 Reflexivity merely expresses the triviality that any sentence \(\alpha\) is a deductive consequence of itself. Monotonicity expresses the fact that adding more premises to a deductive argument allows you to derive all the same conclusions as you could with fewer. Cut says roughly that deductive conclusions are on an equal epistemic footing with their premises: there is no loss of confidence as derivations get longer. Together, these principles imply that “consequences of consequences are consequences” i.e. that \(\alpha \vdash \beta\) and \(\beta \vdash \gamma\) implies that \(\alpha \vdash \gamma\). 