Abstract
According to a standard account of incomparability, two value bearers are incomparable if it is false that there holds a positive value relation between them. Due to the vagueness of the comparative predicates it may also be indeterminate as to which relation that holds - for each relation it is neither true nor false that it holds. John Broome has argued that indeterminacy cannot coexist with incomparability and since there seems to exist indeterminacy there cannot exist incomparability. At the core of his argument lies the collapsing principle. There are several arguments against this principle; Erik Carlson has advanced most of these. In this paper two strategies in dealing with these arguments are discussed. One strategy is to deny the existence of a certain kind of properties; another strategy that has been advanced by Christian Constantinescu is to restrict the collapsing principle. In the paper it is argued that the first of these strategies is the most promising strategy. A novel argument in favour of this strategy is presented and several objections to the strategy are rebutted. Finally it is concluded that, even though this strategy deals with most objections, without a better argument in favour of the principle the debate seems to run into a stalemate.
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Notes
If we assume the supervaluation theory of vagueness it is also a possibility that the disjunction of the relations is true even if none of the relations in themselves are true. In the same sense the disjunctions may be indeterminate.
The following discussion is applicable to most comparatives but I am mostly interested in evaluative and moral comparatives. In fact, I will mostly treat, “Fer than” as a shorthand for “better than”. It should also be noted that, for brevity, I will refer to this principle as the “collapsing principle” and later on as the “dyadic collapsing principle”.
As Wlodek Rabinowicz notes this only proves that determinate incomparability is impossible (2009 p. 80 n. 16). Since for those points, for which it is indeterminate whether they are incomparable with the standard or not, it is not false that the standard is Fer than them, and thus the collapsing principle does not kick in. Thereby indeterminate incomparability may be compatible with indeterminacy.
Rabinowicz has presented an interpretation of Constantinescu’s argument that may widen the scope of the collapsing principle somewhat. But even though this interpretation severely limits the space for incomparability it does not rule it out fully. The interpretation is presented in Carlson 2012 p. 13.
The argument only holds for indeterminacy that is construed in the narrow sense that Constantinescu advocates. As we soon will see there are also other sorts of indeterminacy that is not of the kind that it is indeterminate whether x is Fer than y because it is unclear what it is for x to be F. Perhaps this kind of vagueness also ought to be labelled derivative. However, the argument will not hold for this broad sense of derivative vagueness since it does not presuppose the existence of the indeterminately relevant properties.
Constantinescu does not provide an argument in favour of the restricted collapsing principle. Perhaps it is because he is reasoning along these lines.
That these relations can only exist if there are properties of the indeterminately relevant kind is not surprising. This is the very reason why Constantinescu distinguishes genuine vagueness from derivative vagueness.
I have chosen to present those objections that I find to be the most pressing, but it should be noted that according to Carlson there are more problems with Constantinescu’s strategy. For example it is problematic to understand genuine vagueness in terms of the counterfactual test since the test may yield the result that it is “very implausible that such vagueness exists”. (Carlson 2012, p. 11) I don’t find this objection too worrying though. That the counterfactual test is problematic does not mean that the distinction cannot be made. There may be other ways for us to make the distinction. In other words Carlson’s objection does not conclusively show that the distinction is impossible to make and thus I do not believe this is the most worrisome objection.
Gustafsson’s example has a similar structure as the example I have presented but his example uses bald cavaliers instead of narrow-minded philosophers. (Gustafsson 2011, p. 26)
An anonymous referee expressed a worry that it is question-begging to accept the monadic collapsing principle. The sceptic will claim that what follows from the fact that “it is not false that x is F” and “it is false that y is F” is only that it is not false that x is Fer than y. I.e. there is a need for an independent argument in favour of the monadic collapsing principle. I disagree. Since the “dyadic” collapsing principle entails the monadic collapsing principle there is no need for a separate argument in favour of the monadic collapsing principle. The objection that I am begging the question by assuming the monadic collapsing principle is the very same objection that was discussed when my argument against the existence of indeterminately relevant properties was first introduced. And if I am right in my reasoning there I don’t need an independent argument in favour of the monadic collapsing principle.
An anonymous referee pointed out that if “more shorter than average” is equivalent to “less taller than average” then the cavalier who is taller than average but yet shorter than the other cavalier would be “more shorter than average”. And thus my response fails. This would of course be true if “more shorter than average” is equivalent to “less taller than average”. However, I don’t believe them to be equivalent. Even if “more shorter than” is equivalent to “less taller than”, it does not follow that “more shorter than average” is equivalent to “less taller than average”. To be more shorter than the average one must be shorter than the average and in order to be less taller than the average one must be taller than the average.
Another possible reply to Carlson’s doubts could be to add a condition to P. For example the view could be expressed as: “if Fness contribute negatively to a certain kind of goodness, and x and y are identical in all value relevant aspects, except that y is Fer than x and it is not false that y is F then x is better than y.”
One could object to this. It could be argued that there is vagueness because the criteria of being F is not fully clear. For example, the reason it is indeterminate whether Alf is dead or not is that “is dead” is a vague predicate. Is one dead when one stops breathing? Or must one’s heart stop beating? Or must one be “brain dead”? Or must all of one’s electrical activity have ceased? Say that Alf satisfies the first three criteria. In such a scenario it might be correct that due to the vagueness of “dead” it is indeterminate whether or not Alf is dead. However, in such a case it seems equally intelligible that Alf is more dead than Beth who only satisfies the first two criteria.
As Carlson also notes one cannot argue that the transition is not as sharp as one may first believe by arguing that it may be not false that the standard is Fer than this point but that it is more false than true that the standard is Fer than x, since the collapsing principle would then imply that the point is Fer than the standard.
Semicomparabilism is the view that there is indeterminacy but no determinate incomparability.
I have only discussed Carlson’s and Gustafsson’s objections and concluded that they are not a problem for the collapsing principle. However, there might be other objections that need to be dealt with. For example, an objection presented in Elson (2014) might be of a bigger problem for the adherents of the collapsing principle.
References
Broome J (1997) Is incommensurability vagueness. In: Chang R (ed) Incommensurability, incomparability, and practical reason. Harvard University Press, Cambridge and London, pp 67–89
Broome J (2009) Reply to Rabinowicz. Philos Issues 19:412–417
Carlson E (2012) Vagueness, incomparability, and the collapsing principle. Ethical Theory Moral Pract 16:1–15
Constantinescu C (2012) Value incomparability and indeterminacy. Ethical Theory Moral Pract 15:57–70
Elson L (2014) Borderline Cases and the Collapsing Principle. Utilitas
Gustafsson JE (2011) Preference and choice. Royal Institute of Technology, Stockholm
Rabinowicz W (2009) Incommensurability and vagueness. Aristot Soc Suppl Vol 83:71–94
Acknowledgements
Earlier versions of this paper were presented at the Higher Seminar in Practical Philosophy in the autumn of 2012 at Lund University and at the conference Understanding Value at the University of Sheffield in the summer of 2013. I would like to thank those attending these seminars for helpful comments. I would also like to thank John Broome and Wlodek Rabinowicz for helpful comments on earlier drafts of this paper. Many thanks are also due to the anonymous referees of this journal whose comments greatly helped me to improve earlier versions of this article. I would also like to thank Luc Bovens, Wlodek Rabinowicz and Katie Steele for suggesting me the title of this article.
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Andersson, H. Propping Up the Collapsing Principle. Ethic Theory Moral Prac 18, 475–486 (2015). https://doi.org/10.1007/s10677-014-9533-9
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DOI: https://doi.org/10.1007/s10677-014-9533-9