13 December 2018 Andrew Reisner Normativity: A Unit of (Please note that this is the penultimate draft of an entry for the forthcoming edition of The International Encyclopedia of Ethics edited by Hugh LaFolette. Please consult the IEE for the final version.) Abstract: This entry discusses the notion of a unit of normativity. This notion may be understood in two distinct ways. One way to understand a unit of normativity is as some particular type of assignment of normative status, e.g., a requirement, an ought, a reason, or a permission. A second way to understand a unit of normativity is as a measure of a quantity of normativity, perhaps associated with the numerical assignment given to the strength of reasons. This entry outlines some basic differences among units of normativity in the first sense, noting that they vary slightly depending on whether one is talking about normativity in a more general or more robust sense. This entry also discusses in more detail the question of whether there might be a unit of normativity in the second sense. It discusses the relevant metaphysical questions. It also provides an explanation of why reasons can be assigned numerical strengths, even if there are no units of normativity in the sense of measurements of quantities of normativity. Introduction "Normativity" (see NORMATIVITY), as it appears in contemporary philosophical writings, has two main uses. Its most general use is to denote the property or a concept of being in some sense guiding. These normative properties or concepts include everything from the property or concept of being a conventional rule like those of chess or etiquette, to categorical moral duties like the injunction against harming innocents for pleasure (see DUTY AND OBLIGATION). The more narrow use of "normativity" picks out the property or concept of being guiding in a particularly robust sort of way. It is difficult to describe in independent terms 2 what this robust sort of way is, but one can point to examples. Conventional rules, like those of chess and etiquette, are not typically thought to be normative in this narrower sense. Moral duties, the requirements of prudence (self-interest), and epistemic justification, on the other hand, normally are. In this entry, the more general notion of normativity will be called "general normativity" and the narrower kind of normativity will be called "robust normativity". There are two ways of understanding the concept of a normative unit. One way is as being particular measure of normativity, analogous to a cubic centimeter as a unit of volume or a meter as a unit of length. Another, less literal, way to understand the concept of a normative unit is as reflecting a distinctive normative status, such as being required, prohibited, or forbidden. General normativity only has units on the second, less literal understanding of the concept. Robust normativity may have both kinds. This entry begins with a short discussion of units of general normativity before focusing in more detail on units of robust normativity. The entry concludes with some remarks on the relationship between units of normativity and the measurement of normativity more broadly. The Units of General Normativity General normativity is most often associated with conventional systems of rules, such as those of games like chess, social practices like etiquette and, more controversially, some strong forms of personal evaluation like rationality (see RATIONALITY). There are three main types of units associated with general normativity: requirements, permissions, and prohibitions. Although 'requirement', 'permission', and 'prohibition' are technical terms, their meanings are quite close to their normal natural language uses. The main difference is that in ordinary contexts, these terms are often used in conjunction with particular authoritative individuals or entities. For example, the Kommun of Uppsala prohibits the disturbance of birds' nests during mating and hatching season. In philosophical and some non-philosophical contexts, there need not be a particular individual or entity doing the requiring, permitting, and prohibiting. Instead, there may be some abstract system standards. For example, the rules of chess permit a rook to move either vertically or horizontally across the chessboard. 3 Although there are various controversies about how to understand the general normative units, at least two points are widely agreed upon. One is that each is interdefinable in terms of each of the others (see DEONTIC LOGIC): Required to x =df 1) Forbidden not to x 2) Not permitted not to x Permitted to x =df 1) Not required not to x 2) Not forbidden to x Forbidden to x =df 1) Required not to x 2) Not permitted not to x The other is that the units are strict when unconditional. "Strict" has a special meaning in this context, namely that these units do not come in degrees or ordered lists. For example one is required to x, as opposed to being strongly required to x or required to x more than to y. It is possible to have conditional requirements, permissions, and prohibitions. In that case, one is required, permitted, or prohibited from doing something so long as the conditions obtain. If they do not obtain, one cannot make any direct inference about the general normative status of the action in question. The last important thing to note is that in ordinary philosophical contexts there is little discussion of slack general normative units. A slack unit is one that does come in degrees. With respect to robust normativity, the slack unit par excellence is a normative reason (see REASONS and REASONS, MOTIVATING AND NORMATIVE). The distinction between strict and slack in the normative context originates in (Broome 1999). The Units of Robust Normativity: An Overview The aim of most normative inquiry is to discover what we ought to do, believe, or feel. "Ought" (see OUGHT) is the robust normative equivalent of 'required'. There are other ways to say "ought" in philosophical contexts. One can instead say "should" or "normatively required". If a specific kind of robust normativity is appealed to, for example robust moral normativity, then one might say "morally required", "morally ought", or "should morally". Irrespective of which term is used, the important thing to notice is that one wants to discover what action, belief, or feeling has the property of being robustly normatively required, i.e., to which action, belief, or feeling a strict robust normative unit applies. Just as with general normativity, the strict robust normative units are interdefinable. There are robust normative prohibitions and permissions that can be interdefined with ought. If x is morally forbidden, for example, then one morally ought not x. 4 While the final, strict robust normative unit is the one that plays the ultimate action, belief, or feeling guiding role, much of the current philosophical writing on robust normativity focuses on a slack robust normative unit, a normative reason. The overall balance of normative reasons is usually taken to determine what one ought to do, believe, or feel in a given circumstance. It is an imprecise, but illustrative metaphor to say that normative reasons are treated as the main currency of normativity more generally. Appealing to normative reasons provides a way of describing competing normatively relevant considerations. For example, the fact that Astrid's dog is unfriendly is a reason to avoid him. The fact that Astrid will be offended if you avoid her dog is a reason to meet her dog. If the first reason is stronger than the second reason, and jointly they constitute all the relevant reasons, then you ought to avoid Astrid's dog. Reasons can add up in favor or against something. That plant-based foods are environmentally friendlier is a reason to buy them instead of animal-based foods. The fact that plant-based foods produce less animal suffering is another reason to buy plant-based foods. Even if neither reason on its own were to outweigh a positive reason to choose animal-based foods, for example that you enjoy eating foods derived from animals, they still could do so jointly. In addition to the strict robust normative units and to reasons, there are various quasistrict units. A quasi-strict unit is one that does not feature in weighing relations but which nonetheless is in principle not the sole determinant of what one ought or is permitted to do. These units include prima facie oughts (see PRIMA FACIE AND PRO TANTO OUGHTS) side-constraints, and defeasing and silencing reasons. For more discussion, see (Cullity 2018). Reasons and More Reason The intuitive notion of a reason is a consideration that counts in favor of something for someone. One common view is that reasons are facts that count in favor of an individual agent feeling, believing, or doing something. Reasons are also normally attributed a certain strength or weight. Note that in this article, "strength" and "weight" are used interchangeably as is customary in the literature on reasons. We can express the important elements in the reason relation with a simple reasons schema, derived from the more complicated one developed in (Skorupski 2010: 37): Reasons schema: Fact f is a reason for agent A to ψ to strength s. 5 It remains an open question whether reasons are facts, but it is harmless to think of them that way for present purposes (Morganti and Tanyi 2017 and see REASONS, INTERNAL AND EXTERNAL). Agents are just individuals of the kind for whom there can be reasons. The schematic variable ψ can be an action (e.g., to hammer in a nail), a belief (e.g., to believe birds are dinosaurs), or a feeling (e.g., to feel sad). The question of concern to us is how to understand s, or the strength of a reason. In general, philosophers normally take it that the s place is occupied by a number corresponding to the strength of a reason. The idea that reasons have strengths, or weights, fits with natural ways of speaking and thinking about reasons. One can imagine a situation in which one is rushing one's seriously injured friend to the hospital. At one point on the way, there is a fork in the road. Driving to the hospital via the left fork takes only five minutes, although one passes through a rather nondescript part of town. Driving to the hospital via the right fork takes two hours, but the route goes through idyllic farmland. While there is a weak reason to take the right fork – namely that the scenery is very pleasant – there is a much stronger reason to take the left fork – namely that one's friend will receive care 115 minutes sooner. In such a case, one can say that the reason to take the left fork outweighs the reason to take the right fork. Of course, one need not use terms such "outweighs" or "is stronger than" in comparing reasons. One can also use expressions like "more reason", which perhaps gets most directly to the point. "Outweighs" is just a way of saying "has more weight" and "is stronger than" is just a way of saying "has more strength". Two Senses of 'Unit' and Two Kinds of Scales One sense of a 'unit' of normativity picks up the notions of reasons, oughts, requirements, permissions, and so forth. Different units in this sense can be used to tell us about the overall normative situation. The strict normative units tell us about how things stand overall, at least in a particular normative domain. The slack robust normative unit, a reason, tells us something about how a consideration contributes to determining how things stand overall (in a particular robust normative domain). It is tempting, because of the weighing terminology associated with reasons, to think that there is a second sense of a normative unit, namely a measure of a particular amount of normativity – a weight or a strength. 6 To answer questions about whether there are units of normativity in the second sense, one has to think about what it is one is trying to measure. Ignoring complicated problems about the nature of physical reality, we are usually happy to divide the world into time, space, matter, and energy. At least in our ordinary local environment, the existing time, space, matter, and energy can be partitioned into different amounts corresponding to specific features of reality. For example, a meter is stipulated as being the length equal to the distance travelled by light in vacuum in 1/299,792,458th of a second. The magnitude 1o Celsius is defined as 1/100th of the difference between the thermal kinetic energy of frozen water and that of boiling water at 1 atmosphere of pressure. It is important to note that there is something quite different about the measured values of an object's length in meters and an object's temperature in degrees C. An object with a length of 0 meters would have no extension in the relevant dimension. An object with a temperature of 0o C, however, still has thermal kinetic energy equal to that of frozen water at 1 atm. We can say that 0 meters really is zero of what it is measuring, namely length. On the other hand, 0o C is not zero of what it is measuring, namely thermal kinetic energy. Although subsequent research in physics has led to the discovery that -273 C is equivalent to there being a complete absence of thermal kinetic energy, this was not known when Anders Celsius developed the temperature scale in 1742. The Celsius temperature scale, at the time of its development, did not provide information about the absolute quantity of thermal kinetic energy at any given temperature. But it was nonetheless a very powerful measurement tool. It gave a way to identify temperature relative to the temperature of known substances in known conditions. It also provided information about the relative size of differences in temperature from any measured point. A pleasant spring day in Sweden is 20o C. A deadly hot day in India is 50o C. We can say that the difference in temperature between a freezing winter day and a pleasant spring day in Sweden is only 2/3rds that of the difference between that same pleasant day in Sweden and a fatally hot day in India. A scale that allows us to measure the size of relative differences is called an "interval scale". A scale that allows us to do that and also to measure absolute quantities is called a "ratio scale". A length scale in meters is a ratio scale. The Celsius temperature scale is an interval scale. See (Carlson 2015) for a more detailed discussion the differences in types of scales. There is now no reason why one need use an interval scale for temperatures instead of a ratio scale, since we now know that there is an absolute zero. The Kelvin temperature scale 7 uses the same magnitudes (one does not normally speak of degrees, Kelvin, just 1k, 2k, etc.), but it represents the complete absence of something, i.e., thermal kinetic energy, as zero. Measurements in Kelvin tell us the absolute quantity of thermal kinetic energy in the measured object. Is the Strength of a Reason a Measurement of its Normativity? Having a unit of normativity (or a unit in general) does not require us to be able to measure absolute quantities. We saw this with the Celsius temperature scale, at least as originally conceived. But for reasons that will be apparent presently, it will be helpful to think first about measuring an absolute quantity of normativity. Recall that the project of providing measurements of the physical world occurs in a context where it is assumed, or at least agreed upon for pragmatic purposes, that there is something to measure. Is there stuff, normativity, that is there in anything like an analogous way to physical properties and objects? And if so, is it that kind of thing that can be partitioned and measured in absolute quantities? Should we be inclined to take the analogy between units of normativity and physical units that we suppose there is a ratio scale of normative strength (Horty 2016)? These questions are beyond the scope the scope of this entry, but at least at first blush it seems difficult to imagine what a quantity of normativity would be like, or even what the concept, A QUANTITY OF NORMATIVITY, is. Physical units, whether used as part of an interval scale or a ratio scale, still pick out amounts. That is why in conjunction with a non-arbitrary zero point, units can be used to measure absolute and not just relative quantities. On a ratio scale, one measures how much more of something there is than nothing of it at all. We can try to construct a picture on which there is something like amounts of normativity. Suppose for the sake of argument that the only robustly normatively relevant features of the world are the pleasure and pain experienced by individuals. Let us also suppose that pleasure and pain can be measured in discreet units, hedons (see HEDONISM), and that there is a non-arbitrary zero quantity for each – a total absence of pleasure and of pain, respectively. Finally, let us assume that the normative importance of pleasure or pain is strictly proportional to the quantity of pleasure or pain. On this picture, the numbers used to represent the strength of reasons would be on a scale where 0 represented a complete absence of normativity (corresponding to a fact that had no 8 influence on the total quantity of pleasure or pain in the world). We could create a unit on the scale in several different ways. A convenient one would be to have one normative unit (NU) equal the normative significance of one hedon, assuming the normative significance of a hedon was uniform. For an example of a view developed along similar lines, see (Tännsjö 2011: 27-40). This is a rather narrow example, but it will do for the present purpose. If we assume that there are quantities of normativity, there are at least some conceivable ways the world could be in which we could represent those absolute quantities in NUs. If we could not find a non-arbitrary zero point, we could not represent absolute quantities. That would not preclude there being NUs. We could point to two normatively significant features, say having a mild pain in one's toe and experiencing the grief of losing a pet, and we could assign an arbitrary number to the former (5) and a larger arbitrary number to the second (55). An NU would then be 1/50th of the difference between them. These are partial methods for creating ratio or interval scales with NUs. But notice that in both cases, one must presuppose that there is something to measure, i.e., amounts of normativity. It is one thing to create systems of measurement that use numerical scales, but it is another to think that the numbers on the scale are in fact units of something. Whether the strength of a reason is a unit measurement of its normativity in this particular sense depends in part on whether one things that there a) is such a thing as robust normativity and b) is such that it has measureable quantities. Units of Robust Normativity without Quantities of Robust Normativity? Whether there is robust normativity in some sufficiently strong sense of "there is" remains an open question in the philosophical literature. If there is robust normativity in the relevant sense, whether it is the kind of thing that comes in measurable quantities seems doubtful at first blush, but arguing definitively that it is or is not would be a difficult task. A more straightforward task is to ask whether there can be units of normativity if there are not quantities of normativity. The short answer to this question is "no", at least not if by "units" one means something strongly parallel to the kinds of units that one sees in the natural sciences. But that does not mean that the use numbers to represent the strength of reasons is mistaken or problematic on those grounds. Of course, there may be other grounds on which to worry (Berker 2007). Much depends on what one thinks the role of the strength of a reason is in the wider context of an account of normativity. 9 It may be helpful to start by briefly comparing the role of scorekeeping in baseball and basketball. The unit of scoring in baseball is "a run". A run is also an event in baseball that occurs when a player successfully gets around all the bases in the course of a single inning without being personally out. Because the score in a baseball game is just a tally of runs, one can see it simply as the representation of a quantity, i.e., a quantity of runs. One can define the winner of a baseball game in terms that do not involve referring to the score; a team that has the greater number of runs, in the sense of the event, is the winner. On the other hand, the unit of scoring in basketball is a point. Different scoring events generate different numbers of points. An ordinary basket is worth two points, a free throw is worth one point and three-point basket is worth three points. The score in basketball is a function of the number of each kind of basket made, but it is not a tally of baskets made. Unless a team has scored either zero or one point, it is not possible to infer how many of each kind of basket were made from the score of a basketball game. For this reason, one cannot straightforwardly define the winner of a basketball game without referring to the score. The highest scoring team wins. The non-straightforward way to identify the winner of a basketball game would be to generate a list of the all the possible made-basket combinations possible in the relevant sense for human basketball teams. The combinations could then be organized into tiers, with each tier containing combinations, none of which dominate the others. The tiers could then be ordered such that combinations of baskets in higher tiers count as winning when put up against those in lower tiers. The first method of identifying the winner of a basketball game is of course preferable for practical reasons. When we look at the second method, however, we can see that the score does nothing more than create an ordering over different possible combinations of baskets made. It is not a representation of a quantity of anything. When we look at the point value of each type of basket, we can then also see that its point value is not a representation of a quantity of anything either. It is a representation of that basket's contribution to the ranking of the team's final combination of baskets. Unlike a run in baseball, a point in basketball is not a unit in a sense parallel to that of a unit in physics. It is possible to see the strength of reasons as being like points in a basketball game. The strength of a reason indicates a particular fact or consideration's contribution to the ranking of a set of considerations in an ordering. The ordering is such that the top ranked available option is the one that one ought to do. Of the course, the question remains as to what it is for a reason to contribute to an ought-determining 10 ranking. One possibility is that reasons are weighing explanations of oughts (Broome 2013). Another is that reasons are evidence for oughts (Kearns and Star 2015; Thompson 2008). This picture is consistent with strong forms of realism about robust normativity. The action that one ought to do on such a view has a real normative property, namely being what one ought to do. But the fact that there are real normative properties does not entail, or even suggest, that there are quantities of normativity. The assignment of strengths to reasons may be understood as suggesting that there are quantities of normativity that are being measured, but one can coherently understand them in a different way. The use of "weighing" and "strength" talk with reasons may be little more than a loose metaphor (Liberman and Schroeder 2016). Conclusion This entry has discussed the possibility that there are two senses in which there might be units of normativity. There might be units of normativity in the sense that there are distinct kinds of normative statuses. For general normativity those statuses include requirements, permissions and prohibitions. For robust normativity they include ought and robustly normative permission and prohibition. Another commonly discussed robust normative unit is a reason. Consideration of reasons leads to the second sense of a normative unit, namely something that is a measure of a quantity of normativity. It is intuitively odd to imagine that normativity is the kind of thing that can be partitioned into quantities, but the possibility has not been directly argued against here. The use of strengths with reasons, however, does not require a commitment, even for normative realists, to there being quantities or measurements of normativity. The strength of reasons may just be a way of describing the contribution of a particular consideration to determining whether one ought or ought not to do an action. If that is the right way to understand the strength of reasons, then it would otiose to posit that there are units of normativity in the second sense. REFERENCES: Berker, Selim 2008. "Particular Reaosns," Ethics vol. 118, pp. 109-139. 11 Broome, John 1999. "Normative Requirements, " Ratio vol. 12, pp. 78-99. Broome, John 2013. Rationality through Reasoning. Chichester United Kingdom: Wiley Blackwell. Carlson, Erik 2015. "Organic Unities," in Iwao Hirose and Jonas Olson (eds.), The Oxford Handbook of Value Theory. New York, NY: Oxford University Press, pp. 285-303. Cullity, Garrett 2018. "Weighing Reasons," in Daniel Star (ed.), The Oxford Handbook of Reasons and Normativity. Oxford: Oxford University Press, pp. 423-442. Horty, John 2016. "Reasoning with Precedents as Constrained Natural Reasoning," in Errol Lord and Barry Maguire (eds.) Weighing Reasons. New York, NY: Oxford University Press, 193-212. Kearns and Star 2015. "Weighing Explanations," in Iwao Hirose and Andrew Reisner (eds.) Weighing and Reasoning: Themes from the Philosophy of John Broome. Oxford, Oxford University Press, pp. 232-252. Liberman, Alida and Schroeder, Mark 2016. "Commitment: Worth the Weight," in Errol Lord and Barry Maguire (eds.) Weighing Reasons. New York, NY: Oxford University Press, pp. 104-122. Morganti, Matteo and Tanyi, Attila 2017. "Can Reasons be Propositions? Against Dancy's Attack on Propositionalism," Theoria vol. 83, pp. 185-205. Skorupski, John 2010. The Domain of Reasons. Oxford: Oxford University Press. Thompson, Judith Jarvis 2008. Normativity. Chicago IL: Open Court Press. Tännsjö, Torbjörn 2011. From Reasons to Norms. Netherlands: Springer. 12 SUGGESTED READINGS Brunero, John 2013. "Reasons as Explanations," Philosophical Studies vol. 165, pp. 805-824. Buss, Sarah 2018. "Moral Requirements and Permissions, and the Requirements and Permissions of Reason," in Karen Jones and François Schroeter (eds.), The Many Moral Rationalisms. Oxford: Oxford University Press, pp. 110-144. Chang, Ruth (ed.) 1997. Incommensurability, Incomparability, and Practical Reason. Cambridge, MA: Harvard University Press. Dancy, Jonathan 2004. Ethics without Principles. Oxford: Oxford University Press. Horty, John 2007. "Reasons as Defaults," Philosophers' Imprint vol. 7, pp. 1-28. Olson, Jonas 2018. "The Metaphysics of Reasons," in Daniel Star (ed.), The Oxford Handbook of Reasons and Normativity. Oxford: Oxford University Press, pp. 255-274 Reisner, Andrew 2008. "Weighing Pragmatic and Evidential Reasons for Belief," Philosophical Studies vol. 138, pp. 17-27. Scanlon, T.M. 2004. "Reasons: A Puzzling Duality?" in R. Jay Wallace, Philip Pettit, Samuel Scheffler, and Michael Smith (eds.) Reason and Value: Themes from the Moral Philosophy of Joseph Raz. Oxford: Oxford University Press, pp. 231-246. Wedgwood, Ralph 2007. The Nature of Normativity. Oxford: Oxford University Press.