

Mathematics is a logical method. The propositions of mathematics are equations, and therefore pseudopropositions. 6.21 (1) Mathematical propositions express no thoughts. 6.22 The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations. 6.23 (4) If two expressions are connected by the sign of equality, this means that they can be substituted for one another. But whether this is the case must show itself in the two expressions themselves. It characterizes the logical form of two expressions, that they can be substituted for one another. 6.24 (1) The method by which mathematics arrives at its equations is the method of substitution. For equations express the substitutability of two expressions, and we proceed from a number of equations to new equations, replacing expressions by others in accordance with the equations. 