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The confirmation functions have to meet some basic mathematical conditions.
Sound signals for the orientation and confirmation functions were understood and used by the participants.
Carnap's regular confirmation functions, too, are strongly reminiscent of Bolzano's approach.
We'll now look into how support functions (a.k.a. confirmation functions) represent the logic of hypothesis confirmation.
Note, however, that infinitely many confirmation functions, defined by suitable choices of the initial measure, allow learning from experience.
A sound designer proposed several non-speech sound signals based on two schemas: a pair of sounds for the orientation and confirmation functions, and a timeline sequence for the remaining distance.
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He later generalizes his confirmation function to a continuum of functions cλ.
Firstly, is there a correct setting of λ, or said another way, how 'inductive' should the confirmation function be?
The problem of arbitrariness of the confirmation function also hampers the extent to which the logical interpretation can truly illuminate the connection between probabilities and frequencies.
Carnap approaches the problem by first considering extremely limited artificial languages and trying to find a confirmation function that will work for that.
By Carnap's lights, the degree of confirmation of a hypothesis depends on the language in which the hypothesis is stated and over which the confirmation function is defined.
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