By Louis Auslander, F. Hahn, L. Green
The description for this booklet, Flows on Homogeneous areas. (AM-53), can be forthcoming.
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Extra resources for Flows on Homogeneous Spaces
Classes and subclasses belong to the same ‘kind’ as the whole. In the case of groups, it is reasonable to expect its parts also to belong to the same kind — that is, be subgroups of groups. 50 we can import Lewis’ formulation of parts of classes for groups. 7 What about singletons? Here is where the major problem arises. Is a group a fusion of its singletons? Let me look at the notion of fusion from the opposing direction, namely partition. The equivalence of a class as a mereological sum of its singletons is equivalent to the partition of a class into its singletons.
It is possible that under rotations the spatial location of the object (like a sphere) does not change but those of its parts do. In general, if the rotation does not involve deformation, then the part-whole structure is retained. Suppose we rotate an object. It seems at the outset that no property is lost — the object is Still the same, mass and colour, for example, are unchanged and in general the form or shape is also the same. But the moment we have a frame of reference, then we can notice one particular change, namely the way in which the form is oriented with respect to that frame of reference.
Lombard distinguishes between these two not necessarily in the language of change but as alteration- Thus, objects which change non—relationally seem to be ‘altered’ in some way, which is not exhibited by becoming an uncle. Lombard argues that when an object undergoes relational change, it must necessarily imply that another object has undergone non-relational change. For example, he mots that Xantippe’s becoming a widow because Socrates died is a relational change for Xantippe but this change occurs ' 'only' because Socrates died — a non-relational change of Socrates.