Simon Duffy - Deleuze and the History of Mathematics
Sep 17, 2022
auto_awesome
Simon Duffy discusses the convergence of history of mathematics and philosophy, exploring topics such as perspective in Spinoza, Deliz's work on serialism and calculus, integration of historical mathematics, Lautman's Platonism, consciousness and intensity, differential philosophy, and mathematics as a nomadic science.
The alternative history of mathematics, specifically the power series approach, provides a different perspective on problem solving and challenges standard models.
Dialectics should involve a critical engagement with mathematical theories, highlighting the importance of power series and the integration of different mathematical approaches in problem solving.
Pragmatism and subject naturalism offer an alternative perspective on the relationship between philosophy and mathematics, emphasizing the rigorous evaluation of different vocabularies and problem-solving approaches.
Deliz's exploration of the alternative history of mathematics, influenced by philosophers like Lautman and Vile, showcases the critical and speculative potential of mathematics in problem solving and reimagines the relationship between mathematics, problem solving, and philosophy.
Deep dives
Deliz's exploration of the alternative history of mathematics
Deliz delves into the alternative history of mathematics, specifically the power series approach, which is often overlooked in mainstream mathematics. He traces this alternative history, which emphasizes the importance of integration by series, and highlights how it can provide a different perspective on problem solving. Deliz argues that this approach allows for a critical and speculative engagement with mathematical concepts, challenging standard models and proposing new possibilities. He draws on philosophers like Lautman and Vile, who also explore the connections between mathematics and philosophy, to further support his ideas.
Deliz's perspective on dialectics and problem posing
Deliz's concept of dialectics differs from Hegel's by emphasizing problem posing. Rather than elevating mathematics as the queen of the sciences, Deliz sees mathematics as an important dialogue partner for philosophy. He suggests that dialectics should involve a critical engagement with mathematical theories, particularly those related to problematics. Deliz's exploration of dialectics embraces an alternative history of mathematics, highlighting the importance of power series and the integration of different mathematical approaches in problem solving.
Deliz's approach to pragmatism and subject naturalism
Deliz's views on pragmatism and subject naturalism offer an alternative perspective on the relationship between philosophy and mathematics. Deliz's understanding of pragmatism involves the rigorous evaluation of different vocabularies and problem-solving approaches within a critical framework. He argues for a more grounded and coherent application of Deliz's philosophy in which the history of mathematics, including non-standard analysis and power series, can play a vital role. Deliz's work encourages academics to defend their claims with clear reasoning and to consider alternative approaches in order to enhance the rigor and usefulness of their intellectual endeavors.
Simon Duffy's translation of Lautman and Deliz's engagement with mathematics
Simon Duffy's translation of Lautman's work showcases the importance of the alternative history of mathematics that Deliz explores. Deliz's engagement with this alternative history indicates his interest in problematics and how mathematics can be a valuable dialogue partner for philosophy. By tracing the historical and philosophical implications of power series and integration, Deliz sheds light on the critical and speculative potential of the mathematics he examines. Lautman's ideas, along with other mathematicians and philosophers like Vile and Maimon, contribute to Deliz's overall project of reimagining the relationship between mathematics, problem solving, and philosophy.
The Relationship Between Riemann Surfaces and Power Series Approximations
The podcast episode discusses the relationship between Riemann surfaces and power series approximations in mathematics. The speaker explains how power series approximations can provide an approximation of a curve by using a finite length of the power series. They also discuss the concept of analytic continuity, where curves disappear and are resolved into new surfaces through differential calculations. The speaker highlights the contributions of mathematicians like Plankaré and Viall in connecting different areas of mathematics using surfaces and curves. The episode also touches on the idea of partial objects and how they can be mapped onto surfaces in mathematics.
Deloitte's Approach to Mathematics and Philosophy
The podcast explores Deloitte's approach to mathematics and philosophy. The speaker suggests that Deloitte's does not view mathematics as a language of God or an external truth, but rather as a way of understanding differences of intensity and carving up phenomenal experiences. Deloitte's sees mathematics as a rule-based framework that helps us comprehend and construct new concepts. The speaker also discusses the influence of philosophers like Lautman and Bergson on Deloitte's thinking, as well as Deloitte's engagement with Platonism and his emphasis on imminence and the conditions of the problem.
Examining the Relationship Between Differential Calculus and Deloitte's Philosophy
The podcast episode explores the relationship between differential calculus and Deloitte's philosophy. The speaker discusses the Leibniz diagram, which represents differentials and how they relate to triangles and surfaces. They explain that the moving line in the diagram represents a differential treatment, and the proportions of the triangles are maintained even when one triangle disappears. The speaker suggests that this can be mapped onto Deloitte's concept of surfaces and transversals, and how different surfaces are resolved through differential calculations. They also connect these concepts to Deloitte's ideas of virtual and actual, as well as partial objects on the body without organs.
Cooper and Taylor chat with Simon Duffy about the history of mathematics and the history of philosophy converging in the investigation and determination of problems and Ideas.
https://scholar.google.com/citations?user=IGVRZUMAAAAJ&hl=en
Support us on Patreon:
https://www.patreon.com/muhh
Twitter: @unconscioushh
Get the Snipd podcast app
Unlock the knowledge in podcasts with the podcast player of the future.
AI-powered podcast player
Listen to all your favourite podcasts with AI-powered features
Discover highlights
Listen to the best highlights from the podcasts you love and dive into the full episode
Save any moment
Hear something you like? Tap your headphones to save it with AI-generated key takeaways
Share & Export
Send highlights to Twitter, WhatsApp or export them to Notion, Readwise & more
AI-powered podcast player
Listen to all your favourite podcasts with AI-powered features
Discover highlights
Listen to the best highlights from the podcasts you love and dive into the full episode
