History and Philosophy of Logic 20 (3-4):267-290 (1999)

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Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different formalizations of arithmetic. In Peano's formalization the domain is a restricted class of individuals, while the universe of discourse is the unrestricted class of all individuals. In Gödel's formalization the domain is a restricted class of individuals as in Peano's formalization, but the universe of discourse coincides with the domain. In Whitehead-Russell's formalization the domain is a class of logical notions in Tarski's sense, that are necessarily not individuals, whereas the universe of discourse is the unrestricted class of individuals as in Peano's formalization. The present approach emphasizes the viewpoint that the universe of discourse of a given discourse is important in determining which propositions are expressed by which sentences
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DOI 10.1080/01445349950044198
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References found in this work BETA

From a Logical Point of View.W. V. O. Quine - 1953 - Harvard University Press.
Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.

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Citations of this work BETA

A Verisimilitudinarian Analysis of the Linda Paradox.Gustavo Cevolani, Vincenzo Crupi & Roberto Festa - 2012 - VII Conference of the Spanish Society for Logic, Methodology and Philosphy of Science.
In Defense of Benacerraf’s Multiple-Reductions Argument.Michele Ginammi - 2019 - Philosophia Mathematica 27 (2):276-288.
A New–Old Characterisation of Logical Knowledge.Ivor Grattan-Guinness - 2012 - History and Philosophy of Logic 33 (3):245 - 290.

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