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

Some final notes.

Mathematics does not deal with manipulation of symbols. Set theory and
category theory are two primary examples of mathematics that don't.

There is no homogenous hierarchy in mathematics. There are many branches

Mathematics isn't flawed, it has established its own limitations through
Gödel-Tarski-Turing-Chaitin.

LLMs are flawed from a perspective of neuro and cognitive science and
because of the use of natural language.

Computer science, knowledge representation and artificial intelligence were
all derived from mathematics.

There are many bridges between mathematics, philosophy, neuro and cognitive
science on one side and computer science and artificial intelligence and
its subdomain knowledge representation on the other side.

Which all in all dictates that we must eschew dogmatic thinking and a
priori self-evident truths.

Because the KR for AI we seek to try to develop must lead to computability,
I have tried to use mathematical rigor in pruning all branches that will
lead to nowhere.

I have used the concept of domains of discourse, a linguistic description
for a whole category of formalisms that can be used to describe abstract
and real objects, concepts and all manner of rational structures, with or
without ontological aspects.
This can be either in mathematical or natural language form.

We, I hope, strive to achieve a minimal set of structures and formalisms,
which hints at semantic compression, for KR for AI.

There may be several ways to get there. But the current global path AI
development is taking betting on the generative LLM paradigm for AI we must
recognize for what it is, flawed and having reached its ceiling.

In everything I do in developing AI for Good as the UN and ITU like to call
it I try to avoid all the biases summed up (almost exhaustively) by Paola
in her rebuttal.

The principal question then should be how can we in a practical sense make
an inventory of the types of AI that do not exhibit the flaws inherent in
LLMs, in order to develop KR for such AI?





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.
> .
>
>