℘-𝚺 v1.1

Introduction

“℘-𝚺” stands for “P-System”. The “P” in “P-System” stands alternatively for “philosophy” or “principal” (i.e. “first”). It is a formal system used for structuring ideas. Similar to how arithmetics is strong at dealing with quantities, logic at dealing with truth, this system aims to be strong at dealing with the interconnected structures of ideas. It employs a formal language abstracted from English, aiming to be used natural-language-independently, similar to algebras. It should aid in structuring thought and illustrating patterns and connections between things.

How to Read

  1. “{text}” is meta-text used for talking about f.e. variables.
  2. For “1. Definitions”, “()” contains the glyph for the term.
  3. For “2. Rules”, “()” contains the rule formally written, if applicable.
  4. “text” is an important keyword which is formally defined.
  5. “””” includes a sub-sentence or -phrase or important term.
  6. “1.” is the main sentence.
  7. “1.” is a corresponding example, if under “Examples:”.

1. DEFINITIONS

  1. A “term” (言) is an abstract object representing an idea.
  2. A “symbol” (𝚿) is a physical object representing something else.
  3. A “glyph” (字) is a visual shape used as a symbol.
  4. A “sentence” (文) is a collection of terms that appear together.
  5. A “concept” (©) is a mental idea of something.
  6. A “thing” (Z) is anything.
  7. A “connection” (Y) is a thing that connects two things.
  8. An “element” (X) is a thing that has no special properties.
  9. A “property” (P) is a thing that allows things to have variety.
  10. A “group” (G) is a thing that collects other things within itself.
  11. An “atom” (α) is a thing that cannot be analysed further.
  12. A “compound” (ℂ) is a thing consisting of two or more other things.
  13. A “molecule” (μ) is a thing consisting of three other things.
  14. A “basic sentence” (㊂) is a sentence of type “X Y Z”.
  15. A “predicate” (Ⓟ) is the verb and/or object in a classic SVO-sentence.
  16. A “formula” (𝑓) is a sentence that can be evaluated to get at a value.
Examples:
  1. The term “tiger” represents the idea of a tiger.
  2. The symbol “虎” is a Chinese character representing a tiger.
  3. The glyph “A” is a Latin character representing a phonetic sound.
  4. The sentence “虎 eats” has terms “虎” and “eats” together.
  5. The concept “humanity” is an idea of humanity.
  6. The thing “Z” is something.
  7. The connection “and” connects “sun and moon”.
  8. The element “x” in “x = 1” is an element.
  9. The property “roundness” describes f.e. the sun.
  10. The group “humans” collects all things that are a human.
  11. The atom “x” in “x = 1” cannot be divided further.
  12. The compound “parents” consists of parts “mother” and “father”.
  13. The molecule “虎 eats monkey” consists of three parts: “虎”, “eats” and “monkey”.
  14. The basic sentence “x = 1” consists of “X Y Z”.
  15. The predicate “eats monkey” in “虎 eats monkey”.

2. RULES

2.1. Terms to Sentences
  1. One term has one glyph and vice versa. (言 有 (1 ✕ 字))
  2. One term alone is an atom. (Z = α)
  3. Two or more terms are a sentence. (Z Z = 文)
  4. Three terms are a molecule. (Z Z Z = μ)
  5. A molecule of type “X Y Z” is a basic sentence. (X Y Z = ㊂)
  6. A compound sentence is a sentence with two or more sentences. ()
  7. Two or more sentences are a narrative. (文 文 = 𝇙)
  8. An extended molecule is of type “X Y (Z Y Z)”. (ಗ)
  9. A large molecule is of type “(Z Y Z) Y (Z Y Z)”. (〓)
2.2. Things
  1. An element can stand alone. (X)
  2. A connection needs to connect two things. (Z Y Z)
  3. A connection can connect a thing to itself. (Z Y Z)
  4. A connection cannot connect itself to things. (Y Y Z)
  5. Two or more elements need to be all connected. (Z Y Z)
  6. Two connections cannot only connect to each other. (Y Y)
  7. A sentence needs at least one element. (X Z Z)
  8. A sentence needs at least one connection. (Z Y Z)
  9. Because (N), a molecule cannot have three elements. (X X X)
  10. Because (N), a molecule cannot have three connections. (Y Y Y)
  11. A group is an abstraction of things. (G)
  12. A group can be empty. (G)
2.3. SVO Sentences
  1. A subject is an element. (X)
  2. A verb can be a connection. (V Y)
  3. A verb can be an element. (V X)
  4. An object is an element. (X)
  5. A verb can be written as: “in-the-state-of {verb}”. ()
  6. An action verb can be written as: “do + {verb}”. ()
  7. A modal verb is a modification upon a verb. (M V)
2.4. Reading
  1. Terms in parentheses are processed together, first. ()
  2. Standard variable names are: “A, B, C, …”. (A, B, C, …)
  3. Subscript is used to identify specific things. (Z1, Z2, Z3, …)
2.5. Formulae
  1. There is no universal commutativity. ((A Y B)  (B Y A))
  2. An equation is a sentence of type “Z = Z”. (Z = Z)
  3. An equation is commutative. ()
  4. A sentence has three phases: (a) description, (b) evaluation, (c) result. ()
  5. A formula needs every element to be of the same value-type.
Examples:
  1. The glyph for “tiger” is “虎”. The idea behind “虎” is “tiger”.
  2. The term “虎” alone is an atom.
  3. The sentence “虎 eats” is a sentence.
  4. “sun is shining” is a molecule.
  5. “sun is shining” is a basic sentence.
  6. “(A = B) = (B = A)” is a compound sentence.
  7. “A → B”, “A ← B” is a narrative.
  8. “A = B and C” is an extended molecule.
  9. “(A = B) = (B = A)” is a large molecule.
  10. “虎” can stand alone.
  11. The connection “and” needs to connect two things: “A and B”.
  12. The connection “likes” connects “A” to itself: “A likes A”.
  13. “A and and” doesn’t work.
  14. Instead of “A B”, it needs to be “A and B”.
  15. “and and” doesn’t work.
  16. “A likes to like” contains an element and two connections.
  17. “A B” doesn’t work and needs to be f.e. “A and B”.
  18. “A B C” doesn’t work.
  19. “and and and” doesn’t work.
  20. “animals” is an abstraction of specific animals.
  21. “real unicorns” is a group without elements.
  22. In “sun is shining”, “sun” is an element.
  23. In “sun is shining”, “is” is a connection.
  24. In “shining is good”, “shining” is an element.
  25. In “sun brightens day”, “day” is an element.
  26. “虎 eats” can be written as “虎 is-in-the-state-of eating”.
  27. “虎 eats” can be written as “虎 does eating”.
  28. “sun is (shining modified-by can)” → “sun can shining”.
  29. “虎 eats (fruit of tree)”, where “fruit of tree” gets processed first.
  30. Standard variables are “A, B, C, …”.
  31. In “A1, A2, A3”, subscript differentiates between different “A”s.
  32. “(A Y B) ≠ (B Y A)”, f.e. “A → B ≠ B → A”.
  33. “A = A” is an equation.
  34. “(A = B) = (B = A)”.
  35. “1 + 1” as “one plus one”, then evaluated as “1 + 1”, then resulting in “2”, “two”.
  36. In “2 + rain”, “2” is a quantity, but “rain” isn’t, and needs to be f.e. “2 + 3”.

3. HYPOTHESES

  1. Every sentence can be written as a combination of molecules.
Examples:
  1. “sun and moon are round” → “sun is round” + “moon is round”

4. TRANSFORMATIONS

  1. Terms can get added to each other.
  2. Terms can get subtracted from each other.
  3. Terms can get replaced/exchanged by other terms.
  4. Terms can get quantified by quantities.
  5. Terms can get modified by modifiers.
Examples:
  1. “a = 1” → add “+ 1” → “a = 1 + 1”
  2. “a = 1 + 1” → subtract “+1” → “a = 1”
  3. “a = 1” → exchange “1” with “2” → “a = 2”
  4. “a = 1” → quantify “a” by “3” → “3a = 1”
  5. “虎 eats” → modify “eats” with “slowly” → “虎 eats slowly”


Original: 12.06.2024

Updated: 12.06.2024

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