Chapter 2 (The Basic Concepts of Opposites)

The Concept of Action
   Action is the main concept, since it imparts universe its motion and being – and absence of action means absence of existence. If you are in a motionless room, except your heart beating, your breath, and light reflection; the whole is vanished to you. Action is a synonym for existence – action of a being is what constitutes its existence, and without its action it is null.

   Action is a result of any difference: suppose exactly two homogenous elementary units, but this a contradictory statement, because they amount up to one unit not two, because their complete resemblance makes them one thing. This one unit has been identified because it is different from what is surrounding it, so the effect of difference is an action. As the acuteness of difference increases the effect increases too, so action is increased with the increase of that difference.

  The concepts of opposition and neutrality emerge as two mandatory concepts from action, where action results from opposition (differentiation); and absence of action results from neutrality (equality), irrespective of which is the cause and effect. The neutrality of two opposite states dictates their conduciveness to one similar unit, and the elimination of differences and becoming one unit is what we call neutral state.

   Each action is a result of two opposite actions, e.g. moving a body is not the result of one action without its reverse which is the friction in this case (the justification principle: the impossibility of a state without its opposite). Without the other reverse action, we wouldn't be in need to exert any work to move it. Work or potential doesn't come out unless there is a resistance against the affecting action; otherwise it becomes no need for the force itself, and objects can move by themselves without necessity for any cause or effect.

   The concept of action is a general one in comparison to other concepts like: force, work, or energy. It is applicable to all subjects whether it is tangible or non-tangible. Action is a general meaning which can be excreted from living or non-living things; or from intentional will or accidentally– its functional parameters can be general.

   Motion with a steady speed cannot be observed; we only observe change in motion. This change means existence of opposition, and the value of change is the value of opposition. Irregular (accelerated) motion needs force to take place, so opposition means action or force presence (we notice motion in normal conditions because there are other relatively non moving things, or moving with different velocities, but in completely empty space we can't detect motion). Consequently, change means the presence of opposition, and the amount of change expresses about the amount of opposition. Irregular motion needs a force to happen, so opposition signifies the presence of action or force.

   So, action is a result of opposition, and absence of action is a state of neutrality. Neutrality means conducing to one state, in comparison to opposition means duality. 

The Natural Tendency of Phenomena
   Suppose a virtual system that has many parts which all have only one and the same property – this is in turn negates any possibility to distinguish its parts, it is thus one similar and homogenous unit. Any possibility to differentiate between two parts means that they have different properties; thereby it is two parts not one part.

   Suppose an imaginary system of two exactly equivalent sides, so there is no reason to prefer motion from one side to the other. If shortage is considered to be a cause; this accrues to considering nothingness as a cause, and it becomes capable to do action, but more strictly "excess or surplus" is the only cause, and this is the justification for motion from excess (positive) to the less (negative), other than that logic means that the weaker is more capable than the stronger. "surplus" in itself is the cause, and if the opposite is true, i.e. motion from negative to positive, it would result in accumulation of all things in one global thing, but the contrary means that the tendency is always to reach neutral state, and the surplus is directed to the less with all its meanings.

   Is there any doubt in this simple principle that motion is from positive to negative? If there is an increase of opposition; it means the presence of infinite work from nothing, which is contradictory to the law of conservation of energy, which is not our reference here to affirm this inference, but it is absolutely logical result.

   Water flows from upper level to lower level as a result of this logical principle that imposes the impossibility of occurring the opposite. Have we ever seen water flowing in the reverse direction?!! (Even if the main cause is gravity; and difference is a cause behind cause … it still works) Because the surplus difference moves to attain a state of stability, and if we supposed the opposite - which is impossible and illogical- then there would be no limit for this transfer from negative to positive till the exhaustion of negative, and it would be completely transferred to the positive. But, this does not mean logical impossibility or justification for not happening except that it means the generation of energy from nothing, and the weaker is stronger than the strong – is there a contradiction more obvious than that?. Also with heat transfer it is from the faster particles side to the slower, and the reverse never occurs except by doing work.

   All what can be decided is that the surplus amount is what is transferred between the two opposites, and the reverse is impossible for transfer from negative, because there would be no limit for it, except the negative vanishes, and there would be no condition to stop, except its vanish. In other word, if opposition increases till its maximum value, then at the same moment it changes to the maximum neutral state by accruing to one state, which is unacceptable and contradictory. Accordingly, this is the "justification principle" for sense of motion from positive to negative, whereas justifying the reverse situation in impossible.
State and Quality
   The action manifests itself through transformation, i.e. changing from one state to another. Behind every change, there is an emerging action. And the type of action occurring during this transformation from one state to another is the quality, so quality is a description of the action.

   State is mere an expression about certain property, like: length, width, color, positive, and negative. Properties determine the response when getting into reaction with something else, thus they all are affecting factors, i.e. can be in a functional relationship in a reaction.

   In other words, state is an expression about certain circumstances – e.g. electric circuit is open or closed, or you are standing or sitting down, all of these are states. Taking into consideration that state is a result of action; it is not the action but its result. System state in any moment is the sum of its properties that characterizes it in that moment.

   State is an expression about property, and that property is capable to do action, which is called quality. So quality is doing an action in a someway specific.

   The sweetness of honey expresses about quality because it has an effect and certain action – its action in itself, i.e. causing sweetness is a quality. If we used to describe a state as positive and another as negative, this is an expression about qualitative action for the effect of each one – state is the product (outcome) of quality, and the loop continues, by letting state to be effective quality, and quality results in a new state, which in turn becomes a new quality that results in a new state and so on.

  The action of state is quality. Quality is a typical classification for the occurring action, i.e. the process itself, whereas state is more general; since it means both of the reactors and the process. A positive charge and another negative one represent two states, and before attraction there is no qualitative action, then comes the attraction to express about qualitative action and to express about the nature of the interaction between reactors. So quality is a typical action, and the action of state is a quality.

   Accordingly, quality is a dynamic state; whereas state is a static quality (each of them is defined by the other) and the final situation for quality is state, whereas the act of state is quality.

   Quality is a behavior or action somehow – we realize qualities from its action. As we consider coldness and heat, sweetness and bitterness, greenness and aridity … all those are qualities – they caused their effect because they have actions, otherwise they couldn't leave effect. We do not say that quality is the action itself, but we need a typical classification for action; so quality had come to being.

   In the theory of opposites the word quality is used in place of transformation, state in place of quality (Hamelin's categories consists of trio groups from which: (Transformation, Quality, Causality) namely the relation between state and quality is the causality. So, positive attracts negative, where positive and negative are the states; and attraction is the quality or the classification of action's type, and what relates between state and quality is the causality which interprets how positive and negative attract.

   To recap: State is a specific property capable of action, and its action is called quality. Both of state and quality transforms to each other. State has a certain action that results in a new state; in turn it causes a new quality and so on.

Quality and Quantity
   It was mandatory to go in this logical sequence, starting from action which includes the identification of quality and state – considering quality is nothing but action, and state is a static action. Now comes the turn to distinguish between quality and quantity.

   On the contrary of being the action of any state is a quality, the reality of the quantitative is just a count that does not signify any action. Saying +5 in its qualitative side means just a gain, so gain is a quality or action conduces to richness state. Whereas the counted itself is not so and does not imply any action (the real fact behind that, is that quantity is an epistemological concept, whereas quality is ontological, so the first has no action in contrast to the second). It is just an abstract mental concept, because what really exists is either a quality or state.

   Quantity does not mean any action – is number 5 implies any action or qualitative purport? It is a constant value – it is not even a variable like the symbols x or y that can take different states or values (variability in itself means action, in contrast to constant values), there is no much more than that to assert its non-action, it is a constant and consequently has no action. We will see these meanings verified when testing the laws of physics.

   Quantity is an expression about state – but it is neutral state. With neutral state the there no action or it reaches its minimum – thereby the state of all numbers is considered neutral because of its constancy and un-changeability. The relationship must be clear between: neutral, quantity, and constancy, in correspondence with opposition, quality, and action, which has its implication as we will see (the principle of properties association). If quantity represents the absence of action, thereby all the numeric values are neutral, because it is inert. Quantity is just an abstract mental concept.

   Quality is the action, whereas quantity is the non-action. Whereas non-action is represented by neutral state, thus all numbers are neutral. In other words all numeric values are constant (is there any doubt about that?!!) consequently it is neutral because it is unchanging.

Importance of the Neutral State
   From the view point of factual logic related to nature, not formal logic related to laws of thought, all meanings will be incomplete, and facts will be misunderstood except with the presence of the neutral state, that is because both positive and negative cannot exist without it. The absence of the neutral implies a flaw in the relationships between positive and negative, and this is what we will see in the general context in many subjects. Rationality, justification, and qualitative meanings will all be lost except with the presence of the neutral state.

   It is not only important to know the role played by the neutral state, but also what represents it; which is definitely the unity and number one. We will find number One to play an essential role; unless it is the central essence itself, since it is the reference state and the basis of all explanations as will be discussed.

   Is it reasonable to talk about change without talking about what represents steadiness? How can we talk about inequalities (greater and less than) without talking about equalities?

   If we consider the different geometries from the qualitative viewpoint: Euclidean, Lobachevsky, and Riemannian, we can consider the flat geometry as if it is the geometry of neutral surface, whereas Riemannian and Lobachevsky geometries to represent a positive and negative surface; where one of them deals with concave and the other with convex surface.

   The reverse situation happens with respect to the theory of opposites and the known sign rules, where positive and negative states are present, and the neutral is absent. Indeed, as the upcoming of the non-Euclidean geometries was considered revolutionary and corrected the concepts, also the effect of the neutral advent would be crucial, because any meaning disappears without it, and contradictions arise which can't be solved.

   Between two contradictories if middle exists, the contradiction would disappear – The impossibility of the two contradictories is incurred from the absence of middle – since the neutral state is the main connector. Discrepancy is held as a result of the absence of the neutral state, it is the means of interaction between opposites. How two contradictories coexist and the middle is excluded?! This is exactly the definition of contradiction as will be shown.

   From the first glance it seems that neutral state is an expression about state, but in fact it what creates the quantity of state. Namely neutral is the link between quantity and quality; that is because it is characterized from qualitative side as a state, and from the quantitative side as constant. It is so neutral because it is what actually includes and what connects the two opposites.

   The essence of state is the absolute absence of quantity, but we can't imagine absolute state without quantity, because it is what changes it, also we can't imagine quantity without its relation to any qualitative subject. Considering a state having quantity means it is not an absolute state, i.e. it is not absolute positive nor absolute negative, i.e. the positive includes negative and vise versa, in other words both of the two opposites include a neutral amount responsible for the quantitative side, and thereby neutral is the linkage between quality and quantity.

Neutrality and Unity
   Any absolutely single state is considered referenced to itself, and hence it is neutral- since a standalone state literally is supposed to be absolutely isolated from any other thing, and doesn't interact in any form, and its state is absolutely steady, since it doesn't affect or get affected, hence its neutrality is considered absolute neutral, and it ought to be referenced to another state to determine its state positively or negatively.

   If two states s1, s2 is seeking a neutral state; then they become one thing with one property, since the difference disappeared between them (supposing they have only one property) and the two states become one neutral. The relationship is tight between neutral and unity – whether it is a unity quantitatively or qualitatively. Quantitatively the two objects became one without reason or excuse for their separation, they are homogenous, and qualitatively they became one state with one effect.

   Here we find out that the value "one" is the measure of state and the basic reference of it, like the usual concepts of considering what is greater than zero is positive and what is lower is negative. So if the value of state is equal to one, this implies that the two states are equal and no difference exists, whereas we can put a convention by considering what is greater than one is positive (+) and the smaller is negative (-), thereby "one" is the measure of neutrality.

   Neutral is a synonym for equality of states, even though for the two opposites to attain a neutral state, they pass through many intermediate stages each of them is called the median state, so the final neutral is the last state of the intermediate states till the two opposites equal each other quantitatively.

   Equality is in opposition to difference (always there is equality or inequality and no third at all) and equality is neutrality, and in opposition to equality there is what is different which is opposition. Equality implies the qualitative unity if it is equality in properties, because the effect of the property is the same, thereby comes the correlation between neutral and the qualitative unity.

Conversion Between Quality and Quantity
   The structure of the whole being is eventually hierarchical – its peek is unique representing the qualitatively upper state (or omni power), then the base is getting wider as descending downwards, thus the quantity increases and the quality decreases. Quality is related to the ability to do action also it is associated with the merit to do classification; therefore the upper state represents the maximum value of action then descending down to the least beings with the lowest action.

   Quantity is the opposite category to quality. If action cannot be created or destroyed in a closed system –it would change its form – this change comes out as a mixture between quality and quantity – namely the mixing of action and non-action. Thus both of the action and non-action has its degrees, they are not like affirmation and negation, but the same action changes its form by means of mixing it with quantity, and the way to suppress the action of quality is the quantity- the distribution of action is the way to decrease it by increasing quantity.

   Quality is the ability to act, whereas quantity is the inability for action, thus there is an inverse proportion between them. Hence if the natural tendency and the law of nature is the conversion from higher quality into lower quality (like tendency to increase entropy), which means increase of quantity, in other words it is distributed on larger number and hence quality becomes lower and vise versa. And this is the essence of the principle of conservation of quality that is discussed before.

   In the presence of the quantitative inverse proportionality between opposites (quantity and quality) the qualitative resultant remains the same at the end. As the quality decreases the quantity increases to compensate that qualitative decrease, but the final result is constant, because it is distributed on a different quantity.

   If the tendency of nature is neutrality and attaining a greater stability, there has to be a conversion from quality into quantity, because quantitative has a neutral state (this may differ between living and non-living systems). The second law of thermodynamics implies that the increase of entropy means the transformation from action to non-action, i.e. conversion from quality into quantity. Entropy is the increase of randomness and disorder, whereas the different ordered energy forms is converted into thermal inactive motion (if we are talking about a closed compartment, despite the total number of particles is the same, but quality decreases as a result of distributing what is supposed to be more ordered on all the particles, so comes the decrease).

   The increase of quantity is the cause of decrease of quality. Quantity is the counted (the relative relationships in a series) whereas quality is the action and activeness. The conversion from x5 into 5x4x3x2x1 with successive changes during mathematical differentiation manifests that x5 represents inherent energy; once it is released, different quantitative forms including all the inherent possible states are generated as will be discussed in a detailed chapter. The opposition between quantity and quality plays an important role in formulating the association of properties and the principles and laws of opposites.

Forms of Quantity-Quality Relationships
   The whole being is a mixture of quality and quantity, so, if action is continuous; not swinging between action and non-action it would not exist. However, there can be a relationship between quantity and another quantity, or quality and another quality. The relations come up from the transformation between quantity and quality and their mixture in many forms.

   As the being is the action, then the forms of combination between quality and quantity constitutes all manifestations of the whole being with its two parts: objective and subjective. Where the subjective part represents the pure, abstract, mental concepts (mental relations: quantity-quantity or quality-quality relations) and the objective part constitutes actual relations (quality-quantity relation). So, really the whole being is a mixture of quantity and quality, and the truth of objective and subjective and the distinction between them is a result of quality-quantity relationships.

   Talking about the increase of temperature is different from the increase of values in a series of natural numbers, whereas the first expresses about a relation between quantity and quality, while with a series of natural numbers the increase represents a relation between quantity and quantity. There is a difference between increase of quantity and increase of quality, if the increase means more separation; it causes decrease of action, but if the increase is a result of unifying actions then the effect increases and continuity is achieved instead of separation, thereby quantity decreases, namely it is inverse proportionality between quality and quantity.

   The relation of quantity with another quality ramifies into two directions: Quantity of state, and state of quantity. Quantity of state is like 5+, here is we have five positive states, it is an actual real meaning, as if there are five positive charges, so state is the subject and quantity is the adjective- and since adjective determines the subject, then what is the effect of that quantity on state? Since quantity is neutral it will not change state, and the five states will remain as it is, because the adjective is neutral.

   Whereas state of quantity like +5 means that there are five positive units, it is an abstract mental meaning, as if we are moving five units to the right on the x-axis. Here is quantity is the subject and state is the adjective which determines the nature of quantity, and hence the sense of moving.

   With the state of quantity, state is the adjective (predicate) and quantity is the noun (subject), and since the result should follow the adjective, because adjective determines the nature of the result not the noun – this means that the affecting factor determines the effect, and this is completely logical, otherwise the outcome will be the same for all adjectives irrespective of any adjective because of its dependence on the subject only.

   The relationship of quantity with another results it another quantity, or considering the result a relative state between the two values (quantity/quantity=quantity, quantity/quantity= state, this is not division but relative relationship), but regarding the relation of a state with another, it can be a new state or the numeric value between them (quality/quality=quality, quality/quality=quantity). But regarding the relation of quantity and state, quantity can describe state (quantity/quality=quantity) or quality can describe the quantity (state/quantity=quality). Hence all forms of relationships can be possible.

   All forms of relationships between quality and quantity can be summarized in the following worlds of being:
* Absolute quantity (is not a world): this is represented by increase and decrease, and it represents non-action and it is neutral, because non-action is neutral, also increase or decrease. Can we imagine pure "absolute" quantification? If we suspect we can, this is not true, since pure quantification is not like numbers, because numbers result from relative relationships – and relationships are qualitative. So, pure quantification is mere the increase or decrease. This world does not exist because it is devoid of relations.

   All relations are relative, so with pure quantity or pure quality there are no relations that can be formulated, except by assuming the pure quantity is the numeric values standing alone not in relation with anything else, whereas pure quality may be the state of the mental concepts of the different categories.

* Pure quality (cannot be described as a world): it is represented by the pure states of beings. Pure quality represents absolute states, whereas all what is in our world is relative, hence it is unrealistic world. The basis for our world's construction is the coexistence of quantity and quality, whereby it would be unreal world devoid of relations.

* Quantity with quantity relationship (mental world): this is represented by mathematical properties of numbers, the multiplication table, trigonometry ratios etc. …. The relative relationships of numbers represent relative states or quantities. And since it is a pure mental world it has no action, and this mainly is not by virtue of being mental, but the action needs a mixture of action and non-action. The relation of quantity with another exists only in our minds.

* Quality with quality relationship (mental world): is represented by the sign rules of opposites. And in science there is no sign rules except the first set – and their relationships represent states.

* Quality–quantity relationship has two forms (real world and actual physical phenomena):
- Quantity of state: is represented by physical laws, which includes physical variables and properties that have numeric values, besides including constants and using sign rules. Thus it includes all the other relationships, quantity with quantity, and quality with quality.

Despite the physical laws is a relation of quantity with quality, but it internally uses quantity-quantity relationship (multiplication table) also the sign rules i.e. quality-quality relationship, which are the assisting tools to build the physical structure and the interaction between quantity and quality.

- State of quantity: this relationship seems to be unusual to us and unordinary. It leads to the explanation of universal constants. The interpretation of such values cannot be attained except from its qualitative meaning – but which of those relationships corresponds to this type of relation? Or it is does not absolutely exist, and it represents the final stage in the interpretation of the whole being, so its fact has not been clarified, and no symbolic formulation is established yet, and in what form these relations ought to be? In fact the theory of opposites may play the main role in establishing this relation and the interpretation of constants.

   Till this point the whole perspective has been completed between quantity and quality. And the previous discussion shows the whole scientific content and what should be build on it, and what it needs to be complete, and which are the assisting tools (mental worlds) and which are the facts (real world). It is obvious that what science lacks is the rules of signs, moreover the ability to explain the universal constants. The relation of quantity and quality visualizes the structure of the human knowledge in a holistic perspective; and from where our knowledge is, and where we are and where should we go.

Contradiction and Opposition
   There is a big difference between formal logic and factual logic, the first is related to forms of thought, but the former is related to the logic of nature which is supposed to include the first. The subject of this theory is the factual logic principles.

   Under traditional logic, some kind of relationships is "opposition", which means negation or confrontation; and the two opposing words are those which cannot be said on one subject at the same time and from the same side, opposition has two types:
- Opposition of negate: which is the opposition between affirmation and negation, like white and non-white, since they are contraries, and there is no middle between them, and this purports that the two negated terms cannot meet and raise up (cannot be true and false at the same time, but has to be one of them, but I prefer the words meet and raise up because they can be used with opposition or contradiction and will be applicable), namely no subject can be described with both at the same time, and must be described by one of them.

- Opposition of contrary: it happens between two words points to two subjects completely different, like white and black, and a subject cannot be described by both of them at the same time, and there is a middle between them. This meaning implies that the two opposite terms don’t meet and can be raised both, so a subject cannot be black and white at the same time, but can be anything else like red or green. Notice that we also cannot say red and green at the same time, thereby they are opposites – namely all adjectives are opposites and not necessarily between two adjectives with extreme opposition – from here came the name of this theory, whatever the success or failure in this nomination.

   All these meanings operate only in the range of language, its meanings are not general, and can be reformulated and defined according to a more general viewpoint. So, if logic investigates in the formality of language, it has no relevance to the actual reality, which is our main goal of in this theory.

   Contradiction is the union of what cannot meet (humanistic view point) so contradiction is only there within language, but with physical reality there is no contradictions. Only our minds can do contradictions, but nature is devoid from any contradiction and doesn't do any foolish acts. Contradiction has no meaning or real physical existence, it is only there in our imagination and our thoughts. On the other side we find nature contains opposite states interacting with each other to form new states, so we can mix between white and black to get shades of gray despite the impossibility of describing the object with black and white at the same time in the logic of language. What happens in the real existence differs from what the use of language entails. Whatever it is, language is not our concern here, but it was necessary to clarify the difference between opposition and contradiction.

   Contradiction, is supposed to express about the impossibility of certain events in reality – which means the concurrency of action and its reverse – other than that is not a contradiction. The right logic entails that the two contraries cannot meet and don’t raise up, so it cannot rain and does not at the same time, and the object is either moving or fixed, and in the logic of language affirmation and negation means action and non-action which cannot meet in reality and if met in language the contraction happens. To the contrary of contraction, the two opposites physically can meet and can be raised up, so white and black can meet and cannot be described by any one of them.

  Thereby, physically, the definition of both contradiction and opposition differs from the linguistic logical meaning only in one respect which is the meeting of the two opposites; otherwise no new states will be originated. The traditional logic decrees that there are intermediate states between opposites but does not decree that they can meet (which is in itself a contradiction or represents a flaw somehow, so then how new intermediate states emerge, except by mixing the two opposites).

   Opposition is not necessarily to have extreme value to be called opposition; any difference can be a reason for opposition. And contradiction can go underneath opposition as a special case where the two opposites become not susceptible to blend and the emergence of an intermediate state. So contradiction is considered an opposition with extreme value; that is because between the two contraries there is no middle.

   Thereby, opposition is the most general and includes contraction, because the justification for implication is that what refuses to meet are separate, whereas what refused to meet, no way to be combined actually.

   The two opposing states include opposition and complementarity, where there is opposition between them despite the complementary. Thus, there is opposition and accordance, both has an opposite action to the other, but they complete each other by reason of its opposite action. If the nomination is opposite or opposition, it does not negate the meaning of complementarity, even it purports half the meaning – it is implicit logical meaning.

   Difference goes underneath opposition, because upon any differentiation an opposite and complementary action exists, physically any difference is considered an opposition; and this already what this theory adopts and takes it for granted in the treatment. What assures that is that the two opposites not necessarily to be of the same type, because between different types we cannot say there is an extreme difference, e.g., when we say that the black body absorbs radiation and white reflects it, in spite of the opposition between white (+) and black (-), but this doesn't preclude to consider heat as positive and coldness as negative, and consequently there is an opposition between black and heat, and opposition between white and coldness.

   To sum up: contradiction exists only in the language, but nature does not know it, its occurrence in language is compulsory, but naturally contradictions cannot meet in language or reality, whereas opposites can meet in reality but not in language.

The Basic Relationship of Opposites
   "One" is the relative measure of opposites – and the opposites' relationship is the equal opposition. To express about this equal opposition taking into consideration that one is the measure; it must appear as a link between them, thereby the symbolic representation is reversed with both of them, which can be in the form:
S:1=1:S the relation of "one" is opposite in the two directions, or can be rewritten: s/1=1/s or any other symbolization that can be invented, but the meanings would still be the same, which is the opposite relationship with the "one", or it may be better to be written in the form: p:1=1:n, where p represents positive state, and n represents negative state.

   It may be evident that the origin of inverse and the use of "one" in mathematics and the concepts of division and multiplication resides here – such simple facts are used daily without regard to its origin, and we may be aware of its deep meanings, or just it was a successful form or many trails in the beginning of the modern science, because it was the only right way, and others confronted failure, hence it remained and paved its way, others would result in contradictions so it died, because it is far away from truth, may be.

   The form 1/s or what we call the reverse, has been associated with "one" because it is the separator and connector between opposites. The symbolization of ratio and proportionality agrees with these meanings and the relativity to "one", where "one" is treated one time as nominator and another as denominator, also the terms of proportionality are known with extremes (namely the maxima) whereas the inner terms are called means (the middle terms). The important thing is the opposition regardless of any meanings of division or multiplication, where their meanings will come up.

   We are in a need for non commutative operation, namely its product differs with differing order of terms, and thereby ratio (division or relative relationships and differing in two directions) is the basic operation to achieve that.

   In the statement "set the table upside down", let P stands for the table in its normal situation, and N stands for the situation "upside down" and R for the reverse action. Then, the reversal action has one of two: considering the reversal operator is the same in the two cases, or considering it opposite in the two situations. If there is a doubt to consider the operator opposite in the two cases, the opposition of the table in the two cases has no suspicion.

   Now, consider the action of being the reversal is different in the two operations: with the first reversal in the first time it becomes: R x P = N. then, reversing the table another time, it returns back to its normal position P, which is expressed about in the form: (1/R) x N = P, thus the resultant of the two consecutive actions would be: R x P x 1/R x N = P x N = 1, where "one" indicates state stability and its return back to its origin where both of the actions cancel each other. This form is an expression about the relationship between the two opposites, and the cancellation of opposite actions, thereby: state x opposite state =1.

   Handling the other supposition that reversal action is the same: R x P x R x N= 1, and assuming P x N accrues to unity, thus we get: R2=1, but this is not acceptable except by considering the action is neutral, which is not an action, in return we have to assume the action of reversal is opposite in the two cases even if the performance is the same or what we believe it is so. We can't say that action is neutral and quality comes to classify it, as if it is determined from the result; and it has no special nature and we infer it from the result, namely the action is neutral and gains its state from the qualitative result. And this surely refused and one of the actions should be R and the other is 1/R.

   In Boolean algebra the same example is mentioned as follows: In the statement "Reverse the table upside down" if P sands for the table in the normal position, and N stands for "upside down position", then what expresses about the previous statement is (P x N), if we reversed the table for the second time, it returns back to its original state, which is expressed as: N x N x P = N2 x P, and whereas unity means the stability and being unchanged, then 1P is equivalent to P, thereby: N2 x P=1P, N2=1 (here we can't do the operation N2=P/P=1, because N is called an operator which does not follow the operations of numerals, hence we cannot divide).

   Despite the final result is not the same, but also the detailed meanings are different- I think the interpretation of Boolean algebra is not right, because the action of reversal at the first time is not the same as the second time, and the state of table is not the same in the two cases which is not debatable, so, do we deal with a table or its state, to give ourselves the right to use the same symbol in the two cases?!

   The relationship between the two opposites requires using different symbol for each one, and the same action or what we believed to be so, when was acting for the second time, was it acting on a different state, or it was not the same action, or may be its state determined from its effect? The symbol of the two opposites and the symbol of reversing should not be both same in the two cases which is more acceptable. 

   The state of action is not indifferent; it is definitely positive or negative in spite of the association between them, for example the decrease of hot body causes the increase of cold body – both of the increase and decrease represents the occurring action, namely the two effects happens concurrently, and one of them should be described as positive and the other as negative, and they are associated with each other and a cause for each other, and we can't take one into consideration and overlook the other or considering both is neutral. For every action, there is an equal reaction in magnitude; and different in quality.

    We have to reassert all the matter again another way: if it is supposed that the action is the same in the two cases, namely, the same action is able to reverse state, then: P x R = N , N x R = P, so we get: R=N/P and R=P/N, P/N=N/P, P2=N2 which agrees with the first set of sign rules (+x+=-x-) which is contradictory as will be seen.

   Whereas, by considering the opposition of action in the two cases, then: P x R=N , N x 1/R=P , so we get: R=N/P for both of them, which is un-contradictory and agrees with the second set of sign rules that includes the neutral state as will be seen. And if we are in doubt about the opposition of action in the two cases, just imagine the same example with moving away relative the origin on axes system, then returning back to the origin, and sure the motion is opposite in the two cases.

   Definitely, the actions are opposite from the opposition of their effect, it is not inherent in the state itself– certainly, we infer it from its result and effect –otherwise it would be absolute state which is impossible – where all these meanings will be evident from the sign rules, which follow a causal logic.

 Relativity of States
   The basis of all relationships is proportionality; where the relationship between things means referring each one to the other. Proportion means the same value but in different form, qualitatively they are the same, but quantitatively they are not (the total quality should be the same according to the conservation laws; with varying quantity distribution). The equality of the two sides as a whole is qualitative, but the variation of the inner terms expresses about quantitative variation and different distribution of certain quality on different quantity. Saying 8/4=12/6 means the relative equal quality between (8,4) and (12, 6) despite using different inner terms (ratio is said to be between two terms, but proportion is said to be between four terms).

   Hereby resides the diversity in unity (universe) and resides the unity in diversity, so the whole is one unit, and any change of one thing is reflected on the other things increasingly or decreasingly with keeping the total quality as constant.

   Proportion requires four terms (s1/s2=s2/s3) which represents the relation of the two opposites through neutrality in any natural system or in any physical law. Opposition is a relative relationship between three terms – two terminal states and intermediate one; on which the relative relationship is determined. But this relation actually contains four terms (three states and four terms) where each of the two extremes is referred to the middle term. Only the relationship between the two extremes is determined through the middle. If we said that one opposite is greater than the other – the relation between them is held by the middle, where it is the relative reference and opposition determinant, which will be noticed in all what is coming by.

   Opposition is a relative relationship – it is a sequential proportional link – if it is not so, contradictions would arise that can't be resolved – on the same approach on which the physical laws have been established, the logical correlations is done on the same way.

   Suppose two states s1, s2 where the relation of s1 with s2 is reverse to the relation of s2 with s1, so if s1>s2 then s2<s1, in other words the act of s1 on s2 is opposite to that of s2 on s1, thus: s1/s2 x s2/s1 = s1/s1 x s2/s2 = 1, thereby "one" signifies the cancellation of action. The relative multiplication of the relation of the two opposites with each other is equal to one. Thereby we can consider that s1/s2 represents the action of s1 on s2, whereas s2/s1 represents the opposite action.

   In other words, if we stand for one opposite by the ratio s1/s2 then the other is represented by s2/s3, if s2 increases then the first ratio decreases, whereas the second ratio increases (where s2 is an intermediate link). Thereby is an inverse proportion between them which is expressed as:
s1/s2 = s2/s3, s1 x s3 = s2 x s2 = 1, where s2 represents the connecting middle state. It is the same relation between opposites (P x N = R2 = 1).

   Thereby, the division operation or ratio represents the relation of ordered pair, where the relation s1/s2 is opposite to s2/s1, and both of them cancel each other. Also the relation of any state with neutral, thus: s/1 is opposite to 1/s.

   The basic relation of opposites can be deduced from the relativistic concepts of states in more than way. Considering the direct relation between opposites, and by supposing state s2 is greater than s1, then s1 is smaller than s2, the relation is intentionally opposite in the two directions (simple facts but we have to stress on it). Thus: s1/s2 is opposite to s2/s1, then: s1/s2xs2/s1=1, each action cancels the other.

   Considering the relationship of each opposite with neutral, the ration of each opposite (s1, s3) to the neutral is opposite, so: s1/s2 is opposite to s3/s2, thus the first ratio equals the reverse of the second ratio, namely: s1/s2=1/(s2/s2)=s2/s3 , s1xs3=s2xs2=1, which is the main relationship of opposites.

   Making a relative reference of neutral (s2) to both opposites (s1, s3) which is opposite, we get: s2/s1 opposite to s2/s3, them: s2/s1=1/(s3/s2), s1xs3=s2xs2=1, which is again the basic relation of opposites. In other words considering the opposites relation is the equal opposition, then s2/s3 (the reverse of the last state) has the same state, then: s1/s2=s2/s3, s1xs3=s2xs2=1.
The Corresponding State of Increase and Decrease
   Since the increase of positive state is positive too (except attaining a certain threshold which can be a reasonable cause in some cases), and this is what is entailed by logic, since the increase of honey makes it as it is and does not change to another, and this increase in itself is positive since it is of the same quality of the original one, and this corresponds to (+ x + = +), where the surplus is of the same quality as the added to.

   The same logic goes with negative state since the increase of negative is negative too (+ x - = -) which is also entailed by logic – but what is meant here by increase? Is it an increase of negative or positive value? The meaning of this question is elucidated from the following: a hole of one meter deep becomes two meters deeper, it is said the first depth is greater than the second, i.e. (-1>-2 !!) since the increase of the negative is negative too, then this numeric value has to become more far away from the origin, hence the added is a negative value, thereby the increase here is negative (ex. : -1(+)-3=-4 taking into consideration that the axes system is based upon these concepts, so we can't judge to it). If coldness is negative, then the increase of negative means the increase of coldness, thus the increase is the addition of negative value (-1 + (-2)=-3 , thus -3>-1,  where the temperature 3 under zero is cooler than 1 under zero, and this is the right logic which is different from what is already known, and we will see the reason for adopting this view).

   Thereby, Increase in the first case is positive and in the second is negative according to the associated state, it is related to the addend- this simply means its neutrality, it is thus has no specific state in itself, it is related to the conjugate state. In fact, the increase is a quantitative factor, and cannot be positive or negative in itself, it is in itself neutral Namely, when we say the increase of positive is positive = ±x +=+ , and the increase of negative is negative = ±x - =-, so it must be represented by a neutral state to drive these two rules. The same logic applies on decrease, to get the same latter two rules.

   The traditional mathematical logic signifies that the decrease of positive is negative (-x+=-), and decrease of negative is positive (-x-=+) thereby both of them moves towards the origin in the direction of the other side, consequently the states reverses. So decrease changes state, but increase keeps it as it is – which is very strange logic – it is supposed the decrease of state also does not reverse it, not any decrease can reverse it at least at certain limit (it is not specifically this point, but all the details). It is supposed that the decrease of positive is positive (±x+=+) and decrease of negative is negative (±x-=-) and the state remains the same. The important thing is using a consistent logical scheme, whether we allowed for steadiness of states when a change occurs, or to follow an opposite logic.

   Thereby, both of the increase or decrease is neutral because it expresses about quantity, thereby:
Quantity x state= increase or decrease x positive or negative = the same state  = ± x + or = + or –
Also ± x ± = ±, the increase or decrease of neutral state or pure quantity without states results in the same state. Thus, these sign rules which we call the second set of sign rules that includes the neutral state, satisfy these quantitative meanings.

   The usual axes system considers the increase to be only in one direction, so the origin is not the least value, but below it there exists lower values which are negative, thereby the smallest value is at infinity, despite considering zero is the boundary or separator between positive and negative, but quantitatively it does not get a specific position, whereas another natural axes system (will be explained elsewhere) adopts other than that by making the one the separator between the opposites, and makes the increase in one direction to the infinity and in the other direction to zero in the opposite side.

The difference between the two opposites and what causes opposition is not positive or negative, but it is neutral. That is because if positive is what increases, and negative is what decreases, then the difference between them, and what causes opposition is definitely, not belongs to this or that, but it is neutral (not taking the side of any one of them).

   We say again it is not true or logical to consider increase of state keeps it, whereas its decrease reverses it, but increase or decrease are determined from the associated state, and both is ineffective, namely they are neutral.
    To sum up: the state of increase is related to the state of the addend. If the addend is positive the increase is positive, and if the addend is negative it is negative- so it is neutral, other than that conduces to unsolvable contradictions. Consequently, based on that, not every two opposite are necessarily positive and negative but can be neutral – which is clear from the case of increase and decrease. This happens because they get their meaning from another, which is untraditional, misleading, and tricky to the most extent.

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