Can You Quote me a Mathematical Proof that Uses a Logic Formula other than Syllogism?

[Willem]

There exist many other formulas of mathematical logic in "Principia Mathematica". Is there an example of a mathematical proof that uses one of them (not syllogism)?

 

[Hartmann352]

Are you speaking about Isaac Newton's "Principia" that expounds Newton's laws of motion and his law of universal gravitation?

Or are you discussing "Principia" the three-volume work on the foundations of mathematics written by mathematician-philosophers Alfred North Whitehead and Bertrand Russell, published in 1910, 1912, and 1913?

It is critical to adequately identify which work you suggest that our investigations involve.

However, I suspect you mean Whitehead's and Russell's work because it contains a derivation of large portions of mathematics using both notions and principles of symbolic logic.

Hartmann352

 

[Willem]

It's Whitehead & Russel's work.

 

[Willem]

I mean other than: Modes Ponens, Proof by Contradiction or Proof by Cases.