无差别悖论及其解决(英文)

The Paradoxes of Indifference and Their Solutions

无差别原则及其悖论由来已久。当代归纳逻辑的创始人凯恩斯曾为消除这些悖论付出巨大的努力。本文介绍了若干典型的无差别悖论和对它们的一些尝试性解决,还追溯到贝叶斯方法的创始人曾经受到的类似困扰。笔者提出一种新的解决方案,其核心是对古典无差别原则加以试验机制的限制和提出从参数θ到f(θ)的线性无差别条件。最后指出,古典无差别原则作为经验性的启发原则仍可保留,它同作为逻辑原则或准逻辑原则的试验机制无差别原则是并行不悖和相互补充的。

The Principle of Indifference and its paradoxes are of long-standing. John M. Keynes, one of the founders of contemporary inductive logic, devoted himself to eliminating these troubles. This paper introduces several typical paradoxes of indifference and some ten- tative solutions to them, and traces a trouble related with these paradoxes back to the founder of Bayesian method, who had also been puzzled by it. We propose a solution of all these puz- zles, which imposes restrictions of trial setup on the classical Principle of Indifference and to meet the condition of linear indifference from a parameter 0 to its function f（O）. Finally, we point out that the classical Principle of Indifference can be retained as an experientially heuristic principle, which will function without coming into conflict with the Principle of Indifference, a logical or quasi-logical principle, on the trial setup, while the latter is and we can even say that these two principles are complementary to each other.