A core component of the modern scientific worldview and the beliefs of people and governments in western liberal democracies is that methodological naturalism is true. It is essential to scientific research, historical study, and all fields of academic research. However there seems to be a huge hole in the center of the belief system which I struggle to think that other people have not seen; it also seems fatal to me. A common understanding of methodological naturalism is that the laws of physics are true (there is probably great disagreement about what that exactly means). I am going to focus on the law of the conservation of energy (this seems to have fairly wide spread agreement). Science makes implicit claims to the truth of mathematics, logic, and natural kinds. Conservation laws make appeals to supernatural beings or things in daily life or government policy seem absurd because it would involve immaterial things interacting with material things which would cause there to be energy exchanged. Abstract objects are also immaterial and interacting with them would be no different than a supernatural agent interacting with the world. This energy exchange would violate conservation laws. However the conservation laws and science in general seems to rely on the truth of abstract objects like logic and mathematical objects. Being able to have knowledge of the laws of nature would necessitate their falsity. Are there any other people who have picked up on this and argued for the stance that the law of conservation is self contradictory?

If all of this is true, then in historical or scientific study appeals to abstract objects like logic, norms, or math would be just as unacceptable as appeals to supernatural beings. This result is deeply disturbing.

Side note: I dont think the indispensability argument works in general for abstract objects or a priori reasoning. It seems viciously circular to me. I am not alone (Leng 2005).


1 Answer 1


There is a certain amount of, well, call it clutter, in your question.

The usual attitude towards scientific laws is not that they are true. It is that they work for all known observations, we have good reason to think they could work over a much wider range of observations, and no reason to think they could not work over an arbitrarily wide range of observations.

OR a scientific law has been shown to have a constrained range of applicability within which it still operates correctly. We shall see some examples of that in a moment.

It has somewhat the flavor of logical positivism and the work of Popper. Though there are many statements of the plan. A scientific law is an idea that has not yet been disproved, and that has gone through a lot of determined and clever efforts to do so. Or it's range of applicability has been carefully mapped out, and within its range it works.

However, science is always prepared for our cherished ideas to be trashed by the next observation. And the reason we are prepared for that is because it has happened on so many occasions. We once thought the Earth was flat and the Sun went around the sky. Then we thought that the Earth was a ball and it went around the Sun, but we had little idea about gravity. Then we got Newtonian ideas about gravity, and we expanded our base of knowledge. Then we got observations that were trouble for Newton, and Einstein came and rescued us with relativity. Then we got into observations of atoms and nuclear reactions. And various people in the 20th century brought us quantum mechanics. Heisenberg, Schrodinger, Feynman, Weinberg, and quite a few others.

The point of this series is this. Our basic understanding of the nature of reality changed at each step. From a geocentric idea at the start. Then a heliocentric idea. Then an absolute space and time that we got shiny and new from Newton. Then a relative space-time that can change and dilate and warp. We got that still in its original packing straight from Einstein. Then a quantum foam that we got from the quantum mechanics folks, which we still have not completely managed to get out of its packaging. And these days, we are playing hard with stringy reality. Though so far that has not been as successful as one might hope.

Within the bounds of a couple of kilometers, you can probably work with the idea that the Earth is flat and use "scientific laws" of geometry that we got from Euclid. The curvature of the Earth will not affect your marking off a rose garden to any great degree. Within speed limits of very much slower than light, and where gravity is not important, you can probably stay within Newtonian physics and use Newton's laws of motion. If you are not too accurate you can probably accept the results of Newton's law of gravity. And if you are looking at only the orbital motion of objects in the solar system, you can accept Einstein's theory of gravity. (Be careful about galaxies and dark matter. But it's a fun activity and the people working on it have pizza.)

A personal annecdote, possibly apocryphal, but it gets the idea across. There was this physicist who had been working on his theory for 20 years. He had been publishing papers, training grad students, directing experiments, and he was quite well known for his body of work. One day, a visiting lecturer gave a talk on his results on the Great Man's theory. And he proceeded to show, quite clearly and definitively, that it was wrong. The audience was nervous, glancing at the GM. Who was scowling and frowning through the whole talk. At the end of the talk there was a pause and "Any questions?" And the GM stood up. And he walked up to the visiting speaker. And he shook his hand, grinning widely, and exclaimed: "Thank you sir! You have taught me something today!"

We hope we are getting closer to reality. We hope we are refining and not just thrashing. But we do not expect that we have found absolute final truth. We are always prepared for our current best ideas to be utterly replaced. Indeed, we are kind of hoping for it. Such events mark advance in human knowledge. We hope to be there when it happens.

There are ideas we are more confident of than others. Often we elevate such ideas to the status of scientific law. The attitude of modern physics can be expressed by a quote from Einstein.

“What really interests me is whether God had any choice in the creation of the World.”
― Albert Einstein

There are ideas that seem to be inescapable within the range of observations we currently have. Just as an example, it seems very difficult to avoid Unitarity, although there are speculative theories that explore the idea. This is a very technical thing from QM. But basically, it is difficult to conserve the quantities that we see conserved unless they evolve by a unitary operator.

There are those who think that, given some very basic observations about the universe, a theory based on unitarity is unavoidable. That is "God had no choice." It is a challenging notion.

This brings us to your example of conservation laws. Conservation laws arise from symmetry. We know this because of Noether's theorem. This is one of the Great Results of the 20th century.

The basic idea of Noether's theorem is this:

If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.

The maths to understand this are graduate level. And 40 years in my past. However, there are several easy examples.

  • Conservation of momentum arises from space-translation symmetry.
  • Conservation of energy arises from time-translation symmetry.
  • Conservation of angular momentum arises from rotational symmetry.
  • Conservation of electric charge arises from gauge symmetry, a feature of the electro-magnetic theory of Maxwell.
  • Some quantum numbers (such as the number of certain types of particle) are conserved, and this conservation arises through unitary symmetry.

Fundamentally, Noether's theorem is geometry. The space in which that geometry operates is usually the phase-space of some physical theory, but still, it is geometry. And it is a symmetry argument, one of the strongest arguments we have in all of science.

So, according to these notions, conservation laws arise as so. There is a thing we call reality. It has symmetries. For example, it is symmetric under changes in the origin of location. By that is meant, the behavior of the universe does not change if we set the origin of the x-axis here or instead there, although our angle of viewing may change. Then we do a huge amount of mathematics. Then we conclude that this symmetry implies conservation of momentum.

So, there is no abstract thing to interact with existents. There are objects in reality and their characteristics. If an object has rotational symmetry then it will have conservation of angular momentum. If reality does not have a privilidged time, meaning the origin of time can be set arbitrarily, then energy is conserved. And so on. It is properties of existents, not abstract things, that interact.

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    you are describing an ideal re-imagining of science designed to make it more philosophically respectable, but that is not how science actually works. Most scientists believe that their theories are true and few scientists are willing to give up their theories on the basis of a few observations that contradict it. Oct 21, 2022 at 8:57
  • @DavidGudeman When some 3rd rate researcher fakes some results to get a grant, does this suddenly produce abstract objects that interact with real world objects?
    – BillOnne
    Oct 21, 2022 at 16:21
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    is that supposed to be related to my comment? I don't see the connection. Oct 21, 2022 at 16:43
  • @DavidGudeman Is your comment supposed to be related to my answer? Because I just showed you it was not.
    – BillOnne
    Oct 21, 2022 at 16:46
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    Please stop playing games. I'm trying to have a serious discussion here. My comment offered one general criticism of your answer and two points that you specifically got wrong. Your reply to my comment didn't address anything I said and seemed to be changing the subject. If you see a connection, the proper thing to do is explain that connection to me so that I can see it also. Oct 21, 2022 at 18:59

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