🧠 1. Natural Deduction

Translating writing forms:

🔥 1.2 Primitive Rules - Rules of Inference

• Natural Deduction strategies for conditionals: “If the final conclusion which you are trying to derive (the "target conclusion") is a conditional, set up a sub-derivation which has as its assumption the antecedent of the target conclusion. That is, start your outer derivation by listing the initial premises. Then start a sub-derivation with the target conclusion's antecedent as its assumption. Then reiterate your original premises in the sub-derivation and use them, together with the sub-derivation's assumptions, to derive the consequent of the target conclusion.”

…. Premises A => C Conclusion A Assumption

STEPS

…. List all the premises

      | A        Start an assumption
      | ….       Reiterate premises
      | ….       Reiterate premises
      | .
      | C
      ————————————

A => C Obtain a conclusion

• Reductio Ad Absurdum - Negation introduction: "Negation introduction requires some comment. Once again, natural deduction seeks to capture and make precise conventional forms of informal argument. This time we express what traditionally goes under the name of “reductio ad absurdum,” or “reduction to the absurd.” Here the idea is that if we begin with an assumption from which we can deduce a contradiction, the original assumption must be false. Natural deduction employs this strategy as follows: Begin a subderivation with an assumption, X. If one succeeds in deriving both a sentence of the form Y and its negation, ~Y, write the sentence of the form ~X as a conclusion of the outer derivation anywhere below the subderivation."

    | X            Assumption
    | .
    | .
    | .
    | Y
    | .
    | .
    | .
    | ¬ Y