The Grades of Initiation

[Daniel]

6 hours ago, Michael Sternbach said:

0 can be defined as the infinitely small.

 

What's smaller?

 

A bank account with 0 dollars?

A bank account overdrawn 100 dollars?

 

0 is not infinitely small.

 

-100 is smaller.

[Daniel]

8 minutes ago, helpfuldemon said:

• 0°—Minerval
• I°—Man & Brother
• II°—Magician
• III°—Master Magician
• IV°—Perfect Magician & Companion of the Holy Royal Arch of Enoch
  • P.I.—Perfect Initiate, or Prince of Jerusalem
• because these are the grades of accomplishment in the OTO

 

How are these Jewish?

[helpfuldemon]

perfect magician and companion of Enoch?  Jewish

 

Perfect initiate or prince of Jerusalem?  Jewish

[Nungali]

20 hours ago, helpfuldemon said:

Man of Earth triad[edit]

• 0°—Minerval
• I°—Man & Brother
• II°—Magician
• III°—Master Magician
• IV°—Perfect Magician & Companion of the Holy Royal Arch of Enoch
  • P.I.—Perfect Initiate, or Prince of Jerusalem

The OTO is Jewish, and Thelema isn't.  The two aren't compatible methinks.

 

More than just compatible . You do realize  Crowley re wrote all the OTO rituals to turn them from Christian into Thelema ?  The Book of the Law  holds a central part in those rituals .  The Man of Earth triad gotta be one of the most Thelemic things on the planet !  Its actually  'militantly  Thelemic '  !

 

But this is what happens when one does not have  experiential  direct knowledge  and instead  bases their  conclusions on a word or two.

 

So I assume its due to the companion in IV and the Prince in PI  titles . 

 

For others who might be interested :

 

The Royal Arch  ( 'red lodge' ) , in Freemasonry ,  is a whole different school to the first 3 degrees  ( Blue lodge ) .   It is about the reconstruction of Solomon's temple . . .  and learning certain lessons that are encoded within the masonic version of that story .  Like a LOT of Freemasonry , it is Christian based or focused , and as they do , Christians have a certain crossover into Judaism because they accept the 'Old Testament '.

 

OTO version does none of this  ... in fact , their 4th degree , it could be said, in some ways , makes a mockery of that - not of Judaism or the reconstruction of the temple , but of the  complexity , regalia, titles, degrees, and paraphernalia that clutters the essential teaching of the Masonic  Blue Lodge  and other forms of Masonry [  remember that the 9 degrees of the OTO are a cut down version of the 97 degrees of the Rites of Memphis and Mizriam ( and other things ) ... and yes, Mizriam is a Hebrew cognate of a common Semitic source word for ' Egypt' -  but this doesnt mean  ' it is Jewish ' either  as it is similar to Miṣr in modern Arabic, Misri in the 14th century B.C. Akkadian Amarna tablets, Mṣrm in Ugaritic,  Mizraim in Neo-Babylonian texts, and Mu-ṣur in neo-Assyrian Akkadian (as seen on the Rassam cylinder ). ]

 

But all that gets stripped away in PI .... although there is a title for the person , as shown in the  ceremony title  (it is not a degree as such but more a 'pendant ' to the IV degree )  one certainly does not become a Prince of Jerusalem  after it , in fact one becomes 'not a Prince of Jerusalem '  after it , one becomes  not a Prince of anything after it ... in fact, one becomes not an anything after it - no form of address , no identity,  no magical name or motto , no insignia .... nothing , void .

 

 

[Nungali]

17 hours ago, helpfuldemon said:

perfect magician and companion of Enoch?  Jewish

 

Perfect initiate or prince of Jerusalem?  Jewish

 

• 0°—Minerval
• I°—Man & Brother
• II°—Magician
• III°—Master Magician

?

 

Not Jewish .

[Daniel]

20 hours ago, helpfuldemon said:

perfect magician and companion of Enoch?  Jewish

 

Perfect initiate or prince of Jerusalem?  Jewish

 

Those are reasons.

[Nungali]

Here I was thinking you had to have a Jewish mother to be considered Jewish . 

 

Seems like I cant get anything right  ...    here .

 

[Nungali]

What about being the King of Jerusalem ? Would that make you even more Jewish than being a mere prince would ?

 

Ask Baldwin the First   .

 

  I am pretty sure he remained Christian and didnt automatically become Jewish .

 

Even the  King of Spain retains that title  :  King Felipe VI of Spain holds the title "King of Jerusalem" as a part of the traditional titles of the Spanish monarchy. The Queen of Jerusalem Isabela I, married to the Cypriot royal family through king Amalric II of Cyprus, their daughter Melisende married to the king of Antioch and had her daughter Mary.

 

My favourite non Jewish  King of Jerusalem ;

 

" In 1948 King Abdullah I of Jordan was crowned king of Jerusalem by the Coptic bishop. "

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

 

"

[Nungali]

XVI.

PRINCE OF JERUSALEM.

WE no longer expect to rebuild the Temple at Jerusalem. To us it has become but a symbol. To us the whole world is God's Temple, as is every upright heart. To establish all over the world the New Law and Reign of Love, Peace, Charity, and Toleration, is to build that Temple, most acceptable to God, in erecting which Masonry is now engaged. No longer needing to repair to Jerusalem to worship, nor to offer up sacrifices and shed blood to propitiate the Deity, man may make the woods and mountains his Churches and Temples, and worship God with a devout gratitude, and with works of charity and beneficence to his fellow-men. Wherever the humble and contrite heart silently offers up its adoration, under the overarching trees, in the open, level meadows, on the hill-side, in the glen, or in the city's swarming streets; there is God's House and the New Jerusalem.

 

https://sacred-texts.com/mas/md/md17.htm

[Michael Sternbach]

On 13.9.2023 at 7:32 AM, Daniel said:

 

What's smaller?

 

A bank account with 0 dollars?

A bank account overdrawn 100 dollars?

 

0 is not infinitely small.

 

-100 is smaller.

 

0 is infinitely small as a positive number. Introducing the '-' sign reverses things. Now it might be the largest negative number. Which kind of illustrates my position that zero and infinity coincide.

 

I suspect that you aren't satisfied with my definition of 0 as 1/∞ since you consider zero to be 'disconnected' (as you said elsewhere). You may argue then that, by ongoing division, it can never be reached. But you see... That's the point.

 

On a related note, your equation of 1 and infinity mentioned here actually makes sense to me insofar there's an infinite number of fractions between 0 and 1.

 

It's all a question of perspective, really. 

 

BTW, I constantly find that, at an advanced level, mathematics becomes a surprisingly artistic and intuitive endeavour! 🙂

Edited September 14, 2023 by Michael Sternbach

[Daniel]

4 hours ago, Michael Sternbach said:

 

0 is infinitely small as a positive number. Introducing the '-' sign reverses things. Now it might be the largest negative number. Which kind of illustrates my position that zero and infinity coincide.

 

I suspect that you aren't satisfied with my definition of 0 as 1/∞ since you consider zero to be 'disconnected' (as you said elsewhere). You may argue then that, by ongoing division, it can never be reached. But you see... That's the point.

 

On a related note, your equation of 1 and infinity mentioned here actually makes sense to me insofar there's an infinite number of fractions between 0 and 1.

 

It's all a question of perspective, really. 

 

BTW, I constantly find that, at an advanced level, mathematics becomes a surprisingly artistic and intuitive endeavour! 🙂

 

I distiguish between 'zero' the number and 'null' the concept.  when people speak about 'zero' philosophically, it seems that they are actually talking about 'null' not 'zero', but the two get conflated.  'zero' in my opinion is an object, 'null' is an action.  'null' is something that is happening.  

 

Also, when I consider infinity, it's +/- infinity ( ±∞ ).  I include the negations (was, wasn't, is, isn't, will-be, won't, could-be).Technically, in mathematics, ∞ = ±∞. The ± is implied in the symbolism.  This puts 0, if it were to be included in ∞ in the center, not at the extreme.  It lives in the center of the number-line, doing nothing, contributing nothing, passive.  Absolutley meaningless and without purpose.  But!  That is not what people are speaking about when 'zero', 'emptiness' 'nothingness' is discussed philosophically.  The 'zero' that is being contemplated and considered is active.  a resource, pool of nothingness, so to speak.  like a great heavenly body of water, the 'firmament' for lack of better word.  it's not a boring numeric 'zero' living in the middle of the number line.

 

regarding being disconnected, I prefer the word disjointed, never coinciding.  'null' is the action of removal, like subtraction, like vaccuum.  the operation, not the operator.  it's energetic.

 

Here's a diagram of how I envision 'null' which is often spoken of as 'zero', a source for manifestation.  But I'm trying to illutrate that it's active.  Energetic.  The green arrows are "nullifying".  It just keeps nullifying, forever and ever and always.

 

Edited September 14, 2023 by Daniel

[Daniel]

{ 1, 2 , 3 } ∩ { 4 , 5 , 6 } = null = { ... not -5, not -4, not -3, not -2, not -1, not 0, not 1, not 2, not 3, not 4, not 5 ... }

 

notice null includes "not 0"  and it keeps going forever and nullifying.

 

i haven't read this in a while, but i remember really liking it.  it connects null, to the concept 'mu'.

 

"Enlightenment is the realization of the null, the no-thing, Mu"

 

https://webhome.phy.duke.edu/~rgb/Philosophy/axioms/axioms/Null_Set.html

 

https://en.m.wikipedia.org/wiki/Mu_(negative)

 

Edited September 14, 2023 by Daniel

[whocoulditbe?]

7 hours ago, Daniel said:

{ 1, 2 , 3 } ∩ { 4 , 5 , 6 } = null = { ... not -5, not -4, not -3, not -2, not -1, not 0, not 1, not 2, not 3, not 4, not 5 ... }

Where did you learn this "not" notation from? I'm not sure what it's supposed to mean. If you're getting at the idea that the empty set {} is 𝕌^∁, the complement of the universal set, remember that the universal set doesn't exist.

 

From the page you linked to:

Quote

The algebra of set theory closes under intersection. If we simply consider the empty set {} to be an abstract ``container'' of all sets and hence a ``member'' of all sets in the Universe, then we no longer even have to specify that the intersection of two sets with no members in common [i.e. disjunct sets] is the empty set, we can simply note that ordinary intersection of two sets with no members other than the empty member in common is of course the empty set.

This is misleading. Yes, the intersection of two disjoint sets is the empty set, but that doesn't mean that the empty set is a member of every set! The set {1, 2 , 3, {}} has {} as a member, and is distinct from {1, 2, 3}, which does not. {1, 2, 3} and {4, 5, 6} are disjunct, but neither contains the empty set. If you added the empty set to them, the intersection {1, 2, 3, {}} ∩ {4, 5, 6, {}} would be {{}}, not {}, and they would no longer be disjunct.

 

Errata: For disjunct read disjoint

Edited September 14, 2023 by whocoulditbe?

[Daniel]

30 minutes ago, whocoulditbe? said:

Where did you learn this "not" notation from? I'm not sure what it's supposed to mean. If you're getting at the idea that the empty set {} is 𝕌^∁, the complement of the universal set, remember that the universal set doesn't exist.

 

I'm not getting is from anywhere.  Hee-hee. 

( I'm 'not' getting the 'not' from anywhere. which means the 'not' is coming from 'no-where'. )

 

Yes, I'm of russel's paradox, but, I don't see how it applies here, or invalidates what I wrote.

 

 

30 minutes ago, whocoulditbe? said:

 

From the page you linked to:

This is misleading. Yes, the intersection of two disjoint sets is the empty set, but that doesn't mean that the empty set is a member of every set! The set {1, 2 , 3, {}} has {} as a member, and is distinct from {1, 2, 3}, which does not. {1, 2, 3} and {4, 5, 6} are disjunct, but neither contains the empty set. If you added the empty set to them, the intersection {1, 2, 3, {}} ∩ {4, 5, 6, {}} would be {{}}, not {}, and they would no longer be disjunct.

 

Yes!  If I recall, the point being made is the moniker "empty-set" is a misnomer.  It's not a "set" it can't be.  And the convention/axiom that the "empty-set" is a subet of all sets is actually false.

 

But I'd need to re-read the document to be sure.  Should I do that?  I love this stuff, so I would be happy to do it if it's needed to correct my understanding, or, what I avoid a future mistake.  

[whocoulditbe?]

10 minutes ago, Daniel said:

Yes!  If I recall, the point being made is the moniker "empty-set" is a misnomer.  It's not a "set" it can't be.  And the convention/axiom that the "empty-set" is a subet of all sets is actually false.

The empty set is a set, and an essential one for doing almost anything in set theory. It is also a subset of all sets, just not a member of all sets. It must be a subset of all sets, because B is a subset of A whenever A ∪ B = A, and A ∪ {} must equal A for all A, since there's nothing in {} to add on to A, regardless of what A is.

 

Quote

But I'd need to re-read the document to be sure.  Should I do that?  I love this stuff, so I would be happy to do it if it's needed to correct my understanding, or, what I avoid a future mistake.  

I would say "don't learn set theory from a philosophy website!" but that would be stupid of me, because the SEP has a great intro to it here.

[Daniel]

38 minutes ago, whocoulditbe? said:

I'm not sure what it's supposed to mean.

 

I'm trying to think of a better way to describe it than the way I wrote it.

 

If I consider 2 non-equal sets, A and B, like the picture I posted earlier, what is a real world example of A and B?  My purpose is to better understand the concept of 'null' so, I'd like to slow down the "intersection" the "union", the action which produces "null" in my mind for the purpose of understanding the mechanics of it.  ( in doing so, hopefully, ideally, a realization of Mu is produced , at least temporarily )

 

The easiest example, numerically, is A = { 1 } and B = { 2 }.  But it could be any non-equal pairing. 

{ A } and { B }, { dog } and { cat }, { swimming } and { walking }, { square } and { circle }, etc.

 

If I intersect any of these pairs, what is produced?  how can I imagine it?  is it just an "empty box"?  what does that mean, "empty-box"?

 

{ A } intersected with { B } = ?????

 

it's not A, right?

it's not B, right?

it's not C either, right?

D? nope

E? nope

F? nope

1? nope

not 2 either

not 3

not 4 

not 5

not 6

 

what about negative numbers?

 

nope.

not -1

not -2

not -3

not -4

 

what about symbols?

 

nope.

not circle

not square

not star

not rhombus

 

what about actions?

 

nope.

not walking

not sitting

not standing

not sleeping

not dreaming

 

what about ideas?

 

love?  nope

hope? nope

patience?  nope

 

{ A } intersected with { B } isn't any of those!

See what I mean?  No matter what, nothing is included, and that nothingness is active.

 

If I were to attempt to construct a set of { A } intersected with { B } in my mind, it would look like this:

 

{ ... not-A, not-B, not-C, not-D, not-E, not-F, ... , not-1, not-2, not-3, not-4, not-5, not-6, ... not-negative-1, not-negative-2, not-negative-3, not-negative-4, not-negative-5, not-negative-6, ... , not-circle, not-square, not-star, not-rhombus, ... ,  not-siting, not-standing, not-sleeping, not-dreaming, ... , not-love, not-hope, not-patience, ... }

 

After typing this, maybe this is the easiest clarification of what I mean?

 

{ not-1 } = "{ 1 } is false"

[Daniel]

13 minutes ago, whocoulditbe? said:

The empty set is a set, and an essential one for doing almost anything in set theory. It is also a subset of all sets, just not a member of all sets. It must be a subset of all sets, because B is a subset of A whenever A ∪ B = A, and A ∪ {} must equal A for all A, since there's nothing in {} to add on to A, regardless of what A is.

 

It's just an axiom, just a convention. A beloved convention, a useful tool.  I think I saw it called a "convenient fiction"....

 

Let me see if I can find something for you.... Found it!

 

https://proofwiki.org/wiki/Definition:Empty_Set#

 

1965: J.A. Green: Sets and Groups: §1.3§1.3:

If A,BA,B are disjoint, then A∩BA∩B is not really defined, because it has no elements. For this reason we introduce a conventional empty set, denoted ∅∅, to be thought of as a 'set with no elements'. Of course this is a set only by courtesy, but it is convenient to allow ∅∅ the status of a set.

2) 1968: Ian D. Macdonald: The Theory of Groups: Appendix:

The best attitude towards the empty set ∅∅ is, perhaps, to regard it as an interesting curiosity, a convenient fiction. To say that x∈∅x∈∅ simply means that xx does not exist. Note that it is conveniently agreed that ∅∅ is a subset of every set, for elements of ∅∅ are supposed to possess every property.

3) 2000: James R. Munkres: Topology (2nd ed.): 11: Set Theory and Logic: §1§1: Fundamental Concepts
 

Now some students are bothered with the notion of an "empty set". "How", they say, "can you have a set with nothing in it?" ... The empty set is only a convention, and mathematics could very well get along without it. But it is a very convenient convention, for it saves us a good deal of awkwardness in stating theorems 

 

This might also be useful.

 

https://en.m.wikipedia.org/wiki/Empty_domain

 

In first-order logic the empty domain is the empty set having no members. In traditional and classical logic domains are restrictedly non-empty in order that certain theorems be valid. Interpretations with an empty domain are shown to be a trivial case by a convention originating at least in 1927 with Bernays and Schönfinkel (though possibly earlier) but oft-attributed to Quine 1951.

 

 

 

[whocoulditbe?]

15 minutes ago, Daniel said:

The easiest example, numerically, is A = { 1 } and B = { 2 }.  But it could be any non-equal pairing. 

You mean disjunct. {1, 2} and {2} are non-equal but have {2} as their intersection.

 

15 minutes ago, Daniel said:

{ not-1 } = "{ 1 } is false"

Sets are not propositions. They can't be true or false, but you can say true or false things about them. For example, instead of saying "the room was silent," I could say "The set of all sounds in the room was {}," or "部屋に無音があった."

[Daniel]

1 hour ago, whocoulditbe? said:

It must be a subset of all sets, because B is a subset of A whenever A ∪ B = A, and A ∪ {} must equal A for all A, since there's nothing in {} to add on to A, regardless of what A is.

 

I disgree.  That's not the complete defintion of subset. 

 

A subset is A ∪ B = A *AND* A ∩ B = B.  Both must be true.  

 

A ∪ {} = A But A ∩ {} =/= {}.  It can't, by definition.  {} is disjoint from all sets including itself.  The solution is proper interpretation of {}.  It flips the meaning, it inverts it.  It ( {} ) is "contradicting", the action.  That's it's actual meaning.

 

 

{} is a subset of all sets is just a definition, not a derivation.  Not a proof.  Here, let me see if I can find it.  It's just a mis-application of the law of non-contradiction.  The logic is "If it cannot be proven that {} is NOT a subset, then it is assumed that it must be a subset."  But that doesn't work for negative assertions:  See here:  https://plato.stanford.edu/entries/contradiction/.  Search the page for "Socrates doesn't exist".

 

Definition 1.3 Suppose A and B are sets. If every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is not true that every element of A is also an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B.

 

Looking at the first sentence of the defintion given, If every element of A is also an element of B, then we say A is a subset of B. But this cannot be so because ∅ contains no elements! Thus it is not the case that ∅ ⊆ B, so it must be that ∅ ⊈ B.

 

"Book of Proof, Third Edition, Richard Hammack"

https://math.vcu.edu/directory/hammack.html

 

 

 

See that?  "So it must be..." That's applying the Truth table for implication, the weakest of the weak standards for truth.  And, like I said, it's a defintion.  A convention.  An axiom.  Convenient?  Useful?  Absolutley!  True?  Not really.  It contradicts with the defintion of the empty-set, and empty-set, itself is contradictory.  It's not a collection of elements.  But once {} is interpretted properly, it all falls into place and plays nicely.

 

1 hour ago, whocoulditbe? said:

The empty set is a set, and an essential one for doing almost anything in set theory

 

But there's more than 1 set theory, ZFC is the easiest to learn, so that's what people learn, and assume it's the only one.  They thinks it's law, like scriptural law, religious law.  And let's me honest that's what axioms are.  They're religious.  Useful?  Sure.  But, if someone like me comes along... then the adherents to axiomatic set theory object vehemently :"Blasphemy!  Burn him!  He's a witch!  Burn Him!"  

 

1 hour ago, whocoulditbe? said:

I  would say "don't learn set theory from a philosophy website!" but that would be stupid of me, because the SEP has a great intro to it here.

 

Set theory IS philosophy.  All Math is philosophy.  Anyway, did you check he credentials of the author from Duke University?  PHD in Physics.  Senior Lecturer.  Many many journal articles....

 

https://scholars.duke.edu/person/rgb/publications

 

 

Edited September 14, 2023 by Daniel

[whocoulditbe?]

6 minutes ago, Daniel said:

{} is disjoint from all sets including itself.

... therefore {} ∩ whatever must equal {}, even {} ∩ {}.

[Daniel]

46 minutes ago, whocoulditbe? said:

You mean disjunct. {1, 2} and {2} are non-equal but have {2} as their intersection.

 

Thank you!!!

 

47 minutes ago, whocoulditbe? said:

Sets are not propositions. They can't be true or false, but you can say true or false things about them. For example, instead of saying "the room was silent," I could say "The set of all sounds in the room was {}," or "部屋に無音があった."

 

OK, ok... but, hopefully you know what I mean now?

 

{ 1 } = { ... not-0, not-2, not-3, not-4, not-5, ... } ad inifinitum for everything that wasn't, isn't, and won't with only 1 exception.  

{ shoe } = { ... not-shirt, not-pants, not-glasses, not-hat, ... } ad inifinitum for everything that wasn't, isn't, and won't with only 1 exception.

 

You understand the notation now?  The symbolism?  The meaning of what I wrote?

 

The nice thing about it being completely foreign to you, is, at least, one can see it is my own idea, not a copy from someone else.  Even having minor flaws in how I speak/write about it ( example: { not-1 = "{ 1 } is false" } demonstrates this

[whocoulditbe?]

2 minutes ago, Daniel said:

{ 1 } = { ... not-0, not-2, not-3, not-4, not-5, ... } ad inifinitum for everything that wasn't, isn't, and won't with only 1 exception.  

{ shoe } = { ... not-shirt, not-pants, not-glasses, not-hat, ... } ad inifinitum for everything that wasn't, isn't, and won't with only 1 exception.

A fish is a not-shirt, and a not-pants, and a not-glasses, and a not-hat, but I don't walk about the town on fish. Similarly, a shirt isn't a not-shirt, but it's still a not-hat, so it still looks like you're saying shoes are shirts.

Edited September 14, 2023 by whocoulditbe?

[Daniel]

6 minutes ago, whocoulditbe? said:

... therefore {} ∩ whatever must equal {}, even {} ∩ {}.

 

Can't be, that's not disjointed is it?

 

A ∩ A is not disjointed

B ∩ B is not disjointed

C ∩ C is not disjointed

 

{} ∩ {} = {} is different from any other example of ∩.  Similarly {} ⊆ A is different from any other example of ⊆.  {} is "special".  {} is unlike any other "set".  It is "un-set".  It inverts the meaning of any operator.  It's the basis of "subraction".

 

Edited September 14, 2023 by Daniel

[Daniel]

3 minutes ago, whocoulditbe? said:

A fish is a not-shirt, and a not-pants, and a not-glasses, and a not-hat, but I don't walk about the town on fish. Similarly, a shirt isn't a not-shirt, but it's still a not-hat, so it still looks like you're saying shoes are shirts.

 

Not true.  I'm saying shoes aren't shirt.  I said:

 

"{ shoe } = { ... not-shirt, not-pants, not-glasses, not-hat, ... }"

 

 

[Daniel]

4 minutes ago, whocoulditbe? said:

a shirt isn't a not-shirt,

 

True!

 

Shirt =/= not-shirt.

 

Or

 

Shirt is not (not-shirt). 

Distribute the "not".

 

Shirt is shirt.  Tautology.  Identity.