History of Philosophy Without Any Gaps

Episode 467: "Written in Mathematics: Descartes’ Physics"

Host: Peter Adamson
Date: April 13, 2025

Brief Overview

In this episode, Peter Adamson delves into René Descartes’s physics, exploring his ambition to ground the study of nature entirely in mathematical terms—reducing the physical world to geometric extension and motion. Adamson traces the historical context, the influences and originality of Descartes’s project, his departures from Aristotelian and atomistic paradigms, and the metaphysical implications of Cartesian mechanics. The episode critically examines Descartes’s three laws of motion, the role of God in his system, and the overarching confidence Descartes had in his foundational principles.

Key Discussion Points & Insights

1. The Mathematical Language of Nature

• Drawing from Galileo and Descartes’s predecessors, Adamson sets the stage:
  • Nature is "written in mathematical language," as Galileo famously claimed ([00:20]).
  • Descartes takes this as inspiration, pushing the idea that understanding nature means understanding its geometry.

2. Descartes’s Intellectual Context and Influences

• Humanist Mathematicians:
  • Renaissance scholars like Benedetti, Commandino, Alberti, and Regiomontanus laid groundwork through studies of ancient mathematicians and applications of mathematics to practical fields ([02:00]).
• Corpuscularianism and Atomism:
  • Introduced by thinkers like Daniel Sennert, Taurellus, and Gorlaeus—focusing on the world as composed of tiny bodies ([03:10]).
  • Descartes learned from these trends, though was keen to assert his novelty.

3. Descartes’s Innovations in Physics

• Extension as the Essence of Body:
  • “I am the first to have considered extension as the principal attribute of body.” (Descartes, [04:12])
  • For Descartes, matter is nothing but extension in length, breadth, and depth.
• Mathematics as Physics’ Foundation:
  • Bodies are “the objects of geometrical demonstration made real.” (Dan Garber, paraphrased by Adamson, [07:00])
  • “I recognize no matter in corporeal things, apart from that which the geometers call quantity...” (Descartes, [07:25])

4. Contrast with Aristotelian and Atomist Theories

• Aristotelian Prime Matter:
  • Seen as pure potentiality, lacking determinate features—challenged by Descartes’ conception of solid, filled space ([08:50]).
• Atomists vs. Descartes:
  • Atomists posited indivisible, weighty atoms moving in a void;
  • Descartes denied real atoms and the void—matter is infinitely divisible extension, and all space must be filled ([15:38]).
  • “It is no less impossible that there be a space that is empty than that there be a mountain without a valley.” (Descartes, [15:45])

5. Reduction of Qualities to Motions

• No Substantial Forms or Qualities:
  • All properties (heat, color, etc.) arise from motion and arrangement of parts.
  • On sensation: “...sensible experiences are the result of a causal interaction, but do not wear the underlying cause on their sleeve, so to speak.” (Adamson, [21:34])
• Examples:
  • Burning wood only involves the motion of its parts—there is no special “form of fire” or inherent “quality of heat” ([11:35]).

6. Shortcomings and Ambitious Program

• Empirical Limitations:
  • Descartes didn’t provide quantitative details for most phenomena (smell, color, heat), often lacking experimental means ([25:30]).
  • Color explained tentatively as arising from ratios of types of corpuscular motion ([26:10]).

7. Descartes’s Three Laws of Motion

• Law 1:
  • Bodies continue in motion or rest unless affected by another ([28:50]).
• Law 2:
  • When bodies meet, they push against one another and the 'power' of motion (based on size and speed) determines the outcome ([30:20]).
• Law 3:
  • Natural motion is straight, but can be forced into a curve due to resistance (e.g., a stone in a sling) ([31:35]).
• Notable quote:
  • “All of these laws only concern spatial or local motion, which for Descartes is the only kind of motion there is.” (Adamson, [33:00])

8. Philosophy of Motion and Relativity

• Relative Motion:
  • For Descartes, movement is always relative to surrounding bodies—not an absolute change in spatial coordinates ([36:10]).
  • Playful examples: the swimming giraffe, Adamson lying in bed, etc.

9. Material World as a Mechanistic System

• No Individual Substances:
  • Giraffes, marshmallows, and even beds are just temporary, relatively moving configurations—no underlying forms ([39:30]).
• Critique from Leibniz:
  • The Cartesian universe “is effectively just one big thing with lots of internally shifting parts.” (Adamson summarizing, [40:40])

10. Cosmological Consequences: The Vortex Theory

• Earth’s ‘Rest’:
  • Descartes, a Copernican, says Earth is “at rest” relative to its surrounding vortex, even as it circles the sun ([43:00]).
• Motivation and Sincerity:
  • Unlikely that Descartes is merely bowing to Church pressures—his broader cosmology is too radical ([44:20]).

11. The Role of God in Cartesian Physics

• Lawmaker and Sustainer:
  • Physical laws are decreed by God; their unchangingness reflects divine immutability ([48:15]).
  • “It is a nice trick to make the continual changing of things an argument for divine immutability.” (Descartes scholar Deschene, quoted by Adamson, [49:10])
• Question of Occasionalism:
  • Does God cause every motion? Adamson discusses the later development of occasionalism in Cartesian-inspired thought ([51:10]).
• God as General Cause:
  • Most likely, Descartes sees God as architect and lawgiver, not micromanager, but there’s scholarly debate about this ([52:35]).

12. Confidence in the Principles

• Certainty and Foundations:
  • Descartes is strikingly confident: “the principles on which his physical theory is founded are simply obvious, and that his special achievement is to have realized that these obvious truths could be used as principles of physics.” (Adamson, [53:40])
  • Yet these assumptions are deeply controversial.

Notable Quotes & Memorable Moments

• On the mathematical nature of the universe:

  "Philosophy is written in this all encompassing book that is constantly open before our eyes, that is the universe. But it cannot be understood unless one first learns to understand the language and knows the characters in which it is written. It is written in mathematical language..."
  (Galileo, as quoted by Adamson, [00:22])

• On Descartes' definition of matter:

  "I recognize no matter in corporeal things, apart from that which the geometers call quantity, and take as the object of their demonstrations that to which every kind of division, shape and motion is applicable."
  (Descartes, [07:25])

• Analogies on sensation:

  "Consider how words signify without needing to resemble what they signify, or how tears can represent sadness, even though sadness isn't wet. Just so. Sensible experiences are the result of a causal interaction, but do not wear the underlying cause on their sleeve, so to speak."
  (Adamson, [21:34])

• On the relativity of motion:

  "If a giraffe is swimming in the Gulf of Mexico, it counts as moving because all its parts are traveling together while the surrounding water is being left behind. If, by contrast, the giraffe is standing on the bed of the Mississippi river, we would say that it is at rest because it is not moving relative to the riverbed."
  (Adamson, [36:10])

• Leibniz’s critique:

  "[Leibniz] complained that the Cartesian universe is effectively just one big thing with lots of internally shifting parts. No one part forms an independent substance in its own right, but only earns the honor of being a discrete body because of the way it is presently moving."
  (Adamson, [40:40])

• On Descartes' confidence in his foundations:

  "...he says that the principles on which his physical theory is founded are simply obvious, and that his special achievement is to have realized that these obvious truths could be used as principles of physics."
  (Adamson, [53:40])

Timestamps for Important Segments

| Time | Segment | |------|---------| | 00:20 | Galileo’s vision: universe as mathematical language | | 02:00 | Humanist scholars and pre-Cartesian developments | | 04:12 | Descartes’ claim: extension as principal attribute of body | | 07:00 | Mathematics as the foundation of physics | | 11:35 | Reduction of qualities like heat to motions of parts | | 15:38 | Descartes’ rejection of atoms and the void | | 21:34 | Analogy: sensation as signification and causal effect | | 28:50 | The three laws of motion explained | | 36:10 | Descartes' relativity of motion: giraffes and beds | | 40:40 | Leibniz’s criticism of Cartesian universe | | 43:00 | Earth’s motion and the vortex theory | | 48:15 | The function of God as lawmaker in physics | | 53:40 | Descartes' certainty in his principles |

Tone and Style

Peter Adamson’s delivery is engaging, clear, and often gently humorous—using analogies (like marshmallows and giraffes), vivid historical anecdotes, and witty asides to keep dense philosophical content lively and accessible.

Conclusion

Adamson’s exploration reveals both the radical ambition and the intriguing tensions of Cartesian physics. Descartes aimed to explain all physical reality as geometry in motion, rooted in laws set by God—with confidence that his approach was self-evident and mathematically precise, even as many details awaited experimental validation. The episode prepares listeners for the philosophical challenges Descartes would continue to face, especially regarding the foundation and certainty of knowledge—the focus for coming episodes.