Incommensurability vs. Incomparability vs. Difficulty of Comparison

Introduction

In our last lesson, we explored Isaiah Berlin's theory of value pluralism, which posits that fundamental human goods are multiple, often conflicting, and cannot be neatly harmonized into a single perfect system. A key, and perhaps the most challenging, component of his thesis is that ultimate values can be "incompatible and incomparable." While Berlin often used these terms together, subsequent philosophers have sought to add more precision to this crucial idea.

Today, we will dissect that concept. Our learning outcome is to distinguish incommensurability from incomparability and from the mere difficulty of comparison. This is not just a matter of semantics; the distinction has profound implications for the nature of rational choice. If values are merely difficult to compare, a rational solution is, in principle, findable. But if they are truly incomparable, we face a much deeper challenge to the idea that reason can always guide us to the 'best' choice. This is central to your interest in the "least bad points" of societal design, as it frames the very nature of the trade-offs involved.

1. Incommensurability: The Lack of a Common Measure

The word "incommensurable" has its roots in ancient Greek mathematics. The Pythagoreans discovered that the length of a square's diagonal and the length of its side are incommensurable. They could be ordinally ranked—the diagonal is clearly longer than the side—but their ratio could not be expressed as a fraction of whole numbers. They lack a common unit of measurement.

In value theory, the term has a parallel meaning.

As the reading explains, incommensurability is the lack of a common cardinal scale to measure the value of different goods. You cannot say, for instance, that a certain gain in social justice is worth "5 units of value" while a corresponding loss of economic efficiency is "-3 units of value."

Key points to take away:

• No Cardinal Scale: Incommensurability means there are no interval or ratio differences between values. We can't say a policy is "twice as just" or "20 units more fair" than another. This directly challenges any simple form of cost-benefit analysis or utilitarianism that assumes all values can be converted into a single currency (like "utility").
• Weak vs. Strong Incommensurability:
  • Weak: There is no single unit for measuring all values. This is a claim against monistic theories like classical utilitarianism.
  • Strong: Between any two different values, there is no common unit of measure.
• Incommensurability ≠ Ordinal incomparability: Crucially, two things can be incommensurable yet still comparable. We can often make an ordinal judgment—that this specific gain in liberty is better than that specific loss in security—even if we can't say how much better it is.

2. An Analogy from the Philosophy of Science

Your interest in epistemology makes an analogy to the philosophy of science particularly useful here. The concept of incommensurability was famously used by Thomas Kuhn to describe the relationship between competing scientific paradigms, like Newtonian and Einsteinian physics.

This analogy is powerful. Just as 'mass' in Newton's physics is a fundamentally different concept from 'mass' in Einstein's, a value like 'honor' in a feudal society might be incommensurable with 'utility' in a modern liberal one. They belong to different "conceptual webs."

However, the video's critique provides the perfect pivot to our main topic. The fact that translation between scientific paradigms is difficult does not make it impossible, nor does it make the paradigms radically incomparable. It shows that incommensurability does not automatically imply incomparability. We can still assess whether Einstein's theory is better than Newton's, even if their core concepts are incommensurable. The same applies to values.

3. Incomparability: The Failure to Rank

This brings us to the stronger and more controversial claim: incomparability.

If incommensurability is the lack of a common cardinal scale, incomparability is the failure of even ordinal ranking. Two options, A and B, are incomparable with respect to some value V if it is not the case that A is better than B, B is better than A, or they are equally good.

The Stanford Encyclopedia of Philosophy (SEP) entry on this topic gives a very clear explanation.

The Small Improvement Argument

How can we tell if we are facing true incomparability or just a very difficult choice? The "Small Improvement Argument" provides a test.

Let's use the classic example from Joseph Raz: a choice between a career as a lawyer and a career as a musician.

1. Assume, for the sake of argument, that you've weighed everything up (fulfillment, income, lifestyle, etc.) and you conclude that neither career is better than the other.
2. Now, let's create Lawyer+, a version of the lawyer career that is identical to the original but with a small, unambiguous improvement—say, an extra $100 per month. Lawyer+ is clearly better than Lawyer.
3. Now compare Lawyer+ to the musician career. If the original Lawyer and Musician careers were equally good, then Lawyer+ must be better than Musician.
4. However, for many people, the intuition is that this small improvement is not enough to break the deadlock. The Lawyer+ career is still not clearly better than the musician career.

If you share this intuition, it implies that the original two options were not "equally good" in the first place. This opens the door to the possibility that they are incomparable.

4. Is It Incomparability, or Something Else?

The Small Improvement Argument is suggestive, but not conclusive. Philosophers have proposed alternative explanations for what's happening in these hard cases.

• Mere Difficulty of Comparison: This is the simplest explanation. The choice is just incredibly complex, with many variables and uncertainties. The calculations are hard, but if we had perfect information and infinite cognitive capacity, we could determine which is better. In this view, there's no deep philosophical problem, just a practical one.
• Vagueness/Indeterminacy: Perhaps it is simply indeterminate or vague which relation holds. It's not that the options are incomparable, but that it is neither true nor false that one is better than the other. As the SEP article notes, this is John Broome's position. The boundaries of "better than" are fuzzy, just like the boundaries of "bald" or "tall."
• A Fourth Relation: "On a Par": Ruth Chang argues that the trichotomy of "better than," "worse than," and "equally good" is incomplete. She proposes a fourth relation: "on a par." Two items are on a par if they are comparable, but one is not better than the other, nor are they equally good. The lawyer and musician careers might be on a par. This acknowledges the failure of the Small Improvement Argument without resorting to the radical claim of full incomparability.

The distinctions are subtle but important. Let's summarize them in a table.

Conclusion

Today we have sharpened our understanding of a key claim within value pluralism. By moving beyond Berlin's general use of "incomparable," we can see the distinct philosophical positions at stake.

Key Takeaways:

• Incommensurability is the lack of a common cardinal scale for measuring different values. It challenges simple cost-benefit thinking but does not rule out rational, comparative judgments.
• Incomparability is the more radical claim that no ordinal ranking (better, worse, or equal) is possible between two options. It poses a fundamental challenge to the idea of rationally justified choice.
• The Small Improvement Argument is a key diagnostic tool used to argue for the existence of incomparability (or at least for a relation beyond the standard three).
• Apparent cases of incomparability might instead be explained by mere difficulty, vagueness, or the existence of other value relations like "on a par."

Understanding these distinctions is vital. If values are merely incommensurable, the pluralist project is about finding ways to make reasoned, qualitative judgments in the absence of a single metric. If they are sometimes truly incomparable, then politics must also involve finding legitimate ways to make decisions when reason runs out.

Preview of the Next Lesson:

Having established the possibility of deep conflict between incommensurable or incomparable values, we will now turn to the experiential and political consequences. The next lesson focuses on 'tragic choice' situations, where any course of action involves the sacrifice of a core value, leading to uncompensable loss and rational regret. We will examine what it means to choose when every option is, in some profound sense, a wrong one.