Cresswell, Max - Abstract Entities in the Causal Order

05/23/2008

This is a paper discussing some attempts to argue against the existence, or at least our knowledge of, abstract entities. Author unlocks a short logical argument and shows that it has concealed metaphysical premises that need further argumentation. The argument in question goes as follows:
(1) We can only have knowledge of things which are part of the causal order
(2) Abstract entities are not part of the causal order
(3) We cannot have knowledge of abstract entities

The first section of the paper discusses the proposition as an abstract entity. The knowledge relation holds between a person and a proposition due, some platonist might say, it's part in the causal order. But the existence of a proposition isn't in the causal order-- it's truth or falsity is. Hence there is some equivocation in 'part of the causal order' in (2) (pg2).

To counter this, you might want to make explicit a metaphysical assumption (6): No entity whose existence is logically necessary (a proposition) can stand to any other entity in any contingent (e.g. true or false) relation. (pg3). Author reveals this as a metaphysical premise that needs argumentation. Perhaps, instead of arguing for (6), we'd care to reduce the abstract object 'a proposition' to concrete facts, which would mean we'd have to claim that when such a reduction is possible, propositions don't exist. The problem here is that there can be mutual reduction-- propositions in terms of facts, facts in terms of propositions. This leads to a discussion of possible world theories (pg3-4) where Lewis (concrete objects making abstract objects true) is compared to Plantinga, who uses abstract entities (haecceities) to make concrete facts true.

The second part of the paper discusses abstract propositional knowledge like 'p or ~p'. Here you don't have to know anything about the causal order to know that this is true (pg5). Author explores how to incorporate numbers (abstract entities) into propositions that are quasi-mathematical (pg6-7), or to work with mathematical statements with no empirical content. Author wants to separate our ability to 'access a special class of entities which are not part of the causal order' from empistemological problems of how we are able to do math in the first place. (pg9)