The basic laws of logic are neither arbitrary inventions of God nor principles that exist completely outside God’s being. Obviously, the laws of logic are not like the laws of nature. God may violate the latter (say, suspend gravity), but He cannot violate the former. Those laws are rooted in God’s own nature and govern His own mind. Indeed, some scholars think that the passage “In the beginning was the Word (logos)” (Jn 1:1) is accurately translated “In the beginning was Logic (a divine, rational mind)”. For example, even God cannot exist and not exist at the same time; He cannot both love and hate Jesus Christ; there cannot be one God, no God and many Gods. And even God cannot validly believe that red is a color and red is not a color or that 2+2=73. Divine omniscience is defined as the idea that for all truths, God knows and believes each one, and for all falsehoods, God knows each is false and does not believe it.
Consider Matthew 22:23-33 where the Sadducees raise a reductio ad absurdum argument against Jesus. In such an argument you grant your opponent’s premise, show that it leads to an absurd conclusion, and argue, therefore, that the granted premise should be denied. The argument is also an example of a dilemma syllogism (see below): Formally, the Sadducees argue thusly: If P (there is life after death), then either Q (adultery is permissible in the afterlife) or R (polygamy is permissible in the afterlife). Not-Q (adultery is not permissible, period) and not-R (polygamy is not permissible, period). Therefore, not-P (there is no life after death).
Grasping the heart of this syllogism, Jesus skillfully notes that the either/or dilemma his opponents have placed on him (either adultery or polygamy is permissible in the afterlife) both make an assumption: There is marriage in the afterlife. They argue: If there is marriage in the afterlife, then either there is adultery or polygamy. Jesus denies that there is marriage in the afterlife (Matthew 22:39), and in one simple step, he undermines the dilemma (either adultery or polygamy) they have raised against life after death.
In Mark 11:27-33, Jesus himself uses a dilemma syllogism. Put formally, such a syllogism goes like this: (1) (If P then Q) and (if R the S), and (2) either P or R, then (3) either Q or S. In context, the religious leaders are challenging Jesus’ authority, and he asks, “Was the baptism of John from heaven or from men?” His argument is this: (1) (If John’s baptism is from heaven, then the critics ought to believe John’s teaching about Jesus) and (If John’s baptism is from men, then the critics are in danger from the people). (2) Either John’s baptism is from heaven or from men. Then, (3) the critics should either believe John’s teaching or place themselves in danger from the people. Realizing that Jesus had successfully placed them on the horns of a nasty dilemma, they responded by saying “We don’t know from where John’s baptism came.”
To my mind, Jesus was the greatest thinker who ever lived. And while he did not come to develop a theory about logic or to teach logic as a field of study, it is clear that he was adept at employing logical forms and laws in his thinking and reasoning. We who are his followers should go and do likewise.