Philosophy Explorer wrote: ↑Tue Nov 14, 2017 10:23 pmWhich axioms? All of them? Can you explain this further?Eodnhoj7 wrote: ↑Tue Nov 14, 2017 10:13 pmwtf wrote: ↑Tue Nov 14, 2017 10:02 pm

That's just word salad.

But one question occurs to me. Are you doing math, metaphysics, or poetry? Perhaps I'm taking you too literally and trying to make mathematical sense of your ideas.

Try seperating math from the nature of the "axiom" as "self-evidence" and you will get your answer. Most modern math is just word-salad.

Perhaps you are not trying to make mathematical sense, but are perhaps trying to explain the nature of numbers in the universe or something along those lines.

In which case I still can't understand you, but I would agree that it's not helpful for me to ask you to make mathematical sense.

If mathematics can be "sensed" as you suppose, than it has a subjective nature. Strictly speaking the axioms of modern math don't make sense.

You can pick one if you want but the zero dimensional thread I placed argues one set of points (however it could be taken as geometry). I am not saying that 1+1=3...or anything remotely close to it. What I am saying is the axioms for modern mathematics is determined through a democratic agreement and are strictly and extension of what people percieve "order" as. Is it order? Yes.

But all axioms are by their very definition "self-evidence" and in this respect a largely psychological approach is inevitable.

Serious mathematicians are more prone to mental illness.

https://www.sciencedirect.com/science/a ... 6605000620

PhilX

## Cyclic numbers

### Re: Cyclic numbers

### Re: Cyclic numbers

I don't necessarily disagree with you here.

However earlier, you were saying that your exposition is standard math. You emphasized this by linking to the Wiki article listing the common meanings of the standard mathematical symbols.

But now you seem to be grinding a philosophical axe about how standard math is wrong or doesn't make sense.

Either one of those positions is perfectly sound. To argue in terms of standard math, or to argue that standard math is bullshit, are both perfectly sensible positions.

Just not at the same time.

So which is it?

Also would it be too much trouble for me to ask you to use standard quoting conventions? When you reply to a post by putting your responses in red and then quoting your entire response it's very annoying.

### Re: Cyclic numbers

Well I am sorry you feel that way, however considering the nature of having to specifically address certain points, for the time being, it is a necessary evil.wtf wrote: ↑Tue Nov 14, 2017 11:00 pmI don't necessarily disagree with you here.

However earlier, you were saying that your exposition is standard math.

You emphasized this by linking to the Wiki article listing the common meanings of the standard mathematical symbols.

Yes, the symbol "≡" translates into english as "is congruent to" which also translates as "mirror image"

https://en.wikipedia.org/wiki/Congruence_(geometry).

You are also right about the mod x nature to the symbol.

You are also right about how their are not specific rules saying a symbol cannot be used in a certain way.

So if I take your above perspectives and synthesize them the result is the use of "≡" as a symbol for reflection.

Where I went wrong, if it is to be interpreted in such a manner, is that I did not explain my position thoroughly. But given the nature of this being a dialect, I would hardly count that as a "sin", considering the nature of the dialectic is precisely about that specifically: finding a common bond of definition as a synthesis of axioms.

But now you seem to be grinding a philosophical axe about how standard math is wrong or doesn't make sense.

Nothing noone else has not done before me considering that there is no universal definition as to what mathematics is (Mura), whether it is an art or science (Tobies), or even if it is definable at all (Mura) other than “Mathematics is what mathematicians do” (Mura). It is in this respect the continual observation of symmetry maintains a degree of symmetry within itself, specifically through the axiom as dualism of "symmetry" and "asymmetry".

Either one of those positions is perfectly sound. To argue in terms of standard math, or to argue that standard math is bullshit, are both perfectly sensible positions.

Just not at the same time.

So which is it?

Contrary to popular belief one can hold two different positions at the same time in different respects. Much of logic is founded on this simple premise. From this simple premise of thesis and antithesis we are better able to synthesize further axioms.

Also would it be too much trouble for me to ask you to use standard quoting conventions?

What conventions?

When you reply to a post by putting your responses in red and then quoting your entire response it's very annoying.

### Re: Cyclic numbers

The correct Wiki link for the congruence of integers is here. https://en.wikipedia.org/wiki/Modular_arithmeticEodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 amYes, the symbol "≡" translates into english as "is congruent to" which also translates as "mirror image"

https://en.wikipedia.org/wiki/Congruence_(geometry).

Instead, you linked the geometric meaning of congruence. But you have not explained what you mean by saying that 2 and 4 are congruent in the geometric sense. Until you do, you have said nothing.

Yes of course. That's the standard default meaning of '≡' in the context of the integers.

Correct. If I define '2' to mean 3 and '5' to mean 12 then 2 + 5 = 15.

However if you are going to change the standard meaning of a symbol or technical term, you need to provide a clear, unambiguous definition.

But you have yet to provide a clear, unambiguous definition of your use of the word "reflection." Till you do, your exposition is meaningless. It's devoid of meaningful content.

Agreed. And I would say I'm being patient in being willing to engage with you, and to repeatedly ask for a clear explanation of your terminology and symbols.

What is this, Marxist re-education camp? Where did you get this nutty rhetoric? What does this have to do with your unexplained claim that 2 and 4 are congruent in the geometric sense? You seem to be hiding behind obscure philosophical jargon to avoid dealing with the questions I'm raising.

For a brief moment, you correctly realized that you are being unclear. But instead of then making an effort to be more clear, you decided to wander off into philosophical obfuscation.

I agree that one may question the philosophical basis of math. But that has nothing to do with your making up your own terminology and symbols, and then repeatedly failing to give coherent explanations of what they mean.Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 amNothing noone else has not done before me considering that there is no universal definition as to what mathematics is (Mura), whether it is an art or science (Tobies), or even if it is definable at all (Mura) other than “Mathematics is what mathematicians do” (Mura). It is in this respect the continual observation of symmetry maintains a degree of symmetry within itself, specifically through the axiom as dualism of "symmetry" and "asymmetry".

The fact that philosophers are hard pressed to nail down a precise definition of mathematics, in no way justifies your continued refusal to define your terms and symbols.

What that has to do with your arbitrary and unexplained redefinitions of common terms like reflection and common symbols like the triple equal sign, I have no idea. And again, thesis and antithesis. Are you arguing from a Marxist perspective? What would be the point of that? You still have to define your terms if you want to communicate mathematical ideas.

### Re: Cyclic numbers

I have to agree with "WTF". I still don't understand what you mean by 'reflection' and apparently nearly everything can be a 'median.'

### Re: Cyclic numbers

wtf wrote: ↑Wed Nov 15, 2017 10:28 pmThe correct Wiki link for the congruence of integers is here. https://en.wikipedia.org/wiki/Modular_arithmeticEodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 amYes, the symbol "≡" translates into english as "is congruent to" which also translates as "mirror image"

https://en.wikipedia.org/wiki/Congruence_(geometry).

Yes, the wiki page I posted originally argued that, the above gives greater definition of course.

Instead, you linked the geometric meaning of congruence. But you have not explained what you mean by saying that 2 and 4 are congruent in the geometric sense. Until you do, you have said nothing.

Using the above statement I mentioned prior "is congruent to" which also translates as "mirror image":

1) "≡" translates as "is congruent to" under the mod definition which you provided. "Congruent" means "in agreement or 'harmony' under a general english definition. However, as you correctly pointed out it does not "strictly" translate in such a manner in the field of mathematics. The problem occurs as math and standard english, while having similarities, are not "equal". I believe we both agree here.

2) The geometric meaning of "congruence" further follows the same problem as stated in point 1. The problem occurs that the nature of "congruence", using "≡" has multiple different meanings at the same time in different respects (assuming we equate it to "congruence"). This works if we decide to seperate mathematics, geometry, and language into seperate fields however it does not solve the problem if we are trying to find a common ground in which these different fields must be "rooted" in.

3) Considering that mathematics, geometry, and language are seperate and how "congruence" is portrayed in one field may differ from the other another problem occurs as they are all linked by their very nature to "axioms" as their foundation. Math, geometry, and language differ in varying degrees however, in a great twist of irony, their foundations do not as all are form from "axioms".

4) The nature of subjective and objective realities are inherently united through "self-evidence". This self evidence breaks across all these fields while providing a common bond. So as to the common bond? I can argue a regressive or progressive argument in an attempt to unify them, however considering that each of these fields theoretically could expand ad-infinitum either a regressive or progressive argument in turn would follow that same form and function.

5) So the next question come to mind: What to do exactly? This is considering we develop these fields in such a manner where they continuall differ from eachother to such an extent that any reasonable form of synthetic process would either be difficult or completely impossible. Well going back to point three we have found that all still are united through the "axiom".

6) So what is the most axiomatic structure within math? What can math be reduced to in a atomic state? What can math magnify itself into as a whole? Number specifically, with all "number" being an extension of or being composed of "1".

7) And geometry, assuming the same questions? Western thinking inclines towards the line, however the problem occurs as the line exists if and only if there are "points". So the nature of the "point" being a universal form within geometry follows.

Now if one were to look at the foundation of mathematics as "number through 1" and geometry as "form through point", the next form of synthesis between Quantity (number) and "Quality" (point) would be "1" as "Point".

9)However the problem occurs as the point is viewed as a zero dimensional object, implying the point has no direction and therefore is not a thing in itself. However if the point "directs" itself into itself it becomes both 1 dimensional and simultaneously becomes a stable entity. 1 exists if and only if it is "unified" or "stable". Considering both geometry and mathematics question whether their fields are "abstract" or "physical" entities, a solution can be implied as "Number as Spatial Point(s)".

10) The question occurs going back to the nature of "congruence" is how can number and space find common "ground", formative and functionally speaking? Considering all structure is founded in harmony, or balance, the nature of the meaning of congruence can be argued as "mirroring" or "reflecting" where the quantitative and qualitative aspects of the "Number as Spatial Point(s)" equates to an existence through a "mirroring" or "reflective" process. This nature of 1, point, and mirroring are all axiomatic processes in themselves in the respect that they are the base quantitative, qualitative and form/functional aspects of all observable physical/abstract structures.

11) Now to get back to the example of "2 reflecting/mirroring 4". Considering that (2,4) are composed of 1 reflecting upon itself, they not only find "congruency" or "harmony" through 1, but simultaneously reflect/mirror eachother as structures reflective of 6 (considering they are of positive value, this equates to addition) and 1 at the same time in different respects. Simultaneously, with 1 as point(s), the (2,4,6,1) manifest a variety of geometric structures as points reflecting.

Yes of course. That's the standard default meaning of '≡' in the context of the integers.

Correct. If I define '2' to mean 3 and '5' to mean 12 then 2 + 5 = 15.

However if you are going to change the standard meaning of a symbol or technical term, you need to provide a clear, unambiguous definition.

See above.

But you have yet to provide a clear, unambiguous definition of your use of the word "reflection." Till you do, your exposition is meaningless. It's devoid of meaningful content.

Ambiguity is subjective considering Mathematician, for as long as mathematics existed, provided many "arguments" which were ambiguous for a long time...they still ended up being right. Am I comparing myself to people like "Euler" or "Ramanujan"? No. What I am saying is the Godel's incompleteness theorems argued that truth can exist without proof and what you deem as "meaning" is purely subjective.

With that being said the above "definition/explanation" should provide more clarity.

Agreed. And I would say I'm being patient in being willing to engage with you, and to repeatedly ask for a clear explanation of your terminology and symbols.

[color=#FF0000Thankyou, but remember noone is forcing you other than yourself.[/color]

What is this, Marxist re-education camp? Where did you get this nutty rhetoric? What does this have to do with your unexplained claim that 2 and 4 are congruent in the geometric sense? You seem to be hiding behind obscure philosophical jargon to avoid dealing with the questions I'm raising.

For a brief moment, you correctly realized that you are being unclear. But instead of then making an effort to be more clear, you decided to wander off into philosophical obfuscation.

See above points 1 through 11.

I agree that one may question the philosophical basis of math. But that has nothing to do with your making up your own terminology and symbols, and then repeatedly failing to give coherent explanations of what they mean.Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 amNothing noone else has not done before me considering that there is no universal definition as to what mathematics is (Mura), whether it is an art or science (Tobies), or even if it is definable at all (Mura) other than “Mathematics is what mathematicians do” (Mura). It is in this respect the continual observation of symmetry maintains a degree of symmetry within itself, specifically through the axiom as dualism of "symmetry" and "asymmetry".

The fact that philosophers are hard pressed to nail down a precise definition of mathematics, in no way justifies your continued refusal to define your terms and symbols.

Definition was given, if you don't like it...well then either accept it or provide more questions for me to answer.

What that has to do with your arbitrary and unexplained redefinitions of common terms like reflection and common symbols like the triple equal sign, I have no idea. And again, thesis and antithesis. Are you arguing from a Marxist perspective?

Hegelian Dialectic to be precise, however if you do not agree with that than maybe you should argue against Jan Łukasiewicz who extended “true/false” values to a third value of “possible” in the early 20th century (Zegarelli). Jan Łukasiewicz's and Hegel's work can be further observed as a dualistic (quantitative/qualitative) process of synthesis.

What would be the point of that? You still have to define your terms if you want to communicate mathematical ideas.

Last edited by Eodnhoj7 on Thu Nov 16, 2017 1:25 pm, edited 1 time in total.

- Arising_uk
**Posts:**11694**Joined:**Wed Oct 17, 2007 2:31 am

### Re: Cyclic numbers

wtf wrote:...

What is this, Marxist re-education camp? Where did you get this nutty rhetoric? ...

I think you'll find it is a Hegelian re-education camp.

That'll be the Hegelians for you.... You seem to be hiding behind obscure philosophical jargon to avoid dealing with the questions I'm raising.

### Re: Cyclic numbers

And Jan Łukasiewicz is of no value from a "quantitative" perspective?Arising_uk wrote: ↑Thu Nov 16, 2017 1:46 pmwtf wrote:...

What is this, Marxist re-education camp? Where did you get this nutty rhetoric? ...

I think you'll find it is a Hegelian re-education camp.That'll be the Hegelians for you.... You seem to be hiding behind obscure philosophical jargon to avoid dealing with the questions I'm raising.

- Arising_uk
**Posts:**11694**Joined:**Wed Oct 17, 2007 2:31 am

### Re: Cyclic numbers

Did he use dialectic?Eodnhoj7 wrote:And Jan Łukasiewicz is of no value from a "quantitative" perspective?

I'm guessing he defined his logical notations so that they could be understood.

### Re: Cyclic numbers

Jan Lukasiewicz's observations can comfortably be interpreted as a quantitative dual of the qualitative Hegelian Dialect. Or do you hold a different opinion?Arising_uk wrote: ↑Thu Nov 16, 2017 4:06 pmDid he use dialectic?Eodnhoj7 wrote:And Jan Łukasiewicz is of no value from a "quantitative" perspective?

I'm guessing he defined his logical notations so that they could be understood.

- Arising_uk
**Posts:**11694**Joined:**Wed Oct 17, 2007 2:31 am

### Re: Cyclic numbers

I have no opinion whatsoever, that's why I asked you.Eodnhoj7 wrote:Jan Lukasiewicz's observations can comfortably be interpreted as a quantitative dual of the qualitative Hegelian Dialect. Or do you hold a different opinion?

Your English is good so I assume that its the topic that makes it fairly impenetrable, so are you saying this Lukasiewicz's observations(which ones are you referring to?) are some kind of instantiation of Hegel's idea of Dialectic?

### Re: Cyclic numbers

The are both quantitative and qualitative duals under what "could be" called, at least what I argue, Synthetic (or neutral) Space.Arising_uk wrote: ↑Thu Nov 16, 2017 5:47 pmI have no opinion whatsoever, that's why I asked you.Eodnhoj7 wrote:Jan Lukasiewicz's observations can comfortably be interpreted as a quantitative dual of the qualitative Hegelian Dialect. Or do you hold a different opinion?

Your English is good so I assume that its the topic that makes it fairly impenetrable, so are you saying this Lukasiewicz's observations(which ones are you referring to?) are some kind of instantiation of Hegel's idea of Dialectic?

### Re: Cyclic numbers

Ah, now it all makes sense.

I wish that if people are arguing from a particular viewpoint, they'd simply say so. If @Eodnhoj7 would have begun by saying, "From a Hegelian perspective ..." I'd have simply kept my yap shut, since I don't know much about Hegel and care even less; or else I'd have cruised Wiki and SEP and tried to respond on @Eodnhoj7's own terms.

Instead, I wasted my time trying to converse with someone whose philosophical idol is famously obscure and regarded by many as being full of baloney.

As Schopenhauer famously saidl: "Hegel, said Schopenhauer, was ‘a commonplace, inane, loathsome, repulsive and ignorant charlatan, who with unparalleled effrontery compiled a system of crazy nonsense that was trumpeted abroad as immortal wisdom by his mercenary followers...’

https://www.basicincome.com/bp/schopenhauerdespised.htm

Well enough of that. Thanks Arising for putting this into perspective for me.

- Arising_uk
**Posts:**11694**Joined:**Wed Oct 17, 2007 2:31 am

### Re: Cyclic numbers

I'd have thought this Kant not Hegel?Eodnhoj7 wrote:The are both quantitative and qualitative duals under what "could be" called, at least what I argue, Synthetic (or neutral) Space.

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