Reals by Abstractiont

  title={Reals by Abstractiont},
  author={Bob Hale},
  journal={Philosophia Mathematica},
  • B. Hale
  • Published 1 June 2000
  • Mathematics
  • Philosophia Mathematica
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 began by first defining an equivalence relation on ordered pairs of quantities: E[(a,b), (c,d)] ↔ ∀m,n (ma nb ↔ mc ⇔ nd), and then setting: Ratio(a,b) = Ratio(c,d) ↔ E[(a,b), (c,d)]. Alternatively, if it were felt desirable to avoid reliance on the notion of an ordered pair, we could introduce an… 

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