On Thinking Method of One Effect with Multi-cause

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

Cheng Ping

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The paradox concerning the fundament of negative form ---- upeony paradoxv

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 u<=>v expresses equivalence, u~v negation )

In the article, the author doesnzt 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 unegationv or unegative form v. In history, many famous paradoxes have attracted the attentions of thinkers from ancient to today such as uZeno paradoxv, uthe liar v,uset theory paradoxv, and so on. The following passage will put forward a new case about paradox. Express uThere is peonyv with Q , in that way, uThere isnzt peonyv is paradox.

Proof 1: If uthere is peonyv, we canzt follow logically uthere isnzt peonyv, or, Q -> ~~Q . ( The symbol u->v expresses implication. )

If uthere isnzt peonyv, we canzt follow logically uthere isnzt peonyv; Since there isnzt even any peony, how do you know it is peony which doesnzt exist? Namely, ~Q ->~~Q .

Neither uthere is peonyv nor uthere isnzt peonyv can follow logically uthere isnzt peonyv. Neither uthere is any other thingv nor uthere isnzt any other thingv can follow logically uthere isnzt peony v, therefore, uthere isnzt peonyv is permanently false. It results in:

uThere isnzt peonyv is the permanently false proposition that is in contradiction logically with itself, or is a paradox.

Proof 2: Demonstrate the case of uthere isnzt peonyv according to the method of demonstrating uThe liarv.

From uthis sentence is Fv is T, we can follow logically uthis sentence is Fv is F;

From uthere isnzt peonyv is T, we can follow logically uthere isnzt peonyv is F;

From uthis sentence is Fv is F, we can follow logically uthis sentence is Tv, namely, uthis sentence is Fv is F;

From uthere isnzt peonyv is F, we can follow logically uthere is peonyv, namely, uthere isnzt peonyv is F.

So the paradox of uthere isnzt peonyv is almost equivalent to uthe liarv.

In addition, both ~Q and Q directly follow logically to ~~Q , therefore, for the conclusion, namely, ucanzt follow logically ythere isnzt peonyzv, uthere isnzt peonyv is equivalent to uthere is peonyv, namely, ~Q <=> Q .

We name the above cases as upeony paradoxv in the convenient of narration. It seems as if upeony paradoxv demonstrates that the simplest negative sentence of thought is permanently F, these negations are not reliable or successful. We will face logical mistake like upeony paradoxv as long as we negate something. For example, uthat isnzt Kant v is too paradox. From uthat is Kantv, we canzt follow logically uthat isnzt Kantv; From uthat isnzt Kantv, because there isnzt even shadow of Kant, uthat isnzt Kantv canzt just be out of human thought. If we admit upeony paradoxv or uthe liarv, that is to say, uthis isnzt applev, uthat isnzt moonv, and etc, all these simplest negative propositions will be paradoxes.

Compared with other paradoxes, upeony paradoxv has the following differences: First, upeony paradoxv has no relation with infinity. Secondly, peony paradox has no relation with the concept of uset theory v. 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 thoughtzs subjective standard to judge ulyingv.

The distinguished characteristic of upeony paradoxv is, there is no simpler or more concrete thing than it. It seems as if that human thought almost canzt concern negation, and canzt speak the simplest uNov. As soon as negation is found, it will result in paradox and logical mistake. uPeony paradoxv may be the most basic paradox concerning the negation problem in thought.

This article conceives of upeony paradoxv, 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 upeony paradoxv and uthe liarv.

Concept of One Effect with Multi-cause

This article defines one effect with multi-cause from two aspects. The first is yone effect with multi-causez 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 yone result with multi-causez 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, uThere is waterv is composed of utherev and uwaterv, the proposition utoday I workv includes three elements utodayv, uIv, uworkv.

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 premisezs 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 upremise graduationv, 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 uimplicationzs transmission lawv is found, namely, if A->B , and B->CAthen 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 uImplicationzs non-transitivityv or uimplication recurrence (recursion)v , namely,

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

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

( The symbol u=>v 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 implicationzs transitivity. Implication between polynomial premises may be called pure formal implication or regular implication, which observes implicationzs 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) thoughtzs 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 uherev by A1, upeonyv by A2, then (A1=>A2=>A1)-> uhere is peonyv, (A2=>A1=>A2 )-> upeony is herev. If specific reasoning begin from A1, we can get uhere is peonyv. If location begin from A2, we get upeony is herev. Dual cause and effect structure has only a regular direction.

2. Tri- element. Suppose uthere v by A1, uherev by A2, upeonyv 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 A1BA2BA3 , we getG( A1=>A2=>A3=>A1 )-> uthere is empty space unitv, and uhere is peonyv. According to the direction structure of A1BA3BA2 , we also getG( A1=>A3=>A2=>A1 )-> uthere is peonyv, and uhere is empty space unitv . We may appoint many directions from 3 elements. Suppose utherev by thick circle, uherev by thin circle, upeonyz by u` v.The process of reasoning ( A1=>A2 )N( A2=>A3 ) -> ~( A1=>A3 ) , can be explained by the following draft:

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Suppose uthere isnzt peony v by non-transitivity ~ ( A1=>A3 ). Recursion (A3=> A1) is fixed on A1 after reasoning, namely uthere is empty space unitv and uhere is peonyv.

3. Four elements. We discuss that one is object element and another is time element, the other two units are space elements. Suppose utodayv by A1, utherev by A2 , uherev by A3, upeonyv 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 ) -> utoday here is peonyv and uthere is empty space unitv; We can too get (A1=> A3=> A2=> A4=> A1 ) -> utoday there is peonyv and uhere is empty space unitv.

4. Five elements. We discuss one unit is object element, and another two are time elements and other two are space elements, Suppose uyesterdayv by A1,vtherev by A2, utodayv by A3, uherev by A4, upeonyv by A5 . We can subjectively construct many regular directions, which are enclosed, according to 5 elements. For example, (A1=> A2=> A3=> A4=> A5=> A1 ) -> uyesterday is empty time unitv, uthere is empty space unitv and utoday here is peonyv ; We also get (A3=> A4=> A1=> A2=> A5=> A3 ) -> utoday is empty time unitv , uhere is empty space unitv and uyesterday there is peonyv.

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 uobject sensuous existence propositionv, which isnzt possible to have negative form. Space unit was forced to combine with object unit after two elements is established. It isnzt 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 u proposition that object exists logicallyv 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 uobject sensuous existence propositionv uhere is peonyv. Relying on three elements, in the meantime, after uhere is space empty unitv, it is easily through thought followed logically, by uthere isnzt peonyv. Fourthly, the conclusion proposition on the premise of 5 elements is uobject space-time judge propositionv. After 5 element is established, a certain time unit and space unit may become empty unit, then thought can decide separately the spacezs negative form and timezs negative form of object. Fifthly, the more elements established, the more empty units in plural-cause and effectzs structure, the more negative forms of conclusion proposition, the more effective, accurate and reliable conclusion propositions are made.

Analysis of uPeony Paradoxv

uPeony paradoxv----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 upeony paradoxv. Peony paradox shows that without the condition of sufficient of necessary plural-element, only choosing or recognizing dual-element as premise, human thought doesnzt possess condition and function of constructing negation, and canzt make logical reasoning concerning negation.

Pluralistic-causal structure in thought may be compared with structure principle of computer. Itzs 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 objectzs transformation among units. Computer equally needs to set a certain number of umemory unitsv in advance. For example, it needs at least 8 trillion memory space to control popular Microsoft Windowz95 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 doesnzt set plural element, and donzt build structure of pluralistic- cause-and-effect, it canzt even possess and canzt 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 Kantzs 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 Kantzs dualist philosophy, the logic starting point is ucongenital comprehensive judgementv , but ucongenital comprehensive propositionv canzt 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.