This Latin dictum means “the finite does not (or cannot) comprehend the infinite.” The phrase originated in the Lutheran-Reformed debates about the Lord’s Supper as it related to Christology. The Reformed typically accused the Lutherans of transferring divine qualities to Jesus’ humanity such that Christ could be everywhere, including the Lord’s Supper. Sometimes this resulted in the charge of Eutychianism (mixing Christ’s human and divine natures). The Lutherans typically accused the Reformed of rationalism as well as Nestorianism. The former was thrown at the Reformed because they thought the Reformed depended too heavily on philosophical pre-commitments. There was also the problem of supposedly separating Christ’s human from His divine nature (Nestorianism).
The phrase “finitum non capax infiniti” is related to what is called the “extra Calvinisticum.” The latter phrase refers to the fact that Jesus as God is everywhere, whereas Jesus as human is in heaven at the right hand of the Father. The “extra” then refers to the omnipresence that the divine has outside the human body of Jesus. I just read a brief but interesting article by a Lutheran pastor on this issue, and his claim is that the Lutheran view does not entail a change of the human nature, but rather a display of the very infinity of the divine. He defines the Lutheran capax this way:
In order to see this, it is important to observe what is meant by the Lutheran capax. As the Swedish Lutheran theologian Gustaf Aulén notes, the Lutheran argument is not that the finite has some sort of inherent capability of containing the infinite, but rather that the infinite God is capable of communicating himself to the finite.
This is how he attempts to avoid the communication of divine attributes to the human. He says further, “if the infinite is truly infinite, then it must logically contain an infinite number of possibilities and one of these possibilities must be being contained by the finite.” There are several things that need to be said in response. Firstly, there is simply no way for the infinite to communicate itself to the finite without bursting the boundaries of the finite. We are talking here about the incommunicable attributes of God. So, while initially sounding plausible, the author has not answered the question. Instead, he has tried to shift the question.
Secondly, in answer to his hypothetical situation of the infinite needing to have “being contained by the finite” as a possibility, this fails to take into account the other attributes of God. He is singling out one attribute and separating it from the others. The other attributes include an inability to deny Himself. That God would not communicate divine attributes to the human is not due to inability, but rather to character. This question is in the same category as the age-old conundrum “Can God build a rock so big that He cannot move it?” The answer is no, but not because of a lack of ability on God’s part, but because it is not in God’s character to contradict Himself.
If God communicated the divine to the human, the simple fact remains that the human would no longer be human. It must be noted here that very few Lutherans seem to grasp Calvin’s actual doctrine as expounded by, say, Keith Mathison. We have all the divine and the human that we need in Calvin’s construction of the mechanism of the Lord’s Supper. The Holy Spirit bridges the gap between us and Jesus such that Christ’s humanity is fed to our souls by faith. So Christ is physically given to us in the Supper, but not in the bread and wine. Our reception of it is (S)piritual.