Rigid vs. Non-Rigid Designators: Kripke's Theory

Hello! Welcome to your next lesson in our module on "Reference, Meaning, and Modality."

In our last lesson, we developed the powerful framework of possible worlds semantics to make sense of modal claims about necessity and possibility. We saw how a statement like "Necessarily P" could be formally understood as "P is true in all accessible possible worlds." Today, we will apply this framework to a fundamental question in the philosophy of language: How do our words, specifically names, refer to things?

We'll be focusing on Saul Kripke's groundbreaking work from his 1970 lectures, published as Naming and Necessity. His ideas revolutionized how philosophers think about the relationship between language and reality. This lesson directly addresses the learning outcome: Define 'rigid designator' and distinguish it from 'non-rigid designator' using Kripke's examples.

This concept is a cornerstone of contemporary analytic philosophy and will be essential for understanding the subsequent debates about meaning, necessity, and the mind.

1. From Possible Worlds to Referring Across Worlds

Let's begin with a quick recap. We have the idea of possible worlds—complete ways things could have been. In our actual world, Aristotle was the teacher of Alexander the Great. In another possible world, Aristotle might have died young and never met Alexander. In yet another, Plato might have been Alexander's teacher instead.

This raises a crucial question: when we talk about "Aristotle" in these different scenarios, are we talking about the same individual? What anchors our words to objects across these counterfactual situations? Saul Kripke’s answer revolves around the distinction between two types of referring terms: rigid and non-rigid designators.

Let's get a quick and clear introduction to this key distinction.

As the video explains, the core idea is simple:

• A rigid designator is a term that refers to the same object in all possible worlds in which that object exists.
• A non-rigid designator is a term that can refer to different objects in different possible worlds.

2. Kripke's Definition and the Intuitive Test

Now that we have the basic idea, let's go to the source. Kripke himself introduced this terminology and provided a very intuitive way to test whether a term is rigid or not. Your background in mathematics will make you appreciate the precision he aims for in these definitions.

Let's break down what we've just read.

Kripke contrasts two kinds of terms:

1. Non-Rigid Designators (or "Flaccid" Designators): These are typically definite descriptions.

   • Example: "The inventor of bifocals."
   • Test: In the actual world, this description picks out Benjamin Franklin. But we can easily imagine a possible world where someone else, say, Thomas Jefferson, invented them first. In that world, the description "the inventor of bifocals" would pick out Jefferson, not Franklin. Since the term picks out different individuals in different worlds, it is non-rigid.

2. Rigid Designators: These are typically proper names.

   • Example: "Aristotle" or "Richard Nixon."
   • Test: When we consider a possible world where Richard Nixon lost the 1968 election, are we talking about someone else? No, we are talking about that very man, Richard Nixon, and describing a counterfactual situation he is in. We cannot say, "Nixon might have been a different person." We can only say he might have had different properties (like not being a president). The name "Nixon" seems to stick to the same individual across all these scenarios. Therefore, it is a rigid designator.

To see this contrast in action, let's watch one more short clip.

3. Nuances and Crucial Applications

The distinction between rigid and non-rigid designators has profound philosophical consequences. Let's explore two important cases that highlight its power.

Case 1: Necessary A Posteriori Truths

One of the most famous applications of rigidity concerns identity statements. Consider the statement:

"Hesperus is Phosphorus."

Ancient astronomers used "Hesperus" to name a celestial body seen in the evening and "Phosphorus" for one seen in the morning. It was an empirical, astronomical discovery that these are in fact the same object: the planet Venus. Because this fact was discovered through observation, it seems to be an a posteriori truth. And because it seems it could have turned out otherwise, it also seems to be a contingent truth.

Kripke argues this is a mistake. Let's see why by reading a short, classic explanation.

The argument is as follows:

1. Proper names like "Hesperus" and "Phosphorus" are rigid designators.
2. "Hesperus" refers to the planet Venus in all possible worlds.
3. "Phosphorus" refers to the planet Venus in all possible worlds.
4. Therefore, the statement "Hesperus is Phosphorus" says that Venus is identical to Venus.
5. An object is necessarily identical to itself. Venus is identical to Venus in all possible worlds.
6. Conclusion: The statement "Hesperus is Phosphorus" is necessarily true.

It is a truth that we discover empirically (a posteriori), but it is a truth that, once discovered, is seen to hold in all possible worlds (necessary). This broke the long-held philosophical assumption (popularized by Kant) that all necessary truths must be knowable a priori.

Case 2: Rigid Descriptions

It's tempting to create a simple rule: "Proper names are rigid; definite descriptions are non-rigid." However, this is an oversimplification. Some descriptions can be rigid.

You already encountered one such example in the Kripke excerpt: "the square root of 25."
Let's analyze it:

• In the actual world, "the square root of 25" picks out the number 5.
• Is there any possible world where the square root of 25 is a different number, say, 6? No. Mathematical truths are generally held to be necessary.
• Therefore, the description "the square root of 25" picks out the number 5 in every possible world. It is a rigid designator.

These are sometimes called de facto rigid designators. They are rigid not because of the linguistic form "the...", but because the property they describe is one the object has necessarily. This applies to many mathematical and logical descriptions, like "the successor of 2" or "the smallest prime number."

Conclusion

In this lesson, we have used the possible worlds framework to draw a pivotal distinction in the philosophy of language. By distinguishing how different terms behave across counterfactual situations, Kripke provided a new and powerful tool for analyzing reference.

Key Takeaways:

• A rigid designator (e.g., a proper name like "Saul Kripke") refers to the same object in every possible world where that object exists.
• A non-rigid designator (e.g., a definite description like "the most famous philosopher of the late 20th century") can refer to different objects in different possible worlds.
• The "intuitive test" for rigidity is to ask if the term could have referred to something else. For a name, the answer is no; for a description, it is often yes.
• This distinction allows for the existence of necessary a posteriori truths, like "Hesperus is Phosphorus," which are discovered empirically but are true in all possible worlds.
• While most descriptions are non-rigid, some, especially in mathematics (e.g., "the smallest prime number"), can be rigid because they describe a necessary property of an object.

Preview of the Next Lesson:

Kripke's theory of names as rigid designators was not developed in a vacuum. It was a direct attack on the prevailing theory of names at the time, known as descriptivism. In our next lesson, we will explore Kripke's ingenious modal and epistemic arguments against these descriptivist theories. You will see how he uses clever thought experiments (involving figures like Gödel and Feynman) to argue that the meaning of a name cannot be equivalent to a description or even a cluster of descriptions.