Deutsch's Criteria: Hard to Vary, Reach

Hello! Welcome to your next lesson in our course on Popperian realism, tradition, and rationalism.

In our last session, we began our "Deutschian Turn" by exploring David Deutsch's profound shift in focus from Popper's falsifiability to the search for good explanations. We saw that merely being testable isn't enough; bad, easily-varied theories like the Persephone myth can be tested and patched up without getting us any closer to the truth. In contrast, good explanations, like the axial-tilt theory for the seasons, are powerful because they are constrained and difficult to change arbitrarily.

Today, we will formalize and deepen this understanding. The goal of this lesson is to precisely define the two key criteria that make an explanation "good" in the Deutschian sense. This will equip you with a robust framework for evaluating the quality of any conjecture, from a scientific theory to a political philosophy.

Time to complete: Approximately 45 minutes.

A Quick Recap

In the previous lesson, we established that the engine of progress is the search for hard-to-vary explanations. We used the contrast between the Persephone myth and the axial-tilt theory to build an intuition for this idea. The myth was "easy to vary"—its details were arbitrary. The scientific theory was "hard to vary"—its details were tightly constrained and played a functional role. Today, we build directly on that foundation.

1. Criterion 1: Hard to Vary

While we have an intuitive grasp of this concept, let's look at Deutsch's more formal definition. It's not just about simplicity or having fewer assumptions; it's about the internal logic and structure of the explanation itself.

Please watch the following segment from Brett Hall's reading of Deutsch's The Beginning of Infinity. It succinctly defines what makes a good explanation hard to vary and offers a brilliant critique of the common misconception known as Occam's Razor.

Watch from 00:40:00 to 00:42:04. Pay close attention to the phrase "functional role."

The key takeaway is this:

A good explanation is hard to vary because all of its details play a functional role.

Let's break this down using the axial-tilt theory:

• The assertion of a tilt is not arbitrary; it's the core mechanism.
• The specific angle of the tilt (approx. 23.5°) is not arbitrary; it functions to determine the precise intensity of the seasons we experience. Changing the angle would lead to a falsified prediction.
• The fact that the axis remains pointed in a constant direction isn't an arbitrary add-on; it's a consequence of the physics of spinning bodies, a crucial functional part of the explanation.

There are no superfluous parts. Every detail is doing work to explain the phenomenon. Contrast this with your background in econometrics. A good structural model attempts this: each variable and its coefficient represent a specific, theoretically-justified causal pathway. A "kitchen-sink" regression, where variables are included simply because they show correlation, is the opposite. Its details are not playing a clear functional role; they are just there to improve the fit, making it an "easy-to-vary" and thus poor explanation.

A Note on Occam's Razor

As the video points out, this refines the popular notion of Occam's Razor ("seek the simplest explanation"). Deutsch's criterion is more precise. A very simple explanation like "a wizard did it" or the Greek myth of Demeter is bad, not because it's complex, but because it's too simple to be constrained. Its details are arbitrary and have no functional role. The real principle is to discard superfluous or arbitrary elements. A good explanation might be quite complex, but if every component is necessary and functional, it is not violating this principle.

2. Criterion 2: Reach

Being hard to vary is the first pillar. The second, which is a consequence of the first, is what gives good explanations their world-changing power. Deutsch calls this property reach.

An explanation with reach solves problems beyond the one it was initially created to address. It has an "autonomous domain of applicability" that its creators might not have even anticipated.

To explore this, please watch this next, longer segment from the same video. This is the core of today's new material.

Watch from 00:44:28 to 00:51:35. Focus on how the axial-tilt theory explains phenomena its creators may not have even been thinking about.

Let's unpack this powerful idea.

Definition: The reach of an explanation is its ability to solve problems beyond those that it was created to solve.

The axial-tilt theory is the perfect example:

• Original Problem: To explain the annual cycle of temperature changes and the varying height of the sun in the sky in, say, Greece.
• Its Reach (Unexpected Solutions):
  1. It automatically explains why the seasons are out of phase between the Northern and Southern Hemispheres.
  2. It automatically explains why regions near the equator (the tropics) do not have significant seasons.
  3. It automatically explains extreme phenomena like the midnight sun in polar regions.

The creators of the theory might not have known about seasons in Australia or the 24-hour daylight at the poles. Yet, because their explanation was so good (so hard to vary), it was already a correct explanation of those phenomena. It reached out from the specific problem in one hemisphere to describe the entire planet and, indeed, any tilted, orbiting planet in the universe.

This is a profound point. Reach is not an extra assumption we add to a theory. It is an emergent property of a hard-to-vary explanation. Because the explanation is so tightly constrained by the way reality actually is, it can't help but correctly describe other facets of that reality.

Think of another great example from physics: Newton's law of universal gravitation.

• Original Problems: Explain why apples fall to the Earth and how planets stay in their orbits.
• Its Reach: The same, single law also explained the ocean tides (the Moon's influence), the existence and timing of comets, and the subtle wobble in Earth's axis (precession of the equinoxes).

The theory's magnificent reach was a signal of its quality as a deep explanation of reality.

Conclusion

In this lesson, we have moved from an intuition to a formal definition of David Deutsch's criteria for a good explanation. These criteria provide a powerful, non-justificationist toolkit for evaluating ideas.

Key Takeaways:

• A good explanation has two key properties: it is hard to vary and it possesses reach.
• Hard to Vary: An explanation where every detail is constrained and plays a necessary functional role. This is a more precise concept than simply "simplicity" or Occam's Razor.
• Reach: An explanation that solves problems beyond those it was designed to solve. Reach is not an added assumption but an emergent property of a good, hard-to-vary explanation.
• Together, these criteria allow us to identify conjectures that represent deep insights into the structure of reality, distinguishing them from shallow, ad-hoc stories.

Next Steps

Now that we have this two-part framework for identifying good and bad explanations, we are ready to apply it. In our next lesson, we will turn this critical lens back onto a philosophy of science itself. We will use the "easy to vary" criterion to diagnose Logical Positivism as a 'bad explanation' for how science actually works, tracing the philosophical consequences of that failure.