The following four chapters take up the features of quantities of matter that distinguish them from individuals by their mereological structure. This structure is reflected in the character of certain predicates expressing the property of being a particular kind of substance, say water, and exhibiting one or more phases, such as being liquid and being gas. Such predicates seem to ascribe an amorphous character to their subjects, which authors have tried to more precisely capture in terms of a distributive and a cumulative condition, formulated in terms of the mereological part relation and sum operation, respectively. These conditions are presented in this chapter and generalised to apply to relational predicates. This generalisation is obviously needed for relational predicates like “is the same substance as” and “is warmer than”. But substance and phase predicates, by contrast with the monadic predicates “is a time” and “is a spatial region”, are also taken to be relational, standing between a quantity and a time. The relational interpretation follows the chemist’s understanding of the permanence of matter throughout chemical change, which has been standard at least since the time of Lavoisier. Aristotle and the Stoics can be reasonably interpreted, it seems, to have thought that the distributive condition holds of substance and phase predicates, as discussed in Chap. 5 . Whether the conditions can be upheld from a modern perspective is discussed in Chap. 7 . Substance and phase predicates fall under the linguistic category of mass predicates in accordance with grammatical criteria for their use with articles in singular inflexion and qualification as much/little rather than many/few. This category is more extensive and includes terms whose normal translations into some foreign languages don’t comply with the grammatical criteria for mass predicates whilst lacking terms whose normal translations into some foreign languages do comply with the grammatical criteria. The failure of linguistically-inspired characterisations of mass predicates in general don’t necessarily say anything about the nature of substances and phases. But Quine presents a general reason for rejecting the distributive condition on all mass predicates which he specifically illustrates with substance predicates based on his understanding of what science tells us about the atomic nature of matter. Quine’s case is discussed in this chapter, but as we will see in Chap. 7 , it isn’t the last word on the import of the microscopic view of matter presented by modern science for the distributive condition. Taking advantage of what has been said about the occupies relation in Chap. 2 , versions of the general distributive and cumulative conditions restricted to spatial parts are formulated. This raises the issue of cooccupancy, and some of what has been about this and the very little argument against the feasibility of the idea is reviewed in this chapter. Finally, the tenability of the distributive and cumulative is discussed under non-equilibrium conditions involving substance-changing processes and this final section is rounded off with a discussion of substance-changing processes involving nuclear decay and fusion.

Distributivity and Cumulativity

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发表日期：

2026年

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Paul Needham

摘要

The following four chapters take up the features of quantities of matter that distinguish them from individuals by their mereological structure. This structure is reflected in the character of certain predicates expressing the property of being a particular kind of substance, say water, and exhibiting one or more phases, such as being liquid and being gas. Such predicates seem to ascribe an amorphous character to their subjects, which authors have tried to more precisely capture in terms of a distributive and a cumulative condition, formulated in terms of the mereological part relation and sum operation, respectively. These conditions are presented in this chapter and generalised to apply to relational predicates. This generalisation is obviously needed for relational predicates like “is the same substance as” and “is warmer than”. But substance and phase predicates, by contrast with the monadic predicates “is a time” and “is a spatial region”, are also taken to be relational, standing between a quantity and a time. The relational interpretation follows the chemist’s understanding of the permanence of matter throughout chemical change, which has been standard at least since the time of Lavoisier. Aristotle and the Stoics can be reasonably interpreted, it seems, to have thought that the distributive condition holds of substance and phase predicates, as discussed in Chap. 5 . Whether the conditions can be upheld from a modern perspective is discussed in Chap. 7 . Substance and phase predicates fall under the linguistic category of mass predicates in accordance with grammatical criteria for their use with articles in singular inflexion and qualification as much/little rather than many/few. This category is more extensive and includes terms whose normal translations into some foreign languages don’t comply with the grammatical criteria for mass predicates whilst lacking terms whose normal translations into some foreign languages do comply with the grammatical criteria. The failure of linguistically-inspired characterisations of mass predicates in general don’t necessarily say anything about the nature of substances and phases. But Quine presents a general reason for rejecting the distributive condition on all mass predicates which he specifically illustrates with substance predicates based on his understanding of what science tells us about the atomic nature of matter. Quine’s case is discussed in this chapter, but as we will see in Chap. 7 , it isn’t the last word on the import of the microscopic view of matter presented by modern science for the distributive condition. Taking advantage of what has been said about the occupies relation in Chap. 2 , versions of the general distributive and cumulative conditions restricted to spatial parts are formulated. This raises the issue of cooccupancy, and some of what has been about this and the very little argument against the feasibility of the idea is reviewed in this chapter. Finally, the tenability of the distributive and cumulative is discussed under non-equilibrium conditions involving substance-changing processes and this final section is rounded off with a discussion of substance-changing processes involving nuclear decay and fusion.