The Paradoxy of Observing Systems

In spite of several attempts, it is still difficult to submit formal sciences such as logic or mathematics to a sociological analysis. Such an analysis would entail discovering empirical correlations between specific social conditions and specific formal structures. Both the conditions and the structures would then have to be treated as variables whose values would appear as contingent, despite their claims to be (as society) or necessary (as the principles, axioms, and rules of logic). One would have to assert that the natural is artificial because it is produced by society and that the necessary is contingent because under different conditions it may have to accept different forms. These are paradoxical statements, but we need them when we have to distinguish different observers from each other or when we have to distinguish self-observations from external observation, because for the selfobserver things may appear as natural and necessary, whereas when seen from the outside they may appear artificial and contingent (see L6fgren, Towards System). The world thus variously