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There is no reason to exclude it from regimented theory.
Regimented theory is, of course, an idealization.
Regimented theory contains no abstract objects other than sets.
Regimented theory also has no place for mental entities, most obviously minds, if those are taken to be distinct from physical entities.
What is Quine's justification for relying on the idea of regimented theory, rather than on our ordinary conceptual scheme?
The benefit of including such idioms in regimented theory is not worth the cost in unclarity that it would bring.
Similar(39)
So one might suppose that Quine accepts extensionality reluctantly, as the price to be paid for the advantages of the use of logic in regimenting theory.
Moreover, they sought to account for the presuppositions of scientific theories by regimenting such theories within a logical framework so that the important role played by conventions, either in the form of definitions or of other analytical framework principles, became evident.
He was aware, of course, that there would be disputes over how best to regiment theories within first-order logic.
But or so he thought once theories were regimented, the quantifier criterion would supply unequivocal verdicts.
(The exception here is the case of inconsistent mathematical or scientific theories, which according to the deflationary nominalist, ideally are regimented as consistent first-order theories).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com