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Second order curiosities: MPP, implication

  1. Apr 12, 2015 #1
    In setting up a syntax for a first order theory, one usually includes Modus Ponens as a metarule. However, couldn't MP just be rewritten as a second-order sentence, thereby making all supposedly first-order theories de facto second-order ones?

    While on the subject of second order theories, I have noticed that a rule like ( N(p→q)→(Np→Nq)) uses the same arrow for implications between first-order (p, q) entities and second order (Np, Nq,N(p→q)) ones. Shouldn't they be two different arrows, something like ( N(p⇒q)→(Np→Nq)) ?
     
  2. jcsd
  3. Apr 18, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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