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This question came forth from a discussion I was having. Suppose that the universe is deterministic because of some laws. But those laws themselves exist for no reason.

Does this mean that the laws, but not the universe, exist for no reason? Or does this mean the universe, which the laws are part of as a joint unit, exists for no reason?

Is this purely a semantic issue or would there a correct metaphysical answer to this? I’m not really sure as to what part of philosophy this belongs in. I was guessing this may be related to whether mathematics is “real” or not, but mathematics to me seems like just a language for laws. There seems to be something ontic about laws but I’m not sure what to classify them as and was interested in resources that talk about this.

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    The universe doesn't run by laws: it just runs for reasons we don't understand. The so-called 'laws' are the result of human attempts to 'explain' their observations. Is it deterministic (by people)? Absolutely not, because the 'laws' are incomplete. Nov 24, 2023 at 20:45
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    SEP's Laws of Nature describes the current opposition between Humeanism and realism about laws, which is basically a modernization of nominalism vs realism about universals. Even within realism, there was platonism vs Aristotelian hylomorphism, where on the first view laws/universals would be entities onto themselves, and on the second, matter/form merged with their substrate, the universe in this case. Peirce, for example, used making a proper metaphysical shelf for laws of nature as an argument for a merged relational ontology.
    – Conifold
    Nov 24, 2023 at 22:46
  • The SEP discussion of realism about natural kinds should be pertinent. I think appeal to mechanism-talk in this context might be styled an opposite of strong realism (if the mechanisms are strongly internal to physical objects instead of forces "above" them). Nov 24, 2023 at 23:00
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    You can find additional annotated references on Humeanism vs nomic realism (a.k.a. "necessitarianism") in PhilPapers summaries, Laws of Nature and Anti-Realism about Laws.
    – Conifold
    Nov 24, 2023 at 23:14
  • The universe isn't deterministic, so this question is absurd. I don't think it can be saved, either; there are uncountably many equivalent presentations of typical axiomatic systems, so there aren't "the laws"; see generalized the for formal details.
    – Corbin
    Nov 25, 2023 at 17:08

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You say :

Suppose that the universe is deterministic because of some laws. But those laws themselves exist for no reason.

Here, I see three assumptions :

  1. The universe is deterministic.
  2. The deterministic nature of the universe is a result of some law(s).
  3. The laws exist for no reason.

The assumptions (1) and (2) are related to the concept of determinism, which comes in many flavors.

As of (3), things get tricky. "law" was a word used in classical physics to describe how nature worked, by what was then considered as a divine plan or design by God.

Later on, starting with relativity and then with quantum mechanics, things that were considered simple and clear, as space, time, mass, etc became complex mathematical structures and started to get interrelated in perplexing ways.

Physicists started for the first time to look inside nature and what they saw were not laws, but things that although they were able to model as mathematical constructs, they were in fact unable to describe by language in a meaningful way.

The "laws" you are referring to, ARE the mathematical representations of the way reality appears to us BUT the explanation, the interpretation, the ontological representation is open to speculation.

So, by going back to your question, as we have now redefined the term "law" as the mathematical equivalent of the way reality appears in us and specifically to our measurements, it seems that these "laws" ARE the expression of the universe or in your words ARE an inextricable part of it.

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    +1. The problem of the existence of the objects, though, already appears in classical physics. There are very few things that we can perceive directly. For instance a crucial object in classical mechanics is "force". Mathematically, a force is a vector. If you think about how forces are measured, most of the time you measure distance and then use the theory to talk about the force. Nov 25, 2023 at 10:13
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Any time you are discussing the "ultimate nature of things", you're firmly in the domain of metaphysics.

The answer you seek depends on your metaphysical presuppositions. Many are content to accept mathematical ideas as abstract objects. However, there is another view. The traditional stance that rejects abstract objects is called nominalism. (See SEP's Nominalism in Metaphysics). Since you have the philosophy of mathematics tag, you probably would be more interested in Nominalism in Philosophy of Mathematics (SEP). From the article:

According to nominalism, mathematical objects (including, henceforth, mathematical relations and structures) do not exist, or at least they need not be taken to exist for us to make sense of mathematics. So, it is the nominalist's burden to show how to interpret mathematics without the commitment to the existence of mathematical objects... To achieve that, nominalists in the philosophy of mathematics forge interconnections with metaphysics (whether mathematical objects do exist), epistemology (what kind of knowledge of these entities we have), and philosophy of science (how to make sense of the successful application of mathematics in science without being committed to the existence of mathematical entities).

In this view, a mathematical law is not an abstract object, but rather might be something else, like in Hartry Field's notion of mathematical fiction. What it means to be a mathematical fiction, of course, is what the theory as a whole is devoted to. The point made here is not that mathematical fictionalism is superior to Platonic realism, for instance, but merely that viewing laws as abstract objects is a metaphysical choice and not some sort of necessity.

As to whether things are part of the universe, if one is talking about the physical universe, then certainly not. Mathematical laws are linguistic artifacts that communicate the experience of the regularity of physical systems, but in no way are part of those systems in the same way a mental map describes an island and is not part of the island. The medium of a language is always physical, but the ideas that the language communicates, including all mathematical languages, is mental in nature, and is dependent upon the mental life of beings with minds. This is, in fact, an argument many make for why calculators don't understand math as opposed to people who do.

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You ask the old question: Do we discover scientific laws, or do we invent scientific rules to explain our observations?

The question is old. Until now it has no answer.

  1. Lessons learned: What in the past has been proposed as scientific rules – e.g., on the field of gravitation Aristotle’s law of the natural place, Ptolemaios’ theory of celestial mechanics, Newton’s theory of celestical mechanics, Einstein’s field theory of General Relativity – these are not candidates for the “ontic” objects you are asking for.

    These laws are better and better attempts to find an answer. They teach the lesson that we should not take any intermediate attempt as the final word.

  2. Example: The medieval world view considers the laws of nature as the ideas in the head of God. That’s an example for an answer based on the ontology of the time. But it is not an answer based on present ontology.

  3. Conclusion: One can doubt that we already have the right concepts to formulate such a question. We lack an ontology to discuss your fundamental question.

    The question is a prompt to develop such a metaphysics.

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While I am not an expert in the field of mathematics and/or gravitational physics I can tell you one thing. You mustn't forget that laws themselves are objects of some sort the second you think of them, refer to them, and most definitely put them into language. Objective laws are objects in it of themselves at this point that I am referring to them as a logical construct. Furthermore to imagine the law you cannot imagine it abstractly, in other words no law can be fathomed without use of application and illustration which then turns that law into the idea of a physical manifestation (most definitely a thing) or a physical enactment of the law itself (even more certainly a object). In short anything you and I may ever discuss, fathom, put out of mind, or everything that we haven't thought of our entire lives up until your reading this have now become officially cemented as objects. (to question that which you have not ever thought of you must create a set of things you have not thought of and you cannot declare a element of a set a non-object.)

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  • As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center.
    – Meanach
    Nov 27, 2023 at 8:17
  • I apologize for any misrepresentation this was a free flow response. Nov 27, 2023 at 21:25
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The Universe behaves in a characteristic way, in which we perceive ubiquitous patterns. The laws of physics are labels and symbolic representations for the more fundamental of those patterns. For example, when we see light reflect from a mirror, there is a symmetry to the path of the incident and reflected light. We label that the law of reflection. The patterns seem baked in to the Universe. The laws, however, can be considered separate, as they are approximate maps, not the territory.

Given that, the answer depends on what you have in mind when you speak of the laws of physics. If you mean the actual patterns, then they are part and parcel of the Universe. If you mean the approximate representations, then they are human inventions, subject to being discarded when better ones come along, presumably with the same ontological status as the rest of mathematics and other types of abstract constructs contemplated by human minds.

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What scientists used to call "natural laws" can be considered abstract objects, i.e., objects we cannot perceive with our eyes etc. but that we infer from the observations we make of the universe.

Objects are things that exist independently of our perception of them. Natural laws certainly fall into that category.

One objection maybe is that what may seem at some point a law in fact isn't, such as for example Newton's Law of Universal Gravitation, falsified by the position of Mercury on its orbit around the sun, but this also happens with what we take to be objects in our environment but are only hallucinations, or with interferences in scientific instruments, which may give the impression that there is some new particule when there is nothing except interference.

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