解释概率论
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Classical
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Frequentist
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Subjective
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Propensity
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Main hypothesis
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Principle of indifference
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Frequency of occurrence
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Degree of belief
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Degree of causal connection
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Conceptual basis
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Hypothetical symmetry
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Past data and reference class
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Knowledge and intuition
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Present state of system
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Conceptual approach
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Conjectural
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Empirical
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Subjective
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Metaphysical
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Single case possible
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Yes
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No
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Yes
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Yes
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Precise
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Yes
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No
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No
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Yes
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Problems
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Ambiguity in principle of indifference
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Circular definition
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Reference class problem
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Disputed concept
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Note: frequentist: 常客,propensity: 趋向,propensity accounts 可用于量子力学。
Reference class problem: 引用类问题--different may assign different prior prob.
Classical interpretation (Laplace) :
Laplace’s principle of insufficient reason: if there is no reason to believe that outcomes are not equally likely, take them to be equally likely. However, not believed to be unequally is one thing; known to be equal is another. 这里有逻辑上问题。有点像广义相对论中引力质量与惯性质量等价问题。
Evidential (证据) prob. Baysian prob. :
Subjective interp.
Logical interp. 如,一个恐龙灭绝的假设可能是真。
Eplstemlc (认知) or inductive interp.
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