Let P, Q, R be three statements. Is there a name for the following rule of inference?

If P implies Q, and if P implies R, then P implies both Q and R.

  • 1
    Just for clarity's sake, do you mean for your conclusion to be P -> Q & R (i.e. how the "and" operator works), or do you mean something more like P -> Q,R (i.e. multiple consequents)? – Paul Ross Jul 2 '18 at 7:32

R&W in their landmark work in formal logic : Principia Mathematica, page 110, called it "Principle of Composition" :

if a proposition implies each of two propositions, then it implies their logical product. This is called by Peano the "principle of composition."

The reference is to Giuseppe Peano; see e.g. Logique mathématique (1897).

  • Did the phrase “principle of composition” enter into general use? I found an apparently related idea on SEP at “Propositional Dynamic Logic” > Hoare calculus. Otherwise I have not been able to find the phrase. The most typical search result is “fallacy of composition”. I was able to find several references to Distribution as a rule of equivalence. E.g., math SE math.stackexchange.com/questions/1318235/… – Mark Andrews May 28 '18 at 2:30
  • 1
    @Mark Andrews - I do not think so... but there is no reason to expect that every tautology has a name. – Mauro ALLEGRANZA May 28 '18 at 5:50

If P implies Q, and if P implies R, then P implies both Q and R.

The name of the rule is Distribution. See Barker, Stephen (1965), The elements of logic, p. 124-25 (Truth-functional principles for use in deduction).

  • 3
    The question asks for the name of this rule of inference. – Randy Randerson May 27 '18 at 3:12
  • In short, the name is Distribution. But it takes the two steps to show why distribution works. – Mark Andrews May 27 '18 at 3:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.