On Thinking Method of One Effect with Multi-cause

------ And Discussing Paradox Concerning the Fundament of Negative Form

Cheng Ping

The paradox concerning the fundament of negative form ---- 「peony paradox」

Paradox has much relation with cause and effect. That is to say, paradox is found in thought, or there is some wrong with cause and effect or structure of cause and effect in itself. There are various expressions to define paradox, one of which is:

Paradox is a permanently false proposition, which is in contradiction logically with itself. Its regular form is P <=> ~ P , namely, the premise P may follow logically non-P, and non-P may follow logically P . ( The symbol 「<=>」 expresses equivalence, 「~」 negation )

In the article, the author doesn』t want to discuss the definition of paradox. Otherwise, with the help of the above expressions that are only explained, it is no doubt that all paradox will concern 「negation」 or 「negative form 」. In history, many famous paradoxes have attracted the attentions of thinkers from ancient to today such as 「Zeno paradox」, 「the liar 」,「set theory paradox」, and so on. The following passage will put forward a new case about paradox. Express 「There is peony」 with Q , in that way, 「There isn』t peony」 is paradox.

Proof 1: If 「there is peony」, we can』t follow logically 「there isn』t peony」, or, Q -> ~~Q . ( The symbol 「->」 expresses implication. )

If 「there isn』t peony」, we can』t follow logically 「there isn』t peony」; Since there isn』t even any peony, how do you know it is peony which doesn』t exist? Namely, ~Q ->~~Q .

Neither 「there is peony」 nor 「there isn』t peony」 can follow logically 「there isn』t peony」. Neither 「there is any other thing」 nor 「there isn』t any other thing」 can follow logically 「there isn』t peony 」, therefore, 「there isn』t peony」 is permanently false. It results in:

「There isn』t peony」 is the permanently false proposition that is in contradiction logically with itself, or is a paradox.

Proof 2: Demonstrate the case of 「there isn』t peony」 according to the method of demonstrating 「The liar」.

From 「this sentence is F」 is T, we can follow logically 「this sentence is F」 is F;

From 「there isn』t peony」 is T, we can follow logically 「there isn』t peony」 is F;

From 「this sentence is F」 is F, we can follow logically 「this sentence is T」, namely, 「this sentence is F」 is F;

From 「there isn』t peony」 is F, we can follow logically 「there is peony」, namely, 「there isn』t peony」 is F.

So the paradox of 「there isn』t peony」 is almost equivalent to 「the liar」.

In addition, both ~Q and Q directly follow logically to ~~Q , therefore, for the conclusion, namely, 「can』t follow logically 『there isn』t peony』」, 「there isn』t peony」 is equivalent to 「there is peony」, namely, ~Q <=> Q .

We name the above cases as 「peony paradox」 in the convenient of narration. It seems as if 「peony paradox」 demonstrates that the simplest negative sentence of thought is permanently F, these negations are not reliable or successful. We will face logical mistake like 「peony paradox」 as long as we negate something. For example, 「that isn』t Kant 」 is too paradox. From 「that is Kant」, we can』t follow logically 「that isn』t Kant」; From 「that isn』t Kant」, because there isn』t even shadow of Kant, 「that isn』t Kant」 can』t just be out of human thought. If we admit 「peony paradox」 or 「the liar」, that is to say, 「this isn』t apple」, 「that isn』t moon」, and etc, all these simplest negative propositions will be paradoxes.

Compared with other paradoxes, 「peony paradox」 has the following differences: First, 「peony paradox」 has no relation with infinity. Secondly, peony paradox has no relation with the concept of 「set theory 」. Thirdly, it has no relation with any complicated concept such as motion and silence, the relative and the absolute and so on. Fourthly, it has no relation with human thought』s subjective standard to judge 「lying」.

The distinguished characteristic of 「peony paradox」 is, there is no simpler or more concrete thing than it. It seems as if that human thought almost can』t concern negation, and can』t speak the simplest 「No」. As soon as negation is found, it will result in paradox and logical mistake. 「Peony paradox」 may be the most basic paradox concerning the negation problem in thought.

This article conceives of 「peony paradox」, the aim is to inquire into the condition through which thought makes negation, and into the internal faculty of the most basic negative function of human thought with the method of one effect with multi-cause. This kind of thinking method and new causal structure can wholly avoid something like 「peony paradox」 and 「the liar」.

Concept of One Effect with Multi-cause

This article defines one effect with multi-cause from two aspects. The first is 『one effect with multi-cause』 when thought originally happens, named one conclusion with multi-cause. The second is the logical reasoning of one effect with the pluralistic-cause including complex propositions of a certain number, named 『one result with multi-cause』 reasoning.

One conclusion with multi-cause is that the grasping of some of the simplest conclusions by human thought is necessarily founded on the basis of multi-elements, that is to say, human brain constructs some of the simplest conclusions (namely primary proposition) through multi-elements, named multi-elements to one conclusion. The so-called element, is the objective and single object of thought. The simplest proposition is composed of at least two essential elements. For example, 「There is water」 is composed of 「there」 and 「water」, the proposition 「today I work」 includes three elements 「today」, 「I」, 「work」.

Multi-cause to one result reason is the logical reasoning of a conclusion, which is inferred through the premise of complicated topics, as well as, of polynomial compound simple propositions.

The above two aspects are generally named one effect with multi-cause. We shall attach importance to the following points:

(1) Causal structure of thought in one effect with multi-cause should be founded on the basis of concrete and objective object or process. Generally, thought sets up multi-elements or premise』s relations with a certain fact on the basis of objective object or process.

(2) Multi-element and multi-premise are limited. Thought can only choose finite elements or premises to complete causal function of thought, instead of one or infinite.

(3) Multi-element and multi-premise for a conclusion are equal.

(4) Multi-element and multi-premise for a certain conclusion are independent.

(5) Multi-element and multi-premise have unity. Thought appoints them to a unit, which is called 「premise graduation」, jointly constitute or follow logically to a certain conclusion. After one effect with multi-cause should firstly define them as premise graduation, then a certain conclusion was followed logically by the whole premise graduation instead of one or part of it.

(6) Causal structure of one effect with multi-cause is selective. Human thought should specially choose a certain number of polynomial elements when reasoning constitute, process, and deal with them in thought, and etc. Which or how many elements we specially choose is the key point of studying one effect with multi-cause.

Time and Structure Characteristics of Pluralistic- Causal Relation

Theory of time is the basis of studying cause and effect (including one unit and plural element).

One cause-one-effect observes objective time law, which shows 「implication』s transmission law」 is found, namely, if A->B , and B->C，then A->C. The characteristic of time relation is one-way, diffusive, non-reverse, and the time is objective time. If A is before B, and B is before C, then the proposition A is true before C. One cause-one effect and its time relation are both one-way, diffusive.

One effect with multi-cause observes subjective time law as well as objective time law. First, the time relation between multinomial premise proposition entity and its conclusion is objective, diffusive, one-direction. Premise gradation of the units as cause precedes conclusion as effect. Secondly, multinomial premise follows logically or results in conclusion at a time, time relation between various premises is subjective, multi-directionary, regressive, closed. Subjective time law shows 「Implication』s non-transitivity」 or 「implication recurrence (recursion)」 , namely,

( A1=>A2 )&( A2=>A3 ) -> ~ ( A1=>A3 ) ; or,

( A1=>A2 )&( A2=>A3 ) -> ( A3=>A1 ) .

( The symbol 「=>」 expresses implication between multinomial premise or multi-units. )

One cause-one effect implication between a premise and a conclusion is usually named material implication or objective implication, which observes law of implication』s transitivity. Implication between polynomial premises may be called pure formal implication or regular implication, which observes implication』s non-transitivity law, is a pure subjective implication. Time feature of pluralistic-causal relation designs and constructs comprehensive time frame of which subjective and objective time mix together.

For the reasoning of pluralistic-one effect through the basis of plural elements, thought can subjectively appoint various orders, arrange, pile up and deal with it, constructs various conclusions. For plural-premise or proposition, they can also subjectively appoint orders and subjectively imply.

The following are the structural features of the reasoning of pluralistic-one effect: (1) thought』s choice of plural elements depends on objectivity; (2) the number of plural elements is established through thinking; (3) selective reasoning or building according to the basis of plural elements whose number has been established.

Then we specially discuss causal structure and features of plural elements.

1. Dual-element. According to dual- one result structure of dual element, the time order between dual elements as conditional gradation with its conclusion is objective, namely, dual element precedes conclusion, in total. However, the time order between dual elements is subjective. This kind of order is enclosed, recursive, and subjective time order, which is different from diffusive, non-reverse objective time order. The subjective order is called regular direction. Then we study that two units are objective element and space element. Suppose 「here」 by A1, 「peony」 by A2, then (A1=>A2=>A1)-> 「here is peony」, (A2=>A1=>A2 )-> 「peony is here」. If specific reasoning begin from A1, we can get 「here is peony」. If location begin from A2, we get 「peony is here」. Dual cause and effect structure has only a regular direction.

2. Tri- element. Suppose 「there 」 by A1, 「here」 by A2, 「peony」 by A3, one unit is objective element, the other two are space elements. Two regular directions which is enclosed, can be constructed, it depends on 3 elements. For example, according to the direction structure of A1、A2、A3 , we get：( A1=>A2=>A3=>A1 )-> 「there is empty space unit」, and 「here is peony」. According to the direction structure of A1、A3、A2 , we also get：( A1=>A3=>A2=>A1 )-> 「there is peony」, and 「here is empty space unit」 . We may appoint many directions from 3 elements. Suppose 「there」 by thick circle, 「here」 by thin circle, 「peony』 by 「` 」.The process of reasoning ( A1=>A2 )Λ( A2=>A3 ) -> ~( A1=>A3 ) , can be explained by the following draft:

Suppose 「there isn』t peony 」 by non-transitivity ~ ( A1=>A3 ). Recursion (A3=> A1) is fixed on A1 after reasoning, namely 「there is empty space unit」 and 「here is peony」.

3. Four elements. We discuss that one is object element and another is time element, the other two units are space elements. Suppose 「today」 by A1, 「there」 by A2 , 「here」 by A3, 「peony」 by A4. We subjectively construct that two regular directions, which are enclosed, rely on 4 units. For example, according to the direction structure of A1, A2, A3, A4 , we get (A1=> A2=> A3=> A4=> A1 ) -> 「today here is peony」 and 「there is empty space unit」; We can too get (A1=> A3=> A2=> A4=> A1 ) -> 「today there is peony」 and 「here is empty space unit」.

4. Five elements. We discuss one unit is object element, and another two are time elements and other two are space elements, Suppose 「yesterday」 by A1,」there」 by A2, 「today」 by A3, 「here」 by A4, 「peony」 by A5 . We can subjectively construct many regular directions, which are enclosed, according to 5 elements. For example, (A1=> A2=> A3=> A4=> A5=> A1 ) -> 「yesterday is empty time unit」, 「there is empty space unit」 and 「today here is peony」 ; We also get (A3=> A4=> A1=> A2=> A5=> A3 ) -> 「today is empty time unit」 , 「here is empty space unit」 and 「yesterday there is peony」.

We can draw a conclusion through the above discussions: at first, when we choose plural elements to infer or construct pluralistic-one conclusion, the number of plural elements which is established through thought, has a key influence on structural features of plural- cause and one conclusion. Secondly, the conclusion proposition of dual-cause and effect structure on the premise gradation of dual element is 「object sensuous existence proposition」, which isn』t possible to have negative form. Space unit was forced to combine with object unit after two elements is established. It isn』t possible to be empty unit, therefore, this conclusion proposition is complete sensuously true proposition which is impossible of concerning negation or negative form. Thirdly, 3 cause-one conclusion structure on the premise gradation of 3 elements is 「 proposition that object exists logically」 which has negative form. After 3 elements is established, a certain space unit probably becomes empty unit, it is easily negated in logic through thought that empty unit is piled up with object unit. Relying on dual elements, thought can only construct the 「object sensuous existence proposition」 「here is peony」. Relying on three elements, in the meantime, after 「here is space empty unit」, it is easily through thought followed logically, by 「there isn』t peony」. Fourthly, the conclusion proposition on the premise of 5 elements is 「object space-time judge proposition」. After 5 element is established, a certain time unit and space unit may become empty unit, then thought can decide separately the space』s negative form and time』s negative form of object. Fifthly, the more elements established, the more empty units in plural-cause and effect』s structure, the more negative forms of conclusion proposition, the more effective, accurate and reliable conclusion propositions are made.

Analysis of 「Peony Paradox」

「Peony paradox」----the paradox of concerning the fundament of negative form, substantially results from few element units of reasoning system, under this condition, carrying out causal reasoning by force will result in logical paradox, like 「peony paradox」. Peony paradox shows that without the condition of sufficient of necessary plural-element, only choosing or recognizing dual-element as premise, human thought doesn』t possess condition and function of constructing negation, and can』t make logical reasoning concerning negation.

Pluralistic-causal structure in thought may be compared with structure principle of computer. It』s very important to establishing many element units in advance in it. Reasoning of pluralistic-causal relation allows and even needs many empty units. The set of many units makes it possible that the object』s transformation among units. Computer equally needs to set a certain number of 「memory units」 in advance. For example, it needs at least 8 trillion memory space to control popular Microsoft Window』95 now, In BASIC language, it needs 3 data units (empty units) to finish a program, arranging from little to large from a group of numbers. If thought doesn』t set plural element, and don』t build structure of pluralistic- cause-and-effect, it can』t even possess and can』t be compared with function of computer.

We must emphasize recursion of plural-element in the reasoning of one effect with multi-element. When we concretely arrange, pile up and deal with it, these constructing functions of thought can only be finished among subjective time and background. This is a kind of multi-direction, enclosed, recurrence, and pure subjective time. After we begin to construct or infer from a certain element, arrange it in order among subjective time and pile them up, thought fixes on the element of originally chosen according to time law of recursion. At this time, it makes conclusion after plural-cause-and-effect structure reasoning from primary element, instead of repeating construction or reasoning. Depending on recursion, thought fixes effectively, or it will result in disorder of structure. This point is the same as locating rule of computer.

In Kant』s dualist philosophy, the subjective time parallel with the objective time, unable to intersect or unify. However, structure of plural-cause-and-effect mixes the objective time relation of premise gradation and conclusion with a priori time relation among multi-element, designs and constructs comprehensive time frame in which objectiveness mixes with subjectiveness. In Kant』s dualist philosophy, the logic starting point is 「congenital comprehensive judgement」 , but 「congenital comprehensive proposition」 can』t be looked as the starting point through discussing multi-cause to one result. We can furtherly analyze the simplest primary proposition, step by step, through concretely establishing plural-element, and discuss the process of concrete initialization of thought.

Notes:

Philosophy Big Dictionary, (logic volume), edited by Fen-Qi, Shanghai dictionary publishing house,1988, page 391.

Cheng Ping: Logic Study of Original propositions -------- And discussing one effect with multi-cause, Journal of Dialectics of Nature, 26,Vol.19,No.4, 1997.

BASIC Language, compiled by Tang-Haoqiang, Tian-Shuqing, Science Popularization Publishing House , Page 169,1993.

Kant : Future Metaphysics Guidance , Business Printing House, 32,BeiJing, 1982.

Manuscript Finished on July18, 1997

Email: pcheng65@public.wh.hb.cn  

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Address: Cheng Ping, 430015 Wuhan Academy of Social Sciences,

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Author Introduction: Mr. Cheng Ping, born in April 1965, Bachelor of Physics, Master of Philosophy, vice-researcher in the research institute of Philosophy of Wuhan Academy of Social Sciences.