Gettier Problems and the JTB Theory

Hello! Welcome back to our module on Contemporary Analytic Metaphysics and Epistemology.

In our last lesson, we saw how a single, powerful argument—the Third Man Argument—could expose a deep logical inconsistency in a major philosophical theory. By analyzing its premises, we saw how Platonic Realism, in its simple form, generates a vicious infinite regress. This method of using precise analysis and counterexamples to test a theory is a cornerstone of analytic philosophy.

Today, we shift from metaphysics to epistemology to examine one of the most famous and disruptive papers in 20th-century philosophy. For over two millennia, the definition of knowledge as "Justified True Belief" was a widely accepted starting point. In 1963, a three-page paper by Edmund Gettier showed that this definition was fundamentally flawed.

Your learning outcome for this lesson is to: Explain Gettier's counterexamples to the 'justified true belief' analysis of knowledge.

We will first unpack the traditional "Justified True Belief" account of knowledge. Then, we will dive into Gettier's ingenious counterexamples to see exactly how they demonstrate that these three conditions, while perhaps necessary, are not sufficient for knowledge.

1. The Traditional Analysis: Knowledge as Justified True Belief (JTB)

Before we can see what Gettier dismantled, we need to understand what he was attacking. The philosophical analysis of knowledge typically focuses on what is called propositional knowledge, or "knowledge-that" (e.g., knowing that Paris is the capital of France), as distinct from "knowledge-how" (e.g., knowing how to ride a bike).

For centuries, dating back to Plato, the standard analysis of propositional knowledge held that it has three essential components. This is often called the tripartite or JTB analysis.

The JTB Analysis of Knowledge:
A subject, S, knows a proposition, P, if and only if:

1. P is true. (The Truth Condition)
2. S believes that P. (The Belief Condition)
3. S is justified in believing that P. (The Justification Condition)

Each condition seems intuitively necessary. You can't know something that's false. You can't know something you don't even believe. And you can't know something just by a lucky guess; your belief needs to be properly supported or justified. The crucial claim of the JTB analysis was that these three conditions are not only individually necessary but also jointly sufficient. In other words, if you have a justified, true belief, you have knowledge.

To get a clear overview of this traditional definition and the role of necessary and sufficient conditions in philosophical analysis, please watch the beginning of the following video.

2. The Gettier Problem: When JTB Isn't Enough

In 1963, Edmund Gettier published "Is Justified True Belief Knowledge?", a paper that showed the JTB analysis was insufficient. He constructed scenarios where a person has a belief that is simultaneously justified and true, but which we would intuitively say is not knowledge.

These "Gettier cases" all share a common structure: the justification for the belief is not properly connected to the factor that makes the belief true. The belief turns out to be true purely by luck or coincidence.

The relationship between these concepts can be visualized as follows:

Gettier's argument rests on two key logical points about the nature of justification:

1. Fallibility of Justification: It is possible for a person to be justified in believing a proposition that is, in fact, false.
2. Closure of Justification under Deduction: If S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.

Your background in mathematics should make you particularly attuned to the power of these formal principles. Gettier uses them to build his counterexamples with logical precision.

3. Gettier's Original Counterexamples

The best way to understand Gettier's argument is to see it in action. His paper is remarkably short and clear. I would like you to read it yourself, and then we will break it down.

Now that you've read the cases, let's analyze their structure. The following video walks through both of Gettier's examples, which will help solidify your understanding.

Let's formalize the analysis of these two cases.

Case I: Smith, Jones, and the Coins

• The Belief (P): "The man who will get the job has ten coins in his pocket."
• Justification: Smith has strong evidence for the conjunctive proposition (d) "Jones will get the job, and Jones has ten coins in his pocket." His belief in P is based on a valid deduction from (d).
• Truth: The belief P is true, but not because of Jones. It is true because, unknown to Smith, Smith gets the job and Smith happens to have ten coins in his pocket.
• Not Knowledge: Smith does not know P. His justification is entirely about Jones, while the truth of P is entirely about himself. The connection between justification and truth is severed by luck.

Case II: Jones's Ford and Brown in Barcelona

This case makes explicit use of the closure principle.

• The Initial Justified (but False) Belief: (f) "Jones owns a Ford."
• The Derived Belief (P): (h) "Either Jones owns a Ford, or Brown is in Barcelona."
• Justification: Smith is justified in believing (h) because he has correctly deduced it from (f) using the logical rule of disjunction introduction (if P is true, then P or Q must be true). Since he is justified in believing (f), and (h) is entailed by (f), he is justified in believing (h).
• Truth: The belief (h) is true, but not because Jones owns a Ford (he doesn't). It is true because, by sheer coincidence, the second disjunct is true: Brown really is in Barcelona.
• Not Knowledge: Smith has no idea where Brown is. His belief is true due to a fact for which he has zero evidence. The justification for his disjunctive belief rested entirely on the false part of the disjunction.

Conclusion

Today we've seen how a few carefully constructed thought experiments can overturn centuries of philosophical consensus. Gettier's counterexamples revealed a deep problem in the traditional understanding of knowledge.

Key Takeaways:

• The traditional Justified True Belief (JTB) analysis of knowledge claims that justification, truth, and belief are individually necessary and jointly sufficient for knowledge.
• Edmund Gettier showed that the JTB analysis is not sufficient.
• Gettier cases are scenarios where a person holds a justified, true belief that is not knowledge because the truth of the belief is due to epistemic luck. The justification is not connected to what makes the belief true.
• These cases work by exploiting the fact that one can be justified in believing something that is false.

The "Gettier problem" launched a massive wave of research in epistemology as philosophers scrambled to figure out what was missing. What is the fourth condition—the "X" in a "JTB+X" formula—that can successfully rule out Gettier cases and finally give us a correct analysis of knowledge?

Preview of the Next Lesson:
The search for a solution to the Gettier problem led philosophers to re-examine the nature of justification itself. In our next lesson, we will explore one of the most significant debates that grew out of this: the distinction between internalist and externalist theories of epistemic justification. We will see how these different approaches to justification try, in very different ways, to solve the problem of epistemic luck.