Abstract
Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real numbers.
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Hugly, P., Sayward, C. Quantifying over the reals. Synthese 101, 53–64 (1994). https://doi.org/10.1007/BF01063968
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DOI: https://doi.org/10.1007/BF01063968