Hard to Vary vs Induction: A Response to Kieren

On Twitter “Kieren” has written a short paper where he argues that David Deutsch’s “Hard to Vary” (HTV) criteria for good explanations are really sneaking Induction in via the back door. This article is my attempt to give a short response to Kieren’s argument:

Being unable to vary something implies a constraint. So what is it that constrains a scientific theory? I will demonstrate that the constraint is empirical evidence, or past observations. We can only vary a theory so much before it becomes inconsistent with the evidence at hand (past observations). For example, we cannot easily change any aspect of Newton’s laws whilst still remaining consistent with past observation of the motion of objects, so Newton’s laws are HTV.

This is the very first part of Kieren’s argument and he appears to get the first step of his ‘proof’ incorrect. Everything he writes after this is thus a misunderstanding. So I will address his arguments by only addressing this one paragraph and where he has misunderstood Critical Rationalism and Deutsch’s HTV criteria.

Kieren’s Misunderstanding

Kieren’s mistake is that he incorrectly equates Deutsch’s HTV criteria with constraints only against past observations. In fact, Deutsch’s HTV criteria is a much broader concept. To illustrate this, let me use a very simple intuitively obvious example.

The Milk and the Milkman

Suppose you ordered milk from a milk man and then soon thereafter milk arrives on your doorstep. What is the best explanation for why milk has appeared at your door?

Now there are an infinite number of possible explanations for the sudden appearance of milk, but for the sake of tractability, let’s consider only three possible explanations:

• Theory 1: The milk man you paid for the milk brought it to you
• Theory 2: The milk man you paid pocketed the money, but your nice neighbor is now leaving milk for you because they can see you need it
• Theory 3: Angels saw the milk man pocket the money and started bringing you milk

Now this example seems ridiculous, doesn’t it? Obviously Theory 1 is the best theory. But why is that? Can you explain why our minds naturally recognize Theory 1 as the best explanation? What is going on in our minds that we can so quickly resolve — out of an infinite number of possible theories — that Theory 1 is the only one worth considering? That is the question that Deutsch is trying to answer and that Kieren’s false view of Deutsch fails to answer.

Why Inductivism Can’t Help You

Now Inductivism can not help you understand why Theory 1 is the best explanation. We have only one observation so far — that the milk arrived this morning — and all three theories make the same prediction that the milk should have arrived this morning! Therefore, we can dispense with Inductivism right off the bat as the way we determine if an explanation is good or not.

Now Kieren’s choice to see Deutsch’s HTV criteria as equivalent to only constraint against past observations does no better. After all, Kieren is correct that if Deutsch’s HTV criteria had in fact been only constraint against past observations that “HTV” would be equivalent to Inductivism.

Can you see why? It’s for the same reason as above — all three theories make the same prediction about the one and only observation — that milk arrived today. Therefore Kieren’s (false) view of HTV can’t help us determine why we intuitively know that Theory 1 is the best explanation because it is in fact Inductivism.

It gets even worse when you realize that no matter how many observations you add, the situation doesn’t change for any of these theories. Let’s say that 100 days in a row milk arrives at the door. All three theories predict this will happen. So past observations can not be the basis for HTV criteria in this simple example. Kieren is simply misunderstanding the HTV criteria.

Why HTV Really Means (In This Example)

So how does Deutsch’s HTV criteria help us resolve that the first theory is the good explanation and the rest are bad?

Note that Theory 1 is deeply constrained, not by observations, but by hundreds or maybe even thousands of explicit and implicit theories your mind already has about how the world works.

For example, Theory 1 fits well with your understanding of how human’s behave when they have jobs that earn them income — an economic theory. It fits well with your understanding of human self interest, i.e. a milkman that pockets money and never delivers won’t be in business long and thus this is actually against his own self interest long term — a psychological theory. It fits well with your understanding of just how your neighbors might behave. Sure, maybe they really like you. But why would they bother to give you free milk rather than, say, turn in the bad milkman and get him arrested and get your money back? (A legal theory?) For that matter, where is the neighbor’s milk coming from? Is the bad milkman selectively delivering? Why would he being doing that? Theory 2 doesn’t address these problems in it’s current form.

Note how the various other theories (implicit and explicit) related to Theory 1 are also definitive problems for Theory 2. Theory 2 has a lot to explain that it currently doesn’t even try to do. Theory 2 is a hugely problematic theory that explains very little compared to Theory 1 precisely because it doesn’t interact with all your other implicit and explicit theories about the world you live in that constrain Theory 1.

Note that this tacitly means you can vary Theory 2 any way you want and get an equivalent number of problems — so in that sense, it is an easy to vary theory. But the real problem with Theory 2 isn’t that it fails the HTV criteria, but rather it just has a lot of problems it has to explain and currently can’t. Not to mention the fact that Theory 2 is imminently testable — just go ask your neighbor and he’s going to shortly falsify Theory 2 for you.

But what about Theory 3? Well, this is obviously a supernatural theory. It really is an easy to vary explanation. Why angels? Why not Hindu gods? Why not Elves? Why not friendly aliens?

How to Make Theory 2 Better Than Theory 1

Now consider, for a moment, that we later find out that this Milkman was on his first day and was arrested for cheating everyone. And we found out that our neighbor has a ton of old milk bottles and 100 cows.

Now we have a problem for Theory 1 that can only be solved via a modified Theory 2. It’s only the existence of a problem to solve (why did you receive milk when you now know the milkman you paid skipped town that day and got arrested?) that can make Theory 2 a better explanation than Theory 1. Absent such a problem, Theory 2 is just a bad explanation compared to Theory 1. But with the right problem to solve, Theory 2 might turn into a better theory than Theory 1. But also note that Theory 2 is now constrained by the new observations I just made up that create problems for Theory 1.

Note how we’re dealing constantly with the HTV criteria here, but never with past observations. This proves that Kieren’s understanding of Deutsch’s HTV criteria is incorrect and also that a correct understanding of it is not equivalent to Inductivism.