I’m looking for a text, which presents probability as the only way that subjective reasoning should be done. The argumentation might roughly be similar to the following:

Probability = coherent degree of belief

Probability close to 1 is believed to be practically certain
3.1 Test IID assumption of the weak law of large numbers (utilizing point 2)
3.2 Weak law of large numbers => For large sample size, set probability to relative frequency, because most other beliefs would contradict point 2.

Relate point 3.2 to bayesian updating of beliefs and convergence of posterior distributions.

Interpret models and their parameters as subjective constructs and identify our “reality” with these constructs.

The text I am looking for might be similar to “Howson & Urbach: Scientific Reasoning: The Bayesian Approach”. A concise text book with advanced calculus would meet my needs perfectly, but also any other text on this topic would be helpful.

Interesting blog post, I will have a closer look at the book. Thank you! I wonder whether there is even a more modern and shorter text on the subject. Maybe even a summary of de Finetti’s ideas. Do you have any suggestions?

Jaynes’ book is great. I like the normative approach Jaynes uses when constructing his “robot”. However, I think I’m looking for something more concise. For example, I liked reading the paper

“The Philosophy of Statistics” by Dennis V. Lindley

but I was missing technical details and some a more technical descriptions of how to arrive at intersubjective degrees of beliefs and how to measure these beliefs. I tried to outline such possible technical details above. The subjective role of parameters and models is also interesting to me. In his book

“Understanding Uncertainty” (Lindley 2014)

he talks about chance (say a Bernoulli parameter) and states that “it makes no sense for you to have a believe about your belief” (p. 163), which I do not quite agree with.

What I am actually looking for is some short technical description, of how to create and measure intersubjective beliefs in a subjective framework.