If a person acts and thinks very rationally, the principle motivating them is very irrational. Rationality only applies to back up defending our own fundamental principle, and a fundamental principle existing in our mind is always irrational i.e. emotional, biological, intuitive, superstitious, inspired by experience and sensation, and the reason to obtain some objective value.
Even Mathematics is based on axiom which is totally detached from rationality.
Thus, there is nothing completely rational in this world, we must admit.
If a person is arguing very complicated and unrealistically rational without any irrationality, we must be warned to see this person as an intricatist. An intricatist is only interested in tricking the opponents to be confused, and does not have any spiritual means of living.
The fundamental principle can be the motivation by some objective value which is rationally deriven. But, irrational factors are inevitably involved in the calculus of rationality. So, there is also the case that "The fundamental principle / a priori is rationally deriven, but the methods applied to back up the fundamental principle / a priori can be very irrational". All in all, there is neither 100& irrational nor 100% rational.
My rational thought is also deriven from my rational biological function as well. I have also tried to rationally find the reason why I am existing as a biological-being. I found the rational reason which is because I was born as a member of human-being group which tries to thrive in this world. So, I need to survive and thrive as a human-being, and my biological functional code motivates me to do. This is a rational thought. However, I ended up with wondering why human-beings exist. I was really confused and could not rationally think anymore. T
The fundamental principle can be derived by any assumption based on rationality. I also mentioned the reason to gain the objective value as a fundamental principle. An existence of the objective values is a rational being. For example, the market mechanism and the needs for living are reasoned rationally. However, these factors can be also highly influenced by something not explained by ration.
Plato's ideal state derived from the perfect rationality failed to achieve because those who are in charge of establishing the ideal state and attempted to establish it were not perfectly rational.
Jaspers humiliated Spinoza's perfect rationality by assuming that "Spinoza must have had his own secret God inside his mind".
Science is also not perfectly rational at all. Science is known to be very subjective and intuitive than we tend to imagine. Actually, science was born by being influenced by Neo-Platonist philosophy because science is the philosophy to find "the truth" which is the idea of the reality. Even though the reason that science stands for is rational, the method science exploits is very irrational. Many people tend to believe that scientific analyses find and prove the result. But, the reality is that the already existing result makes the scientific analyses.
The rational process needs to be self-contradicted by a rational principle. Logics fail to be rational at this stage because logics do not have any rational principle which can rationally self-contradict. Therefore, the fundamental principle of logics is often an irrational one or a ration of intricatism. Mathematics is still rational at this stage. However, the tool of the rational fundamental principle which objectively assesses the rational mathematical process is an axiom which has neither a tool nor a principle to objectively and rationally assess and self-contradict. Mathematical axiom is defined by either the excuse to make the theoretical consistency or the measurement of physical outcomes in this real world. The former definition of mathematical axiom is defined by the subjective self-judgement of mathematical schools of thought. The latter definition of mathematical axiom is defined by an experience. An experience is biased because we always interpret what we have sensed into our own different ways.
If there is someone who can explain all the reasons of beings in this world perfectly rationally by rationally backing up these reasons with a rational principle accessed with a rational way of rational thoughts, this figure shall be no longer a human-being; this one shall be God! However, the question still remains to access God's rationality. Why have God created this world? This reason can be it was just an incidence. Why have God created this world? Kierkegaard said it is because God was bored. God, the perfect rational, can do something due to these irrational causes which can be called as chaos. Chaos occurs without a reason. So, we cannot explain what is chaos rationally. God may have rationally planned chaos to take place. So God could have caused the incidence and God's own boredom with his rational reasoning. But, how can we know God's true rational behind his rational action? We have never known because we have never been great as much as God to know all the God's sakes.