To support the claim that some scholars argue conditional probability should be derived from the foundational axioms of probability, rather than defined, and that there is no consensus on how this should be achieved, you can refer to works in the philosophy of probability and mathematical foundations. A prominent reference is:
Hájek, A. (2003). "What Conditional Probability Could Not Be." Synthese, 137(3), 273-323.
In this paper, Alan Hájek critiques the standard definition of conditional probability and explores alternative approaches. He discusses various proposals that suggest conditional probability should be derived from Kolmogorov’s axioms rather than defined separately, but notes that there is no consensus on how to formalize this approach in a way that satisfies both mathematicians and philosophers.
Another relevant reference is:
Popper, K. (1955). "Two Autonomous Axioms for the Conditional Probability." The British Journal for the Philosophy of Science, 6(21), 51-57.
In this work, Karl Popper explores the idea of treating conditional probability as a fundamental concept that can be derived independently, presenting an alternative framework to the Kolmogorov axioms. His approach highlights the lack of agreement on how to extend the axiomatic foundation to include conditional probability.
Both sources discuss the debate surrounding the foundational treatment of conditional probability within probability theory and philosophy, addressing the differing views on whether it should be derived or defined.
To support the claim that some scholars argue conditional probability should be derived from the foundational axioms of probability, rather than defined, and that there is no consensus on how this should be achieved, you can refer to works in the philosophy of probability and mathematical foundations. A prominent reference is:
Hájek, A. (2003). "What Conditional Probability Could Not Be." Synthese, 137(3), 273-323.
In this paper, Alan Hájek critiques the standard definition of conditional probability and explores alternative approaches. He discusses various proposals that suggest conditional probability should be derived from Kolmogorov’s axioms rather than defined separately, but notes that there is no consensus on how to formalize this approach in a way that satisfies both mathematicians and philosophers.
Another relevant reference is:
Popper, K. (1955). "Two Autonomous Axioms for the Conditional Probability." The British Journal for the Philosophy of Science, 6(21), 51-57.
In this work, Karl Popper explores the idea of treating conditional probability as a fundamental concept that can be derived independently, presenting an alternative framework to the Kolmogorov axioms. His approach highlights the lack of agreement on how to extend the axiomatic foundation to include conditional probability.
Both sources discuss the debate surrounding the foundational treatment of conditional probability within probability theory and philosophy, addressing the differing views on whether it should be derived or defined.