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In Mark 13:32, Jesus says that no man knows the day or hour, not the angels, not even the Son, but only the Father. The limit in the knowledge of Jesus is sometimes explained by saying he was speaking from His humanity, and that there are many more examples in Scripture that He was not omniscient in His humanity.
But what about the inference to be drawn from this passage that the Holy Spirit does not (or at least did not) know the day or hour either?
This is related to another matter, actually, that of places where Jesus somehow seems to be ignorant of things -- leading to the question, "How can Jesus be God, yet not know things (i.e., not be omniscient)?" This includes cites like Luke 8:43-5 (where Jesus does not know who in the crowd touched him).
My own ruminations in this area lead me to believe that the typical answer -- that Jesus emptied himself of his power, while making a good point, does not go far enough -- partly because it doesn't explain the Holy Spirit's implicit "ignorance" in Mark 13:32.
What I believe is happening here has to get into some Trinitarian theology, and the crossover temporality of two members of the Trinity which requires them to divest themselves of certain abilities -- what we refer to, in terms of Christ, as a kenotic emptying (Phil 2:6-11).
Note that this should be viewed in line with the "dual nature" (human/divine) of Christ and NOT the "kenotic heresy" which misuses Phil. 2:6-11. In the view being explained here, Christ's "human nature" is the kenoticized one. The divine consciousness remains intact but is not accessed or used under typical circumstances. To put it another way, the incarnated Jesus is divine Wisdom with "half its brain tied behind its back." The attributes are accessible, but not used.
The key for me lies in the verses that indicate a "subordinate" position of Jesus to God the Father. (Like, "The Father is greater than I.") Skeptics often ask how this equates with Jesus being "God" -- the question misses something; we regard Jesus as "God the Son". More literally, Jesus is the Word and Wisdom of God incarnate. (It would take too long to explain here, but for a good start, see my article on Wisdom linked below.)
Now if Jesus is the "Word" of God, and subordinate to God, then Jesus is dependent upon God the Father for his existence. If the Father ceased to exist, so would Jesus. My thought on this related to Mark 13:32//Matthew 24:36 is that Jesus does not know the day or the hour because the Father has not yet "spoken" the word yet (in the temporal realm, related to the human nature; this does not speak to knowledge in the eternal realm and the divine nature) that declares the day and hour.
But Christ "emptied" himself of his divine power to come to earth -- as would be needed, for had he not done so, even practically speaking, it would destroy the world. So in this context, the Father has given some signs to look for, but that is all. (By the way, I hold to a preterist view of this passage, but it doesn't make any difference in the context of this discussion.)
Now shift over to the Holy Spirit. The role of the Spirit is as the person of God's creative power and effect, but it is quite clear that the Spirit is subordinate in the same sense that Jesus is, and so subject to the same restrictions in "knowledge" (again, in the temporal realm) that the Son is -- again, were it otherwise, the awesome power of God would destroy all in this world it came in contact with (notably we sinful humans).
In other words, it may be proper as well to speak of the Holy Spirit undergoing a kenotic "emptying" of his own in order to do its work on earth. It may be that the Incarnation involved, for the Word, an even greater emptying. But this is all speculative, based on philosophical considerations; and it is only implicitly supported by Scripture. However, I do think it is sound in principle.
A scholar gave me another interpretation, noting 1 Cor. 2:11, "For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God." This argues that in Mark 13:32, the Spirit is included in the range of the Father by implication. While I find this a little contrived, and think 1 Cor. 2:11 does not of necessity imply exhaustive knowledge, others may accept it as a viable option.