Big Ideas: The Power of a Unifying Concept

Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 54 (1):149-168 (2023)
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Abstract

Philosophy of science in the twentieth century tends to emphasize either the logic of science (e.g., Popper and Hempel on explanation, confirmation, etc.) or its history/sociology (e.g., Kuhn on revolutions, holism, etc.). This dichotomy, however, is neither exhaustive nor exclusive. Questions regarding scientific understanding and mathematical explanation do not fit neatly inside either category, and addressing them has drawn from both logic and history. Additionally, interest in scientific and mathematical practice has led to work that falls between the two sides of the dichotomy. We might call these less narrow approaches ‘holistic’. Prior to 1918, work in the philosophy of science was also somewhat more holistic and interdisciplinary in nature. An exemplar of this type of approach is found in the work of Henri Poincaré. In this paper I will consider one particularly flexible tool Poincaré uses throughout his philosophical writings about science and mathematics: the tool of the unifying concept. More specifically, I will focus on one unifying concept: that of structure. I aim to show first, that structure is a unifying scientific concept for Poincaré; second, a focus on structure helps explain his scientific and mathematical success; lastly, this case study may provide a model for how unifying concepts can facilitate progress in mathematics and science.

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Janet Folina
Macalester College

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References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
The Aim and Structure of Physical Theory.Pierre Duhem & Philip P. Wiener - 1955 - Science and Society 19 (1):85-87.
Intuitionism and Formalism.L. E. J. Brouwer - 1913 - Bulletin of the American Mathematical Society 20:81-96.

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