# Zolin and Pizzi: Defining Necessity from Noncontingency

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## Abstract

The point of the present paper is to draw attention to some interesting similarities, as well as differences, between the approaches to the logic of noncontingency of Evgeni Zolin and of Claudio Pizzi. Though neither of them refers to the work of the other, each is concerned with the definability of a (normally behaving, though not in general truth-implying) notion of necessity in terms of noncontingency, standard boolean connectives and additional but non-modal expressive resources. The notion of definability involved is different in the two cases (‘external’ for Zolin, ‘internal’ for Pizzi), as are the additional resources: infinitary conjunction in the case of Zolin, and for Pizzi, first, propositional quantification, and then, later, most ingeniously, the use of a propositional constant. As well as surveying and comparing of the work of these authors, the discussion includes some some novelties, such as the confirmation of a conjecture of Zolin’s (Theorem 2.7).

## Notes

### Acknowledgments

I am grateful to Zolin and to Pizzi for correspondence clarifying points from some of the papers dicussed here, to Rohan French for various improvements, and to Toby Meadows for his work (reported in Appendix 1) answering a question left open on as this material was presented to an audience at St Andrews in April, 2012. Thanks also to two Erkenntnis referees for their corrections.

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