Do Caster Levels from different sources stack?

Question

This seems like a glaring oversight, but what are caster levels? Do characters only have one score called caster level just like sneak attack? Why do most classes not state what their caster level increases are? Do all arcane and divine caster levels stack? What about just all arcane caster levels?

I have been playing Spheres of Power lately and it clearly defines when caster levels are gained and how they stack with caster levels from other classes (at least other SoP classes). It got me wondering about original caster levels. So I started doing research.

Under the magic rules for caster level

A spell’s power often depends on its caster level, which for most spellcasting characters is equal to her class level in the class she’s using to cast the spell.

Paladins are one of the exceptions which within their own rules state what the CL of the class is suppose to be.

Through 3rd level, a paladin has no caster level. At 4th level and higher, her caster level is equal to her paladin level – 3.

But the core casting classes of Cleric, Druid, and Wizard have no statement on how their CL increases as you progress in the class so I guess we are forced to assume its equal to the levels in that class.

Under the common terms is another definition of caster level

Caster level represents a creature’s power and ability when casting spells. When a creature casts a spell, it often contains a number of variables, such as range or damage, that are based on the caster’s level.

Finally we have the Mystic Theurge which does seem to have mention that classes have their own isolated caster levels.

This essentially means that he adds the level of mystic theurge to the level of whatever other arcane spellcasting class and divine spellcasting class the character has, then determines spells per day, spells known, and caster level accordingly.

As shown in the FAQ/Editors Note

The increase to his spellcasting level does not grant any other benefits, except for spells per day, spells known (for spontaneous casters), and an increase to his overall caster level.

So would a cleric 1 wizard 1 have an overall caster level of 2, or would each class have their own caster level? What about a cleric 1 and druid 1?

Answer 1

Each class has its own caster level, which is usually equal to its class level. Revisiting your first quotation,

A spell’s power often depends on its caster level, which for most spellcasting characters is equal to her class level in the class she’s using to cast the spell.

^{(emphasis mine)}

The spell’s caster level is equal to the caster’s level in the class casting that spell. The spell’s caster level, usually, pays absolutely no mind to the caster’s level in any other class. When a 1st-level cleric/1st-level druid/1st-level wizard casts a cleric spell—which, to be clear, is a spell prepared in a cleric spell slot, regardless of whether or not that same spell also appears on the druid and/or sor/wiz lists—that spell’s caster level is 1st, the cleric/druid/wizard’s cleric class level. Likewise with druid or wizard spells, using those class levels respectively (all 1st in this example).

The cleric, druid, and wizard class descriptions don’t specify any of this: the general rule in the first quotation instead supplies a default, which none of those classes change. Ergo, they use their full class level as the caster level for their spells. The paladin, on the other hand, does something different from the default, and so its description has to address that change explicitly.

As you note, mystic theurge—as well as all other spellcasting-progression prestige classes, which specify that you have to pick one class to progress—would make no sense if caster level were a property of the character, rather than a separate property for each spellcasting class.

Finally, the common terms definition is context-free and intentionally abbreviated; it is for a reminder, not for the official rules or in any way intended to overrule anything else. It has no place in this discussion.