 tautologies and contradictions do not picture reality or possible states of affairs and possible facts (4.462). Stated differently, tautologies and contradictions do not have sense, which means we cannot use them to make assertions, which means, in turn, that they cannot be either true or false. Analogously, mathematical pseudo-propositions are equations, which indicate or show that two expressions are equivalent in meaning and therefore are intersubstitutable. Indeed, we arrive at mathematical equations by “the method of substitution”: 