Journal of Philosophical Logic

, Volume 30, Issue 1, pp 79–96 | Cite as

Potential Infinite Models and Ontologically Neutral Logic

  • Theodore Hailperin


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.

ontologically neutral logic potential infinite model potential infinite validity generalized tautology 


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  1. Hailperin, T. (1992): Herbrand semantics, the potential infinite, and ontology-free logic, Hist. Philos. Logic 13, 69–90.Google Scholar
  2. Hailperin, T. (1997): Ontologically neutral logic, Hist. Philos. Logic 18, 185–200.Google Scholar
  3. van Heijenoort, J. (1967): From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Theodore Hailperin
    • 1
  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA

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