The frequentist agrees that no reasons can be given for inductive inferences, but holds that reasons can be given for inductive behavior, using certain procedures based on the idea of confidence intervals.
The Bayesian is able to attach personal probabilities, or degrees of belief, to individual propositions. The hard-line frequency dogmatist thinks that probabilities can be attached only to a series of events.
Probability, says this dogmatist, just means the relative frequency of some kind of event produced by a chance setup. Or it refers to the propensity of a chance setup to produce events with a certain stable frequency. Or it refers to certain underlying symmetry properties.
At any rate, we cannot talk sensibly about the probability of a single event, for that event either happens or does not happen. It has “probability” 0 or 1, and that is that.
So the frequency dogmatist will never talk about the frequency-type probability that a particular hypothesis is true.
The hypothesis is either true or false, and there is no frequency about it. At most, we can discuss the relative frequency with which hypotheses of a certain kind are true.
Thus far the dogmatic frequentist is happy to agree with Hume.
INDUCTIVE BEHAVIOR
Nevertheless, continues the frequentist, we may sometimes be able to apply a system for making inferences or drawing conclusions such that the conclusions are usually right.
We can talk about the relative frequency with which inferences drawn by a certain method are in fact correct.
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