Re: limitations of classification systems, fiction, lack of ontological commitment

It seems you have missed the point entirely. Knowledge representation is
about representation of knowledge. You cannot do this without using
mathematical tools. Every tool in the computer sciences, artificial
intelligence and knowledge representation instrumentarium to enable its use
for artificial intelligence is mathematical or natural language based.

You seem to forget from which cross-section of sciences I hail.  The
cross-section of sustainable development and human rights, mathematics AND
computer science and western AND eastern philosophy.

The lack of ontological truth or ontological commitment you attribute to
mathematics is contradictory.

 I know you are trying to make the point that KR deals with real entities
in the real world and thus ontological truth and commitment must hold.
Classical physics did, and I emphasize DID, but the truth of the matter is
that quantum physics has turned everything on its head.
If we want to use KR for AI to apply in all fields of science we must be
very careful with what truths we hold sacred and even the ontological truth
and commitment.
Mathematics without the axiom of choice, causality, or spatiotemporal
characteristics of our observed real world, like philosophy provide a, but
not a definitive tool for sorting out structures.

What should be remembered at all times is that all the angles and tools and
tenets of KR for AI for LLMs can be shown to be flawed.

The only other scientists that use classification systems are library
scientists.
And we use classification systems in summaries of scientific publications.
Do we criticize these for being prone to bias of all kinds?

They seem to serve a useful purpose in representation of knowledge without
ontological truth or commitment.

Your bubbles diagram for KR is flawed, which started the debate in the
first place.

It is IMHO the quest of this CG to arrive at structures and standards for
KR for AI.
This will require insights from mathematics, philosophy,  neuro and
cognitive science and any other discipline that may contribute to adequate
formalization.

The discussion about ontological truth and commitment is just as useless as
the Copenhagen versus multiverse interpretation in quantum physics and all
the "isms" in philosophy describing reality, perception, consciousness,
rationality,  language and formalism.
While they are perfect for debate and honing our vocabulary in the hope of
finding common grounds, they fail miserably in compliance with the
scientific methods used for dealing with existing objects in the observable
real world.

Again the KR for AI, which you state must show ontological truths and
commitment is thus subject to the same problems of the observer in a real
world which doesn't seem to behave according to such truths.

What we at best can aspire to achieve is specific formalisms and standards
for specific use (applications)  in specific domains of knowledge or
real-world world settings.

These may not fit perfectly in the current bubbles diagram.

Ontological truth and commitment are choices out of a set of many options
to arrive at such. We must be careful with considering them absolute.

Milton Ponson
Rainbow Warriors Core Foundation
CIAMSD Institute-ICT4D Program
+2977459312
PO Box 1154, Oranjestad
Aruba, Dutch Caribbean

On Sat, Nov 29, 2025, 21:31 Paola Di Maio <paoladimaio10@gmail.com> wrote:

> 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.
> .
>
>