Analytic-Synthetic: Grounding A Priori Knowledge

1. Two Fundamental Distinctions

To understand the analytic-synthetic distinction, we must first place it alongside another key epistemological distinction: the difference between a priori and a posteriori knowledge. It is crucial to see that these are two separate distinctions that classify judgments along different axes.

• The a priori / a posteriori distinction concerns the justification of our knowledge: how we come to know something.
• The analytic / synthetic distinction concerns the content of a proposition: what makes it true.

To get a clear grasp of these two distinctions and how they differ, please read the following short explanations from a few philosophers.

As the readings suggest, we can define the terms as follows:

• A Priori Knowledge: Knowledge that can be justified independently of any particular sensory experience. For example, knowing that $2+2=4$ or that "no object can be both entirely red and entirely green at the same time."
• A Posteriori Knowledge: Knowledge that can only be justified by appeal to sensory experience. For example, knowing that "it is raining outside" or that "the speed of light is approximately 299,792 km/s."
• Analytic Judgment: A judgment whose truth is determined solely by the meanings of the terms involved. The classic example is "All bachelors are unmarried," where the predicate concept (unmarried) is already part of the subject concept (bachelor). These are often called "true by definition."
• Synthetic Judgment: A judgment where the predicate concept adds new information that is not contained in the subject concept. "All bachelors are happy" is synthetic because being happy is not part of the definition of a bachelor. These judgments are ampliative—they amplify our knowledge.

2. Kant's Framework: The Birth of the Problem

The philosopher Immanuel Kant was the first to systematically deploy these distinctions to tackle a profound philosophical problem: how is metaphysical and mathematical knowledge possible?

This short video explains Kant's original formulation and the motivation behind it. It will also introduce his most controversial and influential idea: the existence of synthetic a priori knowledge.

Kant's analysis gives us a two-by-two matrix of possible types of judgments.

Let's review the categories:

1. Analytic a priori: Uncontroversial. Truths of definition are known independently of experience. "All triangles have three sides."
2. Synthetic a posteriori: Also uncontroversial. These are the standard empirical truths we learn through our senses. "The triangle on the board is blue."
3. Analytic a posteriori: Generally considered to be an empty category.
4. Synthetic a priori: This is Kant's bombshell. He argued that fundamental principles of mathematics and metaphysics fall into this category. They are truths that add genuinely new information to our concepts (they are synthetic), yet they can be known with the necessity and universality that comes from being independent of experience (they are a priori). For Kant, mathematical proof was a process of construction that yielded new knowledge, not merely a process of analyzing definitions.

3. The Traditional Role: Analyticity as the Ground of A Priori Knowledge

Kant's idea of the synthetic a priori was deeply puzzling to many later philosophers. How could mere thinking produce substantive knowledge about the world? For a major philosophical movement of the early 20th century, Logical Positivism, the solution was to reject Kant's fourth category. They argued that Kant was wrong about mathematics. All a priori knowledge, they claimed, is analytic.

This move was intended to demystify a priori knowledge. If mathematical truths are analytic, they are not profound insights into a Platonic realm of numbers. Instead, they are complex tautologies, ultimately true by virtue of definitions and the rules of language.

This "analytic explanation" of a priori knowledge became a cornerstone of analytic philosophy for decades. It promised to explain how we could have certain knowledge in logic and mathematics without appealing to mysterious faculties of intuition. The knowledge isn't about a transcendent reality; it's about our own conceptual scheme.

To make this view plausible, however, a more rigorous account of analyticity than Kant's "containment" metaphor was needed. This is where the logician Gottlob Frege, whose work we will study in depth soon, made a critical contribution. Frege proposed that a statement is analytic if it can be turned into a logical truth simply by substituting synonyms for synonyms.

For example, the statement:

All pediatricians are doctors.

...is not a formal logical truth. But if we substitute the definition "doctors that specialize on children" for "pediatricians," we get:

All doctors that specialize on children are doctors.

This is a logical truth, of the form "All Fs that are G are Fs". Frege's great project, known as logicism, was to show that all of arithmetic could be reduced to logic in this way, thereby demonstrating that mathematical truths are analytic and knowable a priori.

Conclusion

In this lesson, we have untangled one of philosophy's most important conceptual pairings. Understanding this terrain is essential, as the status of the analytic-synthetic distinction has been a major point of contention and has profound implications for how we view the nature of logic itself.

Key Takeaways:

• The analytic/synthetic distinction concerns the source of a statement's truth (meaning vs. facts), while the a priori/a posteriori distinction concerns the justification for our knowledge of it (independent of vs. dependent on experience).
• Kant introduced these distinctions to argue for the existence of synthetic a priori knowledge, which he believed was the basis for mathematics and metaphysics.
• The traditional role of analyticity, especially for the Logical Positivists, was to provide a naturalistic explanation for a priori knowledge. On this view, all a priori knowledge (including mathematics) is analytic. It is true by virtue of language and definitions, not because of insight into a mysterious abstract realm.
• Frege's re-definition of analyticity—as reducibility to a logical truth via substitution of synonyms—was a crucial step in making this logicist project seem viable.

Preview of the Next Lesson:

We have now examined the structure of truth (realism vs. anti-realism), the nature of truth (correspondence, coherence, etc.), and the grounds of truth (analytic vs. synthetic). To complete our toolkit, we need to consider how individual beliefs, once we have them, fit together to form a justified system of knowledge. In the next lesson, we will examine two competing theories of epistemic justification: foundationalism and coherentism. This will conclude our first module and prepare us to begin our historical journey with Kant and Frege.