# A General Theory of Abstraction Operators

@article{Tennant2004AGT, title={A General Theory of Abstraction Operators}, author={N. Tennant}, journal={The Philosophical Quarterly}, year={2004}, volume={54}, pages={105-133} }

I present a general theory of abstraction operators which treats them as variable-binding term-forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically noncommittal… Expand

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#### References

SHOWING 1-7 OF 7 REFERENCES

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

Logic And Existence: Ian Rumfitt

- Philosophy
- 1999

Frege’s logicism in the philosophy of arithmetic consisted, au fond , in the claim that in justifying basic arithmetical axioms a thinker need appeal only to methods and principles which he already… Expand

From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931

- Mathematics
- 1967

The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded… Expand