Page 86 - Contribution To Phenomenology

PHENOMENOLOGY AND COGNITIVE SCIENCE 79

moving: to mechanics, calculus, dynamics
calculating: to algebra, numerical analysis
proving: to logic
puzzling: to combinatorics, number theory
grouping: to set theory, combinatorics

Having listed these different human activities Mac Lane notes their
interrelationships: "These various human activities are by no means
completely separate; indeed, they interact with each other in complex
ways . . . .The two parts of this table should (and do) fit together by
many crosslinks" (Lakoff, 1987, p. 362).
The sorts of relationships that we normally think of as relationships
holding among formal mathematical terms, such as symmetry, asymmetry,
or transitivity, turn out to be rooted and ah*eady exhibited in the more
basic human activities that generate these mathematical formations.
Sequences of human actions are already symmetrical, asymmetrical, etc.
As Mac Lane says, mathematical systems "codify deeper and nonobvious
properties of the originating human activities" (Lakoff, 1987, p. 362).
Mathematical formations thus always retain within themselves what
phenomenologists would call their "meaning-genesis": the forms of the
activities that generate mathematical formations remain embedded within
these higher-level formations, only now emptied of content, i.e., formal-
ized.
Lakoff summarizes Mac Lane's position in the following way:

Mac Lane claims that the branches of mathematics are as they are
because they arise from human activities that each have a general
schematic structure, made up of various substructures, or "basic ideas."
These basic ideas both occur in the structure of the human activities
that give rise to the various branches of mathematics (and in these
branches of mathematics themselves). Mathematics describes them and
their connections and interrelationships in an absolutely rigorous way (p.
362).

Mac Lane's position here resembles Husserl's in "The Origin of
Geometry." Husserl claims that the "meaning-genesis" of geometry lies in
the idealization and formalization of certain human activities. Husserl
mentions in particular the activities of estimating, measuring, designing
buildings, and surveying fields (1970, p. 376). Geometry thus had its roots
in everyday practical life, not in pure theory. As Husserl writes, "in the