Reprint of “Mathematics as verbal behavior”

• Two interrelated principal questions regarding mathematics have been: (a) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are “discovered” as one might discover a new planet; and (b) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was “pure” with applications neither contemplated or even desired?
• I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries.
• How is it possible to understand nature by properly talking about it? Essentially, it is because nature taught us how to talk.

“Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded” (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its “special nature.” Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are “discovered” as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was “pure” with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk.