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Potential Infinite Models and Ontologically Neutral Logic

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Abstract

The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.

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REFERENCES

  • Hailperin, T. (1992): Herbrand semantics, the potential infinite, and ontology-free logic, Hist. Philos. Logic 13, 69–90.

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  • Hailperin, T. (1997): Ontologically neutral logic, Hist. Philos. Logic 18, 185–200.

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  • van Heijenoort, J. (1967): From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA.

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Authors and Affiliations

  1. Department of Mathematics, Lehigh University, Bethlehem, PA, 18015, USA

    Theodore Hailperin

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  1. Theodore Hailperin
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Hailperin, T. Potential Infinite Models and Ontologically Neutral Logic. Journal of Philosophical Logic 30, 79–96 (2001). https://doi.org/10.1023/A:1017576005382

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  • DOI: https://doi.org/10.1023/A:1017576005382

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