Over the last 30 years there have been a number of attempts to analyse the distinction between intrinsic and extrinsic properties. This article discusses three leading attempts to analyse this distinction that don't appeal to the notion of naturalness: the duplication analysis endorsed by G. E. Moore and David Lewis, Peter Vallentyne's analysis in terms of contractions of possible worlds, and the analysis of Gene Witmer, William Butchard and Kelly Trogdon in terms of grounding.
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Marshall, D. (2013). Analyses of intrinsicality without naturalness. Philosophy Compass, 8(2), 186-197. doi: 10.1111/phc3.12004