Carnap from 1950 sets out his exposition on defining a system purely on inductive logic that he attributes with epistemic qualities from probability.
This journey begins with his 'degree of confirmation', which requires evidence and a hypothesis to explicate a confirmed 'scientific sentence'. He details this further with modal logic and various syntactical deductions to define it by ordering finitely-many signs in a language system L, and assigning individual constants (events) to a number of predicates in that system. These signs prove the L-determinate class of sentences and so whether they're True or False.
Applying his method of induction to his own system - we enquire into the relevance of proving a system of reasoning purely under inductive logic. Such that, joining theorems of probability and modal logic to ultimately define probabilities by each sentence and a subset of proposition contained in any set of sentences.
In reference to the original question, how would the degree of confirmation actually apply to these methods of induction which seem psychological. For example: -
A clear sky on a sunny-day at the beach; the perception of colour attributed to the sky remains different to the oceans perceived colour.
If I take a finite number of sentences on a compact set; so a sequence of sentences with a finite subsequence. Assuming the limit point is the colour blue, I may find that the skies colour fits within a neighbourhood around the limit point whereas the oceans colour looks as if it's at some distance. However, I may also conclude the colour of the ocean also converges within that neighbourhood if I take a delta big enough.
How reliable is the evidence in this case - the colour of the sky and the ocean determined under sight and experience. Whereas the hypothesis seems more valid in terms of reliability and evidence because it avoids those sentences defined mainly on the weakness of identifying whether the colour is blue due to defaults in perception.