Intuition plays an important role in all the areas of knowledge. It provides the foundation on which our understanding of each area of knowledge is built. These core intuitions are the fundamental basis for everything we know. Both reason and perception are dependent on intuition. Because many of the areas of knowledge rely on these two ways of knowing, it can be said that they also rely on intuition. Three of the areas that rely on intuition are mathematics, natural science, and ethics. In mathematics intuition is the basis of our theories. Intuition plays the same role in the natural sciences, such as physics. Our ethics are directly formed from our intuitions about what we observe in society.

Mathematics is an area of knowledge that relies mainly on reason to show that things are true. This in turn means that mathematics must be based on intuition. There are several models of reasoning on which we base our mathematical knowledge. One of these models was developed by Euclid and is known as the formal system. His system has three key elements. These elements are axioms, deductive reasoning, and theorems. The axioms are the systems “starting points or basic assumptions”. These axioms are considered to be the self-evident truths that provide the foundations for mathematical knowledge, and show that it is based on intuition. The second element of the formal system is deductive reasoning. Deductive reasoning is an important part of this system. It is built from two or more premises that lead us to a conclusion. It is another fundamental law of reason that can only be justified with intuitive knowledge. This leads to the third element, which are the theorems. These simple theorems are derived from the other two elements. If we know our theorems are true then we must also know that our axioms and deductive reasoning are correct. The first two elements can only be consider true knowledge if we say that our intuitions are correct. If we tried to prove them it would end up at a point were we would just have to say it is true because that is what intuition tells us. There is no way to know if our system is the correct one without saying that we intuitively know that it is. It can be argued that because basic mathematical knowledge is the same throughout the world that our system must be the right one. However it is entirely possible that the whole world is misguided in this belief. That is why we must rely on the intuition that our system is right. If we challenge our intuitions then we must also challenge everything that was derived from those intuitions.

An example of a simple mathematical truth is that parallel lines will never meet. Because the lines continue on forever there is no way to know for certain that the lines will never meet. We cannot see that they will never meet so we must rely on our intuitions that they will not. Another example is the idea that one plus one equals two. There is no way to know that this will always be true because we cannot witness every situation in which it is used. We can also not be sure that our concept of numbers is even true. It is intuitive to us that it is so we accept it as being true. These two examples are considered to be self-observant truths, but because we cannot observe every example of them we must intuitively say that they are.

The natural sciences are another area in which our intuitions allow us to say that our theories are true. Physics is a natural science that is built upon theories. All of these theories are based on data and our observations of what we are testing. These theories are also based upon our perception. We observe many theories through our senses. However our senses can be flawed, so we must rely on our intuitions that they are not. Even though we can see our theories in real world applications and can collect data that supports these theories, there is no way to prove with absolute certainty that our observations and data are correct. It could very well be that what we observe is not correct because our vision is flawed. Our perceptions are tied directly with intuition. We must say that we intuitively know that our perceptions are true because we cannot test them to prove otherwise. If we did not accept our intuition as a valid source of knowledge then we could not accept any thing we perceive in physics or anything else. We must also rely on intuition to say that our theories are and all ways will be true. We cannot observe our theories under every circumstance, so there is no way of knowing that they will always hold true. An example of this is light. For many years it was considered scientific knowledge that light behaved as a particle. However Einstein showed that light would also behave as a wave in some situations. Because of new technology and other advances in science we were able to show that that theory was incorrect for some situations. This could be true of all our theories, so for now we must say we know they are true because our intuitions tells use they are.

Our intuition plays a very large role in defining our ethics. Our ethics are built on moral principles. These principles come directly form our intuition. For example cheating has been deemed as unethical. This is because it goes against what people feel is right. If they were continually question why a person feels cheating is wrong; it would come to the point when they say that they just feel like it is wrong. This is an example that shows that people intuitively know what is right and what is wrong. Intuition is important in defining the basics of our ethics. Every ethical question comes down to the difference between right and wrong. Reason is often used when trying to define what is ethical. This also shows the importance of intuition in ethics. There are many outside sources that can help or hinder an ethical decision. Language can be used to persuade our ethical views. Because of this it can be said that our intuitions are most valuable in making an ethical decision. This is because our intuitions cannot be as easily swayed. Our intuitions provide us with an untainted source of knowledge in this area.

In conclusion, intuition plays an important role in the areas of knowledge. It provides use with the must fundamental knowledge we can have. Both reason and perception are dependent on intuition. Because many of the areas of knowledge rely on these two ways of knowing, it can be said that they also rely on intuition. Some of the areas that require intuition are mathematics, natural science, and ethics. It provides a general knowledge in each of these areas. In mathematics and science intuition is what allows use to have theoretical knowledge. In ethics, intuition is what tells use the difference between right and wrong.

Not sure I concur with your rationalization that intuitive thought forms the basis of our core knowledge. Intuition is instinctive thinking – without the use of rational processes. I offer that the sciences as you describe them are the basis of rational processes — theorems, axioms, basic reasoning, postulates — each imply and are built on deductive, rational understanding of core knowledge. Intuition didn’t guide us there, understanding of patterns, trends and some example of concrete learning did.

There are those extreme, unknown areas of the sciences that require intuitive, instinctive thought to either form a basis of thought or disprove. I concur some level of intuitive thought is imperative, however, disagree that is forms the basis of our understanding and knowledge that guide thought in areas that are founded on rational thinking.