Rationalism: A Priori Knowledge with Descartes & Leibniz

Introduction

In our previous lesson, we followed Descartes on his radical journey of doubt, which led him to his first, unshakeable certainty: "Cogito, ergo sum"—"I think, therefore I am." He established his own existence as a "thinking thing," but this left him isolated in his own mind, with the external world and even mathematical truths still in question.

Today, we will explore the next step in the rationalist project. Having found a truth purely through reason, Descartes and other rationalists argue that this is not an isolated case. They claim that some of our most important knowledge is known a priori—that is, through reason alone, independent of any particular sensory experience. This stands in stark contrast to a posteriori knowledge, which is derived from and justified by experience.

This lesson directly addresses the learning outcome: to explain the rationalist claim that some knowledge is a priori and independent of experience, using examples from Descartes or Leibniz. We will see how Descartes used his theory of innate ideas and how Leibniz used his analysis of necessary truths to argue that reason is a powerful source of knowledge about the world.

A Priori and A Posteriori: A Fundamental Distinction

Before we dive into the specific arguments, we need to be crystal clear on the key epistemological distinction between a priori and a posteriori knowledge. These Latin terms translate to "from what is before" and "from what is after," respectively, where "what is before/after" refers to experience.

To summarize:

• A Priori Knowledge: Justified independently of experience (e.g., "All bachelors are unmarried," "7 + 5 = 12"). We know these things by understanding the concepts involved or through logical proof, not by conducting surveys or experiments.
• A Posteriori Knowledge: Justified by and dependent on experience (e.g., "Water boils at 100°C," "It is raining outside"). We can only know these things by observing the world.

The central debate between rationalists and empiricists is about the scope and significance of a priori knowledge. Rationalists argue it is the source of our most certain and fundamental truths about reality.

The Core Theses of Rationalism

Rationalism isn't just one single idea; it's a family of views built around a few core theses. Understanding these will give you a clear framework for the arguments of Descartes and Leibniz.

These three theses form the rationalist toolkit:

1. The Intuition/Deduction Thesis: We can gain a priori knowledge by first grasping certain propositions as self-evidently true (intuition) and then using logical steps to arrive at further truths (deduction). Your work in mathematics, which starts from axioms to prove theorems, is a perfect example of this process.
2. The Innate Knowledge Thesis: We are born with certain knowledge. It is part of our rational nature. Experience might be needed to trigger our awareness of this knowledge, but it doesn't provide or justify it.
3. The Innate Concept Thesis: We are born with certain concepts (not whole propositions). Experience cannot provide these concepts, as their content "outstrips" what we can derive from our senses.

Now let's see how Descartes and Leibniz put these tools to work.

Descartes and Innate Concepts

We've already seen Descartes use intuition to establish the 'cogito' as his first piece of a priori knowledge. He knows "I exist" not by looking in a mirror, but by reflecting on the act of thought itself.

To rebuild his knowledge, Descartes argues that his mind contains certain innate concepts placed there by God. His most famous example is the concept of God itself.

Descartes' argument is a classic rationalist move:

1. I have an idea of God as an infinitely perfect being.
2. My experiences are all of finite and imperfect things.
3. I cannot create the idea of infinite perfection by simply combining or extrapolating from my ideas of finite imperfection. The effect (the idea) cannot be greater than its cause.
4. Therefore, the idea of God cannot have come from my experience of the world or from my own invention.
5. Conclusion: The idea of God must be innate—part of the original furniture of my mind.

For Descartes, concepts like God, infinity, substance, and even the "true" nature of a perfect triangle are known a priori because they are innate. Experience can give us images of crooked, imperfect triangles, but the concept of a perfect triangle, with its properties knowable through geometry, comes from reason alone.

Leibniz and Necessary Truths

Gottfried Wilhelm Leibniz, a fellow mathematician and rationalist, offers a different but equally powerful argument for a priori knowledge. His argument centers on the distinction between necessary truths and contingent truths.

To see how Leibniz builds his case, let's watch a video that lays out his argument clearly.

Leibniz's argument can be reconstructed as follows:

1. We have knowledge of necessary truths. These are truths that could not possibly be false (e.g., mathematical axioms, logical principles like the law of non-contradiction). They are true in all possible worlds.
2. Sense experience only ever shows us contingent truths—facts about this particular world that could have been otherwise. Experience shows me that when I drop this specific pen, it falls. It might show me that every pen I have ever dropped has fallen. But it can never show me that all pens must fall, necessarily.
3. Therefore, our knowledge of necessary truths cannot be derived from experience.
4. Conclusion: Knowledge of necessary truths must be a priori.

Leibniz called necessary truths "Truths of Reason" and contingent truths "Truths of Fact." For a more formal understanding of this distinction, let's turn to a dedicated text.

This argument is incredibly powerful. Since you have a strong background in pure mathematics, you are intimately familiar with a vast body of knowledge—theorems, proofs, axioms—that seems to be necessary. You know that the Pythagorean theorem isn't just true on Earth in 2024; it's necessarily true. Leibniz's point is that no amount of measuring triangles in the physical world could ever give you that kind of certainty or prove that necessity. That knowledge must come from another source: reason.

Conclusion

In this lesson, we have explored the core rationalist claim that reason is a source of substantial, a priori knowledge about the world. We moved from the general distinction between a priori and a posteriori knowledge to specific arguments from two of the most important rationalist philosophers.

Key Takeaways:

• A Priori vs. A Posteriori: Knowledge is a priori if its justification is independent of experience; it is a posteriori if its justification depends on experience.
• Rationalist Claim: Rationalists believe that we can and do have significant a priori knowledge, often through intuition, deduction, and innate ideas/knowledge.
• Descartes' Argument: Used the Innate Concept thesis to argue that concepts whose content outstrips experience (like God, perfection, infinity) must be part of the mind's native constitution and are thus known a priori.
• Leibniz's Argument: Argued that our knowledge of necessary truths (Truths of Reason, e.g., mathematics and logic) cannot come from experience, which only reveals contingent truths (Truths of Fact). Therefore, knowledge of necessity must be a priori.

Preview of the next lesson:
We have seen how Leibniz divides truths into two kinds. Truths of Reason are governed by the Principle of Contradiction. But what governs the Truths of Fact? Why is this contingent world the way it is, and not some other way? In the next lesson, we will delve into Leibniz's answer: the famous and far-reaching Principle of Sufficient Reason.