Concord/One-Mindedness
Webster’s Dictionary defines Concord as : [Con]Agreeing + [cord]Heart .
1 a : a state of agreement : Harmony
b : a simultaneous occurrence of two or more musical tones that produces an
impression of agreeableness or resolution , on a listener .
It also defines dissemblance as : more at dissimulate .
1 to hide under a false appearance
2 to put on a false appearance: conceal facts, intentions, or feelings under some pretense.
In The Theology of Arithmetic , in the section on The Ennead ,
the author says ,
Surely then , because The Enneaddoes not allowThe Concord/One-Mindedness
of Number to be dispersed beyond Itself ,
But Leads/Draws-Them-Together to The Same and makes Them Play in Concert ,
Hence It is called Single-minded and Limitation ,
and It is also called Sunfrom ItsGathering-together/Salting.
Then Itwasalso calledLack of Strife because of TheRequital and Recompense
of The Numbers from Itup to THE MONAD ;
’
just as it was explained in the Diagram about Righteousness[P97].
Then 9 is also said to contain The Terms of the Symphonies :4, 3, 2 ,
’’’’ :
which make The Sesquitertian Ratio of 4:3 ,
’’
The Sesquialter Ratio of 3 : 2 ,
’’
and The Double Ratio of 4 : 2 .
’’
And finally , THE ENNEADis The First Number to be in
The Sesquioctave Ratio of 9: 8
’’
Now , through the guidance of our Beloved Leader , Dr. Pierre Grimes , we are asked to consider the relationship of the numerical sequence of 2 , 3 , 4 , that is found here in Book One of Plato’s Republic . This series is also an Arithmetical Proportion as described by Nicomachus of Gerasa in hisINTRODUCTION TO ARITHMETIC; Book II Chapter 21.5 or as a one-to-one relationship because “the same term is One and Unchanging if compared to those on either side of it” or what I call a Socratic/Dialectical relationship . For consider :
XI Socrates/Narrator : “And on hearing this , he gave a great guffaw and laughed sardonically and said ,
Thrasymachos : O Heracles , here we have the well-known dissemblance () of Socrates , and I knew it and predicted that when it came to replying you would refuse and dissemble () and do anything rather than answer any question that anyone asked you .”
Socrates : That is because you are wise , Thrasymachos , and so you knew very well that if you asked a man how many are Twelve , and in putting the question , warned him : Do not be telling me , O man , that Twelve is Two-times Six , or Three-times Four or Six-times Two or Four-times Three ; for I will not accept any such foolery as that , as an answer from you . I suspect , that it was obvious to you , that no one could give an answer, to a question framed in that manner .”
2 X 6 3 X 4
12
6 X 2 4 X 3
In other words : The Truth is unacceptable for Thrasymachos .
For earlier Thrasymachos told Socrates : “And do not tell me that It (Justice) is “that which ought to be” , or “the beneficial” or “the profitable” or “the gainful” or “the advantageous” , but express clearly and precisely whatever you say .
The Beneficial (2) The Profitable (3)
JUSTICE
That which necessarily is (1)
The Gainful (4) The Advantageous (5)
Now , who is trying to dissipate all answers and at the same time trying to hinder them from being collected-together ? And , who on the other hand , is trying to prevent the answers that are on the mark from being dissipated and to collect-them-together ?
Furthermore , are these not five aspects of that which is Providential ? Would not the absence of any aspect/part of The Whole keep it from gaining Concord ? For is not Justice something that must necessarily(1 : ) exist ? If there were no Justice , would not existence itself cease to exist ? How could anything exist if it were not necessarily so ? What would impel it to be , if not Necessity ? And once It came to be , how could anything function in its own Proper , Artful , Kosmic way without Justice Itself to serve as its Model ?
What if the Beneficial (2 : aspect were missing ? Did not Socrates prove to the assembly through his discourse with Polemarchus that Justice cannot in any way harm anyone , not even an enemy ? Is not Justice then , only concerned with the Benefit it bestows on all ? For it is not in The Nature of Justice to do harm to anything anymore than it is The Nature of The Sun to make things cold . For that which affects harm is injustice and to affect harm is within its domain . To Benefit is the domain of Justice .
What about the Profitable , The Gainful and The Advantageous ? Are these not different ways of signifying that which is Better ? And is not that which is Better that which has its eye on The Good ? And not just that which is good for a certain part of the city , but Good for all ?
But listen to what comes next in the dialogue and keep in mind what the author of The Theology of Arithmetic says about Concord :
Socrates(continuing) : Suppose he had said to you , ‘Thrasymachus , what do you mean ?
Am I not to give any of the prohibited answers , do you mean to say , not even , if the thing is one of these , but I must say something different from the truth , or what do you mean ?’ What would have been your answer to him?”
Thrasymachus: Oh sure ! How very like are the two cases !
Socrates : There is nothing to prevent this from indeed being the case . Yet if it appears
to the person asked the question , that they are such as these , do you suppose that he will any the less answer such as it appears to him , whether we forbid him , or not ?”
Indeed , The Beneficial , The Profitable , The Gainful , The Advantageous and That which is Necessary , all have a Natural Ring , a True Sound , to them . They all “produce an impression of agreeableness (of Concord) on the listener .” Yet Socrates , being a Lover of Music , fine tunes those reason principles in the soul to fully understand
how they truly are in tune with The Divine .
Before we continue , consider the following section from The Introduction to Arithmetic by Nicomachos of Gerasa . Take notice that The Arts of Number and Music ; The Primary Handmaidens of Philosophy , also bear witness to The Upright and Fair Nature of The Education that Socrates is unfolding before the minds of his audience . For how can any Artist want to out-do another Artist in the tuning of an instrument ? For once an instrument is in tune there is nothing else to be done , other than , to keep it in tune . For being “In Tune” is The Measure that Stands Above Relative Quantity and within The Genus of Absolute Quantity , yet it is established in The Middle byBeing
The Perfect Balance . Furthermore , because of this attunement , every Note has a unique number of vibrations and hence , a unique tone , such as C , and that tone has a direct relationship to certain unique numbers , such as 6 and 12 .
Book I –Chapter 14
[1] Then in turnfrom the beginning , amongThe Simple EVENNumbers ,
some are Superabundant , while others aredeficient , asif they were Extremes set against
each other , but some areIntermediate between both of them , and are called Perfect.
[2] And on the one hand , those which are said to be set against each other ;
The Superabundant and the deficient , are distinguished from one another by the relation of
Inequality in the directions of the more and the less ; for apart from these, no other mode
ofInequality could be conceived , as neither could vice , nor disease , nor disproportion ,
nor indecency , nor any such thing . For on the one hand , in the realm of the more, there
arise excesses andoverreaching , and exaggeration and extravagance , whereas on the other
hand , in the realm of the less, there arise need and deficiency , and privation and lack .
But inThatRealmwhich lies betweenthe more and the less , which isTheEqual , there
AriseTheVirtues, of Health , Moderation , Propriety , Beauty , and The Like, to which
the aforesaid Idea of Number , The Perfect, is most Akin .
NUMBER
THE EVEN THE ODD
2 3 4 5 6 7 8 9 10 11 12 Primary & Incomposite
The Deficient 2 4 6 8 10 12 14 16 18 20 22 24
3 6 9 12 15 18 21 24 27 30 33 36
4 8 12 16 20 24 28 32 36 40 44 48
5 10 15 20 25 30 35 40 45 50 55 60
The Perfect 6 12 18 24 30 36 42 48 54 60 66 72 The Intermediary
7 14 21 28 35 42 49 56 63 70 77 84
8 16 24 32 40 48 56 64 72 80 88 96
9 18 27 36 45 54 63 72 81 90 99 108
10 20 30 40 50 60 70 80 90 100 110 120
11 22 33 44 55 66 77 88 99 110 121 132 Secondary & Composite
The Superabundant 12 24 36 48 60 72 84 96 108 120 132 144
Indissoluble Union Being Intellect Unbounded Wisdom
Beauty
Virtue
Number
Less / more
Need / Excesses
Receptive / Overbearing
Deficient / Superabundant
Privation-lack / Overreaching
Terms x : Y
Relation ofInequality
(evil , disease , disproportion , unseemliness)
Consider that among The Even Numbers what makes Perfect Numbers , Perfect , is that the parts (the lesser) , when joined together , are Equal to The Whole (the greater) . On the other hand , deficient numbers are those that when the parts (Factors) are joined together , are less than The Whole , and the superabundant are those that when the parts (Factors) are joined together ,are greater than The Whole .
Among The Odd Numbers , The Intermediary are those that partake of both Primary andIncomposite and Secondary and Composite qualities ; the former relative to other numbers , and , the latter relative to itself .
Let us take the numbers 6 , 8 , 9 and 12 for example .
The Whole 6 The 1st Actual Perfect Number
The Parts-Factors The Half 3 The Root of The Odd
The Third 2 The Root of The Even 6
The Sixth 1 The Source of Number
The Whole 8
The Parts-Factors The Half 4The 1st Deficient Number
The Fourth 2 7
The Eighth 1
Relative to Itself Secondary & Composite Forithas a9th(1) and a third(3) part
The First 9 Intermediary
Relative to Another Primary & Incomposite with25 , 1= only Common Measure
The Whole The 1st 12 Superabundant Number
The Parts-Factors The Half 6
The Third 4
The Fourth 3 16
The Sixth 2
The Twelfth 1
1