On explanations and causality within physics

I recently watched a video by philosophers Massimo Pigliucci (City University of New York) and Daniel Kaufman (Missouri State University) discussing differences in styles of explanation between the natural sciences and the social sciences. There’s a lot in the video that I agree with, but I want to dissent on one issue. That is, I don’t agree that causality is as central to explanations within physics as the video suggests, and thus the differences with the social sciences are less pronounced than suggested. (Though, having said that, I do agree that there is one very big difference in that biological entities exhibit purpose and intention, whereas physical entities do not.)

Pigliucci and Kaufman suggest that “explanations” within the physical sciences are typically in terms of causation, and thus are of the form of pointing to antecedent causal events that are sufficient to explain subsequent events. They also discuss “laws of physics” as being “widely generalisable causal relations”.

I would instead say that physical laws are often not about causes and are just descriptive. They would thus be “widely generalisable descriptive relations”. The meaning of “explanation” within physics is also much broader than just causal explanations. More generally, “explanations” are linkages between descriptions of different aspects of the system. All systems, simple or complex, can be (partially) described in different ways, and if we show how those descriptions link together then we “explain”.

The unity of maths and physics revisited

A major part of scientism is the idea that maths and logic are not distinct from science, but rather that they arise from the same fundamental root — they are all attempts to find descriptions of the world around us. The axioms of maths and logic are thus equivalent to the laws of physics, being statements of deep regularities of how the world behaves that enable us to describe and model the world.

My article advocating that mathematics is a part of science was recently posted on Scientia Salon. This was followed by an article by Massimo Pigliucci which took the opposite line and criticised the return of “radical empiricism”.

In response I wrote about the roots of empiricism, defending the radical empiricism that Pigliucci rejects. That post was getting rather long, so I have hived off parts into this post where I return to the distinction between mathematics and science. This is essentially a third part to my above two posts, countering various criticisms made on Scientia Salon.

To summarise the above arguments in two sentences, my critics were saying: “Well no, mathematics is anything but studying physical objects. It is the study of abstract concepts”, whereas I was saying, “Yes, mathematics is the study of abstract concepts, abstract concepts that are about the behaviour of the physical world”.

I have argued that maths and logic and science are all part of the same ensemble, being ideas adopted to model the world. We do that modelling by looking for regularities in the way the world works, and we abstract those into concepts that we call “laws of physics” or “axioms of maths” or of logic. Thus axioms of maths and logic are just as much empirical statements about the behaviour of the world as laws of physics. In part one I discussed other possible origins of mathematical axioms, while in part two I discussed the fundamental basis of empirical enquiry.

That leaves several possible differences between maths and science, which I address here:

What are “laws of physics”?

In Sam Harris’s interview with Lawrence Krauss, regarding Krauss’s new book “A Universe from Nothing” (I haven’t read the book yet, it’s on order), Sam asks:

“You have described three gradations of nothing — empty space, the absence of space, and the absence of physical laws. […] Might it not be easier to think about the laws of physics as having always existed?”

Thinking about physical laws like this, as “entities” that can have existence in their own right, is widespread, but in my opinion fundamentally misguided. It seems to regard “laws of physics” as an underpinning “structure” that directs and controls physical matter. If this were true then it would make sense to ask whether “physical laws” have always existed. But if physical laws “exist” in this sense then what are they made of? How do they interact with matter? How do they effect their actions?

That train of reasoning is ill-founded. Physical laws are not entities with existence in their own right, they are simply descriptions of how matter behaves. The “laws” governing a fundamental particle are simply a summary of the nature of that particle and its behaviour when interacting with other particles. Oxford Dictionaries defines the scientific use of “law” as meaning:

Law: (3) a statement of fact, deduced from observation, to the effect that a particular natural or scientific phenomenon always occurs if certain conditions are present.

You can no more have “laws of physics” existing independently of matter than you can have a “description of X” independently of “X”. Thus if matter exists then you can have a description of it (= “laws”). But if there were no matter there could not be a description (and thus one could not have pre-existing “laws”).

To illustrate this let’s take a fundamental physical law, namely conservation of momentum, the fact that summed over all particles the total momentum never changes. Since a force can produce a change in momentum (Newton’s Second Law), this requires that every force be matched by an equal and opposite force (Newton’s Third Law), such that overall forces cancel and momentum stays constant.