Material Equivalence and Paradoxical equivalence

Four valued logic Q&A 1998.8

13:Material Equivalence and Paradoxical equivalence

14:Material Implication and Paradoxical implication

15:Where are the Contradiction of 4 valued logic different from of 2-valued logic ?

16:The logical rule of easy-use-to-live in 2-valued logic can be expanded.

Q&A13：Material Equivalence and Paradoxical equivalence

1.Material equivalence----price

Equivalence of true proposition or false proposition is Material equivalence. It is easy to understand, for example, the equivalence of the Price and a goods. If money is not equivalent to the value of the goods, we can not buy the goods.

2.Paradoxical equivalence---idea

Equivalence of the third valued proposition is Paradoxical equivalence. It is easy to understand, for example, Idea proposition. At any rate, we can do something with idea though we can not understand how to become. This type of proposition have originally special characters whether idea succeeds or idea fails is not made clear. The equivalence of an idea and other idea is therefore same as a contents of the idea and something which the idea invents in future.

As a political idea shall not be easily corresponding with another political idea, it is reasonable to understand the equivalence of this idea proposition is difficult equivalence.

The equivalence of the third valued proposition has a dual implication formally in which two conflicting proposition appears mutually. It is understood whether the idea which looks like another is the same by the trap's of dual implication enduring. Because the idea rolls the submitting person in the trap of painful dual implication, the submitting person should endure a dual implication of idea proposition. The ideal way of such equivalence is Paradoxical equivalence.

Q&A14：Material Implication and Paradoxical implication

1. Material implication----program

Now, think about the computer program. The program which has run to proposition A will stop if the wrong data is input to the following proposition B. This is a result of that the true proposition A imply false proposition B. This case is equal to the truth value of implication which a true proposition imply the false proposition in the truth table of 2-valued logic.

2. Paradoxical implication-----self reference proposition of an idea

Now think about self reference proposition, by which we voluntarily think about an idea itself is an self reference proposition of an idea. However, it is difficult to recognize self reference as a proposition to which the idea is made clear, because this self reference disappears fast by there is not free about which we thinks about either. Also if it is odds and ends of the word which shows the self reference proposition of own idea, it is still better to recognize the self reference. Whether the idea is important or useful is not understood easily, the idea is usually overlooked. However, when we meets the same idea many times repeatedly, we can think at last about that the idea is important or useful. If we think about that idea is wrong or not important, we can not meet the same idea many times repeatedly. It is necessary to repeat such unconscious denials and affirmatives to come to recognize the self reference proposition. This denials and affirmatives is a hidden dual implication of the self reference proposition of our idea. This is paradoxical implication.

If we know the ideal way of the hidden dual implication of the self reference, our hidden consideration to the idea will be able to be recognized early without useless repetition. Moreover, the hidden paradoxical implication of an idea need not appear any longer to recognize the self reference proposition.

Q&A15： Where are the Contradiction of 4-valued logic different from the Contradiction of 2-valued logic ?

A: Contradiction is an most important rule of 2-valued logic which defines that a true proposition and a false proposition cannot exist at the same time. It is easy to understand this exclusive and negative relation true proposition and false proposition in mathematics. The contradiction law of 4-valued logic is very important rule into which a traditional law of 2-valued logic is expanded as it is accurately.

For example, the third valued proposition is that true proposition and false proposition and fourth valued proposition cannot exist at the same time. They are accurately exclusive proposition. This exclusion of these 4 type proposition is especially important for 4-valued logic.

The exclusion of the true proposition and false proposition of 2 valued logic is comprehensible which can be observed as shape of the affirmative and the denial predicate. However, exclusion of the 3^rd valued or 4th valued proposition is not understood in the shape of the predicate of the third or the fourth valued proposition. When the third or fourth valued proposition is accurately made clear a series of paradoxical word or proposition, it is understood that the hiddn series of the third or fourth valued proposition is different from the shape of true or false proposition. Please refer to the shape of the fourth valued proposition or the third valued proposition. (Q&A4,Q&A9)

Q&A16： The logical rule of easy-use-to-live in 2-valued logic can be expanded into 4-valued logic.

Four valued logic can equally treat an intuitive idea proposition and the scientific proposition verified well. That is, the sense and the spirit can use this logic at any time. Therefore, it is thought that four valued logic appears anytime and anywhere.

The true or false proposition is a comprehensible proposition which can be recognized like the mathematical proposition clearly. However, The third valued proposition is a paradoxical proposition which can be barely recognized at careful thinking. For instance, it is also difficult to consider the paradoxical sense which is this third valued proposition as one type proposition of 4-valued logic. Therefore, it is difficult for this kind of proposition to check oneself by a logical rule.

However, when this kind of proposition was able to be recognized slightly, it is useful and necessary to check it logically. For this, the truth table is appropriate. Actually, It is easy for the truth tables in this four valued logic to check the proposition from a logical rule. This is an experience of the author.

4-valued logic adopts and expands the idea of logical rule easy-use-to-live usually like a law of contradiction or the law of excluded middle of 2-valued logic. I think that the other logical rules of easy-use-to-live can be expanded into 4-valued logic.