Chrisw wrote:Because it contains no causal explanation of how the particle follows the path of least action. It is an opaque generalisation that is itself in need of further explanation.

Well, it´s a general principle that requires qualification in terms of phase space geometry. But that geometry then allows the deduction of paths. It´s worth noting that particles don´t follow the parth of least action, but that phase spaces do.

Chrisw wrote:How does the particle "know" to follow this path, what makes it behave like this? The Newtonian formulation provides that explanation in terms of forces acting over time that cause the motion that the principle of least action describes.

But then you might also ask how a particle knows to react to a force by a change in velocity (by definition is the best i can come up with here). You might think of forces as more intuitive, but the same issues arise there.

Chrisw wrote:This is actually a nice example, I think, of why explanation is central to science and why theories are more than the sum of the observations they generate. Though perhaps I just have a broader view of what constitutes science than you do? I'd say that science deals with explanation, not just prediction. Plenty of scientists and philosophers feel this way too (though of course I'm not going to claim that they all do).

Well, the issue is that the explanation is something you get from the expression of the theory, not the theory itself. And since you have multiple expressions, you also have multiple explanations and science can´t distinguish between them, because they make the same predictions. So when you have to expressions of a theory and they can be taken as two different explanations, science can´t pick one over the other.

Chrisw wrote:But scientists do this all the time. I'm not willing to concede that territory exclusively to philosophy, because it takes away the motivation for pursuing science in the first place - the quest for understanding. In fact I don't think that there are clear, fixed lines between philosophy and science. In particular, there is no single, fixed scientific method, so it's quite hard to say that something is notscience when it is something that scientists appear to regard as an important part of what they do.

Well, I do think some scientists do that. And of course they may do so, they just aren´t doing science then. I do think science produces actual knowledge, namely about which theories are false and which are possibly true. That´s the motivator. If you want some additional knowledge that goes beyond the type of knowledge science does produce, you either have to use something that isn´t science or you will commit errors.
I think you have to differentiate between the somewhat abstract scientific method, which we can define rigorously and the stuff scientists do, which might not always fall under this. In the end science tests hypotheses through observation and can only distinguish things that leads to different predicted observations.

Chrisw wrote:I don't follow this argument at all. How do you know that the observations are caused by physical entities rather than immaterial minds? You just seem to declare that this cannot be so, thus assuming your conclusion.

Well, it´s true by definition. You would agree that forces are physical, yet forces only appear as part of specific formulations of physical theories and instead of observing them we observe the change in velocity of particles. If we observe the motion of body parts, then any explanation would be part of one formulation of a hypothesis about the motion of body parts and if we put a "mind" in there, it´d have the same status as putting in the term "force" in some formulations of physical theories.

think wrote:Your observations about the workings of the brain are all sensible enough, yet this first sentence does not follow from them:

But an immaterial mind would have to be responsible for much of the work that is done by the brain, otherwise we wouldn't call it a mind.

I think it follows pretty straightforwardly and directly. How do you think dualism conceives the interaction between mind and body? Is there any possible description, consistent with current knowledge of human antomy, in which the brain does not play an important role?

If I had a theory that physical science could not fully account for the phenomenon of digestion and humans also had immaterial stomachs which partly controlled the workings of physical stomachs I would be a kind of dualist. But not the kind of dualist that philosophers discuss. Stomach's can't think (proof: you don't need one in order to think). Philosophical dualists are primarily concernned with mind/brain dualism.