Violations of the law of identity result in the informal logical fallacy known as equivocation...
In everyday language, violations of the law of identity introduce ambiguity into the discourse, making it difficult to form an interpretation at the desired level of specificity. (https://en.wikipedia.org/wiki/Law_of_identity).

Ambiguity is subjective to the framework of interpreters and suffers from an inherent ad-hominum nature where equivocation is subject to the ad-hominum fallacy as it is subject to the framework of the observer. To argue that an equivocation is an informal fallacy, when other's observe it as a formal fallacy in itself equivocation.

Are you trying to imply that these violations comprise or are derived from a law of logic? As you can see, they are expressly referred to as violations.

By an authority figure, thus necessitating them as not just fallacies under there own nature, but subject to the bandwagon and therefore the ad-hominum fallacy, considering all authorities and "groups" are subjective in nature. To attack an argument from an authority or group is to attack the authority or group themselves.

The law was not developed by Aristotle. Though he made them popular through his literature, they were and have been in use prior to him and since. Philosophers do not adhere to them because Aristotle has any authority over them, but because these laws have been determined to represent logic and have the appropriate significance and utility in all their applications. That is, they are valid to philosophy.

Aristotle did help develop the law, as all development is a progression within the law. New facets of the law did originate with him.
https://en.wikipedia.org/wiki/Law_of_identity
http://importanceofphilosophy.com/Metaphysics_Identity.html
http://oregonstate.edu/instruct/phl201/modules/Philosophers/Aristotle/aristotle_laws_of_thought.html

This origination can be argued by developing the law of non-contradiction which helps define and give extension to the principle of identity:

https://www.objectivistliving.com/forums/topic/8486-aristotle-and-the-law-of-identity/

However this results in a historical argument as "equivocating" this "discovery" to "x" person and falls under equivocation as well considering while the law may originate with x person, the law as developed through "y" person observes a new origin of the law through a new definition.

The laws are defined in accords to progressive definition and exist through continuums.

The laws are adhered to because of majority opinion of specific groups of philosophers and logicians you are saying? This is bandwagon fallacy.

The three laws of logic, as are commonly known, are corollaries of each other:
1. The Law of Identity.
2. The Law of Non-contradiction.
3. The Law of Excluded Middle.

By corollary is meant, each law naturally inferences the other.

@Metaphysician Undercover is right -

P is not defined by not P. — Metaphysician Undercover

Actually the statement proves he is simultaneously wrong at the same time in a difference respect considering The law of identity is defined in accords with the law of non-contradiction as "collaries" of eachother and cannot be seperated. Because one law inferences another the law of identity, and hence "P", is defined by the law of Non-contradiction, hence -P. What you state is illogical and metaphysician undercover is wrong according to your own argument. You and him contradict eachother.


Common language can only be acceptable if it renders the right context. For example, "he is not good" implies he is bad/evil (or any other synonym which maintains the intended meaning). However, in no formal sense does 'not good' offer a definition of 'good'. Informally, as in common use, they're still extensively exclusive and explicit.

The "common" nature of a language is in itself a context and we are left with one context progressing to another context where one context may determine the next, but the next context (if viewed as progressive only) does not determine the prior. In these respects, language as context, is strictly directed movement.

The nature of context, is relative to a subjective group agreement, and what we understand of measurement is psychological (in these respects) where context is an means through which people measure reality and ihherently direct it and form it in such respects. The question occurs dually if "context" forms consciousness, as directed movement considering one context to another is a progressive continuum, and in these respects they are the same.

Context through Context is definition and is inseperable from consciousness as it is consciousness. The fundamental nature of context as directed movement, in accords to time, observes all consciousness existing from, through and as the basic "line" as directed movement.

Rules are group agreement subject to fallacy of authority, equivocation, bandwagon, etc. The fallacies prove this through there own nature.

Regardless, how can you logically argue that I am against these interpretations (perspectives) if I am agreeing with them and say they are correct?

Like in this statement:

The definitions you argue are correct under standard axioms of mathematics. The problem, as axioms, is that they are subject to a multitude of fallacies: authority, bandwagon, no true scotsman (pseudo fallacy for some), straw man (the axioms form a position not previously held), red herring (each axiom diverts to another axiom), etc.

The axioms are determined as true because of the arguments, as strucutures, which stem from them. These argument/structures, in turn are justified according to there symmetry with symmetry being the replication of certain qualities/quantities that show a common bond — eodnhoj7

You are arguing that I disagree with you, when in fact it is false. The argument is premised on a false premise.

Thank you for listing all these things out, it really saves me the trouble, of having to collect them on my own. Now I can address them in one post. I am so flattered you took time out of your day to do all the work for me, thanks.


4)All straight lines are Pi — eodnhoj7

Pi is equal to C/D where Pi is Equal to C if D is 1. This means the diameter, as a line, fits in the 1 length of the Circumferance "Pi times" as one line. Pi as a length, through the circumferance, is straight line. The straight line can be curved to form a radian, which means the curved line can be straightened out as well.


Pi as a line, varies in length with the circle however is always the same measurement. — eodnhoj7

Yes, Pi as a continuous fractal that is irrational and transcendental relative to the context of the framework which defines it.
https://en.wikipedia.org/wiki/Pi

Pi as infinite may be viewed as 3.141, 3.14159, or 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914.

So the application of Pi is determined by how precise we choose to interpret it. Applying 3.141 as pi is not the same as 3.14159, however both definitions are constant. They change relative to where we round them off, hence Pi has a subjective element of interpretation. However one measurement of Pi is relatively more accurate than the other. Pi is subject to equivocation in these respects causing alot of fault in the mathematical community, but considering it is a community which determines these truths we are left with a fallacy of authority and bandwagon.


5) The circle, through infinite Pi's observes the circle composed of infinite angles with these angles equivalent to degrees as a number much less than one approaching 0. — eodnhoj7

Yes, but you will have to quote in context where you got this portion of the argument.

If Pi is a length, observed in Point 4 above, where Pi is a circumferance leading to 3.141 and the Diameter is 1, we are left with Pi Diameter's as one diameter where Pi is a straight line through the Pi Diameter's acting as 1 diameter.

Now if the diameter is Pi, and Pi equals C/D as C/Pi then C = 9.869...

This continually expands when we throw in the Diameter as 9.869... .

Now The circumferance as (n→∞)Pi, and the diameter as Pi observes the Diameter existing inside the circumference equal to (n→∞) times. Pi, as a length through the diameter, and the circumferance composed of (n→∞)D as straight lines observes the circumferance as a number of angles approaching infinity.

Because these angles are continually approaching infinity, the angles are always approaching point zero. This is considering each curve on the line is conducive to a fraction of a radian where the radian as 57.296 becomes a fraction of itself as a fractal degree (as a fractal radian) of 1/(10^(n→∞)).

Now the fractal radian as a degree of 1/(10^(n→∞)) observes a fraction of a curve, but is nonetheless a curve. Now the circumference as composed of radians, is composed of curves with the circumference as continual radians approaching point 0 observing the circumference as infinite fractal curves.

Considering these fractal curves occur through fractal degrees as angles, "the the circle composed of infinite angles with these angles equivalent to degrees as a number much less than one approaching 0".

In these respects the curve is inseperable from an angle, while each curve itself is composed of further angles in itself. The curve as infinite angles, which is composed of further angles, observes a continuum where the angle is always approach a point zero, even though it may be more than one.




6) The line as a quantum angle — eodnhoj7

Yes an angle of 1/(10^(n→∞)) degrees is equivalent to a line as the angle can only be observed as a line. The angle and line are inseperable with the projective nature of the angle in one direction being synonymous to the line as going in one direction.


So a line between two points observes the alternation between being and nonbeing (void) — eodnhoj7

The line as composed of infinite lines is composed of infinite 0d points, which can be observed in the premised definition (commonly accepted in mathematics) as infinite 0d points necessitating infinite 1d lines.

The line as infinite lines and infinite 0d points as the inversion of one line into another, observes the line as a form of alternation being the existing (being) lines and void (points) considering the point is merely inversion of one line into another. The line exists through infinite alternation between line and further lines. Infinite 0d points, with 0d points being the inversion of one line into many lines, observes the line as infinite change conducive to no change.




However if the line connects the points, it necessitates that through the line the points are directed towards eachother simultaneously and the line becomes non directional considering the points are directed towards eachother through eachother as eachother. — eodnhoj7

Yes if Point A is directed to Point B, where Point A and Point B are both 0 both points are the same. So Point B equal to Point A as 0 = 0 observes that the line is simultaneously directed in the opposite direction connecting the points. The line as non-directional, as a connector between points, necessitates the points as directed towards eachother as points. This makes no sense, if it is occurring simultaneously, as the 0d point effectively is nothing. It only makes sense if the point existing through the point observes the point as directed through itself as itself thus necessitating a 1 dimensional nature as well where the line is deficient in direction, except through the 1d points which compose it. Hence the line is negative direction and composed of infinite 1d points:

The negative dimensional line in turn is composed of infinite 1d points. — eodnhoj7

Hence the line a absent of direction as negative dimensional, as a connector and not a thing in itself, observes it as approximator between multiple 1d points in the respect any connection observes multiple points. Multiple points necessitates a deficiency in unity in one respect, while this connection necessitates unity. So the 0d point directed to the 0d point observes:

Void must be void of itself, so the 1d line observes the void of void or the 0d point dividing itself as infinity through the line. This 1d line is an inversion of the of both the 0d point through 0d point (or an inversion of inversion) and the -1 dimensional line. — eodnhoj7

Where the canceling of the 0d point into 1d points, through there self-direction of the line which effectively ceases in direction itself as negative dimensional (described above),

The 0d point cancels itself out to units as multiplicity, but also Unity as pure directed movement. Nothing cancels itself out into pure being. — eodnhoj7

but this nothingness canceling itself out into pure being observes being in a state of multiplicity due to Being exist through void with this void inverting one being into many.


3) The line as composed of infinite points is composed of infinite lines, hence the line is composed of infinite circles as all lines exist as Pi. — eodnhoj7

All lines as diameters considering all lines can be measured in Pi, necessitate these infinite lines as diameters resulting in infinite circumferances where a diameter of x length and a diameter of y length may differ in length, but when observed as 1 diameter in themselves are effectively connected to pi through the equation π = (π=C)/(1=D) ∴ (π=D) ↔ (π=C)*(1=D), where each length as different from another length, as one length in itself is equivalent to Pi where Pi as a length is composed of infinite lengths as observed in Point 4 ("all straight lines are equivalent to Pi" however Pi is constant state of changing numbers.).

Because the line as Pi necessitates the circumference as Pi(Pi), at minimum, the line as different from another line as one Pi different from another Pi (considering Pi is determined by its rounding off), observes each line as a diameter conducive to x(Pi) (with x representing different calculation of Pi observing different degree of accuracy) resulting in x((Pi)Pi). This leads to:

4) The line is composed as infinite circles projecting, hence the line is equivalent not just to infinite points but infinite quantum circles as well. — eodnhoj7

where "quantum" observes a circle much "smaller" than another circle necessitated by the accuracy of Pi in determining the above measurements.

3.141 << 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392

in terms of accuracy with this accuracy determining the size of the circle relative to another size of the circle. This is reflected further in:

5) Each line, as composed of infinite further lines, is composed of infinite "pi's" where the line as Pi is composed of further Pi's. Hence Pi is divided by an infinite number of Pi being divided by Pi. — eodnhoj7


Hence Pi dividing itself observes Pi as its own function of self-division conducive to 1 through the line where 1 is Pi as a function of perpetual self division.

f(x)= 3.14159→(x→∞)
............f(x)= (3.14159→(x→∞) =1
................f(x)= (3.14159→(x→∞)
.........................f(x)=... — eodnhoj7

****where "x" is equal to any number approaching infinity with the fraction of Pi observing all number approaching infinity. Because Pi is statistically random observing x is observing any number which proceeds from Pi and approaches infinity.


4. The radius is half of the diameter.

5. Each radius in itself is a diameter, of another circle. — eodnhoj7

So the Line existing as divided/multiplied by itself results in Pi multiplying/dividing itself considering the line as 1 length is Pi as a length. A line folded in half, results in two lines of equal length, with these lines existing as "1/2" the original line in respect to the original line but relative to themselves strictly exist as 2. The line as a length is the line simultaneously multiplying and dividing when folded through itself.

As the mutiplication/division of a length requires another length, Pi is a constant length of a line — eodnhoj7

Because the line exists as continuous, in the respect it is one infinity (composed of infinite lines), but as one infinity is it composed of further lines considering infinite exists if and only if there are finite phenomenon. The line as one infinity, equates it as well to not just an irrational/transcendental number such as Pi but also Euler's number and any number for that matter. However all lines as one length can be interpreted as any number considering this 1 line as a length is defined by the lengths which composed it (1 inch as 16 parts, 1 foot as 12 parts through 16 parts, etc.).


Pi is a unit of length as one is a unit of length, with both being continuous. All lines as 1 unit of length observes Pi as a unit of length. — eodnhoj7


hence a line equivalent to Pi where Pi becomes a length. — eodnhoj7


So while pi = c/d or c/2r we are left with the circumferance being pi if the diameter is one infinity and the radius is 2 infinities as one infinite. — eodnhoj7


Pi is a length, not just a ratio and alternates with 1 as the foundation of length. — eodnhoj7


All lines are equivalent to Pi just as all lines are equivalent to one in themselves. — eodnhoj7

etc, etc


Since the above quoted information has no basis in any existing mathematical or scientific laws and even seems to contradict them, doesn't that mean it is your own (not yet universally recognised) invention or interpretation (call it what you may)?

What are laws but group agreement? With group agreement determined by proof? And Proof determined by not just the symmetry of the framework but the symmetry between the framework and the observers?

Contradict where exactly if the laws are used as premises? And what laws are you talking about exactly since you no so much. Quote sources. I have for the line as well as fallacies, etc. Where are your sources? Could it not be said your argument is subjective?

2=1+1 is a subjective interpretation as 2 = 1+1, 2+1-1, 2+2-2, 2+3-3, to infinity.

To argue any number is equal to a specific function, is not irrational as all numbers are composed of infinite functions.

Well, lets start with the laws of logic. I will start with the law of identity considering it is the foundation for the law of non-contradiction.



The laws of logic are subject to equivocation.

The law of Identity is written as "P is P" or "P equals P" with "is" and "equal" having multiple interpretations.

is- combining form
variants: or iso-

Definition of is- (Entry 4 of 4)

1 : equal : homogeneous : uniform isentropic

2 : isomeric isocyanate

3 : for or from different individuals of the same species isoagglutinin

https://www.merriam-webster.com/dictionary/is

Now you can look at another source and get the same or similiar, but different, definition and in these respects we are left with equivocation as a problem in the laws.

So in regards to your statement "Equal" does not mean "is", you are performing sophistry which does not match up with the evidence with the evidence being the common perspectives of the community, which in itself leads to further fallacies. Evidence itself falls under certain fallacies in these respects.


The same occurs for the definition of what a line is as well as other axioms you are unaware of.

No, P is not defined by not P. That's not a definition, as a definition gives meaning to P, saying what P signifies. If this were a definition, it would leave P completely without meaning, and that's not what a definition does, it gives meaning. Therefore P is not defined by not P. — Metaphysician Undercover

No, P is not defined by not P. That's not a definition, as a definition gives meaning to P, saying what P signifies. If this were a definition, it would leave P completely without meaning, and that's not what a definition does, it gives meaning. Therefore P is not defined by not P. — Metaphysician Undercover

So The law of Non-Contradiction is not defined by the Law of Identity, and the Law of Identity is not defined by the Law of Non-Contradiction? The Law of Non-Contradiction does not exist through the Law of Identity and defines it? Each law does not define the other?


The Laws of Logic where written and developed by Aristotle. As such we used them based off of a fallacy of authority, as well as bandwagon, considering these laws do not work in modern logic due to there inability to deal with time in a proper manner.

So you are taking a separate stance from the mathematical community then, and it is your own logic?

Here is a mathematical proof that one number is equal to an infinite series of numbers:

3= 3-0,4-1,5-2,6-3,7-4,8-5,9-6...((n+3)-n)...infinity.

Or just

3= ((n+3)-n)

***"n" equals a number approaching infinity

You can replace the number 3 for any value but the statement will be the same.



In regards to the law of concontradiction:

1) A line composed of many lines (hence 0d points) is strictly

2) A person can be composed of a multitude of persons in reference to one person being various persons given a length of time defining that person.

A person may be one person around another person and be a different person in presence of another, with one common person connecting these various identities. Your argument is fail two take into account two distinct phenomena can exist at the same time in different respects.

3. In regards to the law of non contradiction:

A. P is defined by not P.

B. Not P exists if and only of there is P.

C. P is positive and negative where P exists as unified or in a gradient form as deficiency in P hence multiple Ps. Hence not P is an element of P.
***I may have to elaborate on this point.

the point is not defined, except through the line. There is no strictly axiom for the point. A line composed of infinite lines is still one line. It is similar not the same to a set containing infinite numbers, an aleph number, or Cantors work in multiple infinities.

Actually 1/1/1...= 1. The line is its own standard of measurement, hence when it divides itself it is through itself.

Show me your source considering this, according to you is a universal axiom, other wise you are pushing your own theory (which is fine) but does not hold according to its own logic.

Provide a source.

Modern Math. So hyperbolic, elliptic, projective, affine, finite, differential, non-euclidian plane, and angle excess geometry are not real if I take only Euclids arguments?

So if I have infinite lines existing as one line, the line is not composed of infinite points?

x

The mirroring function is premised on all numbers having directional qualities where these directive qualities define the number as a quantitative limit in itself. This directional nature of the mirroring function observes that numbers exist through a replication process that fundamentally is self-direction where a unit is directed into itself to form an approximate unit as an extension of this self-directed unit (with the premise of these self-directed units being quantitatively “1”).

We can see these directional qualities in the basic number line

1→2→3→4→5→∞

Or in the linear form of an equation:

(1+2=3) ∝ (+1→+2)=3


Or the simple fact that all empirically quantifiable entities are directed through time in one direction, hence quantification is grounded in linear 1 dimensional time with empiricism as the premise.


This mirroring function will be observed as the symbol: "⊙"

And the resulting numbers set as “mirrored in structure” or “replicated” will be observed under the symbol “⧂”

Considering all numbers, through the mirroring process are directed to themselves (and towards each other through themselves considering all numbers are extensions of 1) all numbers have an inherent directional quality of cycling observed as (⇄) which is equivalent symbolically in this use to ⟲. In these respects the number as an observation of direction, through the premises of quantities being 1 dimensional linear directions through time, maintain themselves as constants through an intradimensional nature where this “self-referencing” as “self-direction” maintains them as constants through an infinite cycle which is self-maintained and symmetrical.

Direction is the limit through which a quantity exists with the 1 extra-dimensional linear quality observing our standard definition of number as a finite quality which exists as units through time which relate. As intradimensional, all number exists through 1 as “unity” where any percieved multiplicity is an approximation of 1 as all numbers are extensions of 1 through 1 under an infinite cycle as 1 conducive to a geometric form of a circle. In these respects the mirror function is premised in the mirroring process of pythagoreanism of 1 where 1 is conducive to a 1 dimensional self-maintained point (not 0d).


This self-directive quality acts as a form of unification in itself and hence can be observed as “and” where “A and B” can be observed as “C” with “C” being observed as “and” in itself existing as the positive/neutral foundation of a unified relationship between variable in which it projects in itself as its own variable. Considering all numbers are inherently positive or negative they have an inherent nature of additive or subtractive which the form of the number and its function are inseparable, however assumed in all equations in the respect to how positive and negative number relate through addition and subtraction. These additive numbers as “and” or “converging” in nature have an inherent element of directionality where these subtractive numbers (as deficient in positive form and function) are separators and observe an “or” or “diverging” nature (where “A converging with B” observes a unity in direction and “A diverging from B” observes an inherent degree of seperation where one seperates the other into a new direction).

In these respects all numbers have inherent functional qualities inseperable from the number where:

(x) = +x
((x)) = *x
(((x))) = ^x

and inversely negatives are observed as:

)x( = -x
))x(( = /x
)))x((( = x root


The functions are inseparable from the form of the number as the form exists through the function and the function exists through the form. All alternation between the two phenomena of form and function observes an inherent element of directionality as a triadic element which is the neutral median from which both extend. Form as constant, observes direction fundamentally as a limit, while function as change observes direction as no-limit.

The nature of limit exists through no-limit as the limit itself must be constant and unchanging with any change being the application of new limit causing the previous limit to become finite. The nature of no-limit provides the foundation for limit as no-limit cancels itself out under its own terms, as a double negation, which maintains the positive “limit” considering “no-limit” observes “no” through “limit” and not a thing in itself but rather an observation of deficiency.

The mirror function observes an approximation of a unified reflective act in degrees of repitition where while the mirroring process is both one and infinite as all numbers follow this function simultaneously as 1, the function observes the inherent degrees of intradimensional repititition as an approximation of this infinity itself through an inherent multiplicity that exists as an extension of it. For example, all numbers exist simultaneously through 1, however one cannot view all numbers simultaneously. However the numbers are present nonetheless as constants through 1, hence any application of the mirroring of the intradimensional nature of the mirroring process, as one, is in itself quantifiable as 1 direction as all direction with all numbers extending from 1 observing multiple degrees of the process itself, hence it can be calculated through a multitude of degrees.

All resulting numbers are extensions of the numbers being mirrored.

Because of the complexity of the increase in degrees and numbers applied to the function, theoretically speaking it would be more efficient to apply these calculations through a potential computer program.

Premise examples:

1⊙(1) ⧂ ((1,2))

a) (1)⟲ =
((1)→(1)) ∧((1)←(1))=
((1⇄1)) =
((2)) ∋(2),((1)),(1)



2⊙(1) ⧂ ((((1,2,4))))

a) (1)⟲ =

((((1)→(1)) ∧((1)←(1))) → (((1)→(1)) ∧((1)←(1)))) ∧ ((((1)→(1)) ∧((1)←(1))) ← (((1)→(1)) ∧((1)←(1)))) =
((((1⇄1⇄1⇄1)))) =((((4)))) ∋((((2)))),((((1))))*****



Example 1:

1⊙(1),(2) ⧂ ((1,2,3,4))

a) (1)⟲ = ((1)→(1)) ∧((1)←(1))=
((1⇄1)) =
((2)) ∋(2),((1)),(1)

b) (2)⟲ =
((2)→(2)) ∧((2)←(2))= ((2⇄2)) =
((4)) ∋(4),((2)),(2),((1)),(1)

c) (1),(2)⟲ =
((1)→(2)) ∧((1)←(2))=
((1⇄2)) =
((3)) ∋(3),((2)),(2),((1)),(1)


In this above example the numbers 1,2,3 and 4 exist inseperable from addition and multiplication and hence as additive and multiplicative numbers.


Example 2:


1⊙(3),(2) ⧂ (((1,2,3,4,6)))

a) ((3))⟲ =
(((3))→((3))) ∧(((3))←((3))) =
(((3⇄3))) =
(((9))) ∋((9)),(9),(((3))),((3)),(3),(((1))),((1)),(1)


with ((3)) equivalent to: ((1) ⇄ 1 ⇄ 1)


(((1))) ⇄ (1) ⇄ (1))
⇅
(((1))) ⇄ (1) ⇄ (1)) = (((9)))
⇅
(((1))) ⇄ (1) ⇄ (1))


a1) (3)⟲ =
((3⇄3)) =
((6)) ∋(6),((3)),(3),((1)),(1)
***Considering ((3)) contains as an element of (3), and thereby in effect is an extension of it, (3) is observed as self-reflecting as well.


b) ((2))⟲ =
(((2))→((2))) ∧(((2))←((2)))=
(((2⇄2))) =
(((4))) ∋((4)),(4),(((2))),((2)),(2),(((1))),((1)),(1)

b1) (2)⟲ =
((2⇄2)) =
((4)) ∋(4),((2)),(2),((1)),(1)




b) ((3)),((2))⟲ = (((3))→((2))) ∧(((3))←((2)))= (((3⇄2))) =
(((6))) ∋((6)),(6),(((3))),((3)),(3),(((2))),((2)),(2) ,(((1))),((1)),(1)


In the above example the numbers 1,2,3,4 and 6 are inseparable from addition, multiplication and powers; hence are additive, muliplicative and power numbers.

Example 3:

1⊙(1), )2( ⧂ ((1,2,)) ))1,2,4((

a) (1)⟲ = ((1)→(1)) ∧((1)←(1))= ((1⇄1)) =((2)) ∋(2),((1)),(1)

b) )2( ⟲ =
))2((⇄))2(( =
))4(( ∋ )4( ))2(( )2( ))1(( )1(

c) (1),)2( ⟲ =
((1)→ )2() ∧((1)←(2))=
((1)⇄ )2() =
)1( ∋ ((1)),(1),((1)),)2( )1(


In these respects the number line exists as a cycle that maintains itself while simultaneously expanding, hence maintains a dual circular and linear nature through the mirror function.

1→2 = 1⟲ →2


1→2→3→ 4 = (1,2)⟲ →3 and 2⟲ →4





1→2→3→4→5→6→∞ = (2,3)⟲ →5 and 3⟲ →6


Considering the mirroring process is constant and simultaneous for all number, 1 mirrors to infinity and cycles as such. In these respect “1 converges as infinity” exists as the foundation of the mirroring process where quantity as direction is founded in an intra dimensional self-referencing nature. Direction in turn exists as quantity since all number exist if and only if they are directed towards themselves through 1 with 1 existing as infinite direction. In these respects 1 as direction maintains a dualistic nature of “limit” and “no-limit” (with limit being direction as constant and unchanging). Direction as limit, in these regards provides the foundation of both quantity and quality.

(1⇄∞)

This nature of limit is causal in the respect it provides the further foundation for limit with this limit as effect being an approximate cause (as extension of original cause) and cause for further limits. In these respects, 1 as limit through direction observes a nature of cause and effect (approximate cause) where effect as approximation observes an inherent degree of randomness as a deficiency in structure respective of 1. Randomness, as deficiency, exists in turn as a negative dimension (synonymous to a negative number) as an approximator which observes a connection between existing 1 dimensional points in space which can only be observed through an inherent multiplicity.

This connection between multiple 1 dimensional points, through the -1 dimensional line (as an absence of direction which can only be observes through the self-directional nature of the 1 dimensional points) observes that all quantities are a series of connected points. In these respects a geometric quality, such as a triangle (3 1d points connected through 3 -1d lines) or square (4 1d points connected through 6 -1d lines), exists as a quantity in itself. So 3 points observes the triangle as a quantity, or 4 points the square/trapezoid/rectangle/etc. as a quantity in itself. In these respects all base geometric forms, as the foundation of all phenomena are in effect quantitative. These geometric forms as quantities in turn observe an infinite number of geometric shapes as grades which exist within the quantities themselves and hence quantity provides a foundation for quality while dually quality as direction provides a foundation for quantity.

This mirroring process in turn provides a foundation for not just quantitative math but qualitative logic as well considering a gradation of quantity results in quality as an extension of it through “the variable”.

Hence where addition observes an inherent unification as convergence as an extension of whole, multiplication/powers observes this unification as a localized finite version as convergence where convergence exists as a grade in itself resulting in “locality”. Hence the statement:

⊙(a),(b) ⧂ ((a,b,a_a,b_b,c,u))

a) (a)⟲ =
((a)→(a)) ∧((a)←(a)) =
((a⇄a)) =
((a_a )) ∋(a_a ),((a)),(a),(a_a ),((u)),(u)

*****(u) exists as universal
*****((p)) exists as particle/grade of universal which in itself is a universal

b) (b)⟲ =
((b)→(b)) ∧((b)←(b))=
((b⇄b)) =
((b_b )) ∋(b_b ),((b)),(b) (a_a ),((u)),(u)

c) (a),(b)⟲ =
((a)→(b)) ∧((a)←(b))=
((a⇄b)) =
((c=a∧b)) ∋(c=a∧b),((a)),(a),((b)),(b),((u)),(u)

Observes:
1) (a,b,a_a,b_b,c,u) as unified constants in themselves as extensions of “u” (universal) where a_a and b_b existing as grades of “a” and “b” respectively as universal constants in themselves.

2) ((a,b,a_a,b_b,c,u)) as multiples, or localities, which exist as parts or approximates of constants.

1. A line is an infinite number of points, hence is an infinite number of lines.

The line as infinite points is the axiomatic definition of a line:

http://www.bing.com/search?q=the+line+is+an+infinite+number+of+points&qs=n&form=QBLH&sp=-1&pq=the+line+is+an+infinite+number+of+points&sc=1-40&sk=&cvid=C8ED297B32114AA2A7406E89721E7552

"The totality of the points comprising the line is in any case infinite."

"This can be proven rigorously, and it's not hard at all. Basically, between any two distinct points on a line there is a third point between these two points (between should not necessarily mean the mid-point on a straight path connecting the points, and this may get a bit tricky, but not too tricky).
"

You are not just wrong, but lying if you claim that is the common definition. Change my mind and provide a source.

On a side note:

It may be argued the line is a set, however this is not a common mathematical axiom, so don't bother saying it is not a mathematical axiom...I am fully aware of this point as well as all the other "points" you claim.

2. This is blatant contradiction. "If the line is not composed of points, but... [then] the line is composed of points." That's nothing but nonsense contradiction.

Its a contradiction because you misrepresented the argument and took the second portion out. Now you are lying.

If the line is not composed of points, but the line is composed of other lines, then the line must be composed of infinite points.

3. More nonsense. That the numerical value of pi could be given to a length, in no way indicates that pi is a length. That pi is a length is not an accepted axiom. The numerical value of length must be qualified with a unit of measurement. Accepted mathematical axioms clearly indicate that pi is not a unit of measurement


If pi is not a length, then neither is 1 units, 2 units, 3 units, etc. considering quantity is a unit.

The circumferance is a length:

http://www.bing.com/search?q=circumferance+is+a+length&qs=n&form=QBRE&sp=-1&pq=circumferance+is+a+length&sc=6-25&sk=&cvid=C1FA1FB6F46743FE9DD86E053CDFFA91

It also provides the foundation for the radian in trigonometry as a length:

https://en.wikipedia.org/wiki/Radian



I rarely make ad-hominums any more, and I understand you do not have to agree with what I am saying, but between misquoting my argument, misquoting sources, and arguing foundations that are not just fake but are illogical I have one insult.

Now keep in mind, maybe I have been spoiled. Many of the people I have debated, even when they do not understand my argument or I point out deficiencies in theirs are generally kind or at least respectable. So maybe I had it easy as of late.

Not questioning the established authority is a form of deep cowardice not conducive to anyone who is a philosopher. Questioning does not necessitate either doubt or agreement, but rather an understanding a nature of the framework established.

So here is my insult, and you will never understand it:

"I hope you live a long life no different than who you are now."

Actually I made a continuous progressive argument, you keep repeating the same thing over and over again about it not being in mathematical axioms. In fact not only is it in mathematical axioms (line as infinite points), but these axioms are open to further expansion infinitely while each axiom is determined by the framework of proof which extends from it and not the axiom itself.


The line as "a injunctive of infinite points" observes the line as composed of infinite lines through these infinite points. The point is a continuum of further points through the line. The line and point alternate between eachother.

If the line is nor composed of points, but the line is composed of infinite further lines between points, the line is composed of points. You have no argument, you strictly do not understand what you are saying.

There is no misrepresentation of mathematical axioms, as what you have observed is a misrepresentation. You are pushing a belief system nothing more. All mathematical axioms are given structure by there corresponding proofs. A proof is merely the replication of mathematical axioms into a structure. The axioms only exist is a structure stems form them.

As observed in the link, there are infinite number of not just proofs for any mathematical system but these proofs as infinite must continue. Proof is continuity. Whatever finite defintion you are looking for is strictly multiple infinities.

Now relative to pi as a foundation of measurement. Pi can acts as a length of

Pi = c/d where c is equal to Pi and D is equal to one. The circufermance containing a number of lines equal to Pi observes not the circumferance as a length equal to Pi (and the circumferance is a length...Do you want sources?) But the number of diameters as Pi as 1 line in itself.


I am arguing from these axioms, as the proof is that these axioms must continually progress as there are infinite proofs for them. You are unaware of what you are arguing.




Pi as a length results in 1 as a function as stated above.

No fallacy. Hegelian/Fichte synthesis and the Pythagorean nature of 3 observes all contradictions a reconciable and merely approximations of unity.

What rules of logic and I am breaking specifically? I can cover those rules if you wish.

No contest.

Observing unity, duality (mutiplicity), and triads (unity and multipliicty) observes all phenomena as having a numerical base which defines them.

Unity is structure as cause, where all structures as extensions of one are unified through one.

Duality is the opposition of structures through their multiplicity as absence of structure leading to contradiction. Paradox is a reconciable contradiction. All contradictions are reconciable due to there base in a dualism as opposing unities rooted in unity. Quantitatively 2 is composed of one. Duality is acausal as multiplicity is no unity as void. Dualism is the relations of unities as units.

Triad is the joining of causal unity and acausal multiplicity (dualism) as synthesis between being (unity) and non being (multiplicity) as both. Synthesis is the origin of unity and multiplicity and exists as both and is beyond both. Synthesis is existence in the face of nothingness as existence. Considering nothingness cannot exist on its own terms, it is observe through multiplicity.

Thanks for the thought.

So agreement is only an emotion?

Pythagoras viewed God through the Monad(s). Number is both quantity and quality.

Elaborate on Aquinas proofs and why you believe they are sufficient.

God may not me limited to number, but under the defintion of Divine Measurer and One or Many or Triadic, God exists through number.

Any philosopher is a good starting point if it leads to further philosophers.

While math may exist inside the human mind (God as number) it may also exist outside as well.

Atheism has its virtues in the face of blurred truth. Unbelief can alternate to belief.

Emotion does not appeal to truth as well considering it is true that emotion exists?

All fallacies exist as polar negatives to truth statements.

From:

1. ad hominem we understand all axioms are dependent upon the individual.

2. equivocation we understand all axioms a continuum of multiple axioms.

3. Straw man we understand all axioms are dependent upon a framework of axioms outside the axioms or not observed inside the argument.

4. Red herring observes all axioms are divisions from other axioms, and all axioms are subject to entropy and are active entropy.

5. Authority observes all truth axioms are authoritative.

6. Circularity observes all axioms are circular with circularity a foundation of all axioms.

7. No true scotsman observes all axioms as pure and true for what they are.

8. Appeal to ignorance observes all axioms as knowledge.

9. False dichotomy observes all axioms are 1 dualism as triadic.

10. Slippery slope observes all axioms as continuum.

11. Hasty Generalization observes all axioms as evidence.

12. Tu quo que observes all axioms as diversive.

13. Causal obserhas all axioms as cause.

14. Post hoc observes the nature of first is origin point of the axiom.

15. Sunk cost necessitates continuity because of sacrifice.

16. Appeal to pity observes all axiom requiring an emotional stance.

17. The bandwagon fallacy observes group agreement as objectivity.

Russell's logic was given evidence in his Principia Mathematica. It was described through a progressive sequence of non self referencing symbols. It was deemed a failure.

Truth exists, reread the bottom portion of the argument.

All prediction is founded in understanding the nature of a phenomenon. Because prediction must account for unseen variables (variable we know we do not know, and the fact there are variables we know we are unaware of) understanding the structure allows the ability to dually be aware of these unknowns.

I will keep that dogma in mind.

True, we are also chained to a thousand other religions as well with many coming from the same texts.

Its up to you, it may be best to address one subject at a time in different threads (limit and no limit, subjective and objective nature of universal consciousness, multiple types of unified, etc.) for future reference.

Truth be told, the topics we covered could be dealt with in multiple threads.

When dealing with the nature of the infinite (God in this case) be wary of an infinite answer.

In non Euclidean geometry, the parallel postulate is negated. This alters the understanding of a "plane" which is a two dimensional construct, from the Euclidean understanding of a plane. It does not change the definition of "line" (1d), it changes the way that one dimension is related to another dimension, as a plane. It is a different definition of "plane".

That one dimension may be related to another dimension through various means (different geometries), and the correct way has not been firmly established, supports my claim that there is a degree of unintelligibility to the relationship between one dimension and another.


The parrel postulate lead to an open ending to euclidian geometry, through non-euclidian, where the line can have multiple definitions as it is defined through multiple frameworks that are connected through eachother.

The line is subject to the fallacy of equivocation outside of any one framework.

No, as I explained earlier, an infinite number of 0d points cannot construct a 1d line. A segment of line is what lies between two points, the medium between points. There is a fundamental incompatibility between 0d and 1d which makes it impossible that a line is composed of points, it is composed of line segments which are marked by points. 0d provides absolutely no spatial extension, while 1d "line" implies spatial extension. Contrary to what you claim above, a line and a point are fundamentally incompatible and one cannot be reduced to the other.

It's not that I don't understand your argument, but that I reject it as invalid. A point marks a place on a line. A line is not made of points. That is your invalid assumption, and why I reject your argument.


You are not aware of what you are arguing:

https://math.stackexchange.com/questions/1293086/how-to-prove-that-a-straight-line-is-an-infinite-set-of-points

A thesaurus? Continuous means unbroken, uninterrupted, connected. A unit is an individual thing, bounded and complete. Therefore an interruption is implied between one unit an another. When you say that a "succession of units" is continuous, "continuous" is predicated of "succession". But that such a succession (the activity of one succeeding the other) is continuous is just an assertion. There is nothing inherent within a multitude of units to validate your claim of continuity. Nor is there anything inherent within the concept of succession to validate your claim that a succession is continuous. Therefore you have simply predicated "continuous" of "succession", for absolutely no reason, other than to produce an argument from this axiom. That's begging the question.



Infinite interruption is no longer interuption as it is not finite. All continuums, as infinite progressions and regression, are both infinite and one.

All axioms exist through argument, such as those founded in geometric axioms (which you are evidently ignorant of). Proof is structure, structures is the repitition of variables resulting in symmetry as unity.

Reread the argument I presented, you clear do not understand it, nor the axioms of geometry you are arguing.

If they ignore that fact they are aware of darkness, which means they are in the light about something, then yes.

1) The influence of the mental facet is absent when defining the mental faculty according to degrees where one mental facet is greater than or lesser than another mental facet. This necessitates a form of relativity.

Now the nature of the mental faculty as "processing" observes an inherent creative process considering this "process" is the inversion of one experience into another (consciousness in this case).
Hence the mental faculty has a nature of "inversion" so to speak, where it is fundamentally formless on its own accords but exists through the subjective experiences it exists through.

These experiences, that which the mental process inverts into consciousness, in turn form the mental process. This necessitates the nature of experiences, that which impresses upon the void of subjective nature, vary in degrees and this variation causes a variation in the mental processes.

So the degrees, that determine one mental process as less than or greater than another mental process (through relativism), is really the degree of one experience to another. A lower grade mental process, lets say that of a mineral, may be less in degree than that of a human mind. The rock exists under a certain framework of mind where the rock exists through only so through so many states as a rock. The human mind, follows in a similar form and function, however has a higher degree of relations.

A rock may invert into further minerals, which in turn composed organic elements which in turn result in rocks again over time.

A human mind may follow the same course and manner as the rock, however it is able to speed up or slow down this process of the rock changing (mining, industrialization)

In these manners one mental faculty differs from another by not just how they exist through time and effectively manipulate it. This observation of time, with all being existing through it, is what seperates one mental faculty from another as time (parts composed of and composing other parts) is strictly a measuring limit which forms phenomenon. This understanding of time, as a ratio fundamentally, is in itself constant and as constant transcends past itself into an absolute law that is infinite.

Time is a measuring quality, all being exists through, with the grades of various mental faculties being determined by there ability to create it through synthesizing relations.

****This may appear abstract so I may have to elaborate further on it.

2.Every experience is appreciated as form. (Try configuration, circumstance or conditions for better context, but ultimately it refers to a form or manner of expression.) Something formless cannot create an impression on consciousness, awareness, mind, etc. The only difference is the quality of form in comparison with others. Also, as long as an experience is held within the bounds of personal/individual bias, it remains subjective. Memory does not determine objectivity/subjectivity. The degree of interaction, with different selves or distinct external points of references, is what determines objectivity. It is a relation not an independent factor.

a. Formlessness, that which effectively is "void" is an inversion of one structure through another under the dualism of "one/many". I understand that his one/many concept may sound repititive, but it is very important concept to see from different angles considering its foundational nature to not just measurement and reason, but all being in general.

aa. One is seperated from many because of this formless nature of one being observed through many.

ab. Many is seperated from one because its formless nature necessitates we observe it through units which reflect 1 but are not one in themselves.

ac. This division between 1 as formless because of the many, and many as formless because of the one, observes the formless nature of void inverting itself into form through which it continues.

A quality of form in comparison to others, causing this differential, observes all quality as comparitive in nature and hence a common bond. Under this relativistic nature of quality, quality becomes a boundary of movement for further qualities.

b. Individual experience is not limited to a subjective nature when given reflection upon it. An experience maintains a nature of limit when given structure through memory. Now this memory may be subjective in the respect it may only belong to the observer, however it still has an objective property of structure (complex limits). This objective nature becomes "denser" when further objectified to a word or action which is share with others as it encapsulates and gives form to further subjective experience.

c. Memory, as an axiom, is simultaneosly objective/subjective in regards to point b.

d. External and internal are relative terms of perception. What is external is a shallow view, when the external is penetrated to the internal, the internal becomes shallow again. The internal becomes external. The act of self-reflection, as a form of penetration of the self through the self giving form to the self, observes all individual has objective qualities in themselves.


3. Relative to the mother example, the concept of mother as well as similiar qualities shows an objective element. All objectivity is structure, structure is unity. All structure exists through symmetry as unit where certain limits are replicated and maintain a continuum.

4.Your explanations show you are acquainted with certain information, unfortunately, they aren't coherent with the wisdom you are trying to match. There are a lot of holes in your arguments due to lack of strict adherence to logic. It is not enough to regurgitate what someone else has said. If you do not understand it yourself, it is impossible to pass on someone else's knowledge as yours.
"Own knowledge is better than that of another," I'm sure one of those philosophers taught something to the tune of this.

Are you speaking from knowledge or belief?

Yes, one knowledge is better than another. All is better than any one philosophy, but where each philosophy fails is in its observation that it is strictly an angle of "the all" it does not wish to observe. Hence it contradicts itself on its own terms.

Aquinas gave some justice to his argument in this respect as on his deathbed he stated "it is all but straw". Neitzche lost his mind, in face of his philosophy, and ended up canceling out his own nature in the end by defending a whipped horse.

The biological relation, devoid of other unities, still shows that in the face of perplexity and deficiency there is some underlying unity that cannot be erased in the face of any percievable chaos. You claim I am wrong...good...but is it not contradictory to say such a thing without sufficient reason? To believe you would be a fallacy of authority, and a lie considering you admit no authority to any philosophical endeavor. Or do you?

Whatever circumstances brings people into having relations with each other is a synthesis of all the above experiences (the spiritual, mental, emotional, material, etc), it would be wrong to limit it to just one. This is also a key point of spiritual teachings on human relations.

True, but a deficiency in a balance spirituality still does not negate the fact that the biological union has some form of balance and unity to it. The absence of spirituality may have led to a biological union, as all chaos (or deficiency) still moves towards unity. The spirituality, through the breaking of the relationship, may be not be a full unity...but the biological relationship resulting in the child still is.

You claim it is wrong to limit it to just one problem, as all are connected as one, but limiting it two one problem is a reflection of the one.

Interesting points, nihilism reflects a dark night of the soul in many respects.

nihilism cancels itself out into a value system as no moral code as correct observes morality as evil. Morality is a way of being and inevitable.

1. The definition is subject to the framework which proves it. If memory serves in non Euclidean geometry a line is two points on a sphere. Axioms are determined by the frameworks which comes from them and the foundations of mathematics are not universally agreed upon.

The definition of the line is determined by the proofs which follow it, necessitating all axioms as subject to equivocation in light of multiple proofs observing different properties. The agreement of what constitutes a proof is subject to bandwagon and authority fallacies as group agreement determines the nature of the proof.

2. So a line cannot change to a point relative to a much larger line? Geometric forms are determined by the framework of reference, which through the nature of the Monad (point, line and circle), is all forms as size through relation is determined by degree but most specifically quantum degrees (if one gives thought to the nature of fractal degrees). The degree, as one line relative to another, is the foundation of all size.

A line as infinite points can be observed as infinite lines.

3. If a line as infinite points is composed of infinite lines, the line is a continuum of relations...you habe not seem to understood this or much of the above argument for that matter.

4. A succession of units is a continuity of units, from which the word continuum is derived. Look it up in a thesaurus if you don't believe me.

5. Each number is a state of progressive relations.

One state of one, is continual division: 1/1, 2/2, 3/3, to infinity. 1 is a divisive function based upon this continuous nature. Infinite change is no change for change is inversion of unity/multiplicity with continual inversion existing as one continuum.

1. Actually an experience that is not expressed or formulated through thought or memory and translated into word or action is effectively formless. I may experience "now", and now due to its rate of change and its direction to me (impression) is effectively without form and does not contain any objective form until memory replicates it. However This objective natire, occuring through memory as a degree of self reflection, is not fully objective until some act or word allows it to becomes a common median people can find commonality with. Objectivity, as group reflectivity where people can observe the same thing, acts as a unifier or common bond.

2. The objective, as structure, encapsulates the subjective where the subjective is further given form and function as an objective phenomena. So I may have a subjective experience, that subjective experience becomes objective through memory. This memory give form and function to the subjective experience allow it to exist through further objective states. The subjective, as formless and chaotic, is directed and given form and function to further thought, action or word. The memory, as giving boundary, in turn leads to further memory as the further a memory is penetrated, the less subjective it becomes and the more objective and orderly it exits.

An objective phenomena connects subjective states as it is a common limit which effectively defines them into objective existence. For example a common memory may connect subjective states by effectively unififying them by encapsulating them under a common reason. What may separate one subjective state from another is separate objective experiences, which contains subjective formless nature that become objective and defined when further formed.

3. A formless form, or unlimited limit, can be observed as a limit which is continual. The limit as finite in itself, because it must continue if it is to exist has a dual formless nature because of its continuous nature. For example, a memory must continue on and replicate itself in the mind if it is to continue existing. While the memory may exist as limit which exists because it's replication effectively gives it a structure due to the inherent symmetry that comes with replication, this replication as effectively unifying aspects of the memory must continue. So while the memory exists as a limit, the continuous nature of this limit gives a degree of formless, or "no limit", as this continuity is uncertain and undefined. However this limit exists through a continuity.

4. The limit exists through a continuum, but because the limit exists through a continuum it exists as synthesizing with the continuum (limit synthesizes with no lomit) to results in further limit and no limit. ***This point may have to be explained further.

5. Each number can be identified as one set of infinite relations where 2, 3, 4, etc. are composed of infinite see of relations, and that while each number exists relative to other number, this nature of a single unit existing relative to another single unit observes 1 and 1n (through 1) effectively "folding" through itself as a process of continual inversion where the nature of a number as nothing in itself, or void) observes the continual progression of the number (as a means of inversion to further number) as necessary. Each number, on its own, has a dual nature of being 0 units in the respect it exists because of progression.

So 1(n) observes the number (any further axiom) as a unit that inverts through itself to further units.

0(n) observe the number (any further axiom) as nothing in itself.

So (a) for axiom (which can equate to the number example above) is 1(a) as a localization of progressive axioms. 0(a) observes the axiom as nothing in itself but rather a means of inversion, where it exists as a potential localization. This potential acts as a means of inversion where one locality inverts to another.

Example:

0(3) = 1(3) <-> 0(3) -> 1(4)

and

0(a) = 1(a) <-> 0(a) -> 1(b)

***<-> if and only if.
*** -> is directed towards, progresses to

6. The individual in a collective is defined by the collective, hence the individual contains as an element the collective considering the individual exists through collective which simultaneously forms it. While the individual is still an individual, the individual is an embodiment of the collective.

7. The defintion of death is subject to the fallacy of equivocation as it has multiple meanings, with any meaning as group agreement being subject to the bandwagon fallacy with this in turn leading to the fallacy of authority further leading to the quasi fallacy of no true scotsman (absent of identity) and so on and so forth.

The defintion of death is given proof by the framework which contains it, death as change, is a point of inversion within life, but as a point of inversion can observe all degrees of existence as funda,mentally dying in some way shape or form further implying that all existence has some form of life property and consciousness within this given framework of interpretation.

7A) .I will delete an old thread, and replace it with a thread on the nature of fallacies both existing and being subject to there own fallacies as well as the three laws of logic being contradictory. Classical logic is contradictory. However point 7A will need a seperate thread to address this point, so do not bother responding to much, I will address this point further elsewhere.

8. A cow is composed of many parts. So are its legs. So are its atoms. A thing is composed of many things, much like a set.

9. I see what you are saying...do you? You're argument has no unity, as it has no structure...do you need what I am saying?

If a man and woman have a child through cheating, the individual are separating there current unions (and themselves as elements of the union to form a new biological union. The individuals involved respectively as divided by one ritual/biological union and a strict biological union.

If a child is born out wedlock, while the ritual and spiritual union may be left out (or maybe just ritual if the parents stay together) the union is still strictly biological.

10. My arguments are a sythesis of all the research, reading, discussions and practical experience over the years:

As to the reading, it is a sythesis of:

Thales, pythagoras, parmenides, anaximander, laepeducious (wrong spelling), heraclitus, Socrates, plato, Aristotle, Plotinus, Marcus aurellius, seneca, ibn rushed, maimonedes, Thomas Aquinas, Locke, Kant, Neitzche, Kierkegaard, Kant, Hegel, Husserl, Heidegger, Stein (Catholic), Wittgenstein, Popper, Hall (freemason), Jesus (Christianity), Buddha (Buddhism), Nagajeera (buddhism), Muhammad (islam), Crowley (satanist), Lavey (satanist), Liebniz, Newton, Solomon (proverbs), The Kybalion, hermeticism, etc...

And various miscellaneous philosophers and a whole host of asian philosophers stemming past lao tzu (taoism (but I cannot remembee thier names or how to pronounce or spell them)

If an axiom is self aware, to some degree, does it need an independent observer to exist?

If one axiom observes another what determines the relativistic degree of defintion where one forms the other? The degree of self referentiality.

1. All definitions are defined according to the frameworks built around them. "Time" may have one meaning in a x philosophy with there being many philosophies around time. In physics there is no common defintion to time, as some do not believe it exists.

In simpler terms, time has multiple meanings that are not agreed upon and as such is subject to the fallacy of equivocation. As time is equivalent to a variety of definitions, these definitions are determined by the frameworks in which they exist. Time is the relation of parts, acting as a point of inversion in a structure between unity and multiplicity as a form of entropy.

2. An axiom as a self evident truth, which is the dictionary defintion, leads to the question of "what is self evident truth?" In giving answer to the question we are left with breaking it down, at minimum to a subjective state connected with self, and objective state connected with evidence. The axiom exists as both subjectivity and objectivity. Then looking at the nature of subjectivity and objectivity the question occurs as to what there nature is or is not.

Considering a subjective experience is effectively formless in the respect it cannot be viewed by others, or given clear description thrpugh the self, subjectivity is formlessness. The objective, that which is defined and observed by multiple people acts as a common median across subjective states considering many people can observe it. The objective acts a a form and function, or limit, in the respect it brings and maintains a form of unity inseparable from the act of it being structured.

Now the subjective, as formlessness or "no limit", and the objective as limit observes inversely that all phenomena composed of definitive limits and formless no limits (example the rock may have a jagged edge that defines it, but what composes this jagged edge is formless) have a subjective and objective nature.

3. A formless form is a unlimited limit, or a limit which exists through a continuum. A line or circle qualifies as such, as well as the number 1. Qualities such as colors are composed of infinite colors with an individual color merely being a boundary through which further colors exist.

4. One progressing to two is a logical observation of unity inverting to multiplicity. 2 existing as 1 number is a logical progression from multiplicity to unity. A cell individuating into another cell is a other example. 1 cell inverts to two cells as many cells with each cell being a unit in itself.

The inversion from a unified state into a multiple state observes a dualism through opposition (opposites) where inversion itself is void of any defintion because it is nothingness or has no structure.

This opposition, is solved through a form of synthesis, as joining. Where 1 moves to many and moves back to one again. 1 has a synthetic nature of continually moving.

4. Shrodingers cat as both living and dead can be solved by observing the cat as "dying" where both states are observed as one continuum. If the cat is alive, but cells are dying is the cat dead? If the cat is dead, but certain cells keep replicating (such as toenails) is it alive? Shrodingers cat can be solved by a continuum.

The example shows a problem in the principle of identity, and the framework of classical logic being contradictory.

5. A progression is a localization of other progressions and strictly observes the directive qualities of one phenomena to another. In these respects, a logical argument as proof is merely a structure where proof and structure are inseparable. Intuitionist logic observes this in part where proof is merely a creation. The nature of unity and multiplicity, unity and dualism observes a synthetic property thrpugh the triad as one in itself.

Take for example a man and woman, a dualism. They are unified through the function of sex and form of the child resulting. The man, woman and child are individual entities in there own right, while being connected through eachother as 1 family.

Synthesis is continuity with continuity allowing for unity, hence order.

6. The nature of axiom is acausal cause as sythesis where what we observe in all phenomena is:

1) constant structure

2) changing parts.

3. Sythesis as continuity

With these three axioms existing through all phenomena as a foundation for consciousness. These three foundations exist through eachother as eachother. They exist as foundations of measurement as well, with all consciousness being defined in accords to a process of measurement. All phenomena as conscious observes all phenomena as self measuring.

7. Universally accepted for what field exactly? Philosophy? Which school? Science? Which field? Math? Which field? Religion? Which One? Biology? Which field?

What is this "common language" everyone agrees to? English? Which dictionary? What year?

All these perspective invert to further perspective and there is no perspective which will be able to maintain itself without either branching to another one or some argument as to which perspective is best.

In a same respect these multiple perspectives must stem from one source of thinking, due to ther divergent natures necessiating a common bond at some point, so the question is one of where these commonalities occur.

Many schools dependent upon one source requires a form of synthesis.

The only question is one of universal principles with these universal principles being definitions of God.


To define cause is cause.
To define acausality is without cause.
To define synthesis is sythesis.

These principles must be able to maintains themselves as constants, progress in defintion and continually join these new definitions into one in order to maintain them and progress further.

1) There is not a strict definition to a line, or anything for that matter, except through the framework built around it.


2) A line can be both composed of angles (frequency) and exist as an angle within itself without contradiction considering all angles set the premise for size.

For example I may have a frequency of x wavelengths in y length. The frequnecy can ve observed as the repitition of angles.

Now the line appears as a frequency. However if I observe is relative to a much larger angle or frequency, and use that new form as the center point of measurement in which everything is measured against it, then the frequency of x wavelengths and y length "relativistivally" shrinks into a line.

The line, as a unit of relation, is determined by its size relative to other phenomena.

This applies in the same manner to an angle acting as a line. A 1d line exists because of its projection in one direction, this projection from one point to another observes a form of condensation where any phenomenon approaching point 0 (like the number 1) shrinks or turns into a fractal. For the line to shrink would require a previous expansion elsewhere as condensation is a form of shrinking. This shrinking, can be observed in an angle where the apex observes a point of "condensing" where the angle is a projection. Due to size determining the relative nature of the 1d line, an angle of a fractal degree can be observed as a line

3. Keep in mind one phenomena can appear as another due to size which size being the relation of one phenomena to another and using it as a starting point.

4. 1 exists as a unit, as a unit it must continue to exist through further units. It exist through 2 and 1/2, 3 and 1/3, 4 and 1/4, etc. One effectively inverts into one state, then into multiple states with each of these states being 1 number in itself. This progression of numbers manifests as a continuum as each number, composed from and as a unit of one, must follow that same nature and exist through further numbers. 1 along with all numbers composed of 1 as 1 in themselves must exist through a continuum where 1 and 1n exist through infinities as infinities.

Agree with the above.

See the way to long post above.

My apologies if I came off as rude or short earlier, and further apologies for a post which must become necessarily long. Keep in mind, you may want to read this post several times.

With that being said,

The question of an axiom existing independent of an observer, becomes problematic if we view all phenomenon as having a degree of consciousness as the nature of independent observer becomes void if all phenomena have some degree of awareness.

An axiom as self evident is dually subjective and objective. Subjectivity is formless void. Objectivivity is directed movement, or form and function, that exists as a limit conducive to structure.

A. Self referencing subjective nature which gives the phenomenon an objective nature.

All phenomena are composed of some symmetry, where some limit replicates, with this symmetry observing a common bond. An abstract example of this would be a geometric figure as replicated lines. This abstract nature further replicates within nature in the form of a tree or plant, composition of minerals, qualities of an animal (legs, eyes, hair, etc. as replicated qualities).

The replication of certain limits results into complex limits as qualities which replicate so on and so for until some structure occurs. This replication of limits observes structure as perpetual cause considering all cause is premised as order. An effect, is an approximation of a cause, is the replication of a cause through itself with any multiplicity being the mirroring of void causing a perceived variation. All effect contains an inherent element of randomeness to it.

However all effect, as cause through cause, in itself is a cause.

Replication gives foundation to a structure and acts as a self sustaining cause, hence cause is an inherent part of observation as the formation of limits. In these respects all phenomenon have some degree of self referential consciousness to it as an extension of the One Cause (God) which is ever present through creation.

All axioms are self referential due to this causal nature, as all being is connected through structure as cause.


B. A projective subjective nature that gives rise to an objective nature.

All phenomena are composed of and composes other phenomena, with the phenomena existing as a projected movement conducive to time. For example a cow is composed of atoms and composes other cows as a herd. The atoms in there projection through time form the cow, the cow as projecting through time composes a part of the herd. The herd in turn projects through time.

It is the nature of the axiom to project through time, as a time zone in itself, that the axiom must have somewhere to project. The axiom can only project if there is somewhere to project to, neceesstating a further axiom. All axioms exist as relative parts, with this relativity observing a form of multiplicity. Each axiom as an individual part acts as a point of inversion, void in itself, in the respect it can only exist through other axioms.

In these respects the axiom as an individual or, through its void nature, multiplies and divides simulteously. For example a cow individuates (multiplies/divides) itself into further cows through the act of reproduction. It also individuate itself into further particles at death.

The axiom, cow in this example, is a localization of change. As localized directed movement it is an actual locality. In these respects it is objective. However, as an actual locality it must project to another actual locality. Considering there is only existence and order, the projection of one actual locality to another necessitates one locality to take on the form of a potential locality. As potential it is formless in the respect it does not exist in its actualized state.

This may appear confusing, a localized phenomena not being a localized phenomena. It is potential in the respect it is not the embodied form which is about to take place. Take for example the cow again. It's potential state is one of particles (death and decomposition/eaten), it's actual state is the cow. The actual state of the cow must project to another actual state of of being sick then an actual state of being sick.

Each state of the cow is a localization of the cow in a state of time where, due to time, the cow exists as multiple entities or parts. Now the potential state of particles is formless in time, relative to the other localizations of the cow. This potential formless nature is the means through which the actual localized axioms exist, with the potential state being a localized state when observed from a macro localized state. It acts as the formless means through which the actual states invert to other states that exist relative to eachother. The cow actualizes its potential nature (giving the formless nature form) through further actual states. The boundary line between the transition of the actual state into the potential state being actualized when localized appears as a further continuum of actual/potential localites.

Now the localized state as objective, form and function, observes the potential state is subjective. This makes little sense to most. While the potential is relative formlessness, and the subject is formless, how can potentiality be subjective? What we understand of the subjective state is a state of being that is inherently without form through language, thought, whatever in regards to the individual state. The subjective state as potential localization is potential objectivity. One may have a subjective experience and give objective form to it through word, etc. So going back to the cow being potential particles, necessitates the cow as not being a cow is subjective in the respect it is a formless state of the cow. Death, or void, can be viewed as subjective considering objectively a transition of movements occurs.

Potentiality as that without form can be observe as a relative absence of consciousness, death, and the term "reaching ones potential" can be observe as actualizing all that can be actualized before death, as inversion of one degree of consciousness to another (higher or lower) occurs.

In these respects, where the axiom as a locality exists through inversion it is a causal for inversion from one state to another is fundamentally void of being as this inversion of states is an inversion between unity/multiplicity.


C. All axioms are synthetic as the joining of the subjective formless (acausal randomness/potentiality) and objective form and function (causal structure/locality).

All axioms exists as directed movement, woth this directed movement being progressive and self referential. As directed movement they exist as limits. Movement occurs only if it is directed and direction occurs only if there is movement.

This limit exists through no limit as possible limit. A limit may exist if and only if it is possible, all possibilities are that which do not exist, however what is possible occurs through the limits.

This point observes an inherent cycling where possibility and limit occuring through a continual joining that is circular. All phenomena as existing through cycles are maintained for what they are by a process of joining. The birth and death of the cow, are joined as the cow existing as a cycle. Synthesis acts as a means of maintainance. This nature of synthesis is consciousness as it is a form of measurement where A dualism is joined into a unified state observed as triadic in its totality.

I will end it here because the post is way to long.

Long story short, all axioms are conscious because of a synthesis of a causal and causal nature which reflects the nature of God as Universal consciousness.

Will address when have more time but in very simple terms, all axioms exist as limits which replicate to further limits, with this replication allow a form of symmetry to occur that maintains the axiom.

This replication of symmetry, as a reflective or mirroring process, is the foundation of all phenomenon, as well as consciousness (as necessitating a form self referentiality), therefore all axioms have som degree of awareeness. Consciousness exists through a replication of limits.

Yes and No are relative to context of the definition, considering one may defined observation to means several different things relative to certain premises.

It may be defined as an act of reflection, with reflection being the replication of limits either actively (applying limits such as a line to a board), passively (observing the relations between animals or particles physical).

From a defintion where observation exists as a form of reflection, then yes all axioms observe.

The question could be asked, what is form?