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    If incommensurability is treated as indifference, or if '... — Carmelics
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    Supports→Incommensurability can be reframed as a challenge to the Transitivity axiom rather than Completeness

    If incommensurability is treated as indifference, or if 'A is at least as good as B' is defined as the negation of 'B is strictly better than A', then Completeness holds by definition

    Modality & Possibility
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    Modality & Possibility

    Key Terms

    'A is at least as good as B'(used in preference and value comparisons)
    A formal way of saying A is either better than B or equal to B (ruling out only the case where B is clearly better).
    Incommensurability(Decision theory / rational choice theory)
    A relation between two options A and B such that neither A is at least as good as B nor B is at least as good as A, under the standard interpretation of the weak preference relation
    Strictly better than(used in comparisons of value)
    Clearly superior in every relevant way, leaving no room for a tie or equality.

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    Related propositions within the same area of thought.
    by definition(Used to explain what makes something necessarily true based on word meanings)
    Something that is true simply because of how a word is defined, not because of how the world actually is.
    completeness(Used to transfer results from model theory to proof theory)
    The property of a logical system whereby anything valid (model-theoretically) is deducible (proof-theoretically)
    negation(Standard truth conditions for logical negation, used as the basis for arguments against dialetheism)
    ¬A is true if and only if A is not true

    Related

    Incommensurability can be reframed as a challenge to the Transitivity axiom rath...The indifference relation generated by incommensurability is intransitiveUnder these assumptions, incommensurable options satisfy the indifference relati...

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    The indifference relation generated by incommensurability is intransit...83%Incommensurability treated as indifference yields: A is indifferent to...79%Under these assumptions, incommensurable options satisfy the indiffere...78%The existing trichotomy of 'better than', 'worse than', and 'equally g...77%

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    SEP: rationality-normative-nonutility
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    Incommensurability is most directly a challenge to Completeness, since on the most natural interpretation of \(\succcurlyeq,\) the fact that \(A\) and \(B\) are incommensurable means that neither \(A \succcurlyeq B\) nor \(B \succcurlyeq A.\) But incommensurability can instead be framed as a challenge to Transitivity, if we assume that incommensurability is indifference, or define \(A \succcurlyeq B\) as the negation of \(B \succ A\) (thus assuming Completeness by definition). To see this, notic

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