Sociologically, the three levels may be regarded as distinct but inter-related
discursive practices, after Foucault. For each has its own symbol systems, knowledge
base, social context and associated power relationships, although they may be hidden.
For example, at the level of syntax, there are rigorous rules concerning acceptable
forms, which are strictly maintained by the mathematics establishment (although
they change over time). This can be seen as the exercise of power by a social group.
In contrast, the absolutist mathematician’s view is that nothing but logical reasoning
and rational decision-making is relevant to this level. Thus a full sociological
understanding of mathematics requires an understanding of each of these discursive
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practices, as well as their complex inter-relationships. Making these three levels
explicit, as above, is a first step towards this understanding.