Arbitrariness and inconsistency are two signs of a failed worldview. There are others to consider, but these two are major ones to look out for. Ultimately, we want to seek to avoid both of these as we formulate our worldviews and arguments for our perspectives. Additionally, it will help if when we are doing apologetics, we also hold our opponents to these standards. Ironically, there is no reason why these standards should be followed from within a non-Christian worldview, but as all people are created in the image of God unbelievers often seek to follow these standards as well. The Christian worldview requires us to hold to these standards as human beings are created in the image of God, and these principles reflect God's character.
Arbitrariness comes from the adjective: arbitrary. It is defined as follows:
1 based on random choice or personal whim.
Now, I can think of a number of reasons why somebody might do this. Perhaps you don't like me very much and tearing the money up was a way to spite me. Or maybe you are trained at spotting fake money and knew instantly that it was counterfeit. Maybe the reason is even something absurd - you think all $100 bills are poisonous if they are kept on a person for more than 5 seconds. ALL of these reasons are better than tearing the $100 bill up arbitrarily.
If you indeed had no reason whatsoever for tearing the money up and your decision was completely arbitrary, it is worse than if you believed it was poisonous. You see, arbitrariness means making a decision completely randomly and without reason. It is worse than even absurd or failing reasons, because it has no justification whatsoever. Nothing we do in life is arbitrary. Even attempting to do something spontaneously arises out of an inner desire to escape, be free, or be "fun." As such, to believe something arbitrarily runs completely counter to how God created logical and rational creatures in his image. It is like having your web of beliefs in one area and an isolated belief in another that is not derived at all from your web. It is a subversive attempt in thought to return to the false "marbles in a jar" perspective on worldviews.
Christians often believe things arbitrarily. This is unfortunate as it is a major intellectual sin. Sometimes they believe things arbitrarily that are true and sometimes things that are false. This is often due to emotional reasons or considerations. For each of those true beliefs we have that we believe arbitrarily, we should seek to ground those beliefs in the ultimate authority of our worldview, the Bible, thus no longer making them arbitrary. For each of those false beliefs that we hold to arbitrarily, we should reject them and order our lives in such a way as to match true and justifiable beliefs. To find out which beliefs are true and which beliefs are false, we also must consult our bibles.
Now, don't misunderstand me here. I am not advocating rationalism nor dismissing the necessity of faith in the Christian worldview. I am advocating an examining of your individual beliefs to make sure that they fit within your worldview appropriately.
Non-Christians are often arbitrary in their beliefs as well. This is the case necessarily as only the Christian worldview can make sense of all of reality. However, unbelievers also believe both true and false things. The true things are arbitrarily believed, as they do not ground their belief in the Bible, the false things are sometimes tied to their (also false) ultimate authority (thus those are not arbitrary), and are sometimes arbitrary as well.
Let's move on to deal with inconsistency:
1 not staying the same throughout.
▶ acting at variance with one’s own principles or former behaviour.
2 (inconsistent with) not compatible or in keeping with.
Inconsistency is deadly because if two things that are contradictory can both be true at the same time, then truth and objectivity are demolished and we can believe anything that we want. The laws of logic are completely destroyed by inconsistency, which ultimately destroys knowledge itself.
This sin is often visible in the lives of Christians when it pertains to things they are believing arbitrarily. This is because the Bible itself is perfectly consistent. If the believer is making sure that all of his beliefs are grounded in his absolute authority - the Bible - then he will not believe anything inconsistently.
In the lives of unbelievers, inconsistencies run rampant. This is because they have often not made any sort of concerted effort to maintain an absolute authority and to derive their beliefs from it. Typically, unbelievers choose to believe things just because it makes sense to them. For example, naturalistic materialism destroys any foundation for things that are metaphysical in their nature. However, naturalistic materialists will often affirm the existence of immaterial things such as laws of logic, morality, and love. This demonstrates fundamental inconsistency. However, this inconsistency is unavoidable to them because they are created in God's image.
In philosophy, arbitrariness and inconsistency are not allowed. If you can prove that somebody is believing in something arbitrarily or that they are being inconsistent among their own beliefs, then you win. It does not matter if they are convinced by your argument or not. If they are being arbitrary or inconsistent then they either have no reason to believe what they say they do, or they contradict themselves. Both run counter to and destroy the image of God in man, and nobody can live their lives either arbitrarily or inconsistently. Pray for them, that God would bring conviction over their intellectual sins.
Additionally, as Christians, we should also never believe anything arbitrarily or inconsistently. It would behoove each one of us to examine our belief system and see if we are guilty of either of these sins and repent and seek God's forgiveness on the topic.