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Like mathematics, logic may be constructed and developed in the spirit of pure positivity, that is, with inner consistency as the sole concern. Let us take the widest view of logic and define it as the science of possible forms: forms of propositions as well as forms of objects. Among the latter such forms as multiplicities, sets, combinations, permutations, coordinations, relations of every kind, etc., have to be included. In elaborating logic as a positive science, one begins by defining the most elementary forms and the fundamental operations. By applying one of these operations to a given form, a new form is obtained. There is the possibility of indefinite reiteration for every logical operation.² When a higher-order form is constituted through the application of a certain operation to a primitive form, that higher-order form can in turn be subjected to the same or a different operation.

DOI: 10.1007/978-90-481-2942-3_14

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