And that piece is critical. Everybody except magi do two seasons of work to earn a living, and two season of whatever they want.
Magi have four seasons of whatever they want as their mundane needs, food, shelter, new or repaired clothes, etc, are met by the covenfolk. Magi may create things that can be sold, but they never "earn a living", at least in the context used here.
Our Troupe uses this rule, and no, of course the apprentice doesn't also contribute to the Lab Total in that season. Only two Magi have used this rule, one for his Apprentice and one for his Familiar, and both have only done it over two seasons. Just enough to make them useful in a Lab, and actually giving a bonus to Lab Total, which is when you start using them to assist in the Lab, and make a return on being taught.
Also, as far as we were concerned, the training, since it's not a full on teaching, didn't count for the mandatory season of teaching the apprentice.
The "earn a living" seems a bit overly literal to me. Consider a carpenter- generally they spend their time in the workshop earning a living, and can train their apprentice. Should they decide they want an addition to their own house ,however, are they suddenly unable to train apprentices because they are not working for someone else?
Similarly it seems clear to me that magi may train apprentices (while they do not aid the lab total- after all an apprentice being trained may not contribute to the workshop total either) over a season and that what apprentices clarifies is that this does generally count as a season of instruction under Hermetic law (Tribunals may, of course, vary).
Don't forget that it is also a balancing act to make sure that all apprentices received a similar training, are not overpowered compare to non-magical character and allowed to have useful character straight out of apprenticeship while still having a lot of potential to grow.
Once you try to reconcile the mechanical aspect, with the teaching/progression rules and the power balance, concession needs to be made, otherwise the whole system collapse.
Hermetic Art cannot be trained (p164). So helping a master in his laboratory work could only be considered as Exposure (p163, quality: 2), it is spelled out in the rule.
Don't throw a Strawman.
Nobody said anything about training an Hermetic Art. We were discussing Magic Theory, which is an Ability. And yes, Magic Theory can be trained in.
I think the problem is the self-contradictory nature of these two sentences:
However, the master may work at earning a living while training an apprentice. The apprentice may only be taught an Ability which the master is using to earn a living over the whole season.
In the first sentence the “earn a living” is optional and the second mandatory so which is it? I prefer to read it along with the author of Apprentices as earning a living is optional and the important part of the second sentence is that it is an attempt to state that the training must be in the same ability as the master is using that season for their own work.
I think maybe we should consider other scenarios to see what should matter. I'll illustrate. Let's say our Verditius wants to train an apprentice at Craft (Swordsmith). The Verditius is equivalent to a master swordsmith at the Craft, but the Verditius need not earn a living. If the master swordsmith could spend the season crafting several swords while training an apprentice, is there any reason the Verditius could not? They have the same Abilities and matching workshops. I don't see any reason the Verditius could not. If this is the case, then "earn a living" is really being used as a euphemism for "work fully productively" or something like that.
As for nullsettings' contradiction, I think you have to read the second sentence attached to the paragraph of the first sentence and following the first sentence rather than in isolation. I believe the way it is written is supposed to convey, "If the master earns a living while training the apprentice, then the apprentice can only be taught an Ability which the master is using to earn a living over the whole season."
As a continuation, if my last two paragraphs seem reasonable, then we can ask when Magic Theory could be Trained. If we can accept those two paragraphs as valid...
A mage can work fully productively for a season while training an apprentice in an Ability, so long as that Ability is being used to work fully productively over the whole season. A fully productive season for most magi is worked in the lab. Generally Magic Theory must be one of the several things used throughout the season of laboratory work. Note that the rules never claim it must be the only Ability/Art used in the process, just that it must be used for the process. So Magic Theory should generally qualify to be used for Training, regardless of whether the mage is improving their lab, inventing a spell, or similar. Now, I have been saying "generally" because there are situations where a mage may be working in the lab and not using Magic Theory at all. For example, a Merinita substituting Faerie Magic for Magic Theory in a season of lab work could not Train an apprentice in Magic Theory, but could Train and apprentice in Faerie Magic.
Back more to the OP, here is what I would do:
This should leave you churning out some really good spells, hopefully in a useful area, though that depends on the field of Minor Potent Magic. In the process of inventing a whole bunch of these good spells you'll also be advancing toward a breakthrough of some sort relatively early in your career.
My objection to this line of reasoning is twofold.
First, the shift from "spending a season earning a living with an ability" to a far broader "spending a season being productive". While I would accept the former becoming "spending a season doing stuff that, for a character supporting himself through work, would count as a season of work" (so yes, a Verditius can train an apprentice in Craft: Blacksmith), it's a big stretch to me assuming this applies to mystical activities too (from labwork to prayer) which have very different mechanics. One of the reasons I am not convinced is that the current wording is about the best compromise one can find between conciseness and clarity if one indeed refers to Craft, Profession, and similiar Abilities; but a much clearer wording would be possible if one meant instead: "During any season in which you claim exposure experience to an Ability, you can train someone else in that Ability."
My second objection is the way Training is worded seems to imply that you can only train someone in an Ability if that's the focus of your seasonal activity. Instead, it seems to me you assume that any Ability contributing to the seasonal activity would count. So, it seems to me that you assume a blacksmith could train an apprentice, during a season of "blacksmith work", not just in Craft: Blacksmith, but also in e.g. Bargain, Folk Ken and Area Lore (crucial when dealing with clients and suppliers), Living Language (you obviously use it), Athletics (if doing lots of hard labour), etc. etc. I do not think this is what's intended by the rules as written. And here's the other problem with training an apprentice in Magic Theory during a season of labwork: while Magic Theory is certainly important, it's not as central to the work done as Craft Blacksmith is to a season of Blacksmithing - because the 2+ Arts involved are at least as important. As I mentioned, this objection would vanish in a season when Magic Theory would really be as central as Craft Blacksmith for a blacksmith's "work season", e.g. a season spent setting up a laboratory (which you need no other Ability or Art to do).
I hope I've been clear!
Just a quick note:
If one has no Magic Theory, you are forbidden from doing Lab work. I'd say that makes it quite central to work done in the Lab, no less than Craft: Blacksmith.
Central yes, but you can play a game where you just leave MT at 1 and continually boost arts. In fact, given the returns on xp for investing in Arts as opposed to abilities, you are generally incentivized to do exactly that.
If you are playing a craftsman, you are playing with the Craft ability. You want better Craft, you put more xp in. Yeah, Magic Theory is required to do any lab work at all, but that is the big commonality in how they are used in practice, with most else being different.
My personal stance is that training xp is usually intended for NPCs, in order to make math work out, and for Companions to have engaging gameplay. If you have a Blacksmith companion and he wants an apprentice, spending 2 seasons working for exposure xp, and then 2 seasons Teaching an apprentice doesn't leave a lot of time to do anything else. But apprentices are fundamentally a part of medieval production with regards to guilds in the paradigm of the time period. Apprentices are fundamentally a part of the job, and in theory should be more asset than liability. So the game allowing a Crafter to fold Training and Work into one season, albeit at a penalty compared to teaching, makes everything work out again.
The concern my table had, which is why we house ruled it fairly extensively, was that mages fundamentally do not have the same time constraints as non-mage characters. There is no obligation to do a season of work in exchange for exposure xp(which incidentally, is sort of how we ruled it. Seasons in which the only xp that can be gained at all is exposure, including spell xp, are generally allowed for training assuming it is for an ability and the main focus of the season).
The assumption of power level in setting assumes to a degree that if you pick up an apprentice as a mage, you are going to need to use some of your seasons helping them directly, by Teaching them. There is an opportunity cost with regards to time. Flat out ignoring that and allowing training xp is fine, assuming the troupe is all agreed on it, but I am of the opinion that it is a noticeable power creep.
I think the key intent with "earning a living" in a season of training is that the person doing the training is only gaining exposure experience, so you cannot train someone while reading a book or even practicing the same skill you are training.
No, that would be so much broader. For example, you can take exposure in PM any season just because you do it twice a day, but you're really not using it the the sort of full-season effort that is intended by the statement. I think we all agree this is way too much.
How do you get that from what I wrote? Now, I maybe wasn't specific enough. You need to be using it over the whole season to do your work, right? For instance, a blacksmith might bargain some, but that wouldn't be a major part of their work.
But for the mage, when working in the lab they would be using Magic Theory for 10 hours a day, mixed with a Form and a Technique, in order to do their productive work.
And you can play a game where you just leave Craft at 1 and continually boost a Faerie Sympathy. But you still get to Train the Craft. (Well, I forget if there is a minimum.)
Actually, I think the rules state that you need MT 3 to be able to use a Lab. So your Magus or even Apprentice, needs to be at MT 3 to do Lab work, except maybe fixing Arcane Connection.
Not to mention that no Magi will leave their MT at 1, or even 3, since their MT is the limit to how many Shape and Material bonuses they can get, and how much Vis they can handle, and it allows you to refine your Lab.
MT 3 is the minimum to set up a lab.
I don't think there is any stated minimum to use a lab.
If you can continually use a Craft in your work and Train it while it is not the majority of your Workshop Total, is there any reason Magic Theory would need to be the majority of your Lab Total? Does the rule for Training even say it has to be the majority of the total? I'm pretty sure, if the Ability is used continually through the season for the work, then it qualifies.
The issue for me is that you "earn a living" with your Craft knowing that Craft and nothing else in the world. You can't do labwork such as enchantment or spell invention knowing Magic Theory and nothing else in the world.
Well, but what do you mean with "used continually through the season"?
You already made clear that in your view (and I agree on that) you can't train someone in Parma Magica by simply executing the ritual together twice a day and shouting at your student when he gets the motions wrong. Now, in my view, those "few minutes every day" could qualify as "used continually through the season", in the sense that there's no single day in the season you are not doing it. How about using an Ability half an hour every day? Two hours?
And how can you tell that someone doing labwork uses Magic Theory ten hours a day? I mean, in principle, it could be used only sporadically, no more often than a few minutes every day at some crucial moments, with most of the actual "work" done instead via the Arts. If I were to imagine a "lab total" for engineers building bridges, theoretical mechanics would certainly be an essential part of it, but an engineer uses theoretical mechanics only a small fraction of the time when building a bridge.
So, it again seems to me that Craft:Blacksmith is more central to a season of Blacksmithing than Magic Theory is to a season of labwork, in that the former is necessary and sufficient, while the latter is merely necessary. Thus, there is no evidence that Magic Theory used in a season of labwork is enough for Training. And the fact the corebook uses something as Craft:Blacksmith as the example for what can be used for training to me is suggestive of it being the minimum level (or the language would have explicitly put the bar lower, in my view).
You can. But, as I've pointed out, you can do this with minimal Craft, pumping Faerie Sympathy, Characteristic, the workshop, a manual, and assistants instead. So only minimal Craft is needed, just like minimal MT is needed. Meanwhile, you can work in the lab with 0s in the Arts and just MT just like you can have 0s in other things and just have Craft. You also need MT to do this at all. And if you're going to say you need your Arts Opened, I'll counter with you need Touched/Mythic stuff to make a living crafting Wondrous Items, and that qualifies for Training, so this extra thing being needed certainly isn't a disqualifying thing.
You cannot do any lab work without it, and the baseline assumption is 10 hours a day in the lab.