jonathanichikawa / for-all-x

Open-source logic textbook in LaTeX by UBC philosophy professor Jonathan Ichikawa
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reiteration rule shouldn't be basic #4

Closed jonathanichikawa closed 1 year ago

jonathanichikawa commented 5 years ago

The "Reiteration" natural deduction rule is listed as a basic, not a derived, rule. This is unnecessary — it can be derived via or-introduction, negation elimination, and negation elimination. Need to add a discussion of the fact to the derived rules section, and move the R rule from the basic page to the derived page in the appendix.

jonathanichikawa commented 5 years ago

I think I was mistaken about this. Given the way our reductio rules are written, I don't think we can derive R from the introduction and elimination rules after all. I had been thinking along these lines: image

But this is a mistake; line 4 would have needed to reference the double negation, which is not what we have on 1.

So unless/until I figure out how to derive R, I'll leave it as basic.

Nico314159 commented 1 year ago

You can derive R as follows:

  1. φ
  2. φ ∧ φ (∧I, 1, 1)
  3. φ (∧E, 2)
jonathanichikawa commented 1 year ago

I made this change.