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Whole, Parts and Supervenience. A Comparison
by Tommaso Piazza (University of Florence)

1. The concepts of dependent part and husserlian foundation

In his Third Logical Investigation Edmund Husserl introduces the concepts of dependent and independent parts of a whole. Roughly, a dependent part is something that cannot occur but in association with something else, which is what the part allegedly depends on. A part, on the contrary, is independent when it is allowed to occur independently from its being associated with something else. An example of the first kind of part is the colour moments in a perceptual thing, which cannot occur if they are not associated with the extension moments through which the perceptual thing is presented. An example of the second kind is represented by what Husserl refers to as a piece (Stück). The leg of a table, for instance, does not need to be connected with its whole (the table). The colour of a thing, on the contrary, is not even thinkable independently of its being associated with the thing’s extension.

Accordingly, Husserl describes the possible kinds of relations which hold between the parts of a whole. Dependent parts can be mutually dependent parts, as in the case of colour and extension, or univocally dependent parts, as in the case of the relation among a representation and a judgment. While in the first case each part requires the other one, in the second case it is just the second one which depends on the first, while the first does not need, i.e. doesnot depend on, the second.

Even though Husserl explicitly derives his conception from Carl Stumpf’s psychological theory, there is quite an evidence as to the conclusion that the relations among the parts of a whole are meant to hold not only in the psychological realm of the givens of consciousness, but, lato sensu, in every conceivable ontological domain. This fact is worth noticing in the light of the following consideration: in order to evaluate the philosophical significance of the whole-part theory one does not need to embrace phenomenology and its conception of the perceptual constitution of the object of knowledge (or, most importantly, the conception of philosophical activity as related (also) to the description of what is given to the subject). The whole-part theory can thereby be used to try to bridge the gap between analytic philosophy and phenomenology, in the minimal sense in which analytic philosophers can be shown to have at their disposal viable alternatives coming from husserlian phenomenology without being obliged to buy in the full package of his philosophy.

2. Mental and physical properties

For instance it is tempting to apply the theory of whole and parts (and the mutual relations between the various kinds of parts) to legislate many puzzling relationships between different kinds of properties. Here is a sketch of how one could be tempted to proceed:
One of the most intractable problem in philosophy is the relationship between mental and physical properties. The problem, properly stated, relies in the apparently exclusive choice between two paradoxical solutions: either we state that mental properties are identical with physical properties (thereby buying in, together with ontological identity, the following problems: how can our actions be free if every single desire or will or belief that can apparently explain them is identical with a physical property, which, in turn, is causally dependent on other physical properties? How can we be ever (normatively) justified, if according to the ontological reduction, a justified belief amounts to a properly caused state of our brain?); or we state that they are different kinds of properties (thereby buying in the undesirable metaphysical expanse of admitting a family of properties which are incapable of being measured or even detected from our basic sciences). The solution, accordingly, must somehow rely in the middle. We need ontological digestibility, while, at the same time, preserving every single advantage of dualism.
The foundation relationship could conceivably supply the right answer. As distinct parts of a whole mental and physical properties are not identical; as dependent parts they need the other property’s integration. More precisely one could state the foundation in the mental/physical case to be asymmetrical: mental properties do depend on (are founded in) physical properties, while the other way round does not hold. Physical properties do not need (are not dependent on) mental properties. Intuitively stated: instantiating a certain physical structure is a necessary condition to have a mental life, while it is conceivable that having certain physical properties one still lack mental states (properties). Mereologically stated: being physically so and so structured is an independent part of the whole whose dependent part is represented by having such and such mental states.

3. Mental Supervenience

The last two decades have seen the increasing influence of the concept of supervenience. Roughly, a property A supervenes upon property B if (i) things indiscernible in relation to property B cannot be discernible in relation to property A and (ii) things that possess to different degree property A cannot possess to the same degree property B. Since (a) property supervenience entails the negation of property identity, and (b) it apparently entails the fact that property A somehow (non causally) depends on property B, and since claim (b) seemingly renders supervening properties naturalistically less problematic it seems to be what we were looking for in order to legislate the two ontologically distinct domains. Mental properties just supervene on physical properties.

4. Supervenience and Foundation

At a first glance one could be tempted to state the following equivalence:
(E) for property A and property B to be related by supervenience just means to be related by husserlian foundation relation.
Let us check whether this equivalence actually holds, taking as an example of foundation relation the one which Husserl mostly devotes his attention to in the Third Logical Investigation. According to the reciprocal foundation of colour properties and extension properties, tokens of the former kind are always associated with tokens of the latter kind. As an example of supervenience let ustake the relation allegedly holding between the mental property associated with a feeling of pain and its underlying (perhaps disjunctive) physical property of the central nervous system.

According to mental supervenience, first, two distinct subjects, indiscernible in relation to the physical properties of their nervous systems, are indiscernible in relation to their states of pain. Second, two distinct subjects discernible in relation to their pain states must be discernible in relation to the properties of their nervous systems. Therefore, (i) the holding of the supervenience relation between properties P and M seemingly entitles one in drawing the following distinct inferences: if A and B share property P and A has property M, then B has property M; for m n, if A has property M to degree m and B has property M to degree n, then A and B don’t share to the same degree property P. (ii) Since the possession of property P is naturalistically acceptable, supervenience supplies a naturalistically acceptable explanation as to why things come to possess property M, while not reducing property M to the kind of things whose possession is actually explainable in the way available for the possession of property P.
Points (i) and (ii) fix two separate indicators: respectively, they indicate the inferential and explanatory power that husserlian foundation relation must possess in order for (E) to be true.

Let us begin by considering husserlian foundation relation’s inferential power (hence, IP). If colour properties are bilaterally founded in extension properties, we’re entitled to infer from one thing’s possession of a property token of the first kind the thing’s possession of a property token of the second kind. Since in this case the foundation is symmetrical, the other way round also holds. If two things are indiscernible in point of possession of property tokens of colour, though, we are seemingly not entitled to infer that they are also indiscernible in point of possession of property tokens of extension (it is not necessary that two red things share their shape); nor, it would be legitimate to suppose, we are entitled to infer from the discernibility in relation to colour to discernibility in relation to extension (two things are allowed not to share their colour while having the same shape, and vice versa).
The asymmetry with supervenience, it could be argued in defence of (E), is due to the fact that supervenience and foundation have been exemplified by properties of differing generalities. Spelling it out in husserlian jargon, we have chosen, as examples of supervening properties, properties located at the level of the species, while, as example of founded properties, we have chosen properties located at a higher level (one, i.e., that admits a multiplicity of differences below it self). It would have been more fair to check husserlian foundation’s IP with the inferences allowed for supervening properties of the same degree of generality.

I think that this rejoinder is illegitimate. Even if we take properties of the same degree of generality (seemingly the one we should take to meet the requirement are directly mental and physical properties), supervenience still entitles one to draw inferences which are not allowed in the husserlian case. It is certainly true that from the fact that something possesses a mental property, under the hypothesis of mental supervenience, we are entitled to infer its possession of some indeterminate physical property. The point, though, is that supervenience allows one to legitimely expect that whatever mental property a thing actually possesses, if another thing possesses it to the same degree and possesses a certain physical property, then the first one has to possess it exactly to the same degree. In the husserlian case, quite to the contrary, that is precisely what can not be done. Whatever is the colour that two things come to share, what we are entitled to infer is just the fact that both have extension properties, being unable to put any constraint as to what precisely (specifically) the extension properties in question have to be.

The last consideration bring us to the evaluation of the second indicator. Anticipating what we are going to dwell upon, IP and EP connection is secured by the following consideration: the fact that supervenience and husserlian foundation are not on a par in relation to their respective IP is explained by their differences in relation their EP. The point is that foundation is not, while supervenience arguably is, a dependence relation. A dependence relation is one that satisfies the following requirements: it is asymmetric, i.e. it is not compatible with the reversal of the order of explanation; it is exclusive, i.e. it is not compatible with differing explanatory chains. While husserlian foundation seemingly does not imply non exlusiveness it clearly implies symmetry. In the case of colour and extension, the order of explanation can clearly be recast in such a way as to underline the explanatory primacy both of colour and extension.

Obviously one could reply in the following way: again the comparison is not fair. We are discussing the relationship of asymmetric dependence (the one allegedly holding between mental and physical properties) and supervenience, trying to argue for their being on apar as to their explanatorily power, and we are told that they are not on a par, because the first relation is, while the second is not, symmetric. This time the difference between unidirectional and bilateral foundation (the one considered) seems to be crucial in determining the result, and hence somehow seems to be question begging. What the problem of generality (the problem raised about the level of generality at which dependence relations are stated to hold) seems to suggest, anyhow, is that the unidirectional and asymmetric foundation relation, while satisfying the first and the second, unsurely satisfies a third and clearly does not satisfy a fourth further requirement seemingly necessary in order legitimely to count as a dependence relation in apregnant sense. The relation does seemingly entail the indeterminacy at the level of the specifications of the genera among which unidirectional foundation allegedly holds. As in the case of colour and extension, the relation holding between physical and mental properties does not entail, for a given physical property, what the mental property (allegedly depending on the first) specifically is. This conclusion is contradicted by the only example that Husserl put forwards in his Third Logical Investigation. A judgment, we are told, is unidirectionally dependent on the representation upon which it is built. This fact, though, doesn’t imply in and of itself the problem of generality. Contrary to the colour/extension case, from the fact that a subject has in different moments formulated the same judgment derives that the subject must have had the same underlying representation. It is uncertain whether the mental/physical unidirectional dependence should be preferably modelled on the colour/extension case rather than on the judgment/representation one. For the present purpose it suffices to have pointed out the consequences deriving, respectively, from the first and the second alternative. It is in fact possible to put forward a fourth requirement, which we could name the requirement of warranted implication.

It would seem legitimate to require from a dependence relation the fact that the depending property is exhaustively explicated by the property which it depends on, i.e. that the occurrence of the second property is sufficient, in and of itself, to imply the occurrence of the second property. Properties’ supervenience, allowing for generalizations of the form (x) (Px Mx) – where P is the underlying and M the supervening property - , seems to satisfy the warranted implication. Husserlian unidirectional foundation, as exemplified by the judgment/representation case, clearly does not. This conclusion is warranted by the fact that, as we have already seen, husserlian dependence allows one in drawing the inference from one property’s possession to some other property’s possession just in case the inference direction parallels the direction of dependence. Since in the case under discussion a judgment is claimed to depend unidirectionally, i.e. without implying that a representation, in turn, be dependent on a judgment, one is not entitled to infer the other way round, i.e. from the representation to the judgment.

All this, if sound, should suggest the following considerations as regards the truth of (E):


If one constraints the talk of dependence to the satisfaction of (i) asymmetry, (ii) exclusiveness, (iii) non generality and (iv) warranted implication, husserlian asymmetric unidirectional foundation is not a dependence relation (leaving open whether it satisfies or not (iii)).


Since supervenience satisfies requirements (i) – (iv), supervenience is a dependence relation.


(E) is false.

If this is true, we are apparently left with the need of further clarifying the relationship of supervenience and husserlian asymmetric foundation. What we need is, in fact, a position from which evaluate the differences between both relations, aiming, as we do, at some general conclusion as to their respective scope, advantages and costs.
One unattractive way to conclude would be to construe the relationship between supervenience and husserlian asymmetric foundation along the lines of the distinction between dependence and pregnant dependence. That would mean leaving open the choice between the both and limiting our selves to constraint it to the more of less demanding explanatory needs one might found himself to have. But this solution is clearly unsatisfactory. What we want, in fact, is nothing but a satisfactory way to legislate the relations between families of properties, moving in the logical space whose separate and unpalatable horns are represented by identity and sheer dualism. The closer we stay to dualism and the more we hold back from anti-naturalism, the better it is. Since dependence arguably is a naturality-preserving relation, the stronger a dependence relation is, the likeliest and more rational it is for it to be chosen. In this way, i.e., the question of husserlian foundation would be simply ruled out by pointing out, in comparison with alternative accounts, its lower explanatory power.

A much better way to state things would be the following: our analysis is just meant to clarify that, if the correct account of the relationship between physical and mental properties must employ a dependence relation (as defined below), the Husserlian solution can not be correct.

Yet the very claim that the correct account must satisfy a dependence requirement is hardly tenable in the light of the following consideration: dependence, in the case at issue, is meant to explain why (a weak form of) dualism is compatible with naturalism: the very fact that a thing possesses certain physical properties must explain why it comes to possess the mental properties it has, while the latter are not reduced to the former. Yet it could be questioned whether the dependence at issue, while stipulatively being non-causal in nature, can perform the role assigned to it. In order for supervenience to be a good (naturalistically acceptable) explanation, in fact, it would seem quite natural to require thatthe relation at issue be one that holds between ground-level properties according to law-like causal connections, which, in the case at issue, is ex hypothesi not the case.

5. Conclusion

Our moral is somehow paradoxical. I have stated four necessary conditions (asymmetry, exclusiveness, non generality and warranted implication) which jointly suffice for a relation to be a dependence relation. Against the proposed notion, I have maintained that supervenience is, while husserlian foundation is not, a dependence relation. I have thereby drawn the preliminary and conditional conclusion that if the relation needed satisfactorily to legislate the relationship between physical and mental properties has to be a dependence relation, then husserlian foundation cannot supply the right answer to the metaphysical problem. Yet I have contested that dependence, as qualified by acceptance of (1)- (4), does help in solving the problem. It is in fact quite natural to think that, if supervenience has to play any role in explaining what is the status of and the relationship between natural and mental properties, it has to supply some naturalistically acceptable ground to explain the emergence of a mental life against the background of an unconscious series of cerebral event. However, it could be questioned whether, its satisfactions of conditions (1) – (4) notwithstanding, supervenience does supply such a ground. Supervenience is a metaphysical relation whose postulation seems in fact incapable of receiving some naturalistic warrant which is independent form our intuitions about the way mental properties and natural properties should relate to each other, were they separated in nature and closely connected as our unwillingness to accept strict identity and sharp dualism suggests us they should. In fact, from a naturalistic point of view, supervenience is likely to be just a name for the very inferential liaisons we would like to be secured, instead of a genuine tool for explaining the relation between the mind and the body.

If the preceding conclusions are sound, the foregoing asymmetry between supervenience and husserlian foundation does not seem to constitute any definite advantage for the former. While characterizable as a dependence relation, supervenience is on a par with husserlian foundation as regards its explanatory power, and its choice seems to be as rationally recommendable as the choice of husserlian foundation is.