That we cannot doubt of our existence while we doubt, and that this is the first knowledge we acquire when we philosophize in order. (Rene Descartes)
Accordingly, the knowledge, I think, therefore I am, is the first and most certain that occurs to one who philosophizes orderly. (Rene Descartes)
Before examining these inference the famous French mathematician, scientist, thinker Rene Descartes who lived in the 17th century, had done, let us talk about a few aspects.
Can we create an idea?
We think in every second. It’s almost impossible to stop thinking. Is there any idea coming out of nowhere among these many thoughts? Let’s open a little more. Do not all the ideas we think actually originate through an association / stimulation / observation / experiment etc? For example, Newton’s idea of gravity is based on a deduction that depends on the fall of an apple. Einstein’s relativity turned out to be the result of his observations that he had done. It can be said in the simplest sense that the idea actually takes place as conclusion of thoughts which are already processed in our minds. That is to say, an idea can not be created by human beings. If you think carefully, you can see that all ideas arrive at a different point by deduction from a starting point.
This creates a question for us: If all ideas are connected from one point to another, can an idea be produced from absolute nothing? Descartes, too, with or without awareness, would have thought about this question, “.. first and most certain that occurs to one who philosophizes orderly”. So he chose a starting point. He tried to obtain ‘correct’ information through inferences from a point which he assumed is true. There is an important remark we should consider at this stage. If the information I get as a starting point is wrong, we can not talk about the truth for our inferences (stating as wrong, and as not true are two different observations. One has certainty while the other has not!). We will not stay on this for now.
If we turn back to our question, no living or inanimate entity can create ideas. The reason is simple. All ideas are actually based on a starting point, as we have mentioned above, like the starting point of Descartes.
Now let’s talk about certainty. If all ideas are based on a starting point, and all we can examine do is deducing interpretations from an initial point, then we can never be 100 percent sure of the correctness of our base points. Because all of the inferences we make are based on the assumption of the correctness of the starting point, and we need another starting point to prove this is right, for which is not precise by cause of the same reason.
I doubt, therefore I think?
In order to understand the truth of the statement, it is necessary to understand first what thinking is. Do we really think, for instance? Can we be aware of that? When we play a computer game and press some buttons, characters in the game play as we want. Are they aware of that? Can’t it be possible like a simulation game that some ‘creatures’ press a few buttons and for that we presume we think? Can a creature who does not know what will he think after 5 seconds be sure that thinking acts under his own will? How much of this can we take on ourselves if we are programmed to ‘think’? Is it possible to find a right answer of what thinking is when we can not be 100 percent sure that we are not programmed to think? Or is it not a paradox trying to be able to answer what thinking is by thinking? Long story short, the questions of what thinking is and do we really think, especially after the emergence of artificial intelligence, has begun to be described as vague questions. Therefore, we can not be assured of what it is to think in real and propose that doubting implies thinking since we don’t really know what thinking is.
The other issue is, do we really doubt? With the same logic, we can say that we may be programmed to be suspicious. And again, as we have mentioned above, how much of the act of doubt do we possess? We can not be sure of doubting action while the answers of the questions what and how we doubt are pending. So, we are talking about an initial point that we can not prove it is correct (not to be sure it is correct does not imply that we claim the expression is wrong!). In this case, we can not say that the deduction is right.
I think, therefore I am
As we have noted above, we can not be certain of the correctness of this inference because we can not be certain of the act of thinking. (Uncertainty of the accuracy of the base point)
There is also another issue, a paradox. What is being exists? Do we exists? Does really our universe exists? What does existence mean? Does reflection in a mirror exists? Is this illusion which is not occupied in our universe a being?
If we do not consider the reflection as a being, should our universe is a reflection, we may claim that our universe may not exists. More precisely, we may claim that it might be an illusion.
Mathematics and Precision
Mathematics, like other sciences, is based on inferences. This is why mathematics needs the starting point (s) too. For example, most commonly used Euclidean spaces in Geometry is based on 4 axioms . These 4 axioms can not be proved and their validity has to be accepted. All other information is confirmed with the acceptance of these four axioms.
On the other hand, the number 0 in mathematics was unknown for centuries. In fact, the existence of numbers other than rational numbers was unknown. If we could go back to those time zones and ask the people of those times, they would claim without hesitation that their number system is complete. Their number system was far to be complete though. After the irrational numbers have appeared, it is understood that the rational numbers on the number system are so few that the probability of picking a random rational number from the number system is zero percent! That means, rational numbers are almost absent on the number system! Those almost absent numbers have been accepted as the whole number system for centuries… Time has shown that we may be mistaken even in mathematics. So, we can be mistaken in any aspects of science.
In conclusion inferences we now believe in correct can be refuted centuries later. Thus, we can not be sure of anything and we can not talk certainty of any claim including this one!