The same world is viewed differently by different people. Religious people, atheists have their own beliefs according to which they justify the happenings in the world. People stick to their belief systems most of the times. When confronted with contrary evidence, they try to shut it out of their view.
People also have different levels of thinking capabilities. Some can go deep using a particular set of rules and can find inconsistencies in them. Others who cannot go deep are comfortable having opinions which are contradictory.
The beautiful nature of human mind is its ability to hold thoughts which are contradictory as long as it doesn’t perceive them to be inconsistent. This is what makes life move ahead even when faced with difficulties.
Each of us start with a set of axioms we believe in. As we face experiences in life, situations arise where we need to consider our axioms and derive some conclusion from them leading to some contradiction with the event at hand. Note that life always throws things at us so that we don’t have the luxury to derive conclusions from our axioms at leisure. We have to eat, sleep, work and etc. Hence only when faced with some urgent issue, we get to derive that conclusion.
Now, when faced with such situation, we may try to hold on to our axioms and defend them blindly. This may lead to arguments. But over time, when we repeatedly face the same contradiction, we change our axioms which cause the conflict. We may adjust to very similar axioms of others which can justify that particular outcome.
This way we keep on evolving in terms of our worldview. But again, as we repeatedly face everyday situations, we don’t get the luxury to explore all possible conclusions of our new set of axioms. And the cycle repeats.
Difficulties arise when people who have radically different set of axioms come into contact. Both can explain some aspects of the world and both have some limitations. But both cannot co-exist. Also, there is no logical way to disprove others’ axioms without assuming truth to one’s axioms and vice-versa. This leads to conflicts.
Some people may shift from one such perspective to another one. It may be due to bowing down to majority opinion when others are in majority, or an inherent desire to disobey the rules in which they are born into. Or it may be due to brainwashing where repeated exposure to the other perspectives makes one believe in their conclusions.
On the other end of the spectrum are people who are hard to change. Even if their peers change, they try to stick to their set of beliefs.
Whether we believe in some axioms or the other, we assume the world is consistent in some ways that can be explained by those axioms.
But is it really the case?
Take the real numbers between 0 and 1 e.g. 0.023, 0.045 … etc. Cantor’s diagonalization argument shows that natural numbers cannot be mapped to real numbers through bijection. Natural numbers correspond to the set of thoughts or the conclusions that we can derive from them. For e.g. we can number our axioms from 1, 2, and so on say 100. Each derivation of a conclusion involves some steps, which too can be numbered as 101, 102 etc. Now, if the conclusion is a real number, it gets a corresponding natural number N. Since the whole set of natural numbers cannot have bijection to Real numbers, their subset too cannot. Hence, we cannot derive real numbers, ie we cannot explain real numbers using our axioms.
Now the world is clearly composed of more than real numbers. Hence the world which is a superset cannot too be explained by our axioms.
The number of real numbers is called N1. Can we have N1 number of axioms to start with? Our brains have a finite size; hence they cannot produce infinite thoughts. But again, Penrose says consciousness arises at quantum levels. Hence, if thoughts correspond to consciousness, and since quantum states can be in complex superpositions, we can potentially have infinite axioms in our brain.
Hence, it seems that any finite set of axioms cannot explain the world. This effort looks as if trying to make a 3D sphere using planar tiles. We may approximate the sphere, but there will be places where the tiles don’t fit.