Arguing with Atheists
What I mean by "faith" is "accepting something as true and real without having direct experience of it or a perfect proof for it." Many atheists believe that they make no assumptions at all and therefore are "knowers" rather than "believers." This is false, but it is difficult to make them believe (accept as true) that they are operating on belief (unproven assumptions) just as much as religious believers are.
It is ultimately a contest about the right way to understand reason. The Church thinks that we can use our reason to recognize that there is a God (Rom 1:20, solemnly defined as a dogma by Vatican I in 1870). Argumentative atheists believe that reason rules out the existence of God as a conclusion from self-evident principles; if an atheist does not have such an argument, then that person's atheism is simply a matter of presumption--or, in other words, a matter of faith, not reason.
Closed eyes, ears, minds, hearts
Our culture has plucked out its own eyes and plugged up its own ears so that that it cannot hear the gospel and see what it means; then it complains that it can find no evidence to suggest that faith is a reasonable choice. "The lamp of the body is the eye. If your eye is sound, your whole body will be filled with light; but if your eye is bad, your whole body will be in darkness. And if the light in you is darkness, how great will the darkness be!" (Mt 6:23).
Ending the Argument
The Church's teaching that God can be recognized by the right use of reason does not mean that we can convert every atheist we argue with. People have to be willing to be converted in order to let us touch their hearts: "A man hears what he wants to hear and disregards the rest" (Paul Simon, "The Boxer"). God is the changer of hearts. He loves our opponents with His whole mind, with His whole heart, and with all His strength--but He gives His children freedom to resist His Spirit. Those who want to see will see; those who want to hear will hear.
This is one of those many "no rules" situations where all we can do is let our conscience be our guide. When we think that we have made the best case that we can for the Catholic vision of reality, then we may rest from the argument with the knowledge that Jesus does not want us to exhaust ourselves in controversy with those who are unwilling to be converted and healed.
We have Jesus' sayings about "shaking the dust of those towns from our feet" (Lk 9:5) and not throwing pearls before swine (Mt 7:6) to assure us that we may, in good conscience, abandon a fruitless argument. Until then, we should be "as cunning as a serpent and as gentle as a dove" (Mt 10:16) in trying to show our opponents what we mean. It could well be that we are the instrument God has chosen to pierce their defenses. There is no way to tell in the abstract. WE get to make the call about how WE conduct ourselves in the conversation. When we have done all that we personally want to do, then we may say, "We'll just have to agree to disagree."
"Those who sow in tears shall reap rejoicing" (Ps. 126:5). We can't lose by doing the best we can for God, even if we do not see fruit emerge immediately from our labor. We don't plant seeds one day and harvest apples the next. Our job is to sow good seed. After that, it is up to God and to our opponents to do with it as they will.
- Edward Feser, "So you think you understand the cosmological argument?"