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(2003) Philosophy of arithmetic, Dordrecht, Springer.
The concept of calculational technique is customarily taken to be closely associated with that of arithmetic. Indeed, the two are often identified. Arithmetic is usually defined as the science of numbers. This definition is not sufficiently clear. The individual numbers, considered by themselves, give no occasion for treatment with a view to knowledge of them; and where we are concerned with a scientific grounding of particular characteristics of individual numbers, it is always a matter of properties that accrue to them in virtue of certain relations that bind them to other individual numbers (or whole classes thereof). Only out of the relationships of numbers to one another do there arise problems that require a logical treatment. Accordingly, it would be better to define arithmetic as the science of the relations among numbers. In any case, its essential task consists in finding other numbers from given numbers by means of certain known relationships that obtain between them.
Publication details
DOI: 10.1007/978-94-010-0060-4_14
Full citation:
Husserl, E. (2003). The logical sources of arithmetic, in Philosophy of arithmetic, Dordrecht, Springer, pp. 271-301.