Argumentative Strategies Against Bradley's Regress Joshua Woo ________________________________________________________________________ In this paper I will examine the infinite regress arguments pertaining to the unreality of relations that are presented in Francis Herbert Bradley's paper, Appearance and Reality. Then I will suggest two argumentative strategies one can take to undermine Bradley's regress argument. The first option concerns plainly rejecting the regress by stating that Bradley is viewing relations as kinds of objects that are in need of being related, whereas the second option is in regards to adopting an existential-dependence view between objects and their properties to refute the need for relations. I will conclude this paper by comparing these two strategies against each other, alluding to each of their ramifications. ________________________________________________________________________ The first sections of the paper I will provide a brief overview of Bradley's Appearance and Reality, aiming to show how Bradley arrives to his regress arguments pertaining to the unreality of relations. In Chapter II of his essay, called Substantive and Adjective, Bradley provides his reasoning for assuming a bundle theory of particulars through analyzing a lump of sugar. Foremost, we can take the lump of sugar to have the properties of whiteness, hardness, 1 and sweetness. According to Bradley, we may examine and compare the individual properties of the lump of sugar to the object that is the lump of sugar itself and find that the lump of sugar is not identical with any one of its properties: "A thing is not any one of its qualities, if you take that quality by itself; if 'sweet' were the same as 'simply sweet', the thing would clearly be not sweet" (Bradley 1893:16). Also, the lump of sugar does not seem to be merely all of its properties - sugar does not seem to be the plurality of mere whiteness, mere hardness and mere sweetness. Nor is an object something that is distinct from all of its properties; the lump of sugar does seem to contain some aspects of whiteness, hardness and sweetness, after all. Thus Bradley's analysis so far consists of stating that an object is not being identical with (1) one of its properties, (2) with the set of its properties, (3) nor is distinct from all of its properties - and these claims do not seem to be particularly implausible or problematic. The results from this process of elimination lead Bradley to consider a final option, the bundle theory of particulars: the lump of sugar is its properties coexisting in a certain way, or to put it in other words, the lump of sugar is identical to its properties coexisting in a certain relation. In this paper, the terms 'properties' and 'qualities' will be used interchangeably, to mean the same thing.1 2 Bradley provides some definitions regarding the term 'relation' in Chapter III: "Relation presupposes quality, and quality relation. Each can be something neither together with, nor apart from, the other..." (Bradley 1893:21). Although relations and qualities refer to separate terms which refer to different ideas in the world, they are undeniably linked, depending on each other to exist. Bradley states that "You can never... find qualities without relations. Whenever you take them so, they are made so, and continue so, by an operation which itself implies relation. Their plurality gets for us all its meaning through relations; and to suppose it otherwise in reality is wholly indefensible" Bradley 1893:22). An exemplification of this claim may be illustrated through the use of an object, say, a blue ball. We may state that the blue ball has at least two properties: it has the property of being coloured blue, and it has the property of being round. If we try to conceive of each individual mere property of the blue ball, without the properties being related to other properties or objects, it seems quite hard, if not impossible to imagine - it seems that, at least in this sense, Bradley's claim is quite plausible in saying that we can't find qualities without relations. Properties are unified or 'coexist' via relations, and thus if we take the example of the blue ball into consideration, the properties of blueness and roundness (and a collection of various other properties) can be said to become united through relations, composing the object that is the blue ball. Furthermore, Bradley states that relations are also employed to differentiate properties from each other: "...if there are no differences, there are no qualities, since all must fall into one. But, if there is any difference, then that implies a relation...Is it possible to think of qualities without thinking of distinct characters?" (Bradley 1893:25). Therefore relations, according to Bradley, posses the dual task of unifying properties and act as difference-makers of qualities from each other. Although the bundle theory of particulars has prevailed to be the most plausible metaphysical explanation of objecthood, Bradley asserts that the account is problematic because it attempts to explain the identity and relationships of objects and their qualities through the use of relations. Foremost, the explanation offered by the bundle theory of properties is arguably circular - the theory attempts to explain the relationship between an object and its properties by appealing to the facts about the relations that properties have to each other, and thus the connection between an object and its properties is the same as the connection between the properties and the relations in which they stand, so we can hardly use the latter to explain the former (Speaks 2007:2). Furthermore, Bradley states that if relations are the key to understanding the nature of objecthood, they must be independent from the terms they are related to - however, using relations conceived as independent to explain the nature of objects and properties leads to an infinite regress. In the next sections I will briefly present two infinite regress arguments that Bradley offers in efforts to argue for the unreality of qualities. I will also suggest two argumentative reconstructions of the passages employed at the courtesy of Katarina Perovic to make the notions employed more concrete and explicit. Furthermore, due to 3 some of the vague terminology that Bradley employs, potential interpretations and objections to these arguments will be given in the latter sections. In Chapter II of Appearance and Reality Bradley argues against the idea that independent relations can relate, stating that that the use of such relations would lead lead to an infinite regress: "Let us abstain from making the relation an attribute of the related, and let us make it more or less independent. 'There is a relation C, in which A and B stand; and it appears with both of them.' But here again we have made no progress. The relation C has been admitted different from A and B, and no longer is predicated of them...If so, [there] would appear to be another relation, D, in which C, on the one side, and, on the other side, A and B, stand. But such a makeshift leads at once to the infinite process" (Bradley 1893:21). The example here suggests that the independent relation C is the culprit that causes the regress. Bradley does not give an explicitly clear definition as to what the notion 'independent' refers to, but he hints to what a 'real' relation is, and this definition of 'real' might plausibly give us a hint as to what is meant by the use of 'independent' - "If [a relation] is to be real, it must be so somehow at the expense of the terms, or, at least, must be something which appears in them or to which they belong. A relation between A and B implies really a substantial foundation within them" (Bradley 1893:18). Thus the use of 'independent' in this context seems to refer to a kind of relation that does not have a substantial foundation or one that does not belong between the two variables it is trying to relate. An argumentative reconstruction of Bradley's claims here is given by Perovic: (1) Suppose that there is an independent relation C, in which qualities A and B stand. (2) Independent relations are different from their relata and as such cannot relate. (3) Therefore, an independent relation C cannot relate A and B. (4) New relation D is needed to relate C, A, and B. (5) D is an independent relation. (6) From (2), (4) and (5), it follows that D cannot relate C, A, and B. (7) A new relation E is needed to relate A, B, C, and D. And so on ad infinitum. (Perovic 2014:378) From Bradley's arguments it seems that he deems independent relations as entities that cannot do the job of relating properties by themselves - they require further independent relations to relate them to the properties in question, thus triggering an impending infinite regress. In Chapter III, Bradley provides another infinite regress argument, arguing against the reality of relations: "But how the relation can stand to the qualities is, on the other sides, unintelligible. If it is nothing to the qualities, then they are not related at all; and, if so, as we saw, they have ceased to be qualities, and their relation is a nonentity. But if it is to be something to them, then clearly we now shall require a new connecting relation. For the relation hardly can be the mere adjective of one or not of its terms.... And, being 4 something itself, if it does not itself bear a relation to the terms, in what intelligible way will it succeed in being anything to them? But here again we are hurried off into the eddy of a hopeless process, since we are forced to go on finding new relations without end. The links are united by a link, and this bond of union is a link which also has two ends; and these require each a fresh link to connect them with the old." (Bradley 1893:27-28). Perovic provides a reconstruction of this infinite regress argument: (1) Suppose that there is a relation R uniting qualities A and B. (2) If R is nothing to A and B, they are not related. (3) If R is something to A and B, then R itself is something. (4) If R is something itself, then it cannot relate and it needs further relations, such as R' to relate it to A and B. (5) The same process is then repeated with R' and further relations, ad infinitum. (Perovic 2014:382) It is difficult to explicitly tell what exactly Bradley means through phrases such as 'nothing to the qualities' and 'something to to the qualities'. However, while the argument does not explicitly mention independent relations like the first regress, this second regress argument seems to be talking about independent relations through the phrase "but if [the relation] is to be something to them, then clearly we now shall require a new connecting relation" (Bradley 1893:27). The two infinite regress arguments are similar in the sense that they both posit independent relations to require a further infinite supply of different independent relations to relate their relata. And if the relation is 'nothing' to the qualities it is trying to relate, then it simply does not relate. Thus Bradley's second infinite regress may be construed as attempting to argue that all relations cannot relate. So far I have shown that Bradley has assumed the position that relations cannot relate their relata through his infinite regress arguments. In the following sections I will provide two potential ways in which one might oppose his arguments. One interpretation of Bradley's infinite regress against independent relations as unifiers of properties involves understanding the independent relations in question as the same kinds of entities as the relata they are supposed to be relating. This interpretative approach leads to an ultimate rejection of his regress. To show how the Bradleyan regress may be interpreted in this manner we can examine Chapter II of Appearance and Reality, finding his first infinite regress pertaining to relations: "'There is a relation C, in which A and B stand; and it appears with both of them.' The relation C has been admitted different from A and B, and no longer is predicated of them...If so, [there] would appear to be another relation, D, in which C, on the one side, and, on the other side, A and B, stand. But such a makeshift leads at once to the infinite process" (Bradley 1893:21). This argument seems to imply that relations require relatedness. This might seem a bit odd - for is it not the role of relations to relate, or to instantiate relatedness? If relations do not, or cannot relate, what else is their 5 function? Bradley's regress argument here states that the relation C cannot merely relate the relata A and B - another relation must be posited to relate the relation C to the relata A and B, that being relation D, and thus so on. Thus it seems plausible to read Bradley as having a wrong conception of what a relation really is, or what they should be - it seems that he interprets these relations as some kinds of entities that are on the same level or in the same position as the relata themselves, as these relations are treated as entities which require being related. Charlie Dunbar Broad famously objects to Bradley in this fashion: "It is plain that Bradley thinks of A and B as being like two objects fastened together with a bit of string, and he thinks of R as being like the bit of string. He then remembers that the objects must be glued or sealed to both ends of the the bit of string if the latter is to fasten them together. And then, I suppose, another kind of glue is needed to fasten the second drop of glue to the object B on the one side and the string on the other. And so on without end. Charity bids us avert our eyes from the pitiable spectacle of a great philosopher using an argument which would disgrace a child or a savage" (Broad 1933: 85). We can see how this this claim might be illustrated if we take the example 'Mary is the wife of Joseph'. Here, 'is the wife of' is the relation that relates the terms 'Mary' and 'Joseph'. But Bradley states that the relation, 'is the wife of', requires an additional relation to relate the terms 'Mary' and 'Joseph', which seems to construe the relation as a term itself. Blanshard states "[a relation] is not the same sort of being as its terms. It is neither a thing nor a quality. It is a relation, and the business of a relation is to relate" (Blanshard 1986: 215). Thus on this approach, Bradley may be interpreted as misidentifying relations: relations are viewed as particulars in need of being related themselves, while ignoring their proposed function of actually relating terms. One potential problem that this approach may encounter is the problem of explaining how relations relate. The person who takes Bradley to be identifying relations as particular-like entities in need of being related themselves is one who posits relations as primitive - relations just relate; it is simply the role of relations to relate terms to each other. A metaphysical explanation of how it is that relations relate entities may be required for the proponent of this view, and without such an explanatory account a primitivist stance on relations as relating entities may be deemed unsatisifactory. Another way to oppose the problems of the Bradleyan regresses is to relate terms without the use of the 'proper' relations. This feat may be achieved through adopting an existential dependence view regarding objects and their properties. The view involves positing that "substrate and universal stick together not miraculously and inexplicably, 2 but with the help of one of the greatest forces available to the metaphysician: necessity. Universal and substrate are generically dependent on one another: they require for their existence the existence of some entity belonging to the other kind" (Maurin 2010:316). Thus still assuming the bundle theory of particulars, we can choose to forego the view for the purposes of my paper, the term 'universal' will be interchangeable with the terms 'property' and 'quality'.2 6 that an object's identity is its properties existing in a certain relation(s) - disposing of relations and their supposed applications - and instead posit modal claims that link objects to their properties. Maurin provides four modal claims which are attributed to David Malet Armstrong (1978:108): The substrate necessarily exemplifies some universal. The substrate only contingently exemplifies the universals it does exemplify. The universal is necessarily instantiated in some substrate. The universal is only contingently instantiated in the substrate it is instantiated in. Collectively, these claims seem to allow objects and their properties to be 'related' without the use of relations, and the relationship between an object and its properties becomes somewhat clear through the use of modal notions. According to this existential dependence view, an object necessarily has at least some property, and the object contingently has all the properties it has. This seems to be true because an object cannot be an object without having a property, and the collection of all the properties that a certain object has could have been otherwise. This seems true for the case of properties as well - a property is necessarily instantiated in at least some object, and the property is contingently instantiated in the object that it is instantiated in. A property needs to be instantiated in at least some object to exist, to be a property, and it also could have been otherwise that this certain property was instantiated in a different object than the object it is currently instantiated in. In these ways we are able to give an account of the relationship between objects and properties - these two types of entities become dependent on each other, establishing a connection between each other without the use of relations. However, it seems that the existential dependence may not be fully sufficient, facing some difficulties. Maurin states that the aforementioned four modal claims constitute a generic existential dependence between objects and their properties, which does not fully and appropriately address the problems of the Bradleyan regresses. Bradley provides his infinite regress arguments opposing the reality of relations in the context of relating specific terms to each other, not kinds of terms (Maurin 2010:316). In contrast, the modal claims of the generic existential dependence view attempt to explain the nature of the relationship between objects and their properties by talking of the necessary and contingent links between a specific object/property to general kind of property/object. As Maurin states, "the fact that this substrate must be joined to some universal (or that this universal must be instantiated in some substrate) does not explain the union of this specific substrate with this specific universal" (Maurin 2010:316). To exemplify this claim we may take an entity, the particular known as Mary, who has the property of being worshipped, into account. We can take the four modal claims of generic existential dependence and plug our variables into the values to get the following claims: Mary necessarily has some property. Mary contingently has the properties she has. 7 The property of being worshipped is necessarily instantiated in some object. The property of being worshipped is contingently instantiated in the object it is instantiated in. Through this result we are able to see that we cannot obtain a link between the specific particular, Mary, and the specific property she has, the property of being worshipped. Thus while the generic existential dependence view provides an explanation of how specific terms may be necessarily or contingently linked to general terms, it does not seem to account for explanations pertaining to the connections between specific entities. However, a modification of this account may be able to solve the problem in question. To adequately account for Bradley's regresses we must modify generic existential dependence into specific existential dependence. According to Anna-Sofia Maurin, specific existential dependence amounts to "existential dependence holding between the specific particular (and/or universal) constituents of some concrete thing" (Maurin 2010:317). This approach involves linking specific objects to their specific properties, and thus can account for the problem posed by Bradley's regresses. Specific existential dependence involves a different set of modal claims: The object necessarily exemplifies the properties it does exemplify. The property is necessarily instantiated in the object it is instantiated in. On this account, links of contingency between objects and their properties are discarded. The properties that are said to compose an object all specifically depend on each other, meaning that the object in question necessarily has all the properties that it has. Therefore, all objects and properties become necessarily connected to their relevant components and thus we are able to avoid Bradley's regresses by relating entities without the use of relations. The specific existential dependence view is not without some ramifications, however. While it may be able to relate entities without the use of relations, this view implies an assertion of necessitarianism about the world - "a world fundamentally constituted by specifically dependent entities, is a world in which nothing strictly speaking moves or changes. Worse, it is a world in which nothing could have been other than it actually is" (Maurin 2010:317). Thus all contingency is thrown out the window; the proponent of the specific existential dependence view must abandon any potential for possibility and posit that the world could not have been otherwise. The result is the position of necessitarianism, which may seem like a controversial and unattractive position to hold due its complete rejection of contingency. So far I have provided two routes for opposing the Bradleyan regresses. In the next section I will compare the first view that states Bradley as misidentifying relations as particulars to the specific existential dependence view, weighing their theoretical consequences against each other. Proponents of the first view state that Bradley mischaracterizes relations as particular-like entities. On this account, Bradley is interpreted to dismiss the fundamental 8 role of relations, demanding that the notion of relatedness itself requires a relation. Defenders of this view take relations to be primitive - relations function to relate terms, and the Bradleyan regresses are rejected as a result of the collection of these sentiments. However, a metaphysical explanation of how exactly relations relate their terms may be necessary in order to provide a more satisfying and complete refutation of Bradley. On the other hand, specific existential dependence theorists choose to avoid encountering the Bradleyan regresses by positing modal claims to function as links between their terms rather than employing relations. But despite its efficacy and success in dealing with the regresses, advocates of this view are met with a considerable metaphysical commitment in the form of necessitarianism. The Bradley-mischaracterizes-relations view is a more simple, interpretative response towards the regresses, but it lacks a deeper metaphysical explanation of how exactly relations relate, whereas the specific existential dependence view directly avoids the problem of the regresses, but posits necessitarianism. However, necessitarianism may arguably not be that damning of view - as David Lewis states, "the benefits in theoretical unity and economy are well worth the entities" (Lewis 1986:4). In conclusion I have examined Bradley's infinite regress arguments against the reality of relations in Appearance and Reality and have argued for two possible argumentative strategies one can take towards them. The argumentative approaches that I have provided tackle the regresses very differently, and thus have their own set of ramifications. 9 Works Cited Bradley, F. H. (1893). Appearance and Reality. Oxford University Press. Speaks, J. (2007). Bradley's Monist Idealism. Retrieved from https://www3.nd.edu/ ~jspeaks/courses/2007-8/43904/_handouts/bradley-appearance-reality.pdf. Perovic, Katarina (2014). The Import of the Original Bradley's Regress. _Axiomathes_ 24 (3):375-394. Broad, C.D., (1933), Examination of McTaggart's Philosophy (Volume I), Cambridge: Cambridge University Press. Blanshard, Brand, (1986), "Bradley on Relations", in Anthony Manser and Guy Stock (eds.), Philosophy of F. H. Bradley, Oxford: Oxford University Press. Maurin, Anna-Sofia (2010). Trope theory and the Bradley regress. Synthese 175 (3): 311-326. Armstrong, David M., (1978), Nominalism & Realism: Universals & Scientific Realism (Volume I), Cambridge: Cambridge University Press. Lewis, David K. (1986). On the Plurality of Worlds. Wiley-Blackwell.