” However, since the probability of each unobserved raven cannot be assigned 1 without assuming a priori the statement “the next observed raven R will be black,” it follows that every unobserved raven must be assigned a probability of X<1 of having blackness.

Thus, the probability of the infinite conjunction with each conjunct being <1 approaches zero.

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