Assumptions of Coherentism / Categorical Deduction

Assumptions for the system, roughly:

(1) Every term has an opposite, or at least an imaginary opposite, even if no opposite has yet been formalized, it can be thought about in terms of the first term and its opposite properties.

(2) Each opposite may be used to express all associations for the term symbolically, because at least relatively no other term may do so in each case, or alternate terms may be used. Later, terms are compared, so that the relativism is eliminated through relative relativism = degree absolutism, which may also be called iterative positivism.

(3) Opposites can occupy a Bounded Cartesian Coordinate System because by expressing opposites the only term they do not include is zero, although zero could still be used as an opposite for infinity or infinity plus one in some cases.

(4) Opposites are opposed along the diagonal, because opposites must occupy the furthest possible distance, and in a bounded Cartesian Coordinate System diagonal positions meet this criteria.

(5) Relationships must not be directly opposite, that is opposites cannot be compared without cancelling out and equaling zero. Therefore, the only option is to compare opposites indirectly. This happens to result in a clockwise and counter-clockwise formula in quadratics that I call categorical deduction.

(6) Since categorical deduction is the only possible option for any double-pair of quadratic categories and meets the above criteria, it is coherent.

(7) Since categorical deduction tends to have fewer deductions than categories, it is exponentially efficient.

(8) Optionally, it may be important to use a language in which states and qualities are roughly scientifically equivalent, since this makes sentence-forming easier.

The mod 2 set neutral Boolean set operators I discovered are is, as is, just as, when, so, and as such (in ascending numbers of total categories)


For original source, SEE: https://www.quora.com/Is-there-a-logical-system-in-which-anything-can-be-expressed/answer/Nathan-Coppedge/comment/20172336

Demonstrating all the Headache that Can Happen When You Use the Wrong Method

Categorical Deduction for 64-Sq. Diagrams

Note: this paper shows the WRONG METHOD, although with a lot of promise. For the real method, see: https://www.academia.edu/10161352/Categorical_Deduction_for_64_Categories


[THIS METHOD REMAINS INCOMPLETE! (HERE BUT NOT THERE)]



Recall that the method for 16-SQUARE DIAGRAMS


Involved FOUR DEDUCTIONS


Those deductions were:

[A] ABFE-CDHG-KOPL-IMNJ
[B] ABFE-CGHD-KOPL-IJNM
[C] AEFB-CDHG-KLPO-IMNJ
[D] AEFB-CGHD-KLPO-IJNM


Each of the letters shown in the
previous diagram


DCBA
GHFE…

LKJI
PONM


Now refers to four squares in the new diagram.


The new diagram has:

 A first row:
8,7,6,5,4,3,2,1

A second row: 16,15,
14,13,12,11,10,9

A third row: 24,23,
22,21,20,19,18,17

A fourth row: 32, 31,
30,29,28,27,26,25

A fifth row: 40,39,
38,37,36,35,34,33

A sixth row: 48,47,
46,45,44,43,42,41

A seventh row: 56,55,
54,53,52,51,50,49

And,


An eighth row: 64, 63
62,61,60,59,58,57


Remember, there are other
methods

For showing the categories


The categories could be shown
cyclically


Within each quadrant for example.


I will keep the method I showed here


Because I feel it is the most objective.


Now remember, each of the
categories from 16 square


Corresponds to four of the categoiries
In 64 squares.


64 = 16 X 4


Otherwise the method would not
Reveal itself


So easily.


Now we know that:


‘A’ refers to
1.2,10,9


[Listed in cyclical order]

‘B’ refers to
3,4, 12,11

‘C’ refers to
5,6,14,13

‘D’ refers to
7,8, 16,15

‘E’ refers to
17,18,26,25

‘F’ refers to
19,20,28,27

‘G’ refers to
21,22,30,29

‘H’ refers to
23,24,32,31

‘I’ refers to
33,34,42,41

‘J’ refers to
35,36,44,43


‘K’ refers to
37,38,46,45

‘L’ refers to
39,40,48,47

‘M’ refers to
49,50,58,57

‘N’ refers to
51,52,60,59

‘O’ refers to
53,54,62,61

‘P’ refers to
55,56,64,63


Now, we know that opposite
numbers do not combine!


In terms of coherent quadra,


That means position A

Does not go with position C

Position B

Does not go with position D


That process was used once in
The 16-SQ diagram


Now we apply it again in the
64-SQ diagram


AGAIN,

The deductions for 16-SQ.
WERE:


[A] ABFE-CDHG-KOPL-IMNJ

[B] ABFE-CGHD-KOPL-IJNM

[C] AEFB-CDHG-KLPO-IMNJ

[D] AEFB-CGHD-KLPO-IJNM


So, the deductions for 64-SQ.


Merely involve:


Applying the cyclic order


For each quadrant


(within the numbers…)



SUCH THAT:


The two combinations for
Each cycle


Are maintained AT
EVERY SET LEVEL


Before we ascertain that,



We must find the quadra for every level.


The first two quadrant levels refer to the
16-SQ. diagram.


The third quadrant level refers to the
numbers.


We have already determined
the corresponding numbers


Quadrant A refers to:
ABFE

Quadrant B refers to:
CDHG

Quadrant C refers to:
KLPO

Quadrant D refers to:
IJNM


Now we substitute the
numbers:



QUADRANT A =

A: [1.2,10,9]
B: [3,4, 12,11]

F: [19,20,28,27]
E: [17,18,26,25]


QUADRANT B =



C: [5,6,14,13]
D: [7,8, 16,15]

H: [23,24,32,31]
G: [21,22,30,29]



QUADRANT C =

K: [37,38,46,45]
L: [39,40,48,47]

P: [55,56,64,63]
O: [53,54,62,61]


QUADRANT D =

I: [33,34,42,41]
J: [35,36,44,43]

N: [51,52,60,59]
M: [49,50,58,57]


NOW,


Part A of every level
Only relates with part B,D


Of every level


Part B of every level
Only relates with part C,A


Of every level




Part C of every level
Only relates with part D,A


Of every level


Part D of every level
Only relates with part A,C


Of every level


THEREFORE,


Nothing from quadrant A
Relates with quadrant C


Nothing from quadrant B
Relates with quadrant D


And vice versa



This includes the sections of
The numbers which



Correspond to those quadra



At the third set level.



Therefore, we take the 16-Sq.
Deductions:

[A] ABFE-CDHG-KOPL-IMNJ

[B] ABFE-CGHD-KOPL-IJNM

[C] AEFB-CDHG-KLPO-IMNJ

[D] AEFB-CGHD-KLPO-IJNM



The simplest answer is to  apply it


To each of the quadra.


This would leave us with eight
deductions, as predicted



Once the deduction is applied
to the overall quadra.


In QUADRANT A:


ABCDEFGH
IJKLMNOP



Refers to:

1,2,3,4
9,10,11,12

17,18,19,20
25,26,27,28




In QUADRANT B:

ABCDEFGH
IJKLMNOP

Refers to:
5,6,7,8
13,14,15,16

21,22,23,24
29,30,31,32



In QUADRANT C:

ABCDEFGH
IJKLMNOP

Refers to:

37,38,39,40
45,46,47,48

53,54,55,56
61,62,63,64



In QUADRANT D:

ABCDEFGH
IJKLMNOP

Refers to:

33,34,35,36
41,42,43,44

49,50,51,52
57,58,59,60



Now a 16-SQ deduction
for Quadrant A

[A] 1,2,10,9-3,4,12,11-
19,27,28,20-17,25,26,18

[B]1,2,10,9-3,11,12,4-
19,27,28,20-17,18,26,25

[C]1,9,10,2-3,4,12,11-
19,20,28,27-17,25,26,18

[D]1,9,10,2- 3,11,12,4-
19,20,28,27-17,18,26,25


Now a 16-SQ Deduction
for Quadrant B


[A] 5,6,14,13-7,8,16,15-
23,31,32,24-21,29,30,22

[B] 5,6,14,13-7,15,16,8-
23,31,32,24-21,22,30,29

[C] 5,13,14,6-7,8,16,15-
23,24,32,31-21,29,30,22

[D] 5,13,14,6-7,15,16,8-
23,24,32,31-21,22,30,29



Now a 16-SQ Deduction
for Quadrant C


[A] 37,38,46,45-39,40,48,47-
55,63,64,56-53,61,62,54

[B] 37,38,46,45-39,47,48,40-
-55,63,64,56-53,54,62,61

[C] 37,45,46,38-39,40,48,47-
-55,56,64,63-53,61,62,54

[D] 37,45,46,38-39,47,48,40-
55,56,64,63-53,54,62,61


Now a 16-SQ Deduction
for Quadrant D


[A] 33,34,42,41-35,36,44,43-
51,59,60,52-49,57,58,50

[B] 33,34,42,41-35,43,44,36-
-51,59,60,52-49,50,58,57

[C] 33,41,42,34-35,36,44,43-
51,52,60,59-49,57,58,50

[D] 33,41,42,34-35,43,44,36-
51,52,60,59-49,50,58,57




We are nearing our final solution!


Now we simply apply the
Formula:


ABCD and ADCB



On two levels!



In every quadrant
It also takes the order:


ADCB.


Thus, Quadrant A


Is not only:

[A] 1,2,10,9-3,4,12,11-
19,27,28,20-17,25,26,18

[B]1,2,10,9-3,11,12,4-
19,27,28,20-17,18,26,25

[C]1,9,10,2-3,4,12,11-
19,20,28,27-17,25,26,18

[D]1,9,10,2- 3,11,12,4-
19,20,28,27-17,18,26,25



But,

[A] 1,2,10,9-3,4,12,11-
19,27,28,20-17,25,26,18

[D]1,9,10,2- 3,11,12,4-
19,20,28,27-17,18,26,25

[C]1,9,10,2-3,4,12,11-
19,20,28,27-17,25,26,18

[B]1,2,10,9-3,11,12,4-
19,27,28,20-17,18,26,25


Quadrant B is not only:


[A] 5,6,14,13-7,8,16,15-
23,31,32,24-21,29,30,22

[B] 5,6,14,13-7,15,16,8-
23,31,32,24-21,22,30,29

[C] 5,13,14,6-7,8,16,15-
23,24,32,31-21,29,30,22

[D] 5,13,14,6-7,15,16,8-
23,24,32,31-21,22,30,29

But,

[A] 5,6,14,13-7,8,16,15-
23,31,32,24-21,29,30,22

[D] 5,13,14,6-7,15,16,8-
23,24,32,31-21,22,30,29

[C] 5,13,14,6-7,8,16,15-
23,24,32,31-21,29,30,22

[B] 5,6,14,13-7,15,16,8-
23,31,32,24-21,22,30,29


Quadrant C is not only:

[A] 37,38,46,45-39,40,48,47-
55,63,64,56-53,61,62,54

[B] 37,38,46,45-39,47,48,40-
-55,63,64,56-53,54,62,61

[C] 37,45,46,38-39,40,48,47-
-55,56,64,63-53,61,62,54

[D] 37,45,46,38-39,47,48,40-
55,56,64,63-53,54,62,61


But,

[A] 37,38,46,45-39,40,48,47-
55,63,64,56-53,61,62,54

[D] 37,45,46,38-39,47,48,40-
55,56,64,63-53,54,62,61

[C] 37,45,46,38-39,40,48,47-
-55,56,64,63-53,61,62,54

[B] 37,38,46,45-39,47,48,40-
-55,63,64,56-53,54,62,61



Quadrant D is not only:

[A] 33,34,42,41-35,36,44,43-
51,59,60,52-49,57,58,50

[B] 33,34,42,41-35,43,44,36-
-51,59,60,52-49,50,58,57

[C] 33,41,42,34-35,36,44,43-
51,52,60,59-49,57,58,50

[D] 33,41,42,34-35,43,44,36-
51,52,60,59-49,50,58,57


But,



[A] 33,34,42,41-35,36,44,43-
51,59,60,52-49,57,58,50

[D] 33,41,42,34-35,43,44,36-
51,52,60,59-49,50,58,57

[C] 33,41,42,34-35,36,44,43-
51,52,60,59-49,57,58,50

[B] 33,34,42,41-35,43,44,36-
-51,59,60,52-49,50,58,57


Thus, the overall set
takes the order


ABCD and ADCB


With alternation within
each category.


According to the above
dualities…


However, B must
remain opposite of D

And A must remain
Opposite of C…


Thus,

With A.A is
C.B…


With A.B is C.A…


With B.A is D.B…


With B.B is D.A…


With C.A is A.B…


With C.B is A.B…


With D.A is B.B…


With D.B is B.A…


3/4ths of these are
superfluous…


Thus, we have the
combinations:


A.A w/ C.B and
A.B w/ C.A and

B.A w/ D.B and
B.B w/ D.A.


The remaining half of
The categories


Are resolved by
the duality


In which A refers
to B or D…



So we have:

A.A (w/ C.B)
=

A.B (w/ C.A)
=


B.A (w/ D.B)
=


AND

B.B (w/ D.A)
=



Thus, the result is actually
equal to


2^2^2 as predicted…



However, notice, that in spite of the two levels of deductions, the 16-deduction level resulted in four SEPARATE DEDUCTIONS for each quadra, which is inadequate.


Note: this paper shows the WRONG METHOD, although with a lot of promise. For the real method, see: https://www.academia.edu/10161352/Categorical_Deduction_for_64_Categories


[THIS METHOD REMAINS INCOMPLETE (HERE, BUT NOT THERE)]

For Those Doing Research on Categorical Deduction,

You will be pleased to find a new resource available at Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:The_Method_of_Categorical_Deduction.jpg

Distinguishing Between Analogy and Categorical Deduction

We will use the following terms:

'Good', 'Bad'

'Cat', 'Dog'

An analogy would say that:

Good : Bad :: Cat : Dog

The conclusion would be that dogs are bad, and cats are good.

Simple enough.

An analogy would not draw the comparison as follows:

Good : Dog :: Bad : Cat

Because, according to analogies we could only conclude that we are relating two distinct things, a bad cat and a good dog. Or, so goes the reasoning, we could equally compare a bad dog and a good cat.

Suffice to say, in conventional reasoning (that is, conventional analogy), this type of comparison is considered meaningless. It is considered to be relative, or ambiguous. It is a form of amphiboly.

Consider for stark comparison what happens when, instead of analogy, a categorical deduction is implied in the system.

First, we set up four quadrants, in which opposites are held in diagonal locations.

A. Good. B. Dog. C. Bad. D. Cat

The conclusion is that A. A good dog implies a bad cat, or B. A bad dog implies a good cat.

If cat and dog are indeed opposites, then this holds to be true.

And if they are not opposites, then it could only be a rough analogy. In this way it proves what an analogy cannot prove. Furthermore, it establishes complex conditions which an analogy could not establish.

Consider that 'bad' and 'good' (just like 'cat' and 'dog') are really some of the simplest opposites to choose. In other cases the comparisons are more meaningful. In fact, there is even room for imagination, so long as the oppositeness cannot be disproven.

So it may be that geniuses in the large part of recent history have conducted a major mistake, the Folly of Amphiboly, by assuming that nothing could be drawn from comparisons of opposites, except so-called one-to-one-correlations. In the last several months, I have detected people attempting to re-define the meaning of one-to-one. And I think the simple explanation is that there is a new device, with a new standard of definitions. And it's name is the categorical deduction.

Cite my blog. Or better, buy my book and read the source material, if the above material appeals to your intellect. I hope it's infectious.

Nathan Coppedge is the Inventor of the Categorical Deduction

Here are arguments and supporting evidence for a statement that I am promoting, e.g. that I am the inventor of the most important method of philosophical logic ever invented.

A. As of April 2013, the term 'categorical deduction' was rarely used as a set of connected words. Instances included references to Nathan Coppedge's book, published in January of that year.

B. As the term propogated over the internet over the course of the months since January 2013, I saw many instances of its being misused. For example, when I spoke about the term and related terms on Yahoo! Answers, people often mistakenly believed that it was identical first to a categorical imperative (Immanuel Kant's), and secondly to a categorical syllogism (Aristotle's). In fact, neither of these assumptions is correct. Categorical deduction is a diagrammatic or correspondent, non-causal method of inference.

C. Categorical deduction is a coherent theory method which applies to some degree to any type of information (defined as having a quality) that can be measured as relating to one of any two opposite terms. It is thus utterly different from the categorical imperative, which was specifically a moral claim based on general applied reasoning, rather than a general application which applies a neutral system to language statements.

D. Categorical deduction is not a causal method of inference in the normal sense of the word. It's conclusions often refer to genus categories in a highly absolute sense, but always providing an alternative. However, the alternative has different truth conditions. In this sense, it is highly original. A categorical deduction does not depend on premises in the same way as Aristotelian reasoning. Thus, the distinction between categorical syllogisms and categorical deduction is actually very broad.

A More Careful Variation: Coherent Logic with Sixteen Categories

Using the same sixteen-category method:

D, C, B, A
H, G, F, E
L, K, J, I
P, O, N, M

Initially, the categories are reset to correspond with the numeric constituencies:

A-B-F-E is taken to be one category box (quadra diagram), say CC: [1.1] Purity, [1.2] Simplicity, [2.2] Reduction, [2.1] Nothing.

C-D-H-G is taken to be one quadra, say [1.3] Complexity, [1.4] Chaos, [2.4] Paradigmatics, [2.3] Usefulness.

K-L-P-O is taken to be one quadra, say [3.3] Perfection, [3.4] Order, [4.4] Architecture, [4.3] Justice.

I-J-N-M is taken to be a final quadra, say [3.1] Construction, [3.2] Ugliness, [4.2] Injustice, [4.1] Destruction.

Here are the results for the four either-or comparisons:

QUADRA 1
Simple purity is reduced to nothing, or
Nothing pure is reduced to simplicity

QUADRA 2
Chaotic complexity has paradigmatic usefulness, or
Useful complexity is paradigmatic chaos

QUADRA 3
Perfect order is the justice of architecture, or
Perfect justice is the architecture of order

QUADRA 4
Constructed ugliness is injustly destroyed, or
Constructed destruction is an ugly injustice

Now, I use the same balanced method, in which 1 must be abverse of 3, and 2 must be abverse of 4. This time, however, the result is more balanced in terms of the macro-level oppositeness:


A. Simple purity is reduced to nothing so that perfect justice is the architecture of order, when chaotic complexity has paradigmatic usefulness so that constructed destruction is an ugly injustice

B. Simple purity is reduced to nothing so that perfect justice is the architecture of order, when useful complexity is paradigmatic chaos so that constructed ugliness is injustly destroyed

C. Nothing pure is reduced to simplicity so that perfect order is the justice of architecture, when chaotic complexity has paradigmatic usefulness so that constructed destruction is an ugly injustice

D. Nothing pure is reduced to simplicity so that perfect order is the justice of architecture, when useful complexity is paradigmatic chaos so that constructed ugliness is injustly destroyed

Remember that, miraculously, sixteen categories have been reduced to four. There are two primary methods for interpreting the validity of the aphorisms. One is the value method, and the other is the equivalency method. In the value method, it is assumed or determined that one or another end has an advantage in defending a particular set of principles, typically the principles laid out by that description (say, A .or D.). The categories can be re-arranged by cycling them in the same linear positions, if a different value system is desired. The second method, equivalency, involves comparing the aphorisms for differential values. The equivalent sectors are accepted as the standard for comparing the two aphorisms, and the remaining descriptions are used as the primary character of judgment. Axioms can be used of the form that 'the terms differ by the degrees of separation' [in which D. is 1-degree different from A. and 2-degrees different from B.]

Note that, by using the words as variables which have assumed quantifiability, both the opposite subjects A-C and the opposite contexts B-D provide a ground for determining many truths on subjects related to the terms. However, in the case of a sixteen-box diagram, the following assumptions must be made:

A. Two opposites express the entire range of a given notional meaning.
B. What is not an opposite term for anything is determined to be a meaningless context. Note that oppositeness can exist in degrees and still fit into the system.
A. Modal variation allows for multiple opposites for a given term.
B. The terms chosen are in fact opposites, both on a sub-quadra and on a macro-quadra level. E.g. 1.1 opposes both 1.3 and 3.3, 2.4 opposes both 2.1 and 4.1, etc.

With that, it should be possible to assess the validity of the system. Purchases of the Dimensional Philosopher's Toolkit are encouraged for additional insight and organization.

Please cite Nathan Coppedge if this article is chosen for an essay.

For Those Interested in Dimensional Philosophy

I will give a full example of a means to formulate categorical deductions on a sixteen-category diagram. This will allow me (hopefully) to progenitate the method in light of disappointing book sales.

Also, I make the excuse that this expansion of the system is not present in the published book, and deserves recording somewhere. It seems unlikely at this point that I will have the opportunity to publish a condensed version of the methods, as I very much would like to. So here is a way of meeting the prospective reader half-way.

There is an initial context of sixteen categories. I will show how these reduce to four. The method has none of the weaknesses of permutation. The categories are listed in order of closest approximate axialarity, from the beginning point to the oppositemost point.

D, C, B, A
H, G, F, E
L, K, J, I
P, O, N, M

A-B-F-E is taken to be one category box (quadra diagram), say CC: Quantity, Texture, Quality, Amorphous.

C-D-H-G is taken to be one quadra, say Physics, Coherency, Abstraction, Correspondence.

K-L-P-O is taken to be one quadra, say Pessimist, Permanent, Optimist, Temporary.

I-J-N-M is taken to be a final quadra, say Perfect, Subject, Complex, Context.

First, a method yields the following for the first quadra:

Quantity-texture is an amorphous quality, or
Amorphous quantity is texture quality

Second, the same method yields the following for quadra number two:

Physics coherency is abstract correspondence, or
Physical correspondence is abstract coherency

Thirdly, the same method yields the following for quadra number three:

Pessimistic permanence is optimistically temporary, or
Temporary pessimism is permanent optimism

Fourthly, the method yields the following for the fourth quadra:

Perfect subjects are complex contexts, or
Perfect contexts are complex subjects

Since only opposites combine [If, as in the sub-methods, the four macro-categories express opposites, something I was not careful to ensure this time, but which is securable in many cases], and there are two choices for every four opposites when it is determined that the relationship is non-arbitrary by virtue of oppositeness, then there are four large categories produced from the initial sixteen categories:

A. Quantitative texture is an amorphous quality so that temporary pessimism is permanent optimism when physics coherency is abstract correspondence so that perfect contexts are complex subjects.

B. Quantity texture is an amorphous quality so that temporary pessimism is permanent optimism when physical correspondence is abstract coherency so that perfect subjects are complex contexts.

C. Meaningless quantity is texture quality so that pessimistic permanence is optimistically temporary when physics coherency is abstract correspondence so that perfect contexts are complex subjects.

D. Meaningless quantity is texture quality so that pessimistic permanence is optimistically temporary when physical correspondence is abstract coherency so that perfect subjects are complex contexts.

These simply go to demonstrate the method. They would be more rational if opposite macro-categories had been chosen, such as if 1.3 were a suitable but separate opposite from 3.1 (vs. 3.3). The numbers provide a foundation for organizing the properties of the boxes.

Notice again, that the product is four from sixteen, made possible because of the double-tier of oppositeness, a kind of effect in which it is determined that there is one and not two layers of significance. This is not the same as a failed method in which only a fraction of the categories are compared, or in which fallaciously opposites are only compared to opposites, or in which fallaciously any detail is reiterated.

The general form of categorical deduction seems to follow the formula "the nth root of n-dimensions", so 4 = 2, 9 = 3, 16 = 4. If this is the case, it could be considered flat and vastly efficient. This is essentially possible because the property of opposites is protracted over every dimension of the hierarchy.


A simpler example in the extreme is the case of the beautiful stoic, who is said to be sensitive to ugliness.

For those using this article, I highly recommend citing the author, Nathan Coppedge. Further information about how to operate categorical methods may be found in The Dimensional Philosopher's Toolkit (2013), available from Amazon.