¹ See Chang, R., ‘Introduction’, Incommensurability, Incomparability, and Practical Reason, ed. Chang, R. (Cambridge, MA, 1997), pp. 1–34 Google Scholar; and Chang, R., ‘The Possibility of Parity’, Ethics 112 (2002), pp. 659–88CrossRefGoogle Scholar.

² See Scanlon, T., What We Owe To Each Other (Cambridge, MA, 1998)Google Scholar; Rabinowicz, W. and Rønnow-Rasmussen, T., ‘The Strike of the Demon: On Fitting Pro-Attitudes and Value’, Ethics 114 (2004), pp. 391–423 CrossRefGoogle Scholar; Danielsson, S. and Olson, J., ‘Brentano and the Buck-Passers’, Mind 116 (2007), pp. 511–22CrossRefGoogle Scholar.

³ See Rabinowicz, W., ‘Value Relations’, Theoria 74 (2008), pp. 18–49 CrossRefGoogle Scholar; Rabinowicz, W., ‘Value Compared’, Polish Journal of Philosophy 3 (2009), pp. 73–96 CrossRefGoogle Scholar; Rabinowicz, W., ‘Value Relations Revisited’, Economics and Philosophy 28 (2012), pp. 133–64CrossRefGoogle Scholar. Rabinowicz develops, and substantially modifies, a line of thought originally proposed by Joshua Gert (see Gert, J., ‘Value and Parity’, Ethics, 114 (2004), pp. 492–510 CrossRefGoogle Scholar). Since Gert's proposal is subject to some important objections (see Chang, R., ‘Parity, Interval Value, and Choice’, Ethics 115 (2005), pp. 331–50CrossRefGoogle Scholar, at 337–44; Rabinowicz, ‘Value Relations’, pp. 30–6), in what follows I shall focus only on Rabinowicz's FA-analysis.

⁴ Gustafsson, J., ‘Value–Preference Symmetry and Fitting-Attitude Accounts of Value Relations’, The Philosophical Quarterly 63 (2013), pp. 476–91CrossRefGoogle Scholar.

⁵ In this article, I revise and extend my discussion of Gustafsson's arguments in Rossi, M., ‘Sur la symétrie présumée entre valeurs et préférences’, Les ateliers de l’éthique/The Ethics Forum 9 (2014), pp. 82–98 Google Scholar.

⁶ It is worth noticing that, on Rabinowicz's approach, parity turns out to be a non-atomic type of value relation. In fact, within Rabinowicz's framework, parity is the collection of four atomic types.

⁷ In further support of this line of thought, Gustafsson adds that the authors who first proposed the small improvement argument and the chaining argument (i.e. respectively, de Sousa, R., ‘The Good and the True’, Mind 83 (1974), pp. 534–51CrossRefGoogle Scholar, at 544–5; and Chang, ‘The Possibility of Parity’, p. 666) have either formulated these arguments in terms of preferences, rather than value, or explicitly claimed that their arguments apply to preference relations as much as to value relations.

⁸ See Chang, ‘The Possibility of Parity’, pp. 674–5; see also Gustafsson, ‘Value–Preference Symmetry’, p. 484.

⁹ This is not to say that the version of the Small Unidimensional Difference Principle in terms of required preferences is fully convincing. For instance, one may argue against it by claiming that, in cases of small unidimensional changes, one may sometimes be permitted (although not required) to have a preferential gap between the items. Notice that, if one endorses this line of thought, one will also be logically compelled to endorse a weaker axiological version of the principle, stating that, if two items x and y are fully comparable in terms of value and if a third item z differs from y only with respect to one dimension relevant for comparison, then x and z are weakly comparable in terms of value; where two items x and y are fully comparable if and only if one is required to prefer one of these items to the other or to be indifferent between them; and where two items x and y are weakly comparable if and only if one is not required to have a preferential gap between them. For the notions of full and weak comparability, see Rabinowicz, ‘Value Relations’, pp. 27–8.

¹⁰ Gustafsson, ‘Value–Preference Symmetry’, p. 488.

¹¹ One may be tempted to argue that, if we cannot make sense of preferential parity, then we cannot make sense of axiological parity either. Once again, however, this would be true only if we had independent reason to believe the principle of value–preference symmetry. Since we do not, and since there exists an alternative way of making sense of the notion of axiological parity, i.e. Rabinowicz's, then we should simply conclude that, in some cases, there exist value relations that lack corresponding preference relations. In other words, unless Gustafsson can provide a suitable account of preferential parity, we have no reason to think that value and preference relations are symmetric.

¹² The reason for this condition is the following. As we have seen above, if axiological parity exists as a genuine positive value relation, then it exists as a relation that cannot be reduced to the standard value relations. By the principle of value–preference symmetry, it follows that, if preferential parity exists as a genuine positive preference relation, then it exists as a relation that cannot be reduced to the standard preference relations.

¹³ Incidentally, this proposal would also be incompatible with another principle to which Gustafsson subscribes in his article, namely, the principle of Non-irrationality of axiological constrainedness. According to it, if none of a set of value relations holds between x and y, then one is not rationally required to have one of the corresponding preference relations. Since axiological parity holds when none of the standard value relations holds, the principle of Non-irrationality of axiological constrainedness entails that, in such cases, one is not required to have any of the standard preference relations. However, if we define preferential parity as the disjunction of two (or more) standard preference relations, it precisely follows that, when axiological parity holds, one is required to have either one of the corresponding standard preference relations – a clear violation of the principle of Non-irrationality of axiological constrainedness.

¹⁴ See W. Rabinowicz, ‘From Values to Probabilities’, forthcoming in Synthese, fn. 11.

¹⁵ Wlodek Rabinowicz has suggested to me that there exists a third way of reconstructing Gustafsson's argument, i.e. in terms of permissible, rather than actual or required, preferences. When reformulated accordingly, the small improvement argument states that there exist some x and y such that one is not permitted to strictly prefer x to y, nor permitted to be indifferent between x and y, nor permitted to strictly prefer y to x. In turn, the chaining argument states that, in such cases, one is permitted not to have any preferential gap between x and y. The combination of these arguments is incompatible with Rabinowicz's analysis, but compatible with Gustafsson's. The question, then, is whether the small improvement argument and the chaining argument, thus formulated, are as cogent as in the axiological case. In fact, there is reason to doubt that. Let us focus on the small improvement argument. Recall that the axiological version of this argument can be equivalently reformulated in terms of required preferences. When reformulated accordingly, the small improvement argument states that there exist some x and y such that one is not required to strictly prefer x to y, nor required to be indifferent between x and y, nor required to strictly prefer y to x. The important thing to notice is that, in this case, it may still be permissible for one to have any of these preference relations between x and y. By contrast, this is excluded by the version of the small improvement argument in terms of permissible preferences. For this reason, the latter appears to be a considerably more demanding, and less plausible, argument.

¹⁶ Gustafsson, ‘Value–Preference Symmetry’, p. 490.

¹⁷ As Gustafsson suggests elsewhere. See Gustafsson, J., ‘Indeterminacy and the Small-Improvement Argument’, Utilitas 25 (2013), pp. 433–45CrossRefGoogle Scholar, at 445.

¹⁸ Another possibility is that two items x and y may be axiologically weakly on a par when x is equally good as y.

¹⁹ Notice, however, that Gustafsson allows also for the possibility that axiological weak parity may hold when none of the standard value relations holds. See Gustafsson, ‘Value–Preference Symmetry’, p. 490.

²⁰ Arguably, the FA-analysis is a theoretical attempt to clarify, refine and systematize our pre-theoretical understanding of value relations. In fact, the latter seems to be too ambiguous and confused for it to serve as the main evidence in favour of a theoretical principle such as (L).

²¹ Accordingly, we can say that an individual has a preferential attitude c between two items x and y if and only if she both holds x and y preferentially on a par and strictly prefers x to y.

²² I am especially grateful to Wlodek Rabinowicz for his very useful comments as a no-longer-anonymous referee for this article. I would also like to thank Krister Bykvist, Erik Carlson, Denis Courville, Jens Johansson, Christopher Kelly, Sebastiano Moruzzi, Graham Oddie, Niklas Olsson-Yaouzis, Michele Palmira, Jean-Charles Pelland, Daniel Ramöller, Frans Svensson, Jennifer Szende, Christine Tappolet, Giorgio Volpe and one anonymous referee for their helpful comments on previous versions or presentations of the article.