The way that I approach magic is to highlight how little like scientific pursuits it truly is. I can no longer recall where it was, but in the bowels of some Second Edition sourcebook there is an instruction that set me down this path and has served as my watchword ever since I read it those many many years ago. It goes something like this: "Spells are not utilitarian. They do exactly what they were designed to do. You cannot, for example, using a magic missile to knock over an object, nor cast a featherfall spell on a dead body. Magic is not science."
Why not, and how does that make magic not science? Well, there are rules but they aren't necessarily rules of logic. Magic follows rules of theme and poetry. As an Art it has a sensibility of the poetic about it, rather than the mundane. It's not a workhorse, it's a powerful, strange, and sometimes badly understood force. To help give structure to this weird world of magic, I spent a lot of time developing an internally consistent (I hope) philosophy of magic to go with the setting of the 10th Age. I understand how and why, broadly, it functions, and it is not a functioning of set rules and regulations that interact according to hard laws.
For the 10th Age, magic is indeed an art. The discovery of new spells and spell-combinations is generally one that is completely illogical and unstructured. A good deal of magical research is the rote understanding of other people's work. You don't have to know why a particular word in a particular spell produces a particular effect, only that it does. More, magic itself is obscured in a purposefully obfuscating language. Wizards don't want other wizards to understand what they're doing. Magic represents a sort of anti-scholarship, in which the scholars (mages, in this case) actively attempt to prevent each other from puzzling out knowledge.
Magic. The Art, magic is divided by mystical philosophy into three distinct components: the Breath (ter mirarus), the Motion (ter motus), and the Pattern (ter gnomonus). In order for these three components to interact properly and solidify into reality, a latent (or resting) energy-source must be found. This mystical fourth element is the Breath of the Dragon (ter mirari de’ter wyrmus).
Ter mirarus, the Breath. The Mirarus is the expressed form of the Gnomonus (pattern). The gnomonus entire, however, cannot be fit with vocal grammar. Thus, while the mirarus is extremely important to the casting of the spell, it is not the entire work of magic.
Ter motus, the Motion. This comprises the physical grammar of the gnomonus and completes the pattern. In some cases, a third physical expression is required: that is ter materra, the matter. This is most often used as a metaphysical representation of the action or power (potens) of the enacted magic.
Ter gnomonus, the Pattern. The pattern (also called the Weft and Warp) makes up the complete conceptual image of the spell. This also refers to the unspoken and unspeakable portions of the gnomonus, which must be held in the mind until the moment of release.
Ter mirari de’ter wyrmus, the Breath of the Dragon. This element is the most important of all, and generally for some reason not considered to be part of the Three Essentials, possibly as it is generally present. The Breath of the Dragon is the magical tide which encompasses the world. It is so-called based on the ancient Draconic belief that the world itself is an unborn Wyrm; wizards have long postulated that the “tide of magic,” that is, the presence of the latent energy in lesser or greater amounts, is tied to the slow and rhythmic breathing of the Wyrm unborn.
Important related terms: ilmavus and callos refer not to the physical acts or actions of magic (mirare, motus, gnomonus) but rather to the metaphysical concepts occurring behind them. Ilmavus, the abstraction, is essentially ter gnomonus; it is the series of abstract concepts the wizard must focus on in order for magic to function. Callos, the concretion, is the combined concrete aspects of the mirare, motus, and any materra used in the spellcasting. These are concrete actions (as opposed to the abstract “actions” of ter gnomonus).
This is an excerpt from the Kyklor Antiki (the Encyclopedia) of Arunia. While it follows an internal logic, it can hardly be compared with any sort of rational science. Experimentation is essentially impossible outside the confines of a wizard's tower due to the extremely fickle nature of the subject. You can't simply start changing spells around to see their effects: spells that have even the slightest alteration in them fail. The only way to experiment with spells is in the safety of a research facility where you can rewrite whole sections of them according to incomprehensible laws laid down by the mages of old.
Sure, magic still has to follow a real set of sensible rules, because magic otherwise would be unusable in a roleplaying game. Does that mean that it is somehow less magical? I would argue no, since even in a novel or a movie the internal logic of magic must be established and respected, else the audience will become violently upset when things simply stop making sense.
Magic is magic, and science is science. Never the twain shall meet, for one is an art of mystic proportions and the other is a method of understanding the world that precludes the precepts of the other.