On Sharing a Domain

Each conceptual scheme deals with a particular segment of the world. The segments they deal with may be completely different, but they may also partly or completely coincide. In the latter case they may be said to be concerned with the same domain. Even though the idea is intuitively clear, and it is easy to give examples, it needs to be explained what it means. For metaphysical realism it is not a problem. The world has a certain structure, which is ontologically independent of 

The notion of supervenience seems fairly suitable for our purposes. Instead of two different vocabularies, we may now talk about two conceptual schemes, A and 5. They share a domain if at least some of the facts described in one of them supervene on the facts described in the other one, i. e. a subset of the 5-facts supervene on the A-facts. This criterion for the intersection of domains is quite congenial to internal realism. It does not demand going outside conceptual schemes. We do not have to assume any mind-independent structure to mediate between them. Rather, the shared domain can be described from inside any of the conceptual schemes. Also, the intuition we want to capture by the idea of sharing a domain is quite like the intuition which is formalized by the notion of supervenience. What we want to capture is that two sets of facts are not really distinct in a way, they pull together. Nevertheless, supervenience captures more. It also captures that one of the two sorts of facts are more basic, the other sort is derivative . But this is no problem, for two reasons. First of all, internal realism has no problem with one 

This criterion works well for adequate conceptual schemes. But inadequate conceptual schemes seem to pose a special problem. The inadequacy of a conceptual scheme may consist in its leading us to false sentences. Remember the zebralopes. The deficient scheme makes us assert that certain animals belong to the same species, whereas, as a matter of fact, they belong to different species. Or, for a better example, consider what Aristotle says about motion. Many things he says are false. Yet, his theory of motion shares a domain with mechanics. But false sentences do not describe facts. So how can the criterion be applied when one conceptual scheme does not describe facts (This is a problem for metaphysical realism as well. Metaphysical realism holds that sharing a domain means capturing the same mind-independent structures. But inadequacy is just a failure to capture the real structures. So how can two conceptual schemes capture the same structures, if one of them does not capture these structures ) 

There are two other notions in terms of which one may try to provide a criterion for sharing a domain explanation and token-identity. The idea that explanation can do the job comes from the philosophy of science, where it is often said that a new and better theory should explain the successes and failures of its predecessor. The superior theory is expected to make clear why the inferior theory worked in certain cases and why it failed in other cases. One may try to elevate this explanatory relation into a criterion for sharing a domain. So one may say that Aristotelian physics and mechanics intersect because we can account for the successes and failures of Aristotelian physics in terms of mechanics. This solution seems unsuitable for several reasons. One may note that it is theories which explain, not 

However, if we have a closer look at what happens in such cases, it turns out that explanation presupposes supervenience. Aristotle had an account of the motion of unsupported objects. The objects are composed of elements, and each element has a natural place. If we do not interfere with them, the elements move towards their natural place. The unsupported objects which consist mainly of earth move towards the Earth, because that is where their natural place is. So Aristotle describes quite correctly how unsupported stones, trees, people, etc. move. Mechanics, on the other hand, makes no mention of elements or natural places. So how can it explain why Aristotle got right the motion of unsupported objects It reconceptualizes the natural motion of earthen bodies as motion under the force of gravity. But what licenses this claim Why should not we say instead that mechanics describes something completely different The answer is in terms of supervenience. The facts described in Aristotelian terms could not be different without differences in the facts described in terms of mechanics. If this relation did not obtain, mechanics could not explain the success of the Aristotelian account. This shows that explanation presupposes supervenience. Consequently, if supervenience can do the job alone, we do not need the notion of explanation to provide a criterion for the identity of domain. 

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