Philosophy Now Forum

Plato was, to my knowledge, the first person to recommend learning grammar and the principles of predication using geometry. Why?
The definition of a thing tells us that every thing is expressed as a binary construct, a relative constrained by correlatives. When we factor in Symbols and methods of using those symbols to effect binary recursion, we achieve four categories of grammar which we can use traditional names to call: Common Grammar, Arithmetic, Algebra and Geometry.
Three of these are logical, while the fourth, geometry is analogical. Geometry is completely metaphorical. The relative difference, called a line, can represent any relative difference what so ever which makes it a perfect pairing partner to the preceding three logical systems of grammar.
Binary recursion can only produce a binary result, and one of those binary uses is embodied in the words, true and false. Thus, we pair two or more well defined systems of grammar to help guide us in using any particular one of them. Just writing equations to geometric figures teaches one all of the basics of naming in any system of the logical systems of grammar. Therefore, one can learn the principles of grammar by pairing two common programs, Geometer's Sketchpad and MathCad.
However due to the primitive state of geometry when I started my studies, I ended up producing geometry the likes of which has never been seen before and that work, and the different works I produced in geometry is in Universal Language pdf portfolios on the Internet Archive.
One learns first how to write equations to figures, then one learns a very robust form of geometry by which they can write any equation with.
So, one learns grammar by using two or more systems of grammar, pairing one with the other as demonstrated by Euclid. Thus, one learns how to name the parts of a figure and write the mathematics to express it, and then one learns to write equations as the geometric figure itself.
However, if you are as lame as many have demonstrated and cannot even agree with the first step in pairing logic with analogic, it is because no amount of study will keep you from being a babbling mystic.
Line upon line, precept upon precept, i.e., the original metaphor for using geometry to learn how to reason goes back to the Judeo-Christian Book, a book which repeatedly tells the reader that mankind will be to illiterate to read it until after a certain time in human history, so let us, for now, cite just Plato as metaphor is not in the range of most, especially how brilliantly it is used in the JCS.

… „english“s just’a binary – language …
… and this way’s quite’simple …
… beein’free …
… and this way believe …
… in „law“ :
… „do“ !

… purposely computer’s work similar …
… and this way …
… ( globalized - ) people „need“em …
… feelin’like’eden …

… and flew to mars …
… fetchin energy …
… beein’ fed’

… „culture“ seem’s escalatin’ this way …
… several time’s …
… and „stopped“ a thousand year’s ago …
… declarin’ „science“ :

… „re’spect“ !

… Aretha explained …

… some purpose bout „evolutional’grammar“s … „in“ human …
… developed in former time’s …
… by „every’body“ ?
… and may’be’n „Algorithm“ ?
… „I“d consider’ …



… what’s normal’beein’ ?

… from’a humanistic’view …
… people are just considered by action …
… and this way „are“ just …
… and this way „feel“ ( „good“ ) …
… cause human’s „may“ love ?




… but from worker’s’ide …
… action’s considered by „time“ … and bread … and „justice“ …
… cause „real’beein“s ( so’called ) „blurred“ ?
… „is“ ( nowaday’s „real“ ) „production“ …
… „ecologist“s would ask …
… cause’re’s „no“ – time ?





… and this way’s been „negative’deduction“s since ( example ) Popper „the“ – norm :
… beein’free …
… and this way experimente’ …
… feelin’s …
… bout’ „progress“ … or „Reeality“ ?

… Experience …
… or „work“ ?

… ( „emotional“ - ) „fair’ness“ …
… may’be … workin’to’gather ?
… „latin“s word „fare“ mean’s „chang“in re’ality … by thought’n work’n … emotion … „of“ human ?

… humanist’s consider …
… cause’s been „excluded“ by this negative’deduction …
… „be“human … and „have“feelin’s … and cosider’ …
… „past“ ?


… „bove“ aphorism … translated … „mean“s :
… „fare“ mean’s progress … cause human think’s … „bout“ change … cause’s borin’ … doin’a „same“ again … cause human’s „work“ :
… „blurred“ : … by feelin’s … or Sense’s … or Memory … or „inter’action“ … or Thought … or this way religion or speech or „empathy“ … or work ?
… „inter’action“ … or „thought“ ?


… plato considered …
… „speech“ ?

… allegories ?
… „orientation“ ?
… „re’ality“ ?
… „fear“ ?
… „happiness“ ?
… „luck“ ?
… „be“ !

geometry and grammar...



that is a square?

-Imp

… a’long’tim’a’go there’s been „art“ … as Whitehead considered …
… cause people feel’ike „geo’metric“s …
… and „symbol“ize feelin’s and communication and „beein“ …
…
… and so there was found „religion“ :
… „existin“ !

… but now’a’day’s …
… human existence’s determined by „Dualism“ :
… binary’plan’d’future …
… like „season“s …
… cyclin’same’day’s …
… like Mohameddanism’ …
… „growin“ economic’s … linear’ …
… so speech became „sense“less :
… „beein“ – Object !

… „but“I’d consider … bout speech …
… „beein“ – Art !

We must visit Africa to find out, oui?

I am excited to see the approach of learning grammar and logic through geometry being explored. The impact it can have on mathematics education is huge. Do you think Euclid would be proud?

Look in a dictionary. One word leads to another (line), this next word leads back to the original (circle) while leading to a new one (circular progression, thus spiral), and each word acts as a point of awareness (point). We have four geometric symbols that are dualistic circle/line and spiral/point.

To going deeper: each of these symbols occurs through the other by intersecting and fusing and simultaneously negating eachother when laid out as a simple square, this nature of connection and negation best is exhibited by the fifth geometric symbol of the cross +.

Geometry acts as symbolism that guides the psyche in gaining a deeper awareness of language with these symbols fulfilling the nature of language by directing the psyche.

Question to AI:

Given language is the experience of consciousness through the occurrence of applying meaning to symbols which have simultaneously circular self-referentiality and linear progressive variability through the form of recursion that imbues them with contextual definition which fundamentally results in a spiral of expanding self-reference, through which self and interdependent awareness occurs, with the occurrence of this awareness spontaneously emerging and dissolving from a paradoxical singular nothingness as potentiality, as evidenced by the gaps within awareness, can experience be premised and founded upon the geometric symbols of the circle, line, spiral and point as rational guidelines embodied in subjectively and objectively applied symbols of awareness that produce transformation under the processes of a paradoxical fifth symbol of the cross, as the intersection of these four subconscious symbols and the simultaneous negation of moving beyond them into their infinite variations of reality, where this cross symbol, i.e the intersection of lines, embodies the paradoxes of the duality of the line and circle and the duality of the spiral and point?

Response:

This is quite a dense and layered question, so let’s break it down step by step to make it more digestible. At its core, it seems to be a philosophical inquiry into how we understand consciousness, meaning, and experience through the use of symbols—specifically geometric symbols—and how these relate to self-awareness and the nature of reality.
Understanding Symbols and Consciousness

Symbols: When we talk about symbols, we refer to things (like words or geometric shapes) that represent something else (like concepts, feelings, or experiences). For example, the word "dog" symbolizes the actual animal but also conjures different images or emotions for different people.

Language and Meaning: Language is our primary tool for communicating meaning. It operates on two levels:
Circular self-referentiality: This means that symbols can refer to themselves or circularly connect back to other symbols, building a network of meanings.
Linear progressive variability: This suggests that language evolves and changes over time, allowing for new meanings and interpretations to emerge.

The Concept of Recursion and Expanding Self-Reference

Recursion is the process where a concept refers back to itself in a cyclical manner. For example, the definition of "language" may include the necessity of words, which are defined by the language itself.
Expanding self-reference implies that as we contemplate our ideas, the meanings and implications grow and evolve, leading to heightened self-awareness and understanding of ourselves and our context in the world.

Emergence from Nothingness

The mention of "paradoxical singular nothingness" hints at philosophical concepts like emptiness or the idea that everything arises from a state of non-being. The gaps in awareness indicate the moments when we step back and realize our thoughts and experiences are not constant; they can arise and dissipate.

The Geometric Symbols

Circle: Often represents wholeness, unity, or infinity.
Line: Symbolizes direction, movement, or continuity.
Spiral: Represents growth and evolution, a journey that expands outward while returning to its origins.
Point: Denotes a specific location or moment, a starting place or intersection in thought.

The Cross Symbolism

The cross can be seen as an intersection of these symbols. It can represent the confluence of different paths, ideas, or dimensions of experience. This allows for the synthesis of the meanings associated with each geometric symbol, representing the complexities and dualities of existence.

Exploring Duality and Infinite Variation

Your question raises interesting thoughts about how these geometric symbols can represent varying aspects of our awareness and experience, allowing us to explore the interplay between opposites—such as:

Circle vs. Line: The circle is closed and whole, while the line is infinite and open-ended.
Spiral vs. Point: The spiral suggests continuous growth, while the point represents something static or fixed.

This duality—and their intersection in the cross—could symbolize the nuances of our experiences and the dynamic relationship between fixation and fluidity, stability and change.
Reflection and Questions

To further explore this dense inquiry, consider asking or reflecting on questions like:

How do we personally experience the meanings we derive from symbols?
Can we identify moments in our lives where a symbol (like something circular or linear) encapsulated our experience?
What does it mean for our reality to be shaped by both fixed points and fluid movements?

In summary, what you have articulated encompasses an intricate dance between consciousness, symbolism, and the nature of reality, which invites deep exploration and reflection. Each component—from the geometric symbols to the intricate web of meaning—offers rich ground for further philosophical investigation.

AlonsoAcevesMX wrote: ↑Mon Dec 09, 2024 12:27 am I am excited to see the approach of learning grammar and logic through geometry being explored. The impact it can have on mathematics education is huge. Do you think Euclid would be proud?

I never met the guy and I am not sure that it would matter. What matters is starting a revolution in education, aimed at teaching children exactly how they are endowed, by biological fact, with the ability to do their own work commensurate with their own level of intelligence.

Personally, I am still learning just in case I could, by some good fortune, to produce at least a primitive example of a grammar book introducing our Grammar Matrix.

I am currently letting Charles Lyell teach me something.

Most definitely The Elements of Geology will enlighten you!