8/5/2024 - Literary Interpretation Scale

Okay I was screwing around on chat Gpt and I generated literal meaning of a phrase as a heyting algebra. No clue if it actually works.

I also don’t know if it forms a bounded lattice.

But it seems like if you put some limits on things you might be able to squish in that box.

Reversed Scale of Literary Interpretation

1. Irony ( ( A = 0 ) )
   • Description: Expression where the meaning is contrary to the literal interpretation.
   • Mathematical Representation: ( I(x) = (x) ).
2. Symbolism ( ( A < ) )
   • Description: Using symbols to represent broader ideas.
   • Mathematical Representation: ( (x) = (x, z) ).
3. Allegory ( ( A < ) )
   • Description: Narrative where characters/events represent abstract ideas.
   • Mathematical Representation: ( (x) = (x, ) ).
4. Extended Metaphor ( ( A < ) )
   • Description: Metaphor extended over multiple sentences or passages.
   • Mathematical Representation: ( EM(x) = ((x, y)) ).
5. Metaphor ( ( A < ) )
   • Description: Implicit comparison creating resemblance.
   • Mathematical Representation: ( M(x) = (x, y) ).
6. Simile ( ( A < ) )
   • Description: Direct comparison using “like” or “as”.
   • Mathematical Representation: ( S(x) = (x, y) ).
7. Analogy ( ( A < ) )
   • Description: Comparison based on similarities.
   • Mathematical Representation: ( A(x) = f(x_1) f(x_2) ).
8. Literal Language ( ( A = 1 ) )
   • Description: Direct representation with no additional layers of meaning.
   • Mathematical Representation: ( L(x) = x ).

Bounded Lattice and Heyting Algebra

In this reversed scale, we can indeed model it as a bounded lattice where:

• Bottom Element (0): Represents the most abstract form (Irony).
• Top Element (1): Represents the most concrete form (Literal Language).

Bounded Lattice Properties:

• Join (()): The combination of two interpretations could be the more abstract one. For example, combining a simile with a metaphor results in a metaphor or extended metaphor.
• Meet (()): The more concrete interpretation when combining two forms could be the simpler or more direct form. For example, combining a metaphor with a simile results in a metaphor.
• Complement: The complement of a form ( x ) could be its inverse interpretation. For example, the complement of a metaphor might be irony.

Heyting Algebra:

In a Heyting algebra, the implication ( x y ) is interpreted as the largest element ( z ) such that ( x z y ). Applying this to our scale:

• Implication (( x y )): The transformation from one form to another can be viewed as how abstract or interpretive ( y ) is given ( x ). For instance, if we start from a simile and want to move to a metaphor, we look at how much more abstract the metaphor is compared to the simile.

In summary, this scale forms a bounded lattice where the elements are ordered from the most literal to the most abstract, and this structure can indeed be analyzed using Heyting algebra to understand the relationships and implications between different forms of interpretation.