Danielle Macbeth

In Frege's Logic (2005), Macbeth proposes a new reading of Frege’s notation and logical project. Rather than treating Begriffsschrift (Frege's logic) as a notational variant of quantificational logic, Macbeth proposes that reasoning in Begriffsschrift is more like the diagrammatic reasoning of the geometrician or algebraist. She argues that philosophers and mathematicians alike have failed to recognize the revolutionary powers of Begriffsschrift in its expressive and demonstrative capacities.^[2]

Realizing Reason, her most recent book, takes a Hegelian approach to the philosophy of mathematics and traces developments in philosophy, logic, mathematics, and physics beginning with Aristotle in order to illuminate how (pure) reason has come to be realized as a power of knowing. She focuses on three periods: Ancient Greece, early modern mathematics, physics, and philosophy (Descartes to Kant), and late nineteenth-century and early twentieth-century mathematics and physics. Macbeth argues that with her new reading of Frege, we can finally break out of the Kantian framework that remains in place even in twentieth-century analytic philosophy and thereby finally understand how contemporary mathematics enables real extensions of our knowledge on the basis of strictly deductive reasoning. Thus, she demonstrates how pure reason has finally been realized as a power of knowing.^[3]

Macbeth has also published many articles on a wide range of topics in the history and philosophy of mathematics, the philosophy of language, the philosophy of mind, and pragmatism.

• Frege’s Logic (Cambridge, Mass.: Harvard University Press, 2005) ISBN 978-0674017078
• Realizing Reason: A Narrative of Truth and Knowing (Oxford: Oxford University Press, 2014) ISBN 978-0198704751