“The Spirit of…?”

One of the simpler, alleged defenses of the Filioque (Calvin used it) is that the Spirit proceeds from the Son as well because the texts often say “The Spirit of Christ.” Doug Wilson used this argument, too.

Calvin argues for the Filioque along the following lines: Calvin notes in Romans 8 that the Spirit is referred to as “the Spirit of Christ” or “the spirit who raised up Christ.” See also II Peter 1:21. (ICR, 1. 13. 18). (Unless I am missing something, this seems to be the extent of Calvin’s discussion of the Filioque, but it’s been years since I’ve read The Institutes–though I have read them through twice so I do know what Calvin is saying).
Grammatically, while admittedly vague, Calvin’s argument is not a stretch in logic. However, it’s not enough to prove a case, either. The following is from Acolyte4236.

There is biblical material that speaks of the Spirit of God and the Spirit of Christ, but this doesn’t help. First, because the Spirit is also God, so if “of” equals “from” then either the Spirit isn’t God or the Spirit is hypostatically generated from himself as well, which is absurd. Second, the Scriptures also speak of the Spirit of truth, but no one thinks that the Spirit is hypostatically generated from the divine “attribute” of truth.