By intuition, Descartes means those certain things that we just know. Intuition is the concept of a clear and attentive mind which is so simple that there can be no room or doubt for what we are questioning. For example, in geometry, the reflexive principle states that a line always equals itself. This theory does not need to be proven because it is already evident in itself, and is supported by the obvious. In mathematics, beyond the natural numbers, addition, multiplication and mathematical induction are intuitively clear.
By deduction, Descartes describes this as logic that is so obvious it cannot be argued. By deduction we use the absolute to form a relative theory. For example, in the axiom of equality 2+2=4 and 3+1=4, therefore 2+2=3+1. This example can be tested to the maximum, but will still remain true. However, the conclusion has been deduced from the premise making it much more uncertain than intuition. In addition, deduction we know is something man cannot perform wrongly, making it a valid source of reason.
In order to make the obvious conclusions, one must intuit that a number must equal itself or that the value of a number is constant. Without these intuitive thoughts, the logic is not as clear.
By fully explaining these principles in the rules, Descartes integrates them together to inevitably free our mind from any prejudices of the inaccurate senses. Descartes’ principles allow the mind to think intuitively, rather than using the senses to reach a conclusion. The senses are not used in this process because firstly, they are often very inaccurate where the perception is faint, distant and masked. Secondly, the perceptions that we encounter in dreams that often seem real are in fact false. Thirdly, even when we are alert and awake, we can still be deceived by some extraordinary power or “demon”. These three reasons are why the senses should not be the basis of reasoning; instead, we must use our intellect intuitively to free our mind from the prejudices of these senses.
In essence, the method Descartes describes to us seems to be telling us to erase our mind of the senses and consider only the propositions that can be clearly and distinctly intuited. We must believe only what is absolutely certain and make use of intuition by bringing and idea into close attention by the intellect and use deduction to proceed from certain truths, to produce other truths. By doing this, we are freeing our minds by using our intuition and deduction rather than closing our minds by using the senses that constantly mislead us.
