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I want to distinguish between two types of magician. I'm going to provisionally name them magipraxists and magiologists, and my request is for more familiar terminology to replace my invented and silly-sounding words.

Magipraxists are what you probably think of as a magician, in that they perform acts of magic. They cast spells, summon demons, enchant objects, and so forth. Some act essentially as outlaws, taking what supplies they need by force; others make a living performing utilitarian magic for paying customers and purchasing needed supplies; still others are employed on retainer by politically powerful individuals with access to repositories of supplies. Not all persons are capable of performing magic; in addition to the physical implements, one requires a degree of hereditable ability and substantial training.

Magiologists study magic, and may, if able, perform it in controlled settings to further their understanding. In ages past they would try to keep their discoveries secret and gain some proficiency in magipraxy to commercialise their discovery, as a middling magipraxist applying cutting-edge magiology could often outcompete rival superior magipraxists relying on outdated magiology. But there is a sense that recent discoveries have tended to be smaller improvements with narrower applicability, and therefore modern magiologists act more like professors, working collaboratively at facilities where they divide their time between research and teaching future magicians (some students going on to become magipraxists and others magiologists).

What would you call these? I'd be okay with using "magician" for magipraxists if I had a comparably widely recognised word to use for magiologists. No post I was able to discover on this site offered any helpful terminology; there is a lot about the use of magic to confound or assist in conventional sciences, but little about the science of magic itself.

Some flavour to help illuminate the relationship between the two:

Magipraxists regularly summon demons from five alternate realms of existence to perform tasks for them. Magiologists have made contact with a sixth, but it is a two-step process which requires traversing the third one; the environment of the third is lethal to the inhabitants of the sixth, so it is not a viable route for summonings. Further magiological research has established eight as the upper bound on the number of such realms, although the actual number is not known. Magipraxists complain about funding these ivory-tower magiologists who produce such useless results.

Magipraxists learn how to cast weather-affecting spells using stones of a variety of types. These stones usually have natural origins, but magiologists devised methods to synthesise some. Most notably, invoking a fog no longer requires rare heirloom-quality mined stones but can be accomplished with common and cheaply available synthetics. Magipraxists who own mined stones feel unfairly cheated of value by the magiologists, while those who have since purchased synthetics view this development positively.

Magipraxists are employed to enchant various objects, but a spell that confers strength on one material may embrittle another. Magiologists work with structural engineers to ensure that magically-strengthened pieces will not cause harm to nearby parts of the structure. An inquiry into a bridge collapse has divided magicians; the magipraxists have endured criticism of the quality of their spellcasting in its construction, while questions have been raised about the magiologists' claims as to the compatibility of the spells involved.

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    $\begingroup$ What's wrong with the obvious answers, a student, academic or scholar. $\endgroup$ – Pelinore Apr 4 '20 at 23:25
  • $\begingroup$ Plenty of euphemisms & tropes out there like 'the craft' that would be familiar to any reader as well. $\endgroup$ – Pelinore Apr 4 '20 at 23:31
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Theoretical vs practical.

This is borrowed from physics.

https://en.wikipedia.org/wiki/Theoretical_physics

Experimental physics regroups all the disciplines of physics that are concerned with data acquisition, data–acquisition methods, and the detailed conceptualization (beyond simple thought experiments) and realization of laboratory experiments. It is often put in contrast with theoretical physics, which is more concerned with predicting and explaining the physical behaviour of nature than the acquisition of knowledge about it.

The theoreticians study, predict and explain the workings of magic in a manner that is to a greater or lesser degree abstracted from the real world. They might be capable practitioners but their day to day interest is not in the concrete. They are paid to think and talk, not do.

Here I use the term practical instead of experimental - but both connote an emphasis on the real world, results and applications. Practitioners are agnostic empiricists. The practitioner is concerned less about why it works than the fact that it works and predictably so.

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    $\begingroup$ A researcher. Only after arduous study on the Frequency of Leylines can the Archmage of Cambridge publish its moratorium on casting near Stonghenge. $\endgroup$ – Gustavo Apr 5 '20 at 0:02
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    $\begingroup$ @Gustavo - I worry that calling theoreticians the only researchers implies that there cannot be practical, experimental research as well. $\endgroup$ – Willk Apr 5 '20 at 0:11
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    $\begingroup$ And humans got the problem of politics even on Nobel Laureates. Easy to imagine a conflict between Accademia and the down to earth mage contractor. A ton of conflict to spice the story. $\endgroup$ – Gustavo Apr 5 '20 at 0:16
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Our current suffixes used for science will work for your application

A Magicologist. studies magic but may or practice it

A Magicosopher studies the study of magic

If you want to focus on specific skills or knowledge Necrosophy studies the study of using the dead to foretell the future

And Thaumasophy studies the magic of transformation.

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Sadly, it is more or less up to you as it depends entirely on the setting. Real world does not have academic study of how magic and spells function so no "correct" answer exists.

As a practical point, your setting seems too advanced in magic to still have a single name for either. Just like natural philosophers have been replaced by a multitude of specialized titles, your setting would have lots of names for doing different things related to magic.

A person whose job it is to strengthen masonry with magic probably would not be called a "magician". He would have a title that is related to what he works with, what he does, or what the result is. And lots of his skills and work would not involve magic at all, so magic might not even be clearly mentioned. He might be "master mason" or "arcane mason" or "stone caller" or almost anything.

On the academic side you have some obvious general alternatives but even they depend on the specific of the setting and flavour you want. If magic is seen as arcane and mysterious, you might have arcanists. If it seen as wonderful and miraculous you might have "thaumatologists". Pragmatic people might just elect not to use fancy words and talk of "study of magic".

And every "doctor of arcane" or "professor of miracles" would have their specialization. You might have theoretical arcanists who work with theories of magic. You might have experimental thaumatology that is about doing magical experiments. Or analytical arcana analogous to analytical chemistry.

Or the naming might be based on divisions in the magical practice. To return to those magical masons, the academic study of that might simply be a part of architecture. Theoretical study of healing spells might be part of medicine. Theoretical aspects of summoning of demons would be under demonology.

Even if magic is studied separate of the mundane aspects it would be entirely likely for healing magic and demon summoning not to be covered by same study or department.

You probably noticed that all of the above is very vague and confusing. This is because all of this depends entirely on the setting. You should not be thinking about what is the "correct name", none exists. Instead, the questions you need to ask yourself are : "What would the people in my setting think? How would they organize this? How do they see magic and its use? What would these people actually do?"

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