Trying to persuade someone to accept as true propositions based upon principles that he does not accept is fruitless. It’s not going to do any good to appeal to the Bible if the other fellow doesn’t accept it as an authority (or if he has no good reason to accept your authority as an interpreter thereof, for that matter). John Paul II discusses this in Fides et Ratio §36:
The Acts of the Apostles provides evidence that Christian proclamation was engaged from the very first with the philosophical currents of the time. In Athens, we read, Saint Paul entered into discussion with “certain Epicurean and Stoic philosophers” (17:18); and exegetical analysis of his speech at the Areopagus has revealed frequent allusions to popular beliefs deriving for the most part from Stoicism. This is by no means accidental. If pagans were to understand them, the first Christians could not refer only to “Moses and the prophets” when they spoke. They had to point as well to natural knowledge of God and to the voice of conscience in every human being (cf. Rom 1:19-21; 2:14-15; Acts 14:16-17). Since in pagan religion this natural knowledge had lapsed into idolatry (cf. Rom 1:21-32), the Apostle judged it wiser in his speech to make the link with the thinking of the philosophers, who had always set in opposition to the myths and mystery cults notions more respectful of divine transcendence.
One of the major concerns of classical philosophy was to purify human notions of God of mythological elements. We know that Greek religion, like most cosmic religions, was polytheistic, even to the point of divinizing natural things and phenomena. Human attempts to understand the origin of the gods and hence the origin of the universe find their earliest expression in poetry; and the theogonies remain the first evidence of this human search. But it was the task of the fathers of philosophy to bring to light the link between reason and religion. As they broadened their view to include universal principles, they no longer rested content with the ancient myths, but wanted to provide a rational foundation for their belief in the divinity. This opened a path which took its rise from ancient traditions but allowed a development satisfying the demands of universal reason. This development sought to acquire a critical awareness of what they believed in, and the concept of divinity was the prime beneficiary of this. Superstitions were recognized for what they were and religion was, at least in part, purified by rational analysis. It was on this basis that the Fathers of the Church entered into fruitful dialogue with ancient philosophy, which offered new ways of proclaiming and understanding the God of Jesus Christ.
We can and must appeal to conscience and to reason until the other man accepts Scripture’s authority or the Church’s. Nothing else will suffice as a means of rational persuasion.