Fuerza is correct! The concept of “double procession” is, in fact, not what the
filioque was designed to teach. Rather, the
filioque was inserted into the Creed in Spain to counter a version of Arianism that had come to Spain from Germany. The teaching that was erroneous said that the Holy Spirit was not the same as the Father or the Son. We have to recall that the Creed originally taught only the nature of the Father and that the Son was
homoousias (of the same nature, *consubstantionis) *with the Father. The nature of the Spirit was not directly addressed. Thus, the Spanish addition was designed to preclude the erroneous teaching.
Unfortunately, it was, itself, subject to such errors as the teaching of the double procession. Generally, the Latin Fathers understood this teaching as saying that the Holy Spirit is
spirated by the Father but sent to us
through the Son. Thus, the teaching that the Holy Spirit is from the Father through the Son.
There is ample support for this understanding in the Catechism as well as in
recent documents dealing with the Orthodox on this issue.
Deacon Ed