Semi-formal Treatment of Property Structure Terms

Appendix A Semi-formal Treatment of Property Structnre Terms 

A Set of Rules for Obtaining Schenmta for Property Structure Terms 

The schema structure will be called Sps . It contains schema letters and additional operators. 

Note that this fragment does not contain place-holders for modal operators, or something that corresponds to an operator like the fact that. .. (which would make things unnecessary complex) and a considerable number of other operators which might be relevant for scientific discourse. Thus, we should regard the account presented here as a partial account of property structures. We can now recursively define the set of property-structure fem-schemata. I shall talk about terms from now on simpliciter. It should be noted, however, that these terms are schemata for terms. 

The goal of this rule is to build an operator that takes a predicate as an argument. The result is a term referring to the property signified by the predicate. 

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We can now move on to further motivate the proposal, applying it to the reduction debates in the philosophy of mind and the philosophy of science, as well as related issues in Part II. ° The following Appendix contains a semi-formal treatment of property structure terms (it will not be referred to in the remainder of the book). 

Thus, we have outlined a semi-formal treatment of property-structure terms that gives a more precise idea of the metaphysics of property structures. Let me finish these remarks mentioning that the notion of a tuple is nevertheless problematic in this context There can be many property structure terms that are instances of a schema obtainable from Sps for one non-ambiguous natural language expression. For example, a conjunction with only two conjuncts can be modeled in two different ways a natural language predicate of the form is F is G can be modeled as < <[Fy], [Gx]>> and as < <[Gy], [Fx] . Now, intuitively, property structures are less fine grained than tuples. Thus, these tuples should function as a mere model for property structures only. 

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