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.
Similar content being viewed by others
REFERENCES
Hailperin, T. (1992): Herbrand semantics, the potential infinite, and ontology-free logic, Hist. Philos. Logic 13, 69–90.
Hailperin, T. (1997): Ontologically neutral logic, Hist. Philos. Logic 18, 185–200.
van Heijenoort, J. (1967): From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hailperin, T. Potential Infinite Models and Ontologically Neutral Logic. Journal of Philosophical Logic 30, 79–96 (2001). https://doi.org/10.1023/A:1017576005382
Issue Date:
DOI: https://doi.org/10.1023/A:1017576005382