What is important to understand is that the gifts of the Holy Spirit operate in conjunction with the human spirit(pneuma). Paul is not suggesting he is merely praying with his own intellect, or his own 'spirit'; rather, when one operates in the gifts of the Spirit one must understand the Context one is operating in.
Before we delve into Chapter 14, which talks about Context, we must 1st read Chapter 12:
Now there are diversities of gifts, but the same Spirit. 5And there
are differences of administrations, but the same Lord. 6And there are
diversities of operations, but it is the same God which worketh all in
all. 7But the manifestation of the Spirit is given to every man to
profit withal. 8For to one is given by the Spirit the word of wisdom;
to another the word of knowledge by the same Spirit; 9To another faith
by the same Spirit; to another the gifts of healing by the same
Spirit; 10To another the working of miracles; to another prophecy; to
another discerning of spirits; to another divers kinds of tongues; to
another the interpretation of tongues: 11But all these worketh that
one and the selfsame Spirit, dividing to every man severally as he
Nowhere in the above paragraph do we see Paul refuting the gifts of the Spirit, and the same word Πνεῦμα is used-except capitalized to represent the Holy Spirit. However, in Chapter 14, he is talking about "When you come together.."(vs 26), there is an order in which the church should express itself, and that in a public setting with unbelievers in the audience;(vss 23-25)
If therefore the whole church be come together into one place, and all
speak with tongues, and there come in those that are unlearned, or
unbelievers, will they not say that ye are mad? 24But if all prophesy,
and there come in one that believeth not, or one unlearned, he is
convinced of all, he is judged of all: 25And thus are the secrets of
his heart made manifest; and so falling down on his face he will
worship God, and report that God is in you of a truth.
Paul does not discount tongues; in vs 27 he says,
If any man speak in an unknown tongue, let it be by two, or at the
most by three, and that by course; and let one interpret.
He can pray in tongues "more than you all" and he is saying that in truth. But his understanding is unfruitful, therefore he is only edifying himself, rather than the church at large, which is the whole point of Chapter 14.
If Paul prayed in tongues(which he says he does), and it is "unknown"-meaning he doesn't understand what he is saying, then it is a "him and God" dialogue, which is not profitable for a Sunday Morning Worship Service. It is important to note that, "He that speaketh in an unknown tongue edifieth himself"(vs 4), so to speak in tongues without understanding indeed edifies the individual, therefore, one is certainly encouraged to do so-providing it doesn't become a message for the church at large.