Against mechanism

The title might be a tad misleading, so I will need to clarify. But perhaps I should start by pointing out that we really don’t have a good definition of mechanism. So people might disagree about what the word means.

I have a car, clocks, a wrist watch, a cell phone, and many other such things. I am not against that kind of mechanism. I will note, however, that all of those kinds of mechanisms eventually fail. Mechanical things break.

And then there are our scientific laws. Newton’s laws were often described as “Newtonian mechanics”, and Einsteins newer theory is often described as relativistic mechanics. We normally do not expect scientific laws to fail. Of course, these days we normally see relativistic mechanics as having superseded Newtonian mechanics. But that wasn’t because Newton’s laws failed in the way that real mechanisms fail. Rather, it was because relativistic mechanics was better than Newtonian mechanics. And, of course, Newtonian mechanics is still very much in use, because it is easier to use than relativistic mechanics, and in most cases it works well enough.

Ideal mechanisms

Because scientific laws are not expected to fail, we might consider them to be ideal mechanisms. They are abstract, rather than composed of physical gears and levers such as we see with physical mechanisms.

Again, to be clear, I am not in any way opposed to the kind of ideal mechanisms that we see in science. They not what I am against. After all, I am a mathematician, and much of mathematics is about such ideal mechanisms.

So what am I against?

Is everything mechanical?

Some people assume that everything is mechanical, and we just haven’t yet found all of the mechanisms.

That assumption is what I am against. We do not have evidence that everything is mechanical, and there is much that does not seem to be mechanical.

Let’s start with mathematics. For sure, arithmetic can be considered to be mechanical, in the sense of ideal mechanisms. The axioms of arithmetic, usually taken to be the Peano axioms, define the actual ideal mechanisms used. And theorems about arithmetic are all deduced from those axioms. This all fits the idea of ideal mechanisms.

But where did those axioms come from? The axioms themselves are human inventions. There does not seem to be a mechanism for generating axioms systems. Or, if there is a mechanism that all mathematicians are using for this, then nobody knows what that mechanism is.

Similarly, we can look at science. There does not appear to be a mechanical system that generates scientific laws. In practice, laws are creative constructs by scientists.

How does science work?

If the world is not actually mechanical, then scientists must be doing something other than just discovering mechanism that already work. So what are they doing?

Scientists notice apparent regularities in the way things behave. So they construct mechanisms that approximate this behavior. Usually, the mechanisms that they construct are abstract, and fit what I have described as ideal mechanism. But a physical mechanism could also be used for this purpose. For example, a sun dial is a physical mechanism used for telling time. For that matter, mechanical clocks are physical mechanisms for a similar purpose. Some people suggest that Stonehenge may have been a physical mechanism to predict astronomical events.

Once scientists have constructed a mechanism to approximate some behavior of an aspect of the world, they can use that mechanism to make predictions. They then measure the discrepancies between their predictions and what actually happens. These discrepancies are often called “residuals”. They next look for apparent patterns in these residuals, to see if they can construct another abstract ideal mechanism to approximate these residuals. This adds another layer of complexity to our science, but it yields more accurate predictions.

These procedures can be continued iteratively, yielding more and more complex science but with increasingly accurate predictions.

If the world is not itself mechanical, this iterative procedure must eventually break down. And what will be found, at that point, is that it becomes difficult to discern useful patterns in the observed residuals. This will lead to behavior that looks something like quantum wierdness.

Free will and mechanism

The arguments against free will are usually based on the idea that a mechanism is not free. The mechanism can only do what the mechanism requires. If the world is not actually mechanical, then these arguments fail.

Note that I am not arguing for free will. I don’t think we have a good definition of what that means. But I do think that the world is not actually mechanical, and that human choices are not as limited as we expect from mechanical things (such a computer based robots).