Kripke and the Necessary A Posteriori

Introduction

Welcome to our next lesson. In the previous session, we explored the deep metaphysical debate about the nature of possible worlds, contrasting David Lewis's concrete modal realism with the abstract representationalism of ersatzist theories. We saw that possible worlds, however one conceives of them, provide a powerful formal tool for analysing modal claims—statements about what is possible and what is necessary.

Today, we will see this tool put to revolutionary use. We will focus on the work of Saul Kripke, who used the possible worlds framework not just to clarify modality, but to dismantle a long-standing pillar of philosophy. For much of the 20th century, it was widely assumed that three fundamental distinctions were essentially different ways of carving up the same territory:

Metaphysical: The distinction between necessary and contingent truths.
Epistemological: The distinction between a priori and a posteriori knowledge.
Semantic: The distinction between analytic and synthetic statements.

The common view was that these aligned perfectly: necessary truths were the same as a priori truths, which were the same as analytic truths. Kripke's work shattered this neat picture. Your learning outcome for this lesson is to evaluate Kripke's argument for the existence of necessary a posteriori truths and its impact on the analytic-synthetic distinction. We will see how a seemingly abstract point about how names refer can have profound consequences for our understanding of truth, knowledge, and reality itself.

1. Unpacking the Traditional Framework

Before we can appreciate the force of Kripke's challenge, we must be clear on the three distinctions that were traditionally seen as coextensive. These concepts are foundational to analytic philosophy.

Necessary vs. Contingent: This is a metaphysical distinction concerning how things could be. A truth is necessary if it is true in all possible worlds; it could not have been false. A truth is contingent if it is true in our world (the actual world) but false in at least one other possible world; it could have been otherwise.
A Priori vs. A Posteriori: This is an epistemological distinction concerning how we come to know things. A proposition is knowable a priori if it can be known independently of experience (e.g., through reason or conceptual analysis alone). A proposition is knowable a posteriori if it can only be known through experience (e.g., through observation or scientific investigation).
Analytic vs. Synthetic: This is a semantic distinction concerning the source of a statement's truth. A statement is analytic if it is true solely by virtue of the meanings of its terms (e.g., "All bachelors are unmarried"). A statement is synthetic if its truth depends not just on its meaning, but also on the way the world is (e.g., "All bachelors are unhappy").

Necessary; analytic; a priori

To solidify your understanding of these three crucial distinctions and how they were traditionally thought to overlap, please watch the following introductory video.

Watch the first 11 minutes and 51 seconds of this video. The speaker, Kane B, clearly defines each of the three pairs—necessary/contingent, analytic/synthetic, and a priori/a posteriori—and explains why philosophers historically tended to bundle them together.

As the video explains, the pre-Kripkean orthodoxy largely held that if a statement was necessary, it must be analytic and knowable a priori. It is this tidy package that Kripke set out to unravel.

2. The Key to the Puzzle: Rigid Designation

Kripke's argument hinges on a crucial insight about how certain terms refer. He introduces the concept of a rigid designator.

A term is a rigid designator if it refers to the very same object in every possible world in which that object exists. If it refers to different objects in different possible worlds, it is a flaccid or non-rigid designator.

Kripke's central claim is that ordinary proper names (like 'Aristotle' or 'Venus') and many natural kind terms (like 'water' or 'gold') are rigid designators. They act like tags that stick to their referents across all counterfactual scenarios.

In contrast, most definite descriptions are flaccid. For example, the description "the Prime Minister of the UK in 2024" refers to Keir Starmer in the actual world. But in another possible world—say, one where the Conservatives won the election—it would refer to Rishi Sunak. The description picks out whoever happens to satisfy it in a given world.

Kripke on Proper Names

The concept of rigid designation is the engine of Kripke's argument. This next video provides a clear explanation of the idea and contrasts it with the older 'descriptivist' view of names.

Watch the segment from 17:33 to 22:31. Focus on the definition of a rigid designator and the distinction between a proper name like 'Aristotle' and a definite description like 'Plato's best student'.

Once you grasp that names rigidly 'stick' to their objects across possible worlds, while descriptions can 'float' to whatever fits them, you have the key to unlocking Kripke's most famous discovery.

3. The Bombshell: The Necessary A Posteriori

With the concept of rigid designation in hand, Kripke constructs his argument. He does this by producing examples of statements that are both necessary and knowable only a posteriori. Let's examine the two most famous types.

Type 1: True Identity Statements

Consider the statement:

Hesperus is Phosphorus.

The ancient Babylonians used the name 'Hesperus' for the brightest celestial body visible in the evening and 'Phosphorus' for the brightest celestial body in the morning. For a long time, they did not know they were referring to the same object. Eventually, astronomical observation revealed that both names, in fact, refer to the planet Venus.

Let's analyse this statement using Kripke's framework:

Is it a posteriori? Yes. It took empirical, scientific discovery to learn that Hesperus and Phosphorus were the same thing. This truth could not be discovered from an armchair simply by analysing the meaning of the names.
Is it necessary? Yes. According to Kripke, 'Hesperus' and 'Phosphorus' are proper names. As such, they are rigid designators. In our world, they both pick out the planet Venus. Because they are rigid, they pick out Venus in every possible world. Therefore, the statement "Hesperus is Phosphorus" asserts that Venus is identical to Venus. A statement of self-identity, $a = a$ , is a necessary truth. There is no possible world where Venus is not Venus.

The conclusion is startling: "Hesperus is Phosphorus" is a necessary a posteriori truth.

Type 2: Scientific Identities and Composition

A similar logic applies to scientific discoveries about the fundamental nature of things. Consider:

Water is H₂O.

Let's apply the same analysis:

Is it a posteriori? Yes. The chemical composition of water was a major scientific discovery in the 18th century. It is a fact learned through empirical investigation.
Is it necessary? Yes. Kripke argues that a natural kind term like 'water' is a rigid designator. It refers to the substance with a particular underlying microstructure, whatever that turns out to be. In our world, that structure is H₂O. Now, imagine a substance on another planet ('Twin Earth', in Hilary Putnam's famous thought experiment) that looks, tastes, and feels exactly like water but has a different chemical formula, say XYZ. According to Kripke and Putnam, that substance would not be water; it would be something else. To be water just is to be H₂O. Therefore, the statement "Water is H₂O" is true in all possible worlds.

Again, the conclusion is the same: "Water is H₂O" is a necessary a posteriori truth.

[PDF] The Philosophical Significance of The Kripkean Necessary Aposteriori

These examples are the heart of Kripke's philosophical revolution. The following text from a paper by the distinguished philosopher Scott Soames lucidly explains this line of reasoning, which he calls Kripke's 'essentialist route' to the necessary a posteriori.

Please read the first two main sections of this paper (up to the heading 'Kripke’s Second (Attempted) Route...'). Pay close attention to how Soames lays out the pre-Kripkean 'conventional wisdom' and then explains how Kripke's argument, based on rigid designation and essential properties, overturns it with examples like those we've just discussed.

The Illusion of Contingency

A natural objection arises: If these statements are necessary, why do they feel contingent? It certainly seems like we can imagine a world where water isn't H₂O. Kripke provides an ingenious answer: we are confusing two different kinds of possibility.

What we are imagining is not a world where water has a different chemical structure. We are imagining a world that is, from an epistemic standpoint, just like ours, where people encounter a clear, drinkable liquid in their lakes and rivers and call it 'water', but where the underlying structure of that liquid is something else (like XYZ).

This is a world that we could have been in, epistemically speaking, before we did the chemistry. But it is not a world where water is XYZ. It is a world with a different substance altogether. Kripke argues that what we mistake for the contingency of the proposition is actually the contingency of our evidence for it.

Saul Kripke Quote on Necessary Truth — This quote captures the core of Kripke's view. Once we discover a necessary truth (like 'Water is H₂O'), we realize it could never have been otherwise, even if it took empirical work to make that discovery.

4. The Impact: Decoupling Necessity and Analyticity

The discovery of necessary a posteriori truths had a seismic impact on the philosophical landscape. It decisively broke the traditional link between necessity, apriority, and analyticity.

The most significant casualty was the doctrine, central to logical positivism, that all necessary truths are analytic. This view held that necessity arises purely from language—from definitions and linguistic conventions. A statement like "All bachelors are unmarried" is necessary because the definition of 'bachelor' includes 'unmarried'. The positivists wanted to say all necessity worked this way.

Kripke's examples prove this wrong.

"Water is H₂O" is necessary.
But it is not analytic. The definition of the word "water" is not "a compound of hydrogen and oxygen in a two-to-one ratio." People used the term to successfully refer to water for centuries before knowing its chemical formula. The statement's truth is not secured by linguistic convention alone; it required a discovery about the world's essential structure.

Such truths are therefore synthetic a posteriori necessities.

[PDF] kripke on modality - Princeton University

This brief reading from a guide on Kripke's work explains the epistemological fallout of his argument, particularly how it refutes reductionist theories of necessity like logical positivism.

Please read the section titled 'EPISTEMOLOGY OF MODALITY'. Focus on how Kripke's examples refute the idea that necessity is just a matter of 'semantic rules and linguistic conventions' and re-opens the question of how we have knowledge of modal truths.

By showing that necessity could be a feature of the world itself (a metaphysical matter) rather than just a feature of our language, Kripke's work had several profound consequences:

Revitalized Metaphysics: It made the study of essential properties of objects respectable again, pushing back against Quine's influential critique of essentialism.
Separated Domains: It forced philosophers to treat metaphysics (necessity/contingency), epistemology (a priori/a posteriori), and philosophy of language (analytic/synthetic) as distinct, albeit related, domains of inquiry.
Challenged Descriptivism: It provided a powerful argument against the theory that the meaning of a name is a definite description, a view that had been dominant since Frege and Russell.

Conclusion

In this lesson, we have traced one of the most significant arguments in late 20th-century philosophy. By focusing on the simple question of how a name refers to an object, Saul Kripke was able to generate profound and revolutionary conclusions.

Key Takeaways:

The Traditional View: Before Kripke, it was widely held that the distinctions necessary/contingent, a priori/a posteriori, and analytic/synthetic all aligned. Necessary truths were thought to be analytic and knowable a priori.
Rigid Designation: Kripke's key move was to identify proper names and natural kind terms as rigid designators—terms that refer to the same object or kind in every possible world.
The Necessary A Posteriori: Using rigid designation, Kripke showed that statements like "Hesperus is Phosphorus" and "Water is H₂O" are necessary truths (because they state identities involving rigid designators) but are knowable only a posteriori (because they required empirical discovery).
Impact on the Analytic-Synthetic Distinction: These discoveries proved that not all necessary truths are analytic. Statements like "Water is H₂O" are synthetic, as their truth depends on the essential nature of the world, not just the meanings of words. This severed the link between necessity and analyticity.
Philosophical Significance: Kripke's argument dealt a major blow to linguistic theories of necessity (like logical positivism) and rehabilitated metaphysics as a field concerned with the essential properties of things in the world.

Preview of the Next Lesson:
We have just seen a profound philosophical argument that works within the broad framework of classical logic to draw surprising metaphysical conclusions. In our next module, we will pivot to examine arguments that challenge the very rules of classical logic itself. We will begin by analysing the Liar paradox and the principle of explosion, exploring why these ancient and modern puzzles have led some philosophers to believe that classical logic must be revised or even abandoned.

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