A mathematician turned cognitive scientist offers fresh insights into mathematical practice by bridging the gap between abstract theory and empirical science. This provocative essay reframes mathematics as fundamentally experimental—akin to physics—where computation serves as a form of experimentation and mathematical definitions parallel scientific theory-building. By exploring this dual nature of mathematics, the author ultimately aims to uncover deeper truths about human cognition itself, using mathematical thinking as a window into the broader nature of intellectual activity.
The big picture: The essay challenges traditional philosophical divisions by combining platonist and formalist perspectives on mathematics, positioning mathematical practice as surprisingly similar to experimental sciences.
- Mathematics emerges as an experimental discipline where computation plays a role parallel to physical experimentation in the sciences.
- The creation of mathematical definitions and axiomatic frameworks is framed as analogous to developing physical theories like Newtonian gravity or quantum mechanics.
Why this matters: This perspective could reshape how we understand both mathematics and human cognition more broadly.
- By examining mathematics as a test case, the author aims to probe the fundamental nature of human thought processes and knowledge creation.
- The approach bridges traditionally separate philosophical traditions in mathematics, potentially offering new insights for both mathematics education and artificial intelligence research.
Reading between the lines: The author reveals that mathematics serves as a strategic entry point into more ambitious questions about cognition in general.
- The essay’s “secret motivation” is to use mathematics as a controlled environment to study the nature of general cognition and intelligence.
- By focusing on the division between semantics (meaning) and syntactics (formal manipulation) in mathematics, the author is developing a framework that might apply to understanding cognition across domains.
Key details: The philosophical framework emphasizes non-formalistic aspects of mathematical research that often go unrecognized.
- The author proposes a strong division of intellectual activity into semantic (meaning-based) and syntactic (rule-based) components.
- This division, while not fully developed in the essay, represents the author’s core intellectual interest and motivation for the project.
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