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}
}
  • N. Tennant
  • Published 2004
  • Computer Science
  • The Philosophical Quarterly
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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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 alreadyExpand
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