# The Nuisance Principle in Infinite Settings

## TL;DR

This paper investigates the logical relationship between the Nuisance Principle and the HP abstraction principle in infinite settings, showing that their joint consistency fails under certain assumptions.

## Contribution

It demonstrates that the Nuisance Principle is inconsistent with HP in infinite contexts, extending previous results about their compatibility.

## Key findings

- NP is inconsistent with HP in infinite settings
- The inconsistency holds under a modest assumption about infinite concepts
- Joint second-order consistency fails for NP and HP

## Abstract

Neo-Fregeans have been troubled by the Nuisance Principle (NP), an abstraction principle that is consistent but not jointly (second-order) satisfiable with the favored abstraction principle HP. We show that logically this situation persists if one looks at joint (second-order) consistency rather than satisfiability: under a modest assumption about infinite concepts, NP is also inconsistent with HP.