Abstract
Knowing such an elementary truth as 2 + 2 = 4 is essentially a matter of knowing the numbers 2 and 4.
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Notes
In this paper I will operate with the version of this distinction I developed in my “Mathematics as a Science of Patterns: Ontology and Reference” Nous 15, 1981. I am not certain of Ziff’s notion of structure.
See my 1981 paper for further details.
I presented more precise and detailed arguments for these claims in my 1981 paper.
ee my 1981 paper for the definition of pattern/structure occurrence.
Cf. my 1981 paper.
In Physicalism in Mathematics. Andrew Irvine (ed.), Kluwer Academic Publishers, 1990.
See Quine’s Set Theory and Its Logic,Harvard University Press, 1963 or my Frege and the Philosophy of Mathematics,Cornell University Press, 1980. Paul Benacerraf’s “What Numbers Could Not Be” Philosophical Review,74, 1965 also develops this point and draws heavily upon it. If we think of standard number theory as second-order, as I have not, then we need not add the set theory.
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© 1994 Springer Science+Business Media Dordrecht
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Resnik, M.D. (1994). Numbers as Structures and as Positions in Structures. In: Jamieson, D. (eds) Language, Mind, and Art. Synthese Library, vol 240. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8313-8_5
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DOI: https://doi.org/10.1007/978-94-015-8313-8_5
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