I used to worry a lot about the “ontological status of variables”, and I was eventually able to achieve a moderate degree modicum of ontological security, at least, with respect to the simple domains that interested me, by taking up a pattern-theoretic point of view on of variables. In this view, you shift the question from the status of a an isolated variable name like “$x$” to the syntactic entity “$S \ldots x \ldots$” in which the variable name occurs. You may now view “$S \ldots x \ldots$” as a name for a set of denoting the objects denoted by its various substitution instances.
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2 | correct a technical detail about plural denotations | ||
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I used to worry a lot about the “ontological status of variables”, and I was eventually able to achieve a moderate degree of ontological security, at least, with respect to the simple domains that interested me, by taking up a pattern-theoretic point of view on variables. In this view, you shift the question from the status of a variable name like “$x$” to the syntactic entity “$S \ldots x \ldots$” in which the variable name occurs. You may now view “$S \ldots x \ldots$” as a name for a set of objects denoted by its various substitution instances. |
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