A Theory Bite on Infinity: A Companion to Falk

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Notes

Of course, my operational interpretation of Falk's terms may be different from her own. The particularities of the proposed interpretation aside, however, I believe that any lexical explication, being also an epistemological declaration, is bound to lead to adjustments in methods and implications of the study.

To objectify an action means to replace utterances about processes with utterances about independently existing objects, as in the transition from the action of squaring numbers to the object called function x². This is attained in the twin action of reifying, replacing verbs clauses with noun clauses; and of alienation, that is, removing the human subject from utterances.

These are objects in the technical sense described earlier. Mathematically, the relevant kind of object would be called a set.

∗“Theory Bites” are short commentaries on papers that appear in the journal. They aim to highlight and characterize (a) the author's theoretical perspective, (b) alternative ways of thinking about relevant phenomena, and (c) the empirical and educational consequences of taking one or another position. The point of these non-oppositional, dialog-like contributions is to emphasize and contextualize the theoretical commitments behind the research reported in the journal and to advance the capacity of our community to theorize powerfully. A longer discussion of theory bites appears in the Editor's note in Vol. 26, No. 4.