Axiom of thinking II & III

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Reply Sat 10 Oct, 2009 04:46 am
Axiom of thinking II&III

The six elements of thinking have been briefly introduced in the former thesis. But it is not the unique way of classification of human's thinking component. A classical way of classification─categorised by rationality, is a good example.
This comics had expressed a very important point: something is hard to explain logically, just like 1+1=2 in mathematics. Of course I don't think mathematics is a religion...

All thinking can be briefly categorised into two types: Rationality and Irrationality. Rationality is all thinking based upon reason. Contrarily irrationality refers not based upon reason. This is what the axiom of thinking II talks about. The axiom of thinking II claims that the superset of all thinking elements only contains two subsets: rationality and irrationality, which must have no intersection. In mathematics, it is written as:

(If thinking only contains I and R, their intersection doesn't exist)

. According to this axiom, we can easily classify the six elements into these two categories:

Creativity is a "sudden outbreak" of something new. It itself doesn't base upon reason, though in the realistic process of creation a logical plan is necessary. Obviously Desire is not based upon any reason. So does Emotion. For Feeling, when I see a beautiful girl, for example, actually at that time my observation is not based upon reason. Of course the observation will be analysed logically, but I see a beautiful girl is not based upon any reason. I see her not because she is beautiful but because after seeing her I think she is beautiful. Therefore all of these elements must belong to irrationality.

Logic, of course, must base upon reason. But how about Memory? You may think it should be the same as feeling, but actually not. Feeling is a receiver of message. Message is the information that you receive before you "think about" it. But memory is a database of information. The information in it must be processed by thinking before. You will never memorise a French vocabulary without seeing and thinking about it. You can never "suddenly memorise" something as you need to memorise it by spending sometimes to think. Therefore all information in memory must be processed by thinking already. Everything in the memory should be in order, therefore it should be rational. This kind of information is called as data. Simply speaking, these two elements must belong to rationality.

Somebody may think that rationality is "better" than irrationality. However it is totally wrong. At least the axiom itself never claims anything about "which one is better". More importantly both of them are necessary in the set of the six thinking elements. Without desire, an irrational element, for example, human will have no force to do anything, even sleeping and eating (because you don't think you "need" it). Without creativity our society must have no improvement will occur as we have no inspiration. Without emotion we cannot show our expressions and we just like a computer. Of course without feeling, how can we think? And obviously without rationality you cannot think at all. Therefore both of irrationality and rationality are important.

---------- Post added 10-10-2009 at 06:47 PM ----------
Be aware of the importance of both categories. Both rationality and irrationality is imporant in our daily life, for example, business planning, as the figure shown above.

We can make a little ratiocination from the axiom according to the new classification. As the irrationality and rationality have no intersection, all elements must belong to either rationality or irrationality. Nor of them can be irrational and rational at the same time.

Note that the classification above only dealing with each thinking element themselves separately. In the realistic human thinking we cannot only use one element of them to think. Therefore nobody can think purely rationally or purely irrationally. This is a common sense too. How can a poet write a poem without planning its structure? Therefore any other axiom comes about. The axiom of thinking III claims that in realistic thinking actually must be an intersection of the irrationality and rationality contains several elements. Such thinking called realistic thinking. The thinking only contains one type of elements is virtual thinking, can be classified into pure rational thinking (Rp) and pure irrational thinking (Ip). In mathematics, it can be written as:

We can also infer that the whole superset of thinking should be:
All Thinking
= Virtual thinking + Realistic thinking
= Pure rational thinking + Pure irrational thinking - Realistic thinking
= Union of irrationality and rationality - intersection of both
= Pure Irrationality + Pure Rationality - intersection of both

---------- Post added 10-10-2009 at 06:48 PM ----------

This is called as the ratiocination I. In mathematics it should be written as:

Also we can infer the ratiocination II that there must be no intersection between the realistic thinking and the virtual thinking. It should be written as:

Be aware of the differences between two axioms. The superset of the latter is different from the former. It refers to the thinking process whilst the former only refers to the thinking elements. Neither is the set of all thinking elements equivalent to set of virtual thinking, as the virtual thinking is a set of the thinking process consisted of several elements. Here is a short conclusion:

In the axiom of thinking I, we know that all thinking elements must be either rational or irrational. None of them can be both rational and irrational. Then we infer that creativity, desire, emotion and feeling are irrational whilst memory and logic is rational. In the axiom of thinking II, however, for the thinking process, realistically irrational and rational elements must be used. Therefore the thinking process only including rational or irrational elements is just imaginative.

These two axioms is important for the following proof of the theorem of thinking, which is the direct basis of the thinking flow sheet. After this last preparatory theorem, finally we will start to focus on the thinking flow sheet.

10th October, 2009
Reply Thu 15 Oct, 2009 07:31 am
An axiom is really hard to explain its reason...
Reply Fri 16 Oct, 2009 09:11 am
but proof seems to be meaningless as nobody interests in this topic............

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