The principle of indifference cannot be coherently applied when the partition of a possibility space admits multiple non-equivalent descriptions yielding different probability assignments.

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Coherently(as describing how these functions work together): In a way that is logically consistent and doesn't contradict itself.
Non-equivalent descriptions(as used in logic and philosophy): Different ways of describing or organizing the same situation that are not identical and may lead to different conclusions.
Partition of a possibility space(as used in probability theory): A way of dividing up all the possible outcomes of a situation into separate, non-overlapping categories. Think of it like sorting all possible results into distinct boxes where each result goes in exactly one box.
Principle of Indifference(Bayesian epistemology): A norm requiring a doxastic agent to distribute subjective probabilities uniformly across a partition whenever the agent lacks evidence of the relevant kind.

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