  If the LCC is to have a chance of being applicable, then it needs further restriction, beyond atomic sentences and their negations. This is because it has implausible consequences when applied to certain atomic sentences. Consider any increasing function \(f(t)\). Then sentences of the form \(f(t) \lt f(a)\) will hold for \(t \lt a\). By the LCC then, \(f(a) \lt f(a)\). This is surely a gratuitous conclusion even before the contradicting sentence \(-f(a) \lt f(a)\) is taken into account. The present author (1997) therefore proposed to restrict the application to the atomic sentences of equational theories, that is to sentences of the form \(f(t) = 0\). This is not so unreasonable on independent grounds, since the basic laws of nature are expressed in equational form.