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On the indispensability of theoretical terms and entities

Johannesson, Eric (2022) On the indispensability of theoretical terms and entities. [Preprint]

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Abstract

Some realists claim that theoretical entities like numbers and electrons are indispensable for describing the empirical world. Motivated by the meta-ontology of Quine, I take this claim to imply that, for some first-order theory T and formula δ(x) such that T ∃xδ ∧ ∃x¬δ, where δ(x) is intended to apply to all and only empirical entities, there is no first-order theory T such that (a) T and T describe the δ:s in the same way, (b) T ∀xδ, and (c) T is at least as attractive as T in terms of other theoretical virtues. In an attempt to refute the realist claim, I try to solve the general problem of nominalizing T (with respect to δ), namely to find a theory T satisfying conditions (a)-(c) under various precisifications thereof. In particular, I note that condition (a) can be understood either in terms of syntactic or semantic equivalence, where the latter is strictly stronger than the former. The results are somewhat mixed. On the positive side, even under the stronger precisification of (a), I establish that (1) if the vocabulary of T is finite, a nominalizing theory can always be found that is recursive if T is, and (2) if T postulates infinitely many δ:s, a nominalizing theory can always be found that is no more computationally complex than T. On the negative side, even under the weaker precisification of (a), I establish that (3) certain finite theories cannot be nominalized by a finite theory.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Johannesson, Ericjohannesson.eric@gmail.com0000-0001-9128-2565
Subjects: General Issues > Logical Positivism/Logical Empiricism
General Issues > Operationalism/Instrumentalism
General Issues > Realism/Anti-realism
General Issues > Structure of Theories
General Issues > Theory/Observation
Depositing User: Dr. Eric Johannesson
Date Deposited: 06 Apr 2022 03:30
Last Modified: 06 Apr 2022 03:30
Item ID: 20424
Subjects: General Issues > Logical Positivism/Logical Empiricism
General Issues > Operationalism/Instrumentalism
General Issues > Realism/Anti-realism
General Issues > Structure of Theories
General Issues > Theory/Observation
Date: 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/20424

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