in medias res reinforce the a priori conclusions of the sociological cogito. In
both directions, social constructivism leads to sociological realism.
Virtually no one actually doubts the reality of the world of ordinary
experience. It is only within specialized intellectual networks that the question
has arisen whether this banal reality can be proven to a high standard of
argument; and even intellectuals, when they are “off duty,” go back to assum-
ing the reality of the ordinary time-space world. Sociological realism shows
that even within intellectual contention at its most reflexive, it is possible to
support banal realism. It does not follow that every kind of ontological reality
is thereby supported. There are several kinds of realism and anti-realism; let
us see now what sociological realism implies for some of these non-ordinary
realms.
Sociological realism affirms mental and physical realities in human-sized
time and space. Problems arise when statements are made about realities
beyond the human-sized world. These include the objects of science, insofar
as these are entities or structures which are not observed by the naked eye or
acted upon by the unaided limbs; the concepts of mathematics; conceptual or
abstract reality per se, ideas and especially universals; the mind, taken as an
entity or substance. A variety of positions have been taken as to these things,
either to deny their reality or to affirm that they have a higher reality than
ordinary experience. These positions, denying or transcending banal reality,
have been produced by intellectual networks, whose struggles for innovation
in their argumentative attention space have repeatedly pushed beyond the
human-sized world.Mathematics as Communicative Operations
Mathematics is social discourse. The fact is inescapable if we straightforwardly
examine what is given. Here is a mathematical argument of slight technical
complexity:
(1) a bx cy
(2) a bx cy 0The sequence of statements is true, and meaningful, for me only because I
know what the symbols mean, and I know the acceptable procedures for
manipulating them, so that equation (1) becomes equation (2). The symbols,
like any other form of discourse, imply communication. This modest statement
of mathematical abstraction implies that I have had contact with a network of
teachers, no doubt many links removed from those who originated this mathe-
matics. Let us take an example from a higher level of abstraction (Kline, 1972:
1128):
862 •^ Meta-reflections