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Constructive Mathematics and its Implication to Theory of Designing

By Ichiro Nagasaka.

Published by Design Principles and Practices: An International Journal

Designing is a constructive activity that creates certain objects, which satisfy requirements by putting different things together. However, there is apparently no common ground on which we can argue about the constructive aspects of the act of designing. In this study, we analyze the constructiveness of the act of designing on the basis of constructive mathematics, in particular, intuitionism.

Intuitionism in the mathematical sense is that mathematical objects have to be mentally constructed by mathematician to be existed. Therefore, propositions asserting certain objects exist should be verified by proofs, which explain how we can construct the objects.

In order to clarify the constructive characteristic of the act of designing, we examine the three aspects of constructive act of designing in detail, namely, “objects to be constructed”, “processes of the construction” and “semantics of the construction” in comparison to the act of proving in the constructive mathematics.

Finally, we discuss the normative principles of the constructive design activities that are derived from the argument of harmony in the three aspects of constructive activities.

Design Principles and Practices: An International Journal, Volume 3, Issue 5, pp.303-314. Article: Print (Spiral Bound). Article: Electronic (PDF File; 1.354MB).

Ichiro Nagasaka

Associate Professor, Graduate School of Humanities, Kobe University, Kobe, Hyogo, Japan