# The Nuisance Principle in Infinite Settings

@article{EbelsDuggan2015TheNP, title={The Nuisance Principle in Infinite Settings}, author={Sean Ebels-Duggan}, journal={arXiv: Logic}, year={2015} }

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.

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#### References

SHOWING 1-10 OF 17 REFERENCES

Notions of Invariance for Abstraction Principles

- Mathematics
- 2010

The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character ‐ permutation… Expand

Frege Meets Dedekind: A Neo-Logicist Treatment of Real Analysis

- Mathematics
- 2007

objects of mathematics, even implicit ones, ought to determine a unique group of objects which necessarily fall under the definition. If this ‘defining’ abstraction principle is unboundedly… Expand

Reals by Abstractiont

- Mathematics
- 2000

ions like the Direction equivalence and Hume’s principle and that it is reasonable to regard it as one. We might bring EM into line with the characterisation of abstraction principles with which I… Expand

RELATIVE CATEGORICITY AND ABSTRACTION PRINCIPLES

- Computer Science, Mathematics
- The Review of Symbolic Logic
- 2015

It is shown that most other abstraction principles are not naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. Expand

Language, thought, and logic : essays in honour of Michael Dummett

- Philosophy
- 1997

1. Concepts Without Words 2. Has Dummett Oversalted his Frege? Remarks on the Conveyability of Thought 3. Some Senses of Holism: An Anti-Realist's Guide to Quine 4. Another Plea for Modesty 5.… Expand

Logic, Logic, and Logic

- Philosophy
- 1998

Part 1 Studies on set theory and the nature of logic: the iterative conception of set reply to Charles Parsons' "Sets and Classes" on second-order logic to be is to be a value of a variable (or to be… Expand

The foundations of arithmetic : a logico-mathematical enquiry into the concept of number

- Philosophy
- 1951

This volume represents the first philosophically sound discussion of the concept of number in Western civilization. (Mathematics)

Meaning and Method: Essays in Honor of Hilary Putnam

- Philosophy
- 2009

Preface List of contributors 1. The source of the concept of truth Michael Dummet 2. Facts that don't matter Catherine Z. Elgin 3. Has the description theory of names been refuted? Jerrold J. Katz 4.… Expand

Abstraction and Set Theory

- Mathematics, Computer Science
- Notre Dame J. Formal Log.
- 2000

ION AND SET THEORY