The Significance of Value Additivity

Erkenntnis https://doi.org/10.1007/s10670-020-00315-3 ORIGINAL RESEARCH The Significance of Value Additivity Campbell Brown1 Received: 16 August 2018 / Accepted: 24 August 2020 © The Author(s) 2020 Abstract Whether value is “additive,” that is, whether the value of a whole must equal the sum of the values of its parts, is widely thought to have significant implications in ethics. For example, additivity rules out “organic unities,” and is presupposed by “contrast arguments.” This paper reconsiders the significance of value additivity. The main thesis defended is that it is significant only for a certain class of “mereologies”, roughly, those in which both wholes and parts are “complete”, in the sense that they can exist independently. For example, value additivity is significant in the case of a mereology of material objects, but not in the case of a mereology of propositions. 1 Introduction By saying that value is “additive” I shall mean that the value of a whole must equal the sum of the values of its parts. Whether value is additive in this sense has been regarded as important by many philosophers. Moore (1903) famously warned against assuming additivity. He posited “organic unities” whose values are non-additive. Familiar examples abound: a football team of mediocre players who coordinate well together may defeat a team full of individually brilliant lone wolves; a collection of tasty ingredients may combine to form a disgusting dish; a knife paired with a fork may be very useful, while either utensil alone is of only limited utility; and so on.1 Additivity is also widely thought to be implicated in a pervasive, yet controversial, style of argument in moral philosophy. Kagan (1988) calls arguments in this style “contrast arguments”. Perhaps the most famous is advanced by Rachels (1975) in his discussion of active and passive euthanasia. Some believe active euthanasia is 1 On organic unities, see, e.g., Carlson (1997), Hurka (1998), Lemos (1998, 2015), Zimmerman (1999), Dancy (2003), Brown (2007), Fletcher (2010). * Campbell Brown 1 London School of Economics, Houghton Street, London WC2A 2AE, UK 13 Vol.:(0123456789) C. Brown morally worse than passive euthanasia because the former involves killing a person, whereas the latter involves only letting a person die. Rachels rejects this view. He describes another pair of cases which differ only in that one involves killing and the other letting die, but in which, intuitively, neither is morally worse than the other. In both cases, a man sets out to drown his innocent cousin. In one case he carries out his plan, killing his cousin. In the other case, he finds his cousin already drowning, and so instead simply stands by and lets him die. If the bare difference between killing and letting die makes no moral difference in this pair of cases, Rachels argues, then it cannot make a difference in cases of active and passive euthanasia either. According to Kagan, arguments like Rachels’ covertly assume that value is additive.2 On the other hand, one might be sceptical about the significance of additivity. One might doubt whether there’s any substantive difference between additive and non-additive assignments of values, and regard this instead as merely a matter of “bookkeeping”. One source of scepticism may be that it seems possible to divide a set of whole objects into parts in different ways, some of which are compatible with additivity and others not. But there may seem to be no further fact about which is the “correct” division, so it is merely a matter of taste whether one opts for an additive division or a non-additive one. I shall, however, pursue a different line of scepticism. One might fell that, ultimately, only the values of wholes matter. But additivity might not constrain the values of wholes. It might be the case that, for any assignment of values to wholes, one can find an assignment of values to the parts such that these add up in the required way. In that case, additivity may appear to be a non-issue. The main thesis defended in this paper is that whether additivity is significant depends on the sort of mereology involved. By a “mereology” I mean a collection of objects (of whatever kind) related to each other by a parthood relation, so some are parts of others. Parthood relations hold between entities of diverse kinds. Perhaps the most obvious are physical objects: tables, chairs, dogs, mountains, and so on. In this case, parthood is determined spatially (and perhaps also temporally). The parts of a physical object occupy subregions of the space occupied by this object. But we talk also of parthood among abstract objects, such as properties, propositions, and states of affairs. For example, Socrates’ being rational may be a part of his being a person. Here parthood is determined by “modal” space, instead of physical space. The possibilities in which Socrates is a person are a subset of those in which he is rational. The “region” of modal space occupied by the former set of possibilities is a subregion of that occupied by the latter. Notice, however, that the order here is reversed, in comparison to physical objects. For abstract objects, it is the whole that occupies the subregion, whereas for physical objects, it is the part. The unifying general principle governing parthood in all these cases is that you cannot have the whole without the part, but you can have the part without the whole. (By “part” here I mean proper part.) In the case of physical objects, a whole cannot exist without its parts also existing, but each part can exist without the whole. For example, a table cannot exist without a tabletop, but a tabletop can exist without a 2 On contrast arguments, especially Rachels’ “bathtub” example, see, e.g., Philips (1987), Kamm (1996), Asscher (2007), Purves (2011), Woollard (2012). 13 The Significance of Value Additivity table. The same holds for propositions, except what matters here is not existence, but truth. A whole proposition cannot be true without its parts being true, but each part can be true without the whole being true.3 Likewise, a whole property cannot be instantiated without its parts being instantiated, and a whole state of affairs cannot obtain without its parts obtaining. We may evaluate both concrete and abstract objects. We may say, for example, that a dog is good, or a computer is bad. But we may also say that it is good that a person is happy, or bad that she is depressed. When evaluation and mereology are combined, the question of value additivity arises.4 We may ask whether the value of a whole must be the sum of the values of its parts. I argue, however, that additivity is significant only in a certain sub-class of mereologies, namely, those in which the parts are, as I say, “complete”. Consider, for example, the property of being red. It is impossible for anything to be merely red, without being any specific shade of red. This property cannot, therefore, be in (...truncated)