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A couple of comments on a very big topic.
There is a fascinating history of ideas about the objective contents of thought, starting with the Austrians Brentano and Meinong, running through analytical philosophy (Russell and Moore) and phenomenology (Husserl and Heidegger), and also through evolutionary epistemology (Popper and Munz). http://www.the-rathouse.com/EvenMoreAustrianProgram/EMAThreeAustrianStrands.html
On the Bayesian appraisal of theories, with reference to the Duhem problem, it seems that Bayes gives a good result when there is only one major theory in the picture but is not so good when help is most needed, that is to judge between two serious rival theories. http://www.the-rathouse.com/Theses/Duhem-QuineInBayesNewExperimentalism.html