Univocal reasoning: William Edgar, commenting on Van Til writes, "we speak of all forms of reasoning in which man is assumed to be the final or ultimate reference point of predication as univocal reasoning."
Analogical reasoning: "In contrast to univocal reasoning we speak of the form of reasoning employed by the Christian who recognises that God is the ultimate reference point of predication as analogical reasoning."
All men know God exists because God has revealed it to them (Romans 1). Unbelievers know God, yet refuse to honour Him as God and hence argue univocally. They wilfully choose to suppress the knowledge of God (Romans 1). Christians, being regenerated by the Holy Spirit do not reason univocally. They reason analogically and hence regard God as ultimate (Proverbs 1:7; 2 Corinthians 5:18; Colossians 2:3-8; 1 Corinthians 1:20). Isn't it the case that every time we sin, we reason about it in a univocal manner the same way unbelievers do? For example, when we are being tempted and sometimes fall into sin, it's never because we really don't want to sin. We somehow justified that sin and chose to believe the lie over the Truth. (Romans 7:15) Refusing to turn our minds toward God, we believe the lie, argue (in a univocal manner) that it will make us happy (regarding ourselves as ultimate) and that true happiness is not found in God, and hence commit the sin. Now, as we are regenerate Christians, we KNOW that sin won't make us happy and that true happiness can only be found in God, but we suppress the truth of this when we sin and believe the lie. We believe (for the moment) that God is withholding pleasure or happiness*. (James 1:14-15; Romans 15:13)
In the same way, unbelievers KNOW God exists and they that ought to serve Him and give Him glory, but they suppress the truth of this in a constant way and choose to believe the lie over the Truth. As a result their hearts are darkened and their thoughts become futile. (Romans 1:21)
The only difference between the Christian and the unbeliever is the regenerative work of the Holy Spirit. So, the unbeliever is in a constant state of reasoning in a univocal manner despite knowing better. (Van Til regularly states that men ought to know God, but don't). They rebel constantly whereas Christians rebel only when we sin. Our new normative is that of being a slave to Christ, and hence, thinking analogically. Whereas the unbelievers are slaves to sin.
* Sin makes promises to your children, your clients. Sin promises them, “What I have to offer is better, more satisfying, more enjoyable, more hope-giving than Christ.” Hebrews 11:25 calls this “the fleeting pleasures of sin.” Sin promises to be better, longer, deeper, sweeter, more satisfying. And to the degree that we are deceived by those promises, we sin. Nobody sins out of duty, right? Nobody gets up in the morning and says, “I have an obligation: I have to sin some today.”
No, nobody sins out of duty. We sin out of pleasure-seeking. And the only reason we opt for a sinful action is because the devil and our own nature has promised us that action will produce pleasure, satisfaction, fame. Whatever your idol happens to be, the promise is that it will succeed. (desiringgod.org)