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Contents : The Perennial Problem of the Reductive Explainability of Phenomenal Consciousness C. D. Broad on the Explanatory Gap In: T. Metzinger (ed.) Neural Correlates of Consciousness Empirical and Conceptual Questions Cambridge MA: MIT-Press 2000 41-55. Ansgar Beckermann University of Bielefeld Broad's Distinction between Emergent and Mechanically Explainable Properties At the start of the 20th century the question of whether life could be explained in purely mechanical terms was as hotly debated as the mind-body problem is today. Two factions opposed each other: Biological mechanists claimed that the properties characteristic of living organisms (metabolism perception goal-directed behavior procreation morphogenesis) could be explained mechanistically in the way the behavior of a clock can be explained by the properties and the arrangement of its cogs springs and weights. Substantial vitalists on the other hand maintained that the explanation envisaged by the mechanists was impossible and that one had to postulate a special nonphysical substance in order to explain life--an entelechy or lan vital. When C. D. Broad developed his theory of emergence in the early 1920s his aim was to create room for a third position mediating between these two extremes--a position he called emergent vitalism. Broad's first step was to point out that the problem of vitalism is only a special case of a much more general problemthe problem of how the behavior of a complex system is related to the properties and the arrangement of its physical parts. (According to Broad living beings differ from nonliving things only in their specific behavior. That is to say he believed that the property of being alive could be characterized in purely behavioral terms. He strictly distinguished properties of this kind from properties that he called "pure qualities". I will return to this distinction below.) Regarding this question there are in principle only two basic types of answers. One can hold the view that the behavior of a complex system cannot be explained by referring exclusively to its physical parts and their arrangement but only by the assumption that S contains a further nonphysical component which is present in all beings that behave in the way characteristic of S and is absent in all other beings. According to Broad anyone who endorses a theory of this kind is a proponent of a component theory. However one can also hold the opposed view that the behavior of S can at least in principle be explained by its physical parts and their arrangement. In this case however one has according to Broad to distinguish two further possibilities. For even if S's behavior can be explained this way it may be either mechanistically explainable or emergent. (Broad strictly distinguishes between mechanism and pure mechanism. According to the latter the term "mechanistically explainable" means something like "explainable just by reference to the laws of classical mechanics" according to former it means "explainable by reference to all general chemical physical and dynamical laws" (1925: 46). In the following "mechanistically explainable" is always meant to have this second broader meaning.) Mechanistic and Emergent Theories thus concur in denying that there need be any peculiar component which is present in all things that behave in a certain way and is absent from all things which do not behave in this way. Both say that the components may be exactly alike in both cases and they try to explain the difference of behavior wholly in terms of difference of structure." (Broad 1925: 58f.) 41b However mechanistic and emergent theories differ fundamentally in their view of the laws that relate the behavior of the components of complex systems to the characteristic behavior of the systems themselves. On the theory of emergence the characteristic behavior of the whole could not even in theory be deduced 2 from the most complete knowledge of the behavior of its components taken separately or in other combinations and of their proportions and arrangements in this whole. (Broad 1925: 59) 42a Which types of macroscopic behavior are to be regarded as emergent in this sense was controversial even in Broad's days. Broad believed that the behavior of nearly all chemical compounds is emergent in the sense explicated. It was his view for example that so far as we know at present the characteristic behavior of Common Salt cannot be deduced from the most complete knowledge of the properties of Sodium in isolation or of Chlorine in isolation or of other compounds of Sodium such as Sodium Sulphate and of other compounds of Chlorine such as Silver Chloride. (Broad 1925: 59) Naturally mechanists would disagree. For Broad characterizes their theory thus: On the mechanistic theory the characteristic behavior of the whole is not only completely determined by the nature and arrangement of its components in addition to this it is held that the behavior of the whole could in theory at least be deduced from a sufficient knowledge of how the components behave in isolation or in other wholes of a simpler kind. (Broad 1925: 59) Artificial machines are the best examples of complex objects whose behavior can be completely explained in mechanical terms. For instance we surely do not have any reason to assume that the behavior of a clock is based on a specific non-physical component which is present in clocks and only in clocks. Hence component theories are quite inappropriate for the explanation of the behavior of these machines. However we do not have any reason to assume that the behavior of clocks is emergent either. For obviously we can completely deduce its behavior from the specific arrangement of a clock's springs cogs weights and so forth. Put in a nutshell the difference between emergent and mechanistic theories can be explained as follows: Put in abstract terms the emergent theory asserts that there are certain wholes composed (say) of constituents A B and C in a relation R to each other that all wholes composed of constituents of the same kind as A B and C in relations of the same kind as R have certain characteristic properties that A B and C are capable of occurring in other kinds of complex where the relation is not of the same kind as R and that the characteristic properties of the whole R(A B C) cannot even in theory be deduced from the most complete knowledge of the properties of A B and C in isolation or in other wholes which are not of the form R(A B C). The mechanistic theory rejects the last clause of this assertion. (Broad 1925: 61) 42b Broad here stresses two points: First regardless of whether the characteristic behavior B of a class of systems is mechanistically explainable or emergent B nomologically depends on the corresponding microstructures. That is to say if a system S consists of the parts C1 ... Cn arranged in manner R--for short: if S has microstructure C1 ... Cn R then the sentence "All systems with microstructure C1 ... Cn R behave in manner B" is a true law of nature--regardless of whether B is emergent or mechanistically explainable. Obviously this is the reason for Broad's view that emergent as well as mechanistically explainable properties can be explained by reference to the microstructure of the respective system. However Broad here employs a comparatively weak notion of explanation. Second mechanistically explainable behavior differs from emergent behavior in that the former can at least in principle be deduced "from the most complete knowledge of the properties of the components C1 ... Cn in isolation or in other wholes" while this cannot be done for the latter. Broad's concepts of mechanistic explainability and emergence can thus be summarised as follows: (ME) The characteristic behavior B of a complex system S with the microstructure C1 ... Cn R is mechanistically explainable if and only if B can (at least in principle) be deduced from the most complete knowledge of all properties that the components C1 ... Cn have either in isolation or within other arrangements. (E) The characteristic behavior B of a complex system S with the microstructure C1 ... Cn R is emergent if and only if the following is true: 43a 3 (a) (b) The statement "All systems with microstructure C1 ... Cn R behave in manner B" is a true law of nature but B cannot (even in principle) be deduced from the most complete knowledge of all properties that the components C1 ... Cn have either in isolation or within other arrangements. The general upshot of these definitions seems to be clear enough. But why does Broad use the complicated clause "from the most complete knowledge of the properties of the components C1 ... Cn in isolation or in other wholes" To begin with Broad evidently saw that the notion of an emergent property would for quite trivial reasons be empty if one were permitted to use all the properties of the components in the "deduction" of the behavior B. Some twenty years after the first publication of The Mind and Its Place in Nature Hempel and Oppenheim referring to a remark by Grelling phrased this problem thus: If a characteristic of a whole is counted as emergent simply if its occurrence cannot be inferred from a knowledge of all the properties of its parts then as Grelling has pointed out no whole can have any emergent characteristics. Thus ... the properties of hydrogen include that of forming if suitably combined with oxygen a compound which is liquid transparent etc. Hence the liquidity transparency etc. of water can be inferred from certain properties of its chemical constituents. (Hempel/Oppenheim 1948: 260) In order to avoid rendering the concept of emergence vacuous inferences of this kind must be blocked. Broad's formula serves precisely this purpose since it is obviously designed to guarantee that we cannot have recourse to properties like those mentioned by Hempel and Oppenheim when we attempt to deduce the characteristic behavior B of a complex system from the properties of its parts and its structure. However the question remains whether this purpose could have been accomplished with a simpler and more lucid formulation. This much seems clear: It is crucial that in our attempts to deduce some behavior B of a complex object from the properties of its parts and their spatial relations we are not allowed to use ad hoc properties such as the property that certain components if arranged in a specific way form a complex object which behaves in manner B. The question therefore is how we can guarantee this result without at the same time excluding properties which we may legitimately invoke in such an attempt. An answer to this question can be found if we consider which laws we may use in deductions of this type. For here we encounter a related possibility of trivialising the concept of emergence. If we were allowed to employ the law mentioned above i.e. the law "All systems with microstructure C1 ... Cn R behave in manner B" there would be no emergent behavior. Hence Hempel and Oppenheim could have formulated their point just as well in this way: It is a true law of nature that if suitably combined with oxygen hydrogen forms a compound which is liquid transparent and so on. Hence the liquidity transparency and such of water can be derived by means of the laws of nature. Clearly Broad was aware of both possible ways of trivialising the concept of an emergent property (see e.g. Broad 1925: 65ff.). Broad therefore must also rule out recourse to laws of this type. That this is something he actually sought to do can be seen from the following passage discussing the properties of clocks: We know perfectly well that the behavior of a clock can be deduced from the particular arrangement of springs wheels pendulum etc. in it and from general laws of mechanics and physics which apply just as much to material systems which are not clocks. (Broad 1925: 60 italics added) 43b 44a Obviously Broad held that if we attempt to deduce some behavior B of a complex object from the properties and arrangement of its parts we may use only general laws that are valid for the parts of a complex system independently of the specific configurations of these parts. However this constraint provides a way to rule out recourse to ad hoc properties as well. Hence the most straightforward answer to the question "Which properties of a system's parts may we refer to in such a deduction " is apparently this: "to those properties which are mentioned in these general 4 laws of nature". I should therefore like to suggest that we replace Broad's clause with the formula "if B can be deduced by means of the general laws of nature that are true of the components C1 ... Cn from the properties of the components mentioned in these laws". Taken to its logical conclusion this improved version of Broad's formula renders superfluous any reference to admissible properties if we specify which laws can figure in the derivations in question we have implicitly determined which properties may play a role in these derivations. Even after this point has been clarified however the question remains why according to Broad we need to know not only how the components of a system behave "in isolation" but also how they behave "in other wholes". As we have already seen Broad thought that mechanistically explainable behavior differs from emergent behavior in that the former can be deduced by means of the general laws of nature which are true of the components C1 ... Cn from the properties of the components mentioned in these laws whereas the latter cannot. But this provokes the further question of how we can determine which laws are general in the sense required. Broad's own answer to this question has two parts: First we have to observe how the parts behave in isolation and second we have to investigate how they behave in "other" systems. Why do we have to do both Broad was quite obviously thinking of the dynamic behavior of systems that are subject to a number of different forces (see Broad 1925: 62 63f). If we want to find out whether the law that is crucial here the second Newtonian law F m a applies in this case we have to begin by investigating the behavior of objects that are subject to only one force. But if we wish to know how an object behaves generally--that is how it behaves if more than one force acts on it simultaneously-- the knowledge of this law is not enough. We also have to know the law that governs the interaction of the various forces: the law of the vector addition of forces. According to Broad we always need these two types of laws: (a) laws that state how individual factors separately influence the behavior of an object and (b) laws that state what behavior results if different factors simultaneously act on an object. Laws of the second type Broad terms "laws of composition". Moreover he emphatically stresses their indispensability: It is clear that in no case could the behavior of a whole composed of certain constituents be predicted merely from a knowledge of the properties of these constituents taken separately and of their proportions and arrangements in the particular complex under consideration. Whenever this seems to be possible it is because we are using a suppressed premise which is so familiar that it has escaped our notice. The suppressed premise is the fact that we have examined other complexes in the past and have noted their behavior that we have found a general law connecting the behavior of these wholes with that which their constituents would show in isolation and that we are assuming that this law of composition will hold also of the particular complex whole at present under consideration. (Broad 1925: 63) 44b However it is not completely clear what kind of law Broad is alluding to here. The way Broad speaks in the passage just quoted it seems as if laws of composition are meant to relate the behavior of a system to the behavior of its parts. (Only the phrase "in isolation" is puzzling in this interpretation.) In this case laws of composition would have the status of bridge principles relating the level of the parts to the level of the whole. Yet directly after this passage Broad returns to the example of the explanation of the dynamical behavior of objects that are subject to a number of forces: For purely dynamical transactions this assumption is pretty well justified because we have found a simple law of composition and have verified it very fully for wholes of very different composition complexity and internal structure. It is therefore not particularly rash to expect to predict the dynamical behavior of any material complex under the action of any set of forces however much it may differ in the details of its structure and parts from those complexes for which the assumed law of composition has actually been verified. (Broad 1925: 63f.) 45a Obviously the law of composition he refers to in this passage is the law of the vector addition of forces already mentioned. (see Broad 1925: 62). This law however does not state how the behavior of a whole arises from the behavior of its parts but how the parts of a whole behave if they are subject to a number of forces. Thus it might be more apt to call laws of this type "laws of interaction". Fortunately we do not have to decide on one reading for Broad seems to be right in either case. 5 On the one hand we of course need laws of interaction since we cannot deduce the behavior of a system from the properties of its parts and their arrangement if we do not know how the parts themselves move if they are arranged in this particular way. On the other hand we also need laws of composition or bridge principles since we cannot deduce the behavior of a system from the behavior of its parts if we do not know how the behavior of the parts is related to the behavior of the whole. Thus in order to deduce the behavior of a system from the properties of its parts and their arrangement we actually need three types of laws: 1. Simple laws which state how each part of the system S behaves if only a single factor acts on it 2. Laws of interaction which state how the parts of S behave if a number of factors simultaneously act on them 3. Laws of composition or bridge principles which state how S behaves as a whole if its parts behave in a specific way. The fact that any attempt to explain the behaviour of a system S by reference to the properties of its parts and their arrangement requires three types of laws is also pointed out by H ttemann and Terzidis (in press). The indispensability of laws of composition is stressed in McLaughlin (1992). It should again be noted that all these laws must be general laws or must follow from general laws to be usable in what Broad calls the deduction of the characteristic behavior of a system from the properties and the arrangement of its parts. Put precisely what Broad's definitions come to therefore is the following: (ME) The characteristic behavior B of a complex system S with the microstructure C1 ... Cn R is mechanistically explainable if and only if the following is true: (a) The way the components C1 ... Cn behave when arranged in manner R can be accounted for by the general simple laws and by the general laws of interaction holding for objects of the kind C1 ... Cn and (b) there is a general law of composition to the effect that S exhibits behavior B if the components C1 ... Cn behave in the way they do. The characteristic behavior B of a complex system S with the microstructure C1 ... Cn R is emergent if and only if the following is true: (a) The statement "All systems with microstructure C1 ... Cn R behave in manner B" is a true law of nature but (b1) the way the components C1 ... Cn behave when arranged in manner R cannot be accounted for by the general simple laws and by the general laws of interaction holding for objects of the kind C1 ... Cn or (b2) there is no general law of composition to the effect that S exhibits behavior B if the components C1 ... Cn behave in the way they do. 45b (E) 46a Two points should be highlighted here. The first concerns the question of why Broad did not provide a positive example for a law of composition that would render the behavior of a given system mechanistically explainable. My guess is that the laws Broad had in mind are so mundane that he felt no need to mention them. For instance the following seems to be trivially true of spatial movement: (P1) If we know how all the components of a complex system move we also know how the system itself moves. Think for example of a disk whose components all revolve with the same angular velocity and in the same direction around the disk's centre. Then it seems quite clear that the disc as a whole

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