Paul’s drift is to teach what God is. Furthermore, because he hath to deal with profane men, he draweth proofs from nature itself; for in vain should he have cited testimonies of Scripture. I said that this was the holy man’s purpose, to bring the men of Athens unto the true God. For they were persuaded that there was some divinity; only their preposterous religion was to be reformed. Whence we gather, that the world doth go astray through bending crooks and boughts, yea, that it is in a mere labyrinth, so long as there remaineth a confused opinion concerning the nature of God. For this is the true rule of godliness, distinctly and plainly to know who that God whom we worship is. If any man will intreat generally of religion, this must be the first point, that there is some divine power or godhead which men ought to worship. But because that was out of question, Paul descendeth unto the second point, that true God must be distinguished from all vain inventions. So that he beginneth with the definition of God, that he may thence prove how he ought to be worshipped; because the one dependeth upon the other. (John Calvin, Commentary Upon the Acts of the Apostles; emphasis added)
Richard Muller points out (in PRRD Vol. 3, p. 174) that Calvin considered it proper for Paul to begin his Areopagus address with proofs drawn from nature – even citing the pagan Aratus as an authority. I find it interesting that both Calvin and Aquinas seem to adhere to a similar notion of demonstration: pagans do not respect the Scriptures, so we must use reason. Aquinas says:
But on two accounts it is difficult to proceed against individual errors: first, because the sacrilegious utterances of our various erring opponents are not so well known to us as to enable us to find reasons, drawn from their own words, for the confutation of their errors: for such was the method of the ancient doctors in confuting the errors of the Gentiles, whose tenets they were readily able to know, having either been Gentiles themselves, or at least having lived among Gentiles and been instructed in their doctrines. Secondly, because some of them, as Mohammedans and Pagans, do not agree with us in recognising the authority of any scripture, available for their conviction, as we can argue against the Jews from the Old Testament, and against heretics from the New. But these receive neither: hence it is necessary to have recourse to natural reason, which all are obliged to assent to. But in the things of God natural reason is often at a loss. (Thomas Aquinas, Summa Contra Gentiles, I.II, a.3, 4)
Notice also that Calvin did not consider the pagans to need demonstration of God’s existence but they needed their religion to be reformed. The demonstration of the true God was Paul’s starting point not for the purpose of exposing the quiddity of God in a way that could be grasped apart from faith but “that he may thence prove how He ought to be worshipped” since the one depends on the other. Thus, there still remained in Calvin a tinge of the Schoolmen’s high view of reason. And, with a bit of negative theology, perhaps inherited from St. Augustine or St. Bernard, Paul’s purpose is seen to teach what God is. Paul taught what God is precisely by teaching what he is not: a man-made image.