Descartes: Rationalism and the Cartesian Method

Descartes: A Transition to Modern Philosophy

Descartes lived during the Renaissance, a period of transition between medieval and modern philosophy. Key features of this era include:

• Decomposition of feudalism: The emergence of a new class-based society.
• Loss of medieval religious meaning: A shift from theocentrism to anthropocentrism, with the rise of national monarchies.
• Secular spirit: Civil power and politicians distanced themselves from the Church.
• Discoveries: New geographical and scientific discoveries expanded the known world.
• Reformation: The breakdown of religious unity.
• The new science: A focus on mathematizing the observable world.
• Everything: The problem of actually going into the background.

Rationalism in the 17th and 18th Centuries

Rationalism was a philosophical current characterized by:

• Predominance of reason over sense experience: Reason is considered the supreme principle.
• Innate ideas: Rationalists proposed that the human mind possesses certain ideas at birth, independent of sensory experience.
• Universal science: They aimed to create a universal science based on mathematics, valid for all rational beings.
• Rationality of the world: They believed that nothing is casual or random.

The Problem of Method

Idea: To convert philosophical problems into mathematical ones.

The Need for a Method

The preoccupation with method became an "epochal feature." The root cause of errors was believed to come from the senses and imagination. The goal was to reach truth using reason alone. Descartes aimed to end the quarrels of philosophers and restore unity and security in philosophical knowledge. His philosophy is sometimes called "of precaution" because it is guided more by the fear of making mistakes than by the desire to discover the truth.

Descartes defines the method as a set of true and easy rules, which, if correctly observed, will never admit falsehood as truth.

The Origins of the Method

To develop his method, Descartes sought to combine the benefits of three sciences: logic, geometry, and algebra.

• Logic: While useful for developing what is already known, the method must allow for the discovery of new truths.
• Geometry: Too limited to the consideration of lines and shapes, it is inappropriate for the humanities.
• Algebra: Due to its complexity, it fatigues the mind and can be confusing.

The first step in constructing the universal method was the discovery of analytic geometry, which:

1. Made geometry and algebra one science.
2. Managed to tie two sciences together, reducing them to a universal method using mathematics.

The second step was the combination of mathematics with logic:

1. This step captures the essence of mathematical reasoning, applying order and measure to both subject matter (experimental sciences) and objects (human sciences).
2. To make philosophical knowledge more like mathematics, Descartes reduced its objects to three: thinking, extension, and God.

In short, if the most obvious of the more abstract sciences is done, making all sciences as abstract as mathematics, they would become equally obvious.

The Rules of the Cartesian Method

Descartes formulated four rules that summarize the mathematical procedure:

1. Rule of Evidence:
   • Do not consider anything true unless it is obviously so, avoiding any rush. Evidence is the intuition of a clear and distinct idea.
   • Intuition is the design of a single mind in the light of reason.
   • Evidence cannot be doubted. Error arises from rushing.
   • Most ideas are complex and must be reduced to simple ones.
2. Rule of Analysis:
   • Divide the complex into its simplest parts. Eliminate ambiguities.
   • This not only breaks down a simple idea into its elements but also reduces the unknown to the known.
   • This is inspired by geometric thought.
3. Rule of Synthesis:
   • Transform into a complex whole; reconstruct the parts of reality that had been divided.
   • Deductively order from the simple to the derivative.
   • Expand knowledge with new truths.
4. Rule of Enumeration:
   • Check and verify that the analysis is complete and the synthesis is correct.
   • This is part of intuition as it turns.