|Logic: logic is the doctrine of the admissibility or inadmissibility of relations between statements and thus the validity of the compositions of these statements. In particular, the question is whether conclusions can be obtained from certain presuppositions such as premises or antecedents. Logical formulas are not interpreted at first. Only the interpretation, i. e. the insertion of values, e.g. objects instead of the free variables, makes the question of their truth meaningful.|
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|A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967
Logic/Hilbert/d'Abro: Arithmetic is, in fact, to be regarded as a part of logic; however, when looking carefully, we see that certain fundamental concepts of arithmetic have already been employed in the formulation of the laws of logic, e.g. the concept of quantity and, in part, of the number.
So we get into a circle. To avoid this, a simultaneous development of logic and arithmetic is required.