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Formal Formulations


Form and Substance
As The Sentient Perception of Objects
has evolved over The Realms of Consciousness,
The Paradigm of Form and Substance
serves as a touchstone reference example,
of what our consciousness experiences.

The Formal And Substantive Foundations for
The Paradigm of Form and Substance will be established by:

Analogy and Analysis
of the
Form and Substance
Quality and Quantity

These strong Analogies of Form
allows the Substance of the Initial Distinction to be
projected across the The Realms of Consciousness
such that
it can be measured in the Physical Realm,
with ever increasing Distinction.

This triad of strong Analogy of Dialectics spans the The Realms of Consciousness, while preserving the import of Spiritual Objects across the Realms. Thus, this trinity may serve as a touchstone reference for all Other Dialectic Distinctions.

For a deeper understanding how Objects have been experienced, by our consciousness over the ages, the reader is invited to explore the history of The Clarification of Form and Substance.


Realms of Consciousness

As sentient beings,
our consciousness has the potential
to sense and experience
the Form and Substance
of an Object
on any of the four so-called
Realms, or Planes, of Consciousness.

Intellectual Emotional


The Paradigm of Form and Substance

An Analytical distinction,
between Form and Substance,
allows Form and Substance,
to manifest
as distinct attributes of an Object.

As sentient beings, we experience
the Substance of water
as three common Forms of water:

Solid ~~~~~~~~~~~~~~~~~~ Liquid ~~~~~~~~~~~~~~~~~~ Vapor

In an existential or Spiritual sense,

As the Form is formed,
The Substance is experienced,
In an intuitive or Emotional sense,
As the Form is different,
The Substance is similar,
In a sentient or Physical sense,
As the Form has shape,
The Substance has mass,
In a mathematical or Intellectual sense,
As the Form is correlated approximately as macroscopic energy levels,
The Substance is measured precisely as 2 hydrogen and 1 oxygen atoms,

The above series of Analogies and Analyses span the The Realms of Consciousness and provides a specific example of the experience of Form and Substance in each of the Realms.

This distinction of Form and Substance strictly conforms to The Canonical Form of Distinction, as detailed in the treatment of Non-Numerical Arithmetic. As such, it establishes a touchstone for the conformity, with reasoning by Analogy , of all Other Dialectic Distinctions.

In turn, this allows the formalism of Form and Substance to be applied to any Object, in any Realm. Understanding the Form and Substance of an Object can provide great insight into our possible experiences of an Object.


Formal And Substantive Foundations

In this task, The Homeless Mathematician is confronted with a "Which came first, the chicken or the egg?" problem. Although the foundations arise from drawing a single distinction, without the foundations, it is meaningless to draw a distinction.

Thus, for the formal construction,
of the foundation for the Paradigm,
The Homeless Mathematician, as a mathematician, must:

Ultimately, the validity of The Formation of the Formal Form rests on its conformity to The Canonical Form of Distinction, as detailed in the treatment of Non-Numerical Arithmetic. However, as an Intellectual or Physical Object, no arithmetic can manifest until the Formal Form has manifested.

The Homeless Mathematician notes that, although he was able to nullify the recursive element of the original "chicken or egg?" problem, the recursive element persists. This is relatively free from contradiction with, or conforms to, the Form of The Canonical Form of Distinction. This is a direct and immediate validation of the Formal Form, but recursively forces a treatment of Substance.

Fortunately, Substance was left undefined, with a single exception: the definition of Analysis as the Substance of Distinction. To assure that Substance is not otherwise specified, two conditions are imposed:

With Reasoning by Analogy, the Substance of any Realm of Consciousness may be seen as forming a weak or strong Analogy with any other Substance.

As the Form and Substance of Objects is clarified, the strength and utility of such Analogies is revealed. The strong Analogy between

and is one example of such utility.


Experience Beyond Existence

The Homeless Mathematician begins with the Spiritual Realm as being:

the Realm of Consciousness
before the Beginning
of the Space and Time
of the Physical Realm
of our consciousness.

As such, direct sensory experience of the Spiritual Realm is meaningless. In order to experience itself, or anything else, this Spiritual Realm must draw an existential distinction between "being" and "becoming".

The Homeless Mathematician takes this act of drawing a distinction as the Substance of Reasoning by Analysis. As such, Reasoning by Analysis is an intrinsic Object of the Spiritual Realm.

However, it is necessary to maintain a balance among any Objects of the Spiritual Realm. Only then will the Objects produce a net effect which is null, and which can not be directly experienced.

The balance is achieved with Reasoning by Analogy as another intrinsic Object of the Spiritual Realm.


Formal Forms of Reasoning

To conforms to The Canonical Form of Distinction, as detailed in the treatment of Non-Numerical Arithmetic, there are four distinct Forms of Reasoning as follows:

Analysis Analogy

Note well how Analysis and Analogy correspond to the representational Forms, while Spirituality and Empathy correspond to the experiential Forms. Ironically, the mathematical interpretation refers to the representational Forms as the "real roots", while the experiential Forms are called the "imaginary roots".

There is an elegant subtlety in that Reasoning by Spirituality is both the source and a result of the Initial Distinction in The Formation of the Formal Form. This serves to import a recursive element, but also obscures the full spectrum of the Initial Distinction by an apparent collapse of four Forms into three.


The Formation of the Formal Form

As a sentient being, The Homeless Mathematician constructs the formal framework for the non-Spiritual Realms as follows:

I always imagine the Null Set

( also called The Void, or NoThing ), until,

Reasoning by Analysis, I draw a Distinction;

Reasoning by Analogy, I erase the Distinction.

This produces a Zero-Sum Game and represents a Form of Void without Substance .

Reasoning by Empathy,
I empathize with this Form of The Void
to experience the Substance of The Void.

This allows me to experience the Form and Substance of the Void.


paradigm (pre-dm, -dm)


  1. An example that serves as pattern or model.
  2. A list of all the inflectional forms of a word taken as an illustrative example of the conjugation or declension to which it belongs.

[Middle English, example, from Late Latin parad gma, from Greek paradeigma, from paradeiknunai, to compare : para-, alongside. Also, para-1 + deiknunai, to show.]

The Formal Paradigm of Substance essentially fixes the Physical experience of Substance as what can be measured and quantified. At first, this may seem very limiting and the ultimate in Descartian arrogance. In fact, all it really does is to shift Quality into the realm of Form , and there are few limitations on Form . This allows us to deal with Substance on the Physical Realm in a precise, knowledgeable, and reliable manner. What remains aside from the Substance is pure Form and may be viewed in terms of conformity to canonical Form .

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