limitations of classification systems, fiction, lack of ontological commitment

Some participants come to this list to learn about KR, and thus, about the
world
Other may come to impose their views of the world
I only share some thoughts in the hope to inspire newcomers to the
discussions to be skeptical of the reductionist views, especially
when they are fictional

The metaphor  of ' finger pointing at the moon  may be useful to explain
how maths relates to the real world
*moon=object in the real world,  finger=pointer to an object

Lack of ontological commitment in mathematics does *not reduce its
usefulness*.It allows mathematics to serve as a *symbolic, structural, or
fictional framework* that organizes knowledge, supports reasoning, and aids
scientific modeling, *without asserting that numbers, sets, or functions
exist as real entities*.

*Just some side notes for the record  *no problem if some participants have
different views!*

1. The limitations of classification systems are well understood in science
!
All classification systems have representational limitations—structural,
cultural, and epistemic constraints that prevent them from perfectly
capturing the complexity of real-world subjects, and are sometimes
misaligned

Subject classification systems simplify and distort the vast complexity of
knowledge. Their limitations stem from:

   -

   Structural constraints (hierarchies, reductionism)
   -

   Cultural and historical biases
   -

   Linguistic and epistemic factors
   -

   The ever-changing nature of knowledge


2. *Ontology captures and represents 'what exists*'  *
Ontic categories describe what exist


3. *MORE ON Lack of Ontological Commitment of Mathematics*
*Fictionalism* Mathematics is akin to a story: numbers, sets, and functions
are characters or constructs in a narrative.

Statements like “2+2=4” are “true” within the story, but there is no
metaphysical commitment to numbers actually existing.

Hartry Field’s Science Without Numbers demonstrates how physics can be
formulated nominalistically, showing mathematics is dispensable to physical
ontology.

*Nominalism* Mathematics is a linguistic or conceptual system, describing
patterns, relations, or structures without positing entities.

Mathematical objects are seen as placeholders or names, not actual beings.

* Formalism*

Mathematics consists of symbol manipulation according to rules.

Truth is internal to the formal system, not dependent on entities existing
in reality.

There is no ontological claim beyond the consistency of the formal
structure.

________________________________

*Implications of Lack of Ontological Commitment*

Philosophical: Avoids metaphysical debates over the existence of abstract
objects.

Scientific: Shows that mathematics can be used as a tool for modeling,
explanation, and prediction without assuming mathematical objects exist.

Epistemic: Shifts focus from discovering “real” entities to understanding
structures, patterns, and relations.

Practical: Emphasizes that mathematical work is justified by utility,
coherence, and explanatory power rather than ontological truth.
------------------------------


*MORE LIMITATIONS OF CLASSIFICATION SYSTEMS*

1. Reductionism

Classification systems force complex, multifaceted subjects into
predefined, discrete categories.

Real-world topics often span multiple domains.

Example: “Climate change” involves science, politics, economics, ethics—but
often must be placed in one dominant category.

Limitation: Nuanced or interdisciplinary knowledge becomes oversimplified.

________________________________

2. Rigid Hierarchies

Most classification systems are hierarchical (trees), assuming that
knowledge can be arranged from general → specific.
But many fields do not follow clean hierarchies.

Consequences:

Relationships between subjects that are lateral, cyclical, or network-like
are lost.

Some topics fit multiple parent categories but must be assigned only one.

________________________________

3. Cultural Bias and Eurocentrism

Many widely used systems were created in Western institutions during
specific historical periods.
Thus they often reflect:

Western cultural priorities

Colonial perspectives

Christian or Euro-American worldviews

Gendered assumptions

Examples:

Dewey Decimal once grouped non-Christian religions as a single minor
section.

Indigenous knowledge systems do not map neatly onto Western categorizations.

________________________________

4. Static Categories in a Dynamic Knowledge Landscape

Knowledge evolves, but classification schemes update slowly.

Limitations:

Emerging fields (e.g., AI ethics, quantum biology) lack appropriate
categories.

Outdated terminology persists long after it becomes obsolete.

________________________________

5. Ambiguity and Boundary Problems

Subjects don’t always have sharp boundaries.

“Digital humanities,” “bioinformatics,” “neuroeconomics”—these hybrid
fields strain rigid category structures.

Result: Misclassification or forced placement into inadequate categories.

________________________________

6. Language-Based Constraints

Classification systems often depend on the language in which they were
originally created.

Concepts with no direct translation get misrepresented.

Polysemous words (one term, many meanings) complicate categorization.

________________________________

7. Ethical and Social Framework Limitations

Some subjects carry social or moral implications the system fails to handle
gracefully.

Examples:

LGBTQ+ topics historically hidden or marginalized

Mental health categories shaped by outdated frameworks

Stigmatizing terminology baked into classification labels

________________________________

8. Practical Space Constraints

Especially in library systems:

Only a finite number of codes or shelf spaces exist.

Broad areas get subdivided excessively; others receive disproportionately
little granularity.

Outcome: Arbitrary compression or over-expansion.

________________________________

9. Authority and Gatekeeping

Classification presumes that experts can definitively decide how knowledge
should be structured.

But:

Some knowledge systems (e.g., community knowledge or oral traditions)
resist systematization.

Marginalized groups often have limited influence over classification design.

________________________________

10. Interoperability Problems

Different systems don’t align cleanly.

Translating between Dewey, LCC, MeSH, or scientific taxonomies can distort
meaning.

Metadata loss occurs during crosswalks (mapping between classification
systems).




However, if it helps, a reminder that it is what is generally accepted,


1. maths is  type of KR
2. is not NL KR *which is what we use in LLM

Subsumption
Subsumption is a key concept in knowledge representation, ontology design,
and logic-based AI. It describes a “is-a” hierarchical relationship where
one concept is more general and another is more specific.
mathematics *is* a knowledge representation *although it may be understood
or defined in other ways because  it provides:

   -

   Formal symbols (numbers, variables, operators)
   -

   Structured syntax (equations, functions, relations)
   -

   Precise semantics (well-defined meanings)
   -

   Inference rules (logical deduction, proof)

and much more not related to what we are discussing here


 Other views may also exist, in the vast universe of discourse, that may or
may not contribute to the discussions in hand.
.