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Okay,so I have an occultist, and I've run into this one problem, and none of my friends or I can parse it out. Either there is a printing error in the book, or I'm just not getting it, or whatever.
So let's start off by defining our terms:
Spell List: Throughout most of the pathfinder books, a "Spell List" refers to the list of spells that a class CAN cast, conceivably. That is to say, a level 20 caster with a sufficient casting stat could cast that spell, if they learned it/chose it/whatever.
If a spell is on your spell list, you don't have to UMD a wand of it, and you don't have to UMD a scroll of it (though you might have to make a caster level check if the spell on the scroll is not something your character can cast yet.)
List of Spells Known can refer to two things: It either refers to the spells that a spontaneous caster (like a sorcerer) actually can cast (as in, the spells they know and can cast without needing a scroll, wand, etc.), or it can refer to the spells in a particular wizard/archaist/magus/yadda yadda yadda's spellbook.
Here's where it gets tricky. An Occultist's list of spells known, and spell list, changes over their career.
An occultist casts psychic spells drawn from the occultist spell list, limited by the implement groups he knows.He can cast any spell he knows without preparing it ahead of time. Every occultist spell has an implement component (see Implements). To learn or cast a spell, an occultist must have an Intelligence score equal to at least 10 + the spell level. The Difficulty Class for a saving throw against an occultist's spell equals 10 + the spell level + the occultist's Intelligence modifier.
An occultist can cast only a certain number of spells of each spell level per day. His base daily spell allotment is given on Table: Occultist. In addition, he gains bonus spells per day if he has a high Intelligence score.
The occultist's selection of spells is limited. For each implement school he learns to use, he can add one spell of each level he can cast to his list of spells known, chosen from that school's spell list. If he selects the same implement school multiple times, he adds one spell of each level from that school's list for each time he has selected that school.
When the occultist learns to cast a new level of spells, he immediately adds one spell of that level to his list of spells known from each implement school he knows (plus any extra spells from schools he has selected multiple times).
At 5th level and every 3 occultist levels thereafter (8th, 11th, and so on), an occultist can choose to learn a new spell in place of one he already knows. In effect, the occultist loses the old spell in exchange for the new one. The new spell's level must be the same as that of the spell being exchanged, and it must be at least one level lower than the highest-level occultist spell the occultist can cast. The spell learned must come from the same list of spells provided by the implement school of the spell lost. An occultist can swap only a single spell at any given level, and must choose whether or not to swap the spell at the same time that he gains new spells known for that level.
An occultist need not prepare his spells in advance. He can cast any spell he knows at any time, assuming he has not yet used up his allotment of spells per day for the spell's level.
At 1st level, an occultist learns to use two implement schools. At 2nd level and every 4 occultist levels thereafter, the occultist learns to use one additional implement school, to a maximum of seven schools at 18th level. Each implement school adds one spell per spell level of that school of magic to the occultist's spell list. No spells from any other school are considered to be on the occultist's spell list until he selects the associated implement school. He can't use spell trigger or spell completion magic items from unknown schools without succeeding at the appropriate Use Magic Device check. An occultist can select an implement school more than once in order to learn additional spells from the associated school.
(Snip)
So, that's a lot of text, but the tl;dr version is this:
It says that the only spells that you have chosen as your SPELLS KNOWN are on your SPELL LIST (In other words, you cannot use scrolls/wands of spells you don't know because they aren't considered on your SPELL LIST.)
Then it goes on to say that only spells of unchosen schools are not on your SPELL LIST.
So, trying to parse this, there are three interpretations.
1) The worst way (for players)
When you chose an implement, you choose spells known. Those spells are the only spells to be considered on your spell list. As you gain new levels and gain access to new spell levels, you gain access to new spells which are then considered on your spell list, but only the ones you've chosen.
2) The average way (in-between)
When you chose an impliment, choose 7 spells (0th lvl to 6) from that impliment's school. Those spells are considered on your spell list, and those are the spells you will learn when you hit the appropriate level.
3) The best way (for players) The line:
"Each implement school adds one spell per spell level of that school of magic to the occultist's spell list."
Should read something like:
"Each implement school adds one spell per level of that school to an occultist's LIST OF SPELLS KNOWN. Choosing an implement also adds all that implement's school's spells to an occultist's spell list for the purposes of using wands or other magic items. Note that an occultist must have an appropriate spell slot to cast that spell (thus a first level occultist would have two implements, and know two sixth-level spells, but cannot cast them until at least level 16"
I believe you have spotted a printing error. To take any approach other then your third option would set the occultist at odds with every other class. it isn't like the class has a dazzling array of class abilities to offset such a disadvantage.
It really does seems to be an editing mistake. It seems pretty clear to me that, as you suggest, "Each implement school adds one spell per spell level of that school of magic to the occultist's spell list" is meant to say "Each implement school adds one spell per spell level of that school of magic to the occultist's spells known."
That makes it match the earlier statement "For each implement school he learns to use, he can add one spell of each level he can cast to his list of spells known, chosen from that school's spell list." And as Haldrick says, it makes the Occultist match the rules for other casters.
As I see it, a first level Occultist who selects the Divination and Transformation Implements would know one cantrip and one first level spell from each of those two Implement lists, would be able to use Scrolls or Wands for any spells on those two lists, but would have to use UMD if they were from other Implement School lists.
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I was just hunting around for an answer to this same question. It seems like most people agree on how this should work, but has there ever been official word from Paizo? I'm thinking of making an occultist for PFS, and I don't want to run into table variation on whether or not I can use a wand of CLW after taking a conjuration implement.