  Classical logic fits very well with the multiple-succedent sequent calculus. There we do not need any additional principles beyond those assumed in the intuitionistic case. Just the structural feature of allowing for more than one formula in the succedent suffices to obtain classical logic. As there are plausible approaches to establish a harmony between right-introductions and left-introduction in the sequent calculus (see  section  3.3),  classical logic appears to be perfectly justified. However, this is only convincing if reasoning is appropriately framed as a multiple-conclusion process, even if this does not correspond to our standard practice where we focus on single conclusions. One could try to develop an appropriate intuition by arguing that reasoning towards multiple conclusions delineates the area in which truth lies rather than establishing a single proposition as true. However, this intuition is hard to maintain and cannot be formally captured without serious difficulties. Philosophical approaches such as those by Shoesmith and Smiley (1978) and proof-theoretic approaches such as proof-nets (see Girard, 1987; Di Cosmo and Miller, 2010) are attempts in this direction.