Naturalism generally refers to the belief that the only things that exist are the laws of Nature; nothing supernatural exists and the Universe is the consequence of these laws. It also states that nothing outside the natural universe exists or if it does it does not affect the natural universe. However this definition is not very satisfying; the biggest problem is with how the term “natural universe” is used. Here, I am going to present a more general description of Naturalism which is essential to the scientific method and understanding of Nature.
What is Nature? It is the physical world. It is our Universe and the Multiverse (if it exists). Nature refers to all physical existence and it can be expressed with mathematical models. It has laws which can be written down in the form mathematical structures and relations. This fact is the basis of all Science; Mathematics is our tool of understanding everything around us. So, what is Naturalism? It is the basic principle behind all scientific research: we seek to represent physical reality with equations and other structures as more accurately as we can, and we assume that nothing supernatural will intervene with this quest. After all, there is no evidence that anything supernatural ever intervened. But what exactly is the supernatural? Does it have its own laws? Can they be understood or written down mathematically? I am going to call the world of the supernatural (as viewed by superstitious and religious people) “SuperNature“. If SuperNature exists then, along with Nature, it formulates the whole Reality and existence: everything that existed, exists, can exist, or will exist is a part of this Reality. Supposing that SuperNature exists then we as rational beings with minds capable of understanding and modeling the perceived reality will be able to understand SuperNature too (if we ever entered it in the form of “souls”, for example). I am not sure if mathematics would be the same tool used in SuperNature, but I am almost certain it would be the main one. We would create new mathematics anyway, if needed. The power of mathematical modeling actually can even be applied to an all-powerful being like God, but I will not discuss this here.
To see an example of basic mathematical modeling of the supernatural we will use sets in order to represent reality:
N is the set of Nature, SN is the set of SuperNature and R is Reality. All that can know or will be able to know about Nature is in its set (maybe there are some things about Nature which we won’t be able to comprehend but they are in the set too of course). Assuming that SuperNature can sometimes interact with Nature we might be able to know some things about it too and therefore enter the SN set theoretically. Nevertheless, there has been no indication that SuperNature interacts with Nature so far, which leads us to seriously doubt its existence. We can however say that SN does exist but its empty: SN = Ø, and therefore there is nothing supernatural to understand or explain. Strict Naturalism states that SN doesn’t exist and this seems more likely. It is very important for a scientist’s research that they accept st first that SN doesn’t exist or that it’s equal to an empty set, because SuperNature only brings more truble to the quest. We need to make sure that the phenomena we examine are not in Nature if we will to hypothesize that they might be in SuperNature. So far no such need was presented and we can safely write for the time being:
which is the very definition of Naturalism. In N we can include everything that is qualified as physical or material: the laws of Nature, the Universe, the multiverse and the physical reality in general (it is better not to use the word universe in the definition cause nowadays the Multiverse hypothesis plays a significant role in our understanding of the nature and origins of our Universe). One can only speculate about whatever can exist outside it. But think about it, if SuperNature has laws that are comprehensible with models (scientific/mathematical in nature) then there isn’t anything particularly special about it; we just need to discover those laws. Maybe SN is actually the same set as N, but we don’t know it yet. There is no “supernatural” mystery and no “divine power” behind anything. If we can understand the laws of SN then why not labeling it physical or a different form of physical reality in the same manner as we label N physical too? If there are laws in SN and we have access to it, then we will most likely find them.
One way or the other, it all works, because it has to.