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.
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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