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Theoretical Functions with Special Forms

In: The Logical Structure of Mathematical Physics

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  • Joseph D. Sneed

Abstract

In this chapter one final proposal for using set-theoretic predicates to make empirical claims is considered. The motivation for considering this proposal is provided by examples of situations in which we apparently “postulate” or “hypothesize” that theoretical functions have some special form in certain applications of a theory. It appears that a logical reconstruction of theories with such claims will require something more than claims of form (3). The proposal for dealing with such theories is roughly this. A number of predicates are employed, all of them defined by restrictions of the definition of the same basic predicate. These predicates are used to construct a sentence which says that there are theoretical functions which make all intended applications models for the basic predicate, make some designated sub-sets of intended applications models for the “restrictions” of this basic predicate, and satisfy certain constraints. The “restrictions” of the basic predicate are to characterize various special forms that the theoretical function is hypothesized to have. This claim is regarded as the central empirical claim of the theory.

Suggested Citation

  • Joseph D. Sneed, 1971. "Theoretical Functions with Special Forms," Springer Books, in: The Logical Structure of Mathematical Physics, chapter 0, pages 96-109, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-3066-3_5
    DOI: 10.1007/978-94-010-3066-3_5
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