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It is not the case that A perfect single-number hedonimeter measuring happiness with full precision may be impossible even in principle.
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Reasons For
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Reason for
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1.
Happiness might involve multiple dimensions.
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2.
Those dimensions either cannot be precisely quantified or cannot be summed into a single value.
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Reasons Against
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Reason against 1 of 2
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1.
Bentham's own felicific calculus required seven independent dimensions (intensity, duration, certainty, propinquity, fecundity, purity, extent), each raising distinct incommensurability problems.
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2.
Ruth Chang's work on 'on a par' relations demonstrates that value comparisons can be neither equal, greater, nor lesser, making aggregation into a single number formally incomplete.
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3.
If even two hedonic states can stand in a 'parity' relation resistant to cardinal ordering, then a single-number hedonimeter would systematically misrepresent the structure of hedonic value.
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Reason against 2 of 2
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1.
Pleasure and pain involve phenomenal qualia whose intrinsic character resists reduction to any uniform cardinal scale, as argued by Nagel's 'what it is like' framework.
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2.
Interpersonal comparisons of hedonic intensity require a common unit that cannot be grounded in either behavioral or neurological data without begging the question.
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