The link between probability theory and logic is most opportune. There is a whole—albeit not very popular—branch of probability theory and statistics that goes by various names (e.g., logical inference) that considers probability an extension of logic in the sense that it helps us come up with adequate solutions to problems whose premises are not stated in terms of true or false but are assigned some credibility. Names associated with this school of though are Keynes (because of his 1921 book on probability theory), Carnap and, more recently, Ian Hacking.
In this program, of course, Bayes Theorem plays an important role. If you consider logic more important than probability is, think again how many times do you work with premises that are 100% true or false and whether it would make sense to extend it to allow for plausibilities rather than certainties.
Actually, I said above that “Bayes Theorem plays an important role” but I did not state which or how. In a sense, Bayes Theorem is the soft version of Modus Tollens.
That’s interesting. I’ve heard about probabilistic modal logics, but didn’t know that not only logics are working towards statisticians, but also vice versa. Is there some book or videocourse accessible to mathematical undergraduates?
The link between probability theory and logic is most opportune. There is a whole—albeit not very popular—branch of probability theory and statistics that goes by various names (e.g., logical inference) that considers probability an extension of logic in the sense that it helps us come up with adequate solutions to problems whose premises are not stated in terms of true or false but are assigned some credibility. Names associated with this school of though are Keynes (because of his 1921 book on probability theory), Carnap and, more recently, Ian Hacking.
In this program, of course, Bayes Theorem plays an important role. If you consider logic more important than probability is, think again how many times do you work with premises that are 100% true or false and whether it would make sense to extend it to allow for plausibilities rather than certainties.
Another key work here is Probability Theory: The Logic of Science by ET Jaynes. (you can download the entire book here). The early chapters are focused on deriving the probability calculus from logic.
Actually, I said above that “Bayes Theorem plays an important role” but I did not state which or how. In a sense, Bayes Theorem is the soft version of Modus Tollens.
That’s interesting. I’ve heard about probabilistic modal logics, but didn’t know that not only logics are working towards statisticians, but also vice versa. Is there some book or videocourse accessible to mathematical undergraduates?