Chapter Five – The Reality of Abstractions

In this chapter Deutsch makes me reconsider reductionism – sort of. He also makes me reconsider, and ultimately change my mind, on science and morality. Before I get to those, though, I want to discuss how Deutsch shakes me up about the nature of knowledge.

Consider Newton’s vision of gravity. Newton essentially explained Kepler’s Laws by providing a mechanism, the gravitational force operating by the inverse square law. It was a great advance in knowledge – we now had an explanation with enormous reach, an explanation that showed why Kepler’s Laws worked for the Solar System, for the Moon-Earth system, for the Galilean satellites, and in fact for the galaxy itself.

But then Einstein improved Newton’s explanation with his own explanation, General Relativity. In the new explanation, gravity was no longer a force. But wait, was it ever a force? If Newton was wrong after Einstein, surely he was wrong before Einstein, too. As Deutsch points out, this sort of evidence was used to argue that science never actually adds to our knowledge, because new theories wipe out the old ones. If Einstein’s curved spacetime does away with Newton’s gravity, then Newton’s gravity was never there in the first place.

But this is wrong, and here’s why: “it is true that something real (the curvature of spacetime), caused by the Sun, has a strength that varies approximately according to Newton’s inverse square law.” (p 108) Much else was also true in Newton’s theory – or at least approached the truth. Compared to what came before it, Newton’s theory was “more right.”

“Wherever (a theory) made true predictions this was because it had expressed some truth about reality.” (p 108)

Deutsch again states quite plainly why explanations are so crucial to science. “(I)n order to make progress in any field, it is the explanations in existing theories, not the predictions, that have to be creatively varied in order to conjecture the next theory.” (p 109).

So better explanations always approach the truth, but of course never get there. We’re always at the beginning of infinity. The next explanation will correct some of the errors of the previous theory, but it will also preserve the truth inherent in the previous theory. Remember, there are lots of ways to be wrong, but only one way to be right. Therefore, any explanation that correctly models some portion of the real world must have some element of truth to it. It is that element that will be preserved in the next, better, but still infinitely far from perfect, explanation.

Before this discussion, though, Deutsch goes after reductionism. As a committed reductionist, I of course at first reacted angrily. But a closer listening and reading of the section on reductionism convinced me of two things:

1) I’m not really a reductionist, not in Deutsch’s sense (and neither is anyone else who’s given it any thought).

2) He has a very good point.

First, Deutsch says this:

“The behavior of high-level physical quantities consists of nothing but the behavior of their low-level constituents with most of the details ignored.” (p 109)

This is all I’ve ever meant when I say I’m a reductionist. Stop there, and we already agree. But Deutsch’s real beef with reductionists is over the meaning and importance of explanation. As Deutsch points out, good explanations don’t have to be at a low level. His description of Douglass Hofstadter’s domino computer is an effective example. The explanation of the computer is meaningless on a physical level. It only takes on meaning when we understand the point of the program, which is to determine whether or not a number is prime. As Deutsch points out, there’s nothing in nature that insists on good explanations being reductive, and in fact he can show me many (like the domino example) that are not reductive and yet are still good explanations. I can’t argue with that. But, as I said, I’m happy to define my reductionism solely in terms of Deutsch’s first sentence. That’s all it really needs to mean, because this sentence, all by itself, does away with supernatural explanations. That’s all I really was after.

More shocking than the lesson on reductionism is Deutsch’s convincing argument that science is not mute on morality. Of course it isn’t, how could I have ever been so blind? I’ll use the question of race as an example. Before Deutsch, I was convinced that we couldn’t use scientific truth about race to inform our morality. The reason seemed straightforward. Scientific conclusions are always tentative. What if scientific truth changes? Does that mean our morality changes, too?

For instance, scientific consensus says that all humans derive from common ancestors who lived in Africa around 200,000 years ago. What if we discover that this is incorrect, that in fact human races really are genetically separate. Is racism then ok? Of course not!

Here’s where I was wrong. Humans are all people. We’re all universal explainers. We’ve all made the jump to universality. This makes us unique entities, well deserving by any sensible measure of equal treatment as stakeholders in humanity. If this weren’t true (and it might not be if, for instance, we found a living group of australopithecines, or even Homo erectus), we’d need, without question, to reexamine our attitudes about human rights. Morality is absolutely informed by factual knowledge, and if factual knowledge changes, then it is absolutely sensible that morality might (even must) change, as well.

But none of this, of course, is the point of Chapter Five. Instead, Deutsch is trying to convince readers that abstractions are real. He succeeds, but it’s an interesting sort of success. Consider Newton and Einstein again. In Newton’s time, the force Newton called gravity was real, because it was part of the best explanation existent at the time. But Einstein’s better formulation showed that the force Newton called gravity wasn’t real at all. It no longer played a role in our best explanation, and so had to be abandoned. In the same way, any explanation that is replaced by a better one also changes what is real (at least, real to us).

This begins to give a hint at the power Deutsch sees in explanation. Reality is defined by our best explanations. If something, including an abstraction like gravity or curved spacetime, appears in our best explanation, it is real. If it doesn’t appear there, it’s not real. Reality is always changing as our knowledge increases – but how could it be otherwise? For, as Deutsch here so vividly points out, we define reality – and, as the subtitle of the book claims, transform the world – through our explanations.

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