About learned Magicians and all their variants... Philosophy, Artes Liberales and Craft: Charms are their Magic theory similar abilities or only are used like one without to be actually?
Pardon?
Sorry... I'll explain better.
Learned Magician from HMRE, Mathematici use Artes Liberales like their Hermetic Counterparts use Magic Theory on Lab totals. The Alternate tradition of Mythic Alchemists uses Philosophiae and not Artes liberales, and the Cunning-Folk use Craft: Charm instead.
I am asking if that Abilities iequal Magic Theory to all, being like Hedge Magic Theory or only are important to Lab, that i mean/i am asking.
No.
Hedge magicians have things like Gruagachan Lore (for initiations) or Hedge Witch Magic Theory (used in lab work), but these are far more limited in usage than Hermetic Magic Theory. The abilities you quote above are just useful in their magic, like (realm) lore is to a summoner not an underlying theory of how magic works.
Does that help?
Yes, but i think that Pictish (Jotun Language or Koldovali Theory), Rune Magic and Folk Witch Magic Theory are theirs Hedges Magic Theories, because they are listed like that on the book; and on the Introduction says that ther are traditions with and without.
But i get that ther are usefull abilities on lab and spellcasting and not.
Another point, the hermetics need have Mystery Cult Lore to Initiations too, just like the Organizations hedge traditions need ownselfs Organizations Lores for that.
I disagree. I see Learned Magician magic as basically a magical expansion of Experimental Philosophy. Therefore, for Mathematicia, Artes Liberales is their version of Magic Theory. The theory and principles of astrology (which is part of Artes Liberales) provides the underlying theory of how their magic works.
Wow, i think that i opened the Pandora-topic cage!
To resume, hedge traditions with some type of "pure" Hedge Magic Theory:
Folk Witches
Gruagachan (and variants similar) - Pictish and Jotun Language work like Languages too.
Vitkir - use 3 abilities on his magic: Craft Runes, Run Magic and Old Norse
Without Hedge magic Theory:
Elementalist
Nightwalkers
And, with one Ability that works like Hedge Magic Theory:
Learned Magicians (Mathematici, Mythic Alchemists and Cunning-folk) - Philosophiae, Artes Liberales and Craft: Charms.
Fine for you, but for me the distinction is that any scholar can learn artes liberales, and have absolutely no clue how learned magicians perform their magic, because that is not what the ability covers. Non hermetic magi who manage to learn the Magic Theory ability can be used as lab assistants I believe. For me artes liberales is a 'sympathetic' knowledge that is helpful to learned magicians understanding of their magic in the same way that summoners use realm lores, but nothing more.
I am more than happy to admit that this is probably just a symantic distinction, and I'm probably in the minority here.
The same way I don't see how pictish can be a magic theory, as it is a langauge. Latin is helpful to Hermetic Magi in several ways, but it isn't the theory.
Ah well.
Except for...
HMRE page 56:
I think that THE RULES have no discussion, or free interpretation.
Fair enough. 
I think I probably went wrong there with my remembering of 3rd and 4th edition gruagach who had both the Pictish langauge and Potency the later of which acted as the magic theory and was limited by the pictish langauge. It's been streamlined in 5th.
It always struck me as funny that Hedge Magic says that some "technically naïve traditions" lack practitioners with this skill. But by some they seem to mean Elementalists and Learned Magicians because all the other ones in the book either have it by default (Vikter, Folkwitches, and Gruagachan) or really have no use for it at all (Nightwalkers).
It's funny because if I had to choose the two least technically naïve traditions I would probably pick the Elementalists and Learned types.
Agreed, though as I recall, there is a note to the effect that very few folk witches actually know their own magic theory ability?
I always thought there was too, but I looked and couldn't find it. I think that I just might have been thinking of the whole technically naïve thing. The fluff sort of leans that way.
When you read the actual crunch of folk witchery their Hedge theory is required. Literaly it's actualy a required ability if your a Gifted hedge witch. Also practically. Most hedge witch magic is based around laboratory work, er kitchen work. Many of their abilities will not function if they don't make components in their kitchens. And you seem to need theory to set up a kitchen just like hermetics.
...thanks for reminding me why I disliked the Hedge Magic book.
Nothing really serous, but every tradition s nearly (but not quite) Hermetic in it's mechanics.
Easy to understand and evaluate, I agree, but I miss ye olden days of yore, when what few hedge traditions we had were really unique - fundamentally different from hermetic magic in game mechanics as well as concept and 'feel'.
And yes, I know I'm using far too big a brush there. The nightwlkers are very different, and the Vitkir kinda actually have their own mechanics, but still.
I would say that the tradition are "ars magica" in its mechanics, more than hermetic. ArM5 has a tradition of having characteristic + ability 1 + ability 2 for everything that is supernatural or seasonal work. That is a virtue or a flaw (depends on your POV) of the whole system, not of hermetic activity.
I would say that the HMRE traditions are quite different from hermetic magic. In fact quite a few other threads have shown a dislike a dislike of them because they are different from basic hermetic mechanics. Vitkir do not resemble hermetics at all. Nightwalkers are basically a kind of companion V&F package and the other traditions have lab activities and spells. So what? So do legends. 
And they do not resemble hermetics much, really, heh. I fail to see how a folk witch is really a hermetic spin of. I do not really like the witches as designed, but that is because of the V&F chosen, not because they resemble hermetics. The only tradition that could be seen as somewhat hermetic IMo is the natural magicians. I thought they would be more based on natural philosophy than they are, but this is not how they are designed in the setting. Different people, different takes on the material, I guess. Easy to adapt in any case. I fact you can build ALL the traditions in HMRE and ROP:F out of ROP:I and its mechanics with very little adaptation if you want something somewhat different.
Cheers,
Xavi
Well thanks.
So we can close the discussion with that the Learned Magicians hasn't really one own Hedge Magic Theory, but they use one Ability to the same, but they need one Hedge magic Theory first, then they can grow their own Innovations.