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The thaumaturge is confusing. The class progression table has "invocations" at several levels, and the entry for the ability does not state how many they know:

Thaumaturges control power in its purest form; whether through bargains with outsiders, the summoning of primal spirits, or simply an untamable spark in their soul, a thaumaturge can invoke a limited amount of truly wondrous power.

A thaumaturge may use invocations a number of times per day equal to his casting ability modifier, which refreshes when he rests to regain spell points. Whenever an invocation calls for a saving throw, the DC is equal to 10 + 1/2 the thaumaturge’s level + the thaumaturge’s casting ability modifier. A thaumaturge may only use invocations of his level or lower. Using an invocation is a free action that may be taken even when it isn't the Thaumaturge's turn.

I checked in the extra X feat section, and extra invocations only allows 2 more daily uses.

So I am prone to believe they know all invocations, but given the pattern from other PF/SP classes of pick N from the list below at the given levels the thaumaturge may seem to follow this, from the table progression.

Does a thaumaturge knows all invocations up to the class level they can cast?

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Yes, you know all of them

Invocations have a minimum required level to be used, so a 1st level thaumaturge can only use Meditation, Lingering Pain and Lingering Blessing. Once they reach 3nd level, both Empowered Defense and Empowered Attack will unlock. Then 4 levels later (7th) they will unlock Channel Punishment. And so on, unlocking new Invocations every 4 levels in the class.

So, it may seem like they have too many abilities, but they are unlocked gradually, not all at once. This is similar in design on how bards and skalds gain their new songs automatically once they reach a certain level.

You will also notice that thaumaturges gain magic talents similarly to half-casters like the Armorist or Mage Knight, capping at 10/11 talents. But they have a full caster level progression, like the Fey Adept or Soul Weaver, which cap at caster level 20. This means that the class, though a full caster, is not as versatile as other full caster classes, and they balance that out with their Invocations.

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