Related to this Question.
In the linked question I asked how a spell I am granted as known by some ability is treated when the spell is normally of a level higher than the highest level I can cast.
To only ask one question at a time I want to separately ask: Is it possible (allowed by the rules) to have a spell known that is of a spell level you can't cast yet?
Conceivably, the typical wizard could have a whole spell volume filled with spells that were copied from scrolls or from other wizards' spellbooks that the wizard understands but cannot yet cast (see Adding Spells to a Wizard's Spellbook on Spells Copied from Another's Spellbook or a Scroll). Likewise, a typical alchemist can be in the same position as the wizard with the alchemist's formula book plus a rules quirk allows an alchemist to have, technically, started play with one or more formulae in his formula book that he can't cast. (That is, unlike the wizard that enters play having selected "a number of additional 1st-level spells equal to his Intelligence modifier to add to the spellbook," the alchemist enters play having picked "two 1st level formulae of his choice, plus a number of additional forumlae equal to his Intelligence modifier," with no level limits! Good for trading with high-level alchemists in an alchemist-heavy campaign, perhaps?)
The same can happen to a caster that casts spells without preparation. For example, a 2nd-level sorcerer can happen upon an extremely valuable page of spell knowledge (wish), but while "that spell [is] on her class spell list," the sorcerer can't "use her spell slots to cast that spell as if it were one of her spells known" as she has no 9th-level spell slots yet!
Allowing a caster to have knowledge of a spell he can't yet cast permits the GM to develop plots that will hinge on the character being able to cast those spells later. Further, such access doesn't leave the player feeling utterly cheated, for example, after his low-level character finds a high-level wizard's spellbook filled with low-level spells the character already knows: the character can transfer the higher-level spells into his own book so that he needn't pick such spells himself upon advancing levels.
Yes, why couldn't you?
Actually note that "to know a spell" doesn't mean the same thing for all casters. For example:
Clerics don't have "known spells": they just have spells or their list and can cast them.
Wizards have to write them on their spellbook and for that have only one restriction: to learn a spell (with the regular way) they must have an Intelligence score equal to at least 10 + the spell level. That doesn't prevent a 16 Int wizard to get a 7th level spell from some other capacity if it doesn't precise the wizard has to learn it.
The way to acquire spells for different casters varies, but nothing (no rule) forbids someone to actually know a spell of a level too high for him to cast it. (even if he still won't be able to cast it).
