INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)  
ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue XI November 2025  
Mathematics as Ontological–Cognitive Participation: Reconstructing  
Ethical and Metaphysical Foundations within a Humanized  
Mathematical Universe  
Md. Zahir Alam1, Jahangir Alam2, Zawad Rami3*  
1Department of Philosophy, Shachindra College, Pukra-3351, Habiganj, Bangladesh  
2Department of Computer Science and Mathematics, Bangladesh Agricultural University, Mymensingh-  
2202, Bangladesh  
3Department of Languages, Bangladesh Agricultural University, Mymensingh-2202, Bangladesh,  
*Corresponding Author  
DOI: https://dx.doi.org/10.47772/IJRISS.2025.91100302  
Received: 01 December 2025; Accepted: 05 December 2025; Published: 08 December 2025  
ABSTRACT  
The status of mathematics on the ontological or epistemological level is still undetermined even though it has  
been debated by realist, constructivist and formalist traditions. This paper pursues a dual-aspect view of  
mathematics with the Humanized Mathematical Universe (HMU), where it is assumed that mathematics lives as  
metaphysical structure and as embodied cognitive activity. Through reconstructing some foundational positions,  
the paper illustrates how currently available frameworks fail to account for mathematical universality and  
(human) access to mathematical structure as well as their ethical implications. According to the HMU model,  
mathematical entia are cosmological potentialities needing human cognition for actualization, causing a  
participative ontological relationship between mind and cosmos. The analysis adds that doing logic today is  
morally significant as a practice because of its role in the mechanics of algorithmic governance, artificial  
intelligence, genetic computation, and financial automation. The results reveal that mathematical warrant needs  
to encompass three kinds of evaluation: structural congruence, epistemic deeming and normative adequacy.  
Hence HMU synthesis refashions mathematics as epistemologically unified, where ontology, cognition and  
ethics are mutually enmeshed. The thesis argues that mathematics should be considered not as a neutral formal  
language, but as a metaphysically real and ethically responsible world-building process in which we participate.  
Keywords: Philosophy of mathematics, embodied cognition, metaphysical realism, ethical epistemology,  
mathematical ontology, algorithmic ethics, participatory realism.  
INTRODUCTION  
The status of mathematics concerning ontology and epistemology is one of the most persistent but still  
unresolved problems in all history of philosophy (‘An Aristotelian Realist Philosophy of Mathematics:  
Mathematics as the Science of Quantity and Structure’, 2015; Ebert, 2007; Glattfelder, 2019). Shall we say that  
mathematical entities should be understood as having one shape or communicating only in the language of  
accord? Platonic realism, common in its traditional and modern versions, is an approach where mathematical  
truths reside within the metaphysical realm apart from human knowledge, and are uncovered through rational  
analysis (Rytilä, 2021; Szabó, 2023; Wolff, 2019). On the other hand, constructivist, empiricist and historicist  
narratives assert that mathematical systems are no inevitable outcomes of human thought processes and depend  
on linguistic-cultural-cognitive limitations (Rami, 2024; Rami et al, 2024; Rami et al, 2023; Hassan & Rami,  
2024; Rami et al, 2025; Belbase, 2019; Hartimo & Rytilä, 2023; Kilpatrick, 1990; Lerman, 1989; Rodin, 2022;  
Stemhagen,2007).  
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Neither argument goes far enough, however, to “account for the twofold character of mathematics as an  
internally consistent symbolic system and yet as the most exactively descriptive framework we have for physical  
reality” (Longo, 2005; Sfard, 1991). This philosophical tension is exemplified by Wigner’s articulation of the  
“unreasonable effectiveness” of mathematics (Bărboianu, 2019; Woźny, 2018): if mathematics is the product of  
a human invention, its predictive success in cosmological and physical scales appears ungrounded or explicable;  
if it constitutes an autonomous metaphysical sphere detached from any form of human activity then the means  
through which humans have access to/approximations with such a realm remain philosophically unclear  
(Ferreirós, 2017; Fillion, 2012; Soto, 2020). Now appeals to formalism, intuitionism or linguistic  
conventionalism are partial solutions (Blanchard & Longo, 2021; Glattfelder, 2019; Longo, 2005), but do not  
enable the embodiment and a metaphysical universality nor the normative responsibility together in one single  
philosophical model (Longo, 2005; Tall & Katz, 2014).  
Contemporary developments intensify this problem. Mathematical formalisms now underpin global decision  
systems, algorithmic governance, artificial intelligence and massive biotechnological intervention (Monte-  
Serrat and Cattani, 2023; Rittberg, 2022). Since mathematics is playing a more and more operative role in  
building material, social and existential worlds (Ernest 2020), the philosophical interrogation cannot be reduced  
to issues of epistemic justification or metaphysical grounding anymore. Any thorough philosophical account  
must also address the ethical dimensions of mathematical practice (Müller & Chiodo, 2023; Skovsmose, 2020).  
And, if mathematical knowing contributes to world-making conducts, then reasoning in mathematics is open to  
moral appraisals— and not a value-free area (Chiodo & Müller, 2024; Kant & Sarikaya, 2020; Rittberg, 2022).  
In this paper, we advocate a dual aspect framework called Humanized Mathematical Universe (HMU). The  
model opposes the invention–discovery divide and posits that mathematics is a product of participation by  
cognitive bodies within a structural cosmic order. Human Cognitive capacities are necessary conditions of  
realization with mathematical structure is a transcendental potential that exists regardless of particular minds.  
This synthesis considers mathematics both to be ontologically real, epistemically constructed and ethically  
actionable.  
This HMU paradigm presents a new philosophical framework that unites metaphysics and moral philosophy,  
on which in turn can be placed elements of cognitive theory. Mathematics is not read as passive reflection of  
reality or sheer signification, but as mediations in the play between mind and cosmos, with ethical responsibilty.  
The paper at hand further develops the model and explores its implications for philosophy of mathematics,  
epistemology, metaphysics and technology ethics.  
LITERATURE REVIEW  
The philosophy of mathematics has been structured around three main interpretive paradigms: mathematical  
realism, anti-realist constructivism and formalistic reductionism. Both traditions harbor an explanatory lacuna,  
for they cannot combine a theory of knowledge and value with the ontological machinery needed to make sense  
of philosophical questions simply in general.  
Mathematical Realism and Transcendent Ontology  
Platonic realism is the view that mathematical objects exist as an independent reality, thereby being uncreated  
and created, abstractions (abstract objects) of a transcendent world of platonism. According to Plato's version of  
realism, it is the nonphysical entities (and not their instances in spacetime) which are real. Modern realisms,  
Balaguer and Parsons to the fore (Jonas 2023; Kosecki 2019; Paseau & Baker present business-as-usual (Weir  
2023): the indispensability of mathematics in physics gives itself evidence of a mind- independent ontological  
domain. Versions like Aristotelian realism understand mathematics as immanent form, as part of the structure  
of the world itself and not in a ‘higher’ or transcendent place (“An Aristotelian Realist Philosophy of  
Mathematics: Mathematics as the Science of Quantity and Structure,” 2015).  
Yet, realism encounters epistemological objections: it supplies no satisfactory philosophical means for  
explaining how finite, physically located human agents possess knowledge of abstracta that are non-  
spatiotemporal (Aboites 2022; “An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science  
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of Quantity and Structure” 2015; Ebert 2007; Jonas 2016; Pedersen 2021; Startup 2024a and Sterpetti 2018).  
Increasingly, it seems that such competing philosophical analyses are not grounded in cognitive theory and are  
open to question of the basis on which rational intuition, structuralist abstraction, or quasi-empirical justification  
can resolve these problems.  
Constructivist and Cognition-Based Accounts  
Anti-realism perspectives, as exhibited by intuitionism, constructivism, historicism and social epistemology  
view mathematics from the standpoint of a human activity and not an abstract discovery (Belbase, 2019; Hartimo  
& Rytilä, 2023; Kilpatrick, 1990; Lerman, 1989.1 Stefan Rodin above n5.RodinStefan,, MüllerVladimir),  
Stemhagen2007). Lakoff and Núñez (2000)’s embodied cognition hypothesis claims that mathematical ideas  
stem from perceptual-motor schema and metaphorical mapping in neural architecture (Baggio, 2025; Friedman,  
2024; Sabena, 2018; Winter & Yoshimi, 2020). Ernest, and other social constructivists add a further level of  
sophistication at the sociocultural argument by suggesting that mathematical truth arises out of intersubjective  
consensus and disciplinary practices (Belbase, 2019; Hartimo & Rytilä, 2023).  
These are important contributions with respect to such matters of embodiment, linguistic mediation, and  
historical variability, but they do not account for the trans-contextual deployment of mathematics in prefounders’  
spin-offs fundamental physics and cosmology as well as in computational systems (Stemhagen 2007). They  
contribute to, but do not feature an explanation of mathematical necessity, universality and predictive power.  
Formalism, Structuralism and Logical Reduction  
Formalist mathematics is nothing more than syntactic manipulation in arbitrary symbol strings. Hilbert's  
program and further structuralist understanding leave mathematics uncompromised by metaphysics; validity is  
exclusively based on internal coherence of reasoning (Blanchard & Longo, 2021). But post-Gödelian advances  
established intrinsic incompleteness, that no formal system can prove all its own truths (Blanchard & Longo,  
2021).  
Logical empiricism and structuralism remove metaphysical dimensions.6 But they both leave (pure)  
mathematicsmetaphysically indeterminate and epistemologically tautological. They neglect embodiment,  
interpretation and ethics, and thus the practical and ontological consequences of mathematical systems within  
technological and sociopolitical reality.  
Participatory and Neo-Realist Frameworks  
Postured emergent positions (and these are the ones I find to be numeral) merge metaphysics with physics by  
claiming that mathematics is not a language we use to describe reality but the fabric of reality itself. Tegmark’s  
Mathematical Universe Hypothesis states that there is no distinction between physical and mathematical  
existence (Woźny, 2018). Non-computational realism is the approach which Penrose suggests and says that -  
mathematics is at an objective ontological level, which can be reached by awareness (Allegrini et al., 2003;  
Gupta, 2021; Shakespeare, 2023; Simeonov, 2010).  
Parallel trends in quantum cosmology and information theory suggest observer-dependent ontology, where  
consciousness plays a role in the actualization of mathematical form. These theories are similar to HMU,  
although they are incomplete as health in this respect were not part of their frameworks and they do not integrate  
ethical considerations and embodied cognition.  
Criticisms of Mathematics and Technological Rationality in Ethics  
Recent discussion in philosophy turns towards the ethical implications of mathematical practice (Chiodo &  
Müller, 2024; Ernest, 2020; Kant & Sarikaya, 2020; Müller & Chiodo, 2023; Rittberg, 2022; Skovsmose, 2020).  
O’Neil, Floridi and Mittelstadt show how algorithmic systems in the digital environment make mathematics  
operational toward injustice, surveillance and epistemic damage (Mittelstadt et al., 2016; Monte-Serrat &  
Cattani, 2023; Rittberg, 2022; Tsamados et al., 2020). Such criticisms reveal the ethically non-neutral nature of  
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mathematics, but do not provide a metaphysical reason to think that wrong with the 795 misuse is a violation  
(as opposed merely to causing social harm).  
Identified Theoretical Gap  
The current literature, for its part, displays the following discontinuities:  
1. Ontological–epistemic disjunction: Realism accounts for universality but not cognition, while  
constructivism accounts for cognition but not universality.  
2. Lack of moral basis: Mathematical philosophy does not have much to do with the normative pervasive  
role of mathematics in the world.  
3. Absence of Integrative Metaphysics: There is no dominant framework which embodies the body that  
reconciles physical structure with metaphysical, and ethical responsibility in one philosophical model.  
Positioning of This Study  
The Humanized Mathematics Universe model attempts to address some of these shortcomings by:  
● Affirming both a metaphysical reality to mathematics but also the cognitive participation in it.  
● Reading mathematics as a relational phenomenon between the mind and the cosmos, rather than as a binary  
of invention vs. discovery.  
● Construct ethical responsibility as an essential philosophical category of mathematical existence.  
This synthesis locates mathematics as ontologically based, epistemically embodied and normatively responsible  
in such a way as to offer an extensive reorientation in the philosophy of mathematics that is incident appropriate  
for the technological and cosmological circumstances of our time.  
METHODOLOGICAL ORIENTATION  
This research uses a philosophico-analytic methodology, consisting in the use of conceptual analysis based on  
ontological synthesis and normative reasoning. The first is not to find empirical evidence but rather the  
production of a logically cogent, metaphysically sound and ethically acceptable explanatory framework for what  
mathematics are.  
The methodological framework unfolds according to three different, though mutually related stages:  
Analyzing Foundational Categories Conceptually  
The first level investigates the fundamental ontological and epistemological concepts enacted by big  
“conception philosophies” of mathematics – existence, truth, cognition and normativity. Classical realism,  
constructivism and formalism are re-assessed to elucidate their metaphysical presuppositions and epistemic  
propositions. This is a model of analysis which goes back at least as far as Frege, Husserl and Putnam and it is  
one that believes in the primacy of conceptual over normative or metaphysical dispute.  
The analysis shows that the current paradigms suffer from either:  
● Metaphysical reduction (mathematics reduced to the physical), or  
● Epistemic closure (of mathematics as pure formal manipulation devoid of afflatus, of the metaphysical/ethical  
kind).  
This conceptual map reveals the need for a two-aspect model that accommodates both embodiment and  
metaphysical structure in relation to moral responsibility.  
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Philosophical Model Building and Synthesis of Ontology  
The second stages of the methodology constructs a humanized mathematical universe (HMU) as an example of  
metaphysical model based on dual-aspect ontology. The synthesis is a structured reasoning process:  
⒈ Mutual interpretation of explanatory domains:  
– Cognitive embodiment.  
– Cosmological mathematical structure.  
⒉ Argument for I and II Reasons for I and II:  
– The mathematical structure is metaphysically already possible>false without entering in the human cognition  
agenda.  
– Mathematical meaningfulness is realized by human cognition.  
⒊ Constructing Ontology of Relation (days):  
– By contrast, mathematics lies at the confluence between structural objectivity and embodied subjectivity.  
– Mathematical existence is not just discovered, nor is it just invented but co-enacted.  
The proposed ontological structure is relational, non-reductionist and in line with participatory interpretations  
within quantum epistemology and embodied cognition investigations.  
Normative–Ethical Reasoning  
The third methodological moment suggests that if mathematics is co-constituted with human activity it cannot  
be ethically neutral. The moral dimension arises from two underlying philosophical assumptions:  
1) If the structure of the world is predicated by mathematical reasoning, it has moral import similar to  
technological and political action.  
2) If mathematical form is evidence of cosmic intelligibility, abuse represents a perversion of rational and moral  
order-- not just social harm.  
This moral expansion is based on ethical philosophical theories such as:  
● Neo-Aristotelian virtue-ethics (practical rationality in terms of human flourishing)  
● Kantian formal ethics (universalizable duty within rule-governed action)  
● Relational ethics in technologically mediated interaction  
The methodology therefore marries descriptive metaphysics with normative philosophical justification, making  
mathematics a moralized ontological playground rather than a neutral playground whose application in social  
and scientific tools is hence politically and socially contested.  
Theoretical Model: The Humanized Mathematical Universe (HMU)  
The HMU framework can be expressed through the following foundational claims:  
Philosophical Dimension HMU Position  
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Mathematical structure exists as cosmic potentiality independent of  
human minds  
Ontology  
Epistemology  
Ethics  
Mathematical knowledge is actualized through embodied cognition and  
symbolic reasoning  
Mathematical action bears moral responsibility due to its world-  
constituting effects  
HMU Theoretical Diagram  
Figure 1. Humanized Mathematical Universe (HMU) Model  
Mathematical structure is in potential cosmological, actualization embodied and morally meaningful operational.  
Dual-Aspect Metaphysical Structure  
Mathematics is simultaneously:  
● Structurally Real  
– Fundamental levels of reality which condition physical order, logical intelligibility, and cosmic consistency  
● Cognitively Enacted  
– A symbolic conceptualization mediated by neural embodiment, linguistic schematization, and evolutionary  
cultural processes  
This kind of dualities avoids reductionism and so is a relational, metaphysical field mathematics.  
Participatory Realism  
The reality of mathematics is not out there to be seen, nor in here to be invented, but something we participate  
in. So, human cognition brings the mathematical structures out of hiatus meaning using reasonning,  
symbolization, proof and numerical intuition.  
4.3 Ethical state of the Art of Mathematics  
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As mathematical systems now govern:  
● Predictive policing  
● Autonomous weapons  
● Financial automation  
● Biomedical computation  
● AGI: Artificial general intelligence  
The act of mathematical reasoning is an institutionally significant activity. The HMU framework maintains that  
mathematical justification must involve moral justification, not just logical validity.  
Implications for Philosophical Inquiry  
The HMU model generates four research directions:  
1. Metaphysics in mathematics  
– Mathematics as relational ontology of mind/cosmos  
2. Moral Responsibility and the Problem of Many Hands Enlightenment Engineering: The Meanings of Making  
as Revealed in the Design of a Solar Powered Light which is a Tale Yet to be Told: A Historiography of Canadian  
Instructional Technology and Open Education  
– The assessment of algorithmic mathematics in the moral and political realms  
3. The Phenomenology of Mathematical Consciousness  
– Subjective mathematical intuition and insight as ordered sharing in cosmic rationality  
4. The Philosophy of Technology and AI  
– Rethinking the mathematics responsibility in case of machine-performed reasoning  
Data Analysis  
The analysis includes three types of philosophical data:  
⒈ Ontological Claims  
– Realist claims that mathematical objects exist independently of all cognition.  
– Anti-realist assertions of mathematics as a cultural-linguistic fabrication.  
⒉ Epistemic Mechanisms  
– Intuitionistic and rationalistic accounts of the acquisition of mathematical knowledge.  
– Models advocating for embodied cognition in mathematics as neural-conceptual mapping.  
⒊ Normative Status  
– Claims of mathematical neutrality in classical philosophy.  
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Contemporary anti-algorithmic mathematics critiques as a form of power.  
Rationale analysis goes on from cross-level conceptual mapping, highlighting internal consistency, explanatory  
lacunae and philosophical incompatibilities.  
The analytical outcome reveals:  
● Universality is to be accounted for by realism alone, but not explanatorily accessible to it.  
● Cognitivism accounts for cognition but not cross-cultural invariance.  
● [Formalism] does not settle metaphysical status or ethical effects.  
The only consistent path calls for a model which combines:  
● Metaphysical structure  
● Cognitive embodiment  
● Ethical normativity  
This is the analytical basis of the HMU paradigm.  
FINDINGS  
The formal analysis results in three philosophical findings:  
Findings 1. Mathematics is a Dual-aspect Ontological Field of Reality:  
Mathematics neither purely as mental construction nor totally self-sufficient metaphysical abstraction. It is as  
cosmological structural potential in need of cognitive fulfilment to be epistemically operational.  
Formally:  
Mathematical Being = Metaphysical Structure + Embodied Instantiation  
Findings 2. Mathematical Cognition is an Embodied Phenomenon:  
Mathematics is not a passive representation, but co-actualization of embryo structural order through  
symbolization, proof, and conceptual abstraction.  
Human cognition is involved with the ontology of mathematics, rather than only describing this entity.  
Findings 3. Mathematics is Ethically Respondable:  
When mathematical reasoning rules the technology that mediates material and political reality, the decisions  
made by mathematicians are virtually normative acts.  
Therefore:  
The correctness of mathematical statements should be judged by three criteria: logical consistency, ontological  
adequacy, and ethical neutrality.  
DISCUSSION  
The paper shows that the classical separation between ontology, epistemology and ethics in philosophy of  
mathematics is no longer tenable in the present.  
Ontological Implications  
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The dual-aspect architecture abolishes the dichotomy between invention and discovery. The mathematics turns  
into relational metaphysics in ways reminiscent of, say, quantum participatory realism and phenomenological  
intentionality.  
This follows new positions in:  
● Neo-structural realism  
● Cosmology: The theoretical interpretation of the infinite information in a finite universe.  
● Second-order post-positivist philosophy of science  
Epistemological Implications  
If cognition contributes to the ontology of mathematics, mathematical knowledge is neither purely a priori nor  
arbitrary stipulation. It's an epistemic activity insofar as this is a modal matter; the latent structure of reality  
simply gets itself signified by human rationality.  
It recasts proof, intuition, and abstraction as features of jobsite metaphysical interaction rather than mere  
symbolic shuffling.  
Ethical Implications  
Philosophical traditions regarded mathematics as inherently neutral. However, mathematical systems now  
constitute:  
● Algorithmic judgment infrastructures J. Zittrain 43 decision making, but to prop up systematized judgments  
with input from people about what decisions should reflect or look like.  
● Self-determining decision architectures  
● Predictive computational governance.  
In HMU, misuses of mathematics are metaphysical and moral disarray, not mere technical failure.  
It follows that mathematical ethics should go beyond external regulation and develop into internal philosophical  
necessity, just as bioethics and legal philosophy.  
CONCLUSION  
This work shows that extant philosophy of mathematics perspectives, being realism, constructivism, and  
formalism cannot account for the metaphysical nature of mathematical objects (metaphysical problem), how we  
are able to access these objects (epistemological problem), or what will be our responsibilities towards those  
who fail in their attempts to attain this optimal end during training (practical/ethical problem). The Humanized  
Mathematical Universe (HMU) model negates these discontinuities by treating mathematics as a dual-aspect  
metaphysical entity whose constitution in the course of nature is co-actualized via embodied cognition and  
cosmological structure.  
The following conclusions emerge:  
1. The ontology of mathematics as an essential structural possibility of the universe.  
2. Mathematical knowledge is constitutively, epistemically embodied as symbolic rationality.  
3. Mathematics is a morally relevant activity, and so moral reasoning should be part of it.  
Hence, any further philosophy of mathematics should consider mathematics as:  
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● An ontological link between mind and universe  
● A cognitive way of relating to rational structure  
● A moral act with implications for civilization  
The HMU paradigm presents a philosopher's stone powerful enough to overcome the history and signs of  
metaphysical coherence, epistemic justification, and ethical responsibility in one model-and hence to re-situate  
the philosophy of mathematics within its inevitable stance towards an algorithmic/usability-  
visible/cosmologically meaningful/ethically precarious world.  
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