Author: Luo Xiaomao (Luo Han)
Nature: Metascientific Critique / Incision Paper on Foundations of Mathematics and Philosophy of Science
Positioning: Minimal Defensible Presentation for External Communication of the Non-Evident Choice, Tri-Source System. Publishable Prototype, System Seed, Door-Opening Paper.
Abstract
Modern science and modern mathematics exhibit extraordinary formal capability at the intermediate structural level: they can compute, predict, classify, model, and achieve remarkable effectiveness in a vast range of complex problems. However, formal effectiveness does not equal completeness of origin explanation. This paper points out that a noteworthy "first-principle immunity mechanism" is widespread in modern mathematical and physical sciences: while theoretical systems demand rigorous proof, rigorous definition, and rigorous verification at the intermediate level of reasoning, they allow their most fundamental primitive concepts, axioms, constants, operational definitions, or basic units to escape origin-level interrogation of comparable intensity.
This paper does not deny the scientific value of axiomatic methods, effective theories, operational definitions, or empirical modeling. On the contrary, it acknowledges that they are necessary tools for the great success of modern science. What it criticizes is a different kind of overreach: when provisional axiomatic settings, empirical constants, operational definitions, or model languages are mistaken for ontological endpoints, science may slide from an open truth-seeking activity to a self-exempting closed system.
Using examples from the foundations of natural numbers in mathematics, fundamental constants in physics, photons and wave–particle duality, and the history of model replacement in chemistry, this paper illustrates that science often exhibits high rigor at the complex level while retaining explanatory debt at the first-principle level. In response, this paper proposes the "Principle of Origin Proof": whatever is taken by a theory as a first principle, primitive term, fundamental unit, or an unquestionable starting point cannot obtain ontological immunity solely through formal effectiveness; it must be constructed, generated, derived, proven non-arbitrary, or explicitly marked as an as-yet-unpaid explanatory debt.
This paper also emphasizes that this principle cannot be used only to judge established science; it must also constrain any new system in reverse. Any alternative theory that proposes new first-principle concepts must likewise submit to the tests of origin proof, refutability, explanatory gain, and structural self-consistency. The purpose of this paper is not anti-science, but opposition to scientistic first-principle immunity. Truly thorough science should not only question complex issues, but also permit and encourage questioning of the most superficial, most fundamental, and most origin-level questions.
Keywords: first principles; axiomatic method; explanatory debt; philosophy of science; foundations of mathematics; origin proof; effective theory; falsifiability; scientism
I. Problem Statement: The Success of Science and the Immunity of Science Are Not the Same Thing
Modern science is undeniably successful.
Mathematics provides extremely powerful formal reasoning capabilities; physics can predict celestial motions, particle scattering, spectral structures, and engineering systems using equations; chemistry can explain and control a large number of material reactions; modern technology directly demonstrates the practical power of these theoretical frameworks.
Therefore, this paper does not start from "science is invalid."
What this paper truly asks is:
Does the computational success of a theory equal its completion of first-principle explanation?
The answer is clearly no.
A theory can be effective yet incomplete;
A model can be useful yet not the ontological endpoint;
An axiomatic system can be formally rigorous yet its primitive terms may not have been origin-proved;
A physical constant can be measured and used with high precision yet its particular value may not have been explained;
An operational definition can ensure reproducible communication within an experimental community yet may not reveal the ultimate structure of the object.
The danger of modern science does not lie in its unknowns. Any genuine science must confront unknowns.
What is truly dangerous is:
Disguising the unknown as an unquestionable starting point.
When a theory says, "we temporarily treat this as an axiom," that is a reasonable methodological restraint.
But when it goes further and says, "this need not and should not be questioned," the situation changes.
The former is a temporary working strategy of science.
The latter approaches a dogmatic stance.
In the real world, if a system demands that people "don't ask, just accept" its starting points, that is typically called a belief structure, not a scientific structure. Science can certainly set temporary starting points, but it cannot sanctify temporary starting points as permanent exemptions.
This paper terms this phenomenon:
first-principle immunity mechanism.
II. Core Definitions: Formal Proof, Origin Proof, Explanatory Debt, and First-Principle Immunity
To avoid misunderstanding, this paper first gives four basic definitions.
2.1 Formal Proof
Formal proof, as used here, means deriving a proposition within a given axiomatic system or formal rule system, according to accepted axioms, definitions, and inference rules.
For example, in ZFC set theory, Peano arithmetic, type theory, or other formal systems, once axioms and rules are accepted, many propositions can be rigorously proved or refuted.
The advantages of formal proof are:
Clarity;
Testability;
Reproducibility;
Avoidance of linguistic ambiguity;
Ability to establish high-strength chains of reasoning.
But formal proof also has a boundary:
It generally cannot prove within the system why the system's initial axioms themselves hold.
This is not a failure of formal systems, but a structural feature of formal systems.
2.2 Origin Proof
Origin proof, as used here, does not require an axiom to prove itself within the same system. That would lead to circular reasoning or infinite regress.
Origin proof means that a concept, unit, principle, or constant placed in a foundational position must be defended at a higher meta-level, through generative mechanisms, constructive processes, ontological analysis, or empirical anchoring.
In other words:
A first principle does not necessarily have to be proved within its own system, but it cannot rest on "I stipulate it so" as its ultimate justification.
It should satisfy at least one of the following:
It can be constructed;
It can be generated;
It can be derived from deeper principles;
Its non-arbitrariness can be demonstrated;
It can be stably anchored in empirical structure;
Or it is explicitly marked as an unpaid explanatory debt.
2.3 Explanatory Debt
Explanatory debt refers to the fact that although a theory can describe, compute, or predict certain phenomena, it has not yet explained their first-principle source, generative mechanism, or ontological structure.
Explanatory debt does not mean the theory is wrong.
For example, Newtonian mechanics had enormous predictive power before relativity, but it did not explain why gravity exists in that form. Classical electromagnetism was extremely successful before quantum theory, but it did not complete the origin explanation of radiation, quantum jumps, etc.
Therefore, explanatory debt is not an accusation, but a marker.
It reminds us that:
Effectiveness is not the endpoint.
Beyond effectiveness, there may still be deeper explanations.
2.4 First-Principle Immunity Mechanism
First-principle immunity mechanism refers to the situation in which a theoretical system demands rigorous proof, rigorous definition, and rigorous verification at the intermediate level of reasoning, while allowing its most fundamental primitive concepts, axioms, constants, operational definitions, or basic units to escape origin-level interrogation of comparable intensity.
Its typical structure is as follows:
Intermediate-level problems: must be proved, must be rigorous, must be testable;
Bottom-level starting points: this is an axiom, this is a definition, this is a constant, this is an operational convention, no further questions.
This practice is understandable methodologically, but cannot be absolutized ontologically.
If a system merely says:
"We temporarily start here."
That is reasonable.
If a system says:
"This need never be questioned."
That constitutes first-principle immunity.
What this paper criticizes is not the axiomatic starting points in science, but the immunity that arises after those starting points are sanctified.
III. The Fatal Double Standard: Rigorous at the Intermediate Level, Immune at the Foundational Level
The greatest strength of modern science is its extreme rigor on intermediate-level problems.
Once within an established theoretical framework, the scientific community typically demands:
Clear concepts;
Rigorous derivations;
Reproducible experiments;
Testable data;
Refutable conclusions;
Analyzable errors;
Comparable models.
These demands are entirely reasonable and are important reasons why modern science is superior to pre-science, pseudoscience, and purely belief-based systems.
The problem is that when questioning goes deeper to the foundational level, the same strict requirements are often relaxed.
For example:
Mathematics can study the complex structure of natural numbers, yet often does not ask how "one as a unit" is established;
Physics can use fundamental constants for high-precision calculations, yet may not explain why those constants take their specific values;
Quantum theory can accurately predict experimental results, yet still has multiple non-equivalent ontological interpretations;
Chemical models can effectively predict reactions, structures, and properties, yet often mistakenly package scale models as ontological images.
Thus, a structural asymmetry is formed:
For external theories: your first principles must be proved;
For internal starting points: our first principles are axioms, definitions, constants, or operational conventions.
This is what this paper calls "the fatal double standard of science."
It does not mean modern science is invalid; it means:
Modern science often covertly substitutes "methodologically temporary starting points" for "ontologically unquestionable endpoints."
Once this substitution occurs, science ceases to be purely open truth-seeking and partially exhibits dogmatic tendencies.
IV. Case Study in Mathematics: The Natural Number Structure and the Origin Problem of "One"
Mathematics is one of the most rigorous disciplines. Therefore, first-principle issues in mathematics are particularly worth discussing.
Modern mathematics can certainly provide rigorous formal foundations for natural numbers.
For example, in ZFC set theory, common definitions are:
0=∅0=∅1={∅}1={∅}2={∅,{∅}}2={∅,{∅}}
In Peano arithmetic, starting from 00 and the successor function SS, one can define:
1=S(0)1=S(0)
In type theory, natural numbers can also be viewed as an inductive type constructed from zero and successor.
These formalizations are very effective and very important.
But this paper points out:
Formal representation is not origin explanation.
When mathematics says:
1={∅}1={∅}
it indeed gives a formal construction.
But this construction still presupposes several more fundamental things:
How is the empty set established;
How is set boundary established;
How is the distinction between element and set established;
How is identity established;
How is the membership relation established;
How is the successor operation established;
What does it mean for a unit to be countable.
Thus, this paper does not say standard mathematics has not defined 0 and 1.
What it asks is:
How is "one as a unit" established?
4.1 "One" Is Not the Absolute First Principle of the Complete System, but It Is the Unit First Principle in Mathematics
It should be noted that this paper does not equate the mathematical "one" directly with the highest ontological first principle.
In a complete origin system, "one" may still be a derived layer, not the ultimate starting point. That is, the mathematical "one" can be a first principle in counting, unit, difference, and structural identification, but it may not be the final first principle of complete ontology.
This paper adopts a restrained formulation:
"One" is not the ultimate first principle of the complete system;
but in the counting structure of mathematics, "one" functions as the unit first principle.
Therefore, questioning "one" is not a surreptitious replacement of mathematical problems, but a question about the origin conditions of the mathematical unit structure.
4.2 Proposition on Unit Structure
If an object xx is called "one," it must at least satisfy the following conditions:
xx and non-xx are distinguishable;
xx maintains self-identity under some judgment;
There is a boundary between xx and its background;
xx can serve as a unit for counting or repeated construction;
xx can enter into the generative relation of "one, another, many."
Therefore, "one" cannot be understood as a completely structureless empty point.
Because as long as it can be called "one," it already contains at least:
self/non-selfself/non-selfinner/outerinner/outeridentity/differenceidentity/differenceboundary/backgroundboundary/background
These are not complex number-theoretic structures, but the minimal structural conditions for a unit to be established.
In other words:
"One" is not a simple structureless point, but a minimal distinguishable structure.
This does not negate modern mathematics' formal definitions of 11; it points out:
Formal systems can start from 00, 11, successor, axioms, or set-theoretic constructions;
but if one asks how "one as a unit" is established, a deeper origin explanation is still needed.
4.3 Mathematics' Explanatory Debt
Mathematics can say:
"We do not discuss ontology; we only discuss formal systems."
If mathematics strictly maintains this position, then this paper's critique of mathematical ontology would partially fail.
But the problem is that mathematics is not always a mere formal game. It is often assigned a higher status:
It is regarded as the language of natural science;
It is regarded as the universal expression of structure;
It is used to describe physical reality;
It is thought to reveal deep orders of number, space, continuity, infinity, symmetry, etc.;
It is used to judge whether other theories are rigorous.
Once mathematics moves from pure formal game to "describer of world structure," its primitive terms cannot entirely escape origin questioning.
Therefore, this paper's judgment on mathematics is:
Mathematics is highly successful in formal reasoning;
but on issues of unit, identity, boundary, infinity, continuum, etc., it still retains origin explanatory debt.
This is not a denial of mathematics, but a re-marking of its boundaries.
V. Case Study in Physics: Constants, Photons, Wave–Particle Duality, and Operational Success
The success of physics is likewise undeniable.
Modern physics can predict planetary motions, design semiconductors, explain spectra, build lasers, establish nuclear technologies, and achieve extremely high-precision predictions through quantum electrodynamics, the standard model, and general relativity.
Therefore, this paper does not claim physics is invalid.
What it points out is:
Predictive success in physics does not automatically equal completion of origin explanation.
5.1 Fundamental Constants: Measurable Does Not Mean Explained
Physics contains many fundamental constants, for example:
cc
the speed of light;
hh
Planck's constant;
GG
the gravitational constant;
αα
the fine-structure constant.
These constants can be measured with high precision and play core roles in theories.
But the question is:
Why do they take these values?
In effective theories, treating constants as input parameters is reasonable. Science must start from measurable, computable, and experimentally accessible points.
But if a theory long maintains only:
"It is just this number."
without acknowledging that there remains explanatory debt, then the constant shifts from a working parameter to an ontological immunity point.
More rigorously:
Fundamental constants are not errors;
fundamental constants are markers that the theory has not yet fully generated them.
When a theory can derive constants from deeper structures, or explain their non-arbitrariness, it truly reduces explanatory debt.
5.2 The Photon: Formal Concept Effective, but Ontological Language Still Tension
Common language often says "the photon is a particle."
But in modern quantum field theory, the photon is not a small ball in the classical sense, but a quantum excitation of the electromagnetic field. The photon has no rest mass, which does not constitute a formal contradiction within standard theory, because "particle" here is no longer a classical entity particle but a quantized mode of field excitation.
Thus, this paper does not adopt a crude critique:
"Since it is called a particle, how can it have no mass?"
Such critique can be easily dismissed by professional physicists.
What this paper truly points out is:
The photon concept reveals the ontological linguistic tension in modern physics.
On the one hand, physics needs to use concepts such as "particle," "wave," "field," "excitation," and "quantum state" for computation and experiment; on the other hand, these concepts do not all correspond to everyday entity images.
Thus, the theory is extremely successful formally, but the ontological explanation has multiple layers of linguistic misalignment:
LevelExpression
Experimental levelDiscrete detector clicks
Mathematical levelField operators, state vectors, propagators
Model levelPhoton, wave packet, quantum excitation
Ontological level"What light truly is" still has room for explanation
Therefore, this paper does not deny the effectiveness of photon theory, but points out:
The photon as a computational object is successful;
Whether light as an existential structure has been fully explained remains an open question.
If a new system proposes that "light is not a classical particle, but a certain kind of fissure, perturbation, or manifestation in spatial structure," then it should not remain at the metaphorical level, but must further provide:
Mathematical expression;
Testable predictions;
Regions of compatibility with existing optics and quantum electrodynamics results;
New experiments distinguishable from existing theories.
Otherwise, it remains merely new language, not new science.
5.3 Wave–Particle Duality: Predictive Success Does Not Equal Explanatory Unity
Wave–particle duality is often regarded as one of the core features of quantum theory.
Objects such as electrons and photons exhibit wave-like or particle-like properties under different experimental conditions. Quantum theory can accurately predict these experimental phenomena, such as interference, diffraction, photoelectric effect, single-particle double-slit experiments, etc.
But from the explanatory perspective, quantum theory does not have a uniquely recognized ontological picture.
At least multiple interpretive paths exist:
Copenhagen interpretation;
Many-worlds interpretation;
de Broglie–Bohm theory;
Objective collapse theories;
Relational quantum mechanics;
QBism;
Information-theoretic interpretations.
These interpretations are identical or nearly identical in many experimental predictions, yet give different answers to "what quantum objects truly are."
This indicates:
Quantum theory as a predictive framework is highly successful;
but the origin explanation of quantum objects has not been closed by a single approach.
Therefore, if someone proposes a new ontological interpretation, it should not be directly shut down by "quantum theory is already successful."
The correct attitude should be:
As long as the new interpretation does not break verified results and can propose additional testable differences, it qualifies for entry into scientific discussion.
VI. Case Study in Chemistry: Effective Model Chains and Ontological Explanation Gaps
The history of chemistry is not simply a history of errors, but a history of continuous replacement and refinement of effective models.
From Dalton's atomic theory, to Thomson's "plum pudding model," to Rutherford's nuclear model, to the Bohr model, quantum orbitals, valence bond theory, molecular orbital theory, density functional theory, chemistry and physical chemistry have continuously developed stronger explanatory and computational capabilities.
These models have great value.
But the problem is:
Effective model does not equal final ontology.
For example, chemical bonds can be described categorically using concepts such as covalent bonds, ionic bonds, metallic bonds, hydrogen bonds, van der Waals forces; at deeper levels, they can be described using electron clouds, orbital overlap, energy levels, symmetry, exchange interactions, etc.
These descriptions are effective at different scales, but they do not automatically answer:
Why does matter stably exist at this hierarchical level;
Why do elemental properties form periodic structures with nuclear charge;
Why does chemical affinity have specific directionality;
Why do molecular configurations form stable spatial skeletons;
Why are reaction pathways allowed in some structures and forbidden in others;
Is a "bond" an entity, a relation, an energy valley, or a model language.
At the professional level, chemists certainly know that models have applicability boundaries. But in teaching and popular science, effective models are often told as "the world is actually like this."
Thus, chemistry also exhibits a kind of first-principle immunity:
Models are continually replaced, but each generation of models, when used, is easily mistaken as the ontological endpoint.
This paper's evaluation of chemistry is not "chemistry is invalid," but:
Chemistry is an extremely powerful system of effective models;
but many of its foundational concepts still carry origin explanatory debt.
VII. The Principle of Origin Proof: No Absolute Immunity for First Principles
The mathematical, physical, and chemical issues discussed above can be summarized into the same principle question:
Does a theory have the right to demand that others prove their first principles while exempting its own first principles?
This paper's answer is: No.
Therefore, this paper proposes:
The Principle of Origin Proof
Whatever is taken by a theory as a first principle, primitive term, fundamental unit, fundamental constant, or an unquestionable starting point cannot obtain ontological immunity solely through formal effectiveness. It must satisfy at least one of the following conditions:
Be constructed;
Be generated;
Be derived from deeper principles;
Be proven non-arbitrary;
Be stably anchored in empirical structure;
Or be explicitly marked as an unpaid explanatory debt.
This principle has two directions.
7.1 Constraint on Established Science
Established science cannot, because of its own success, declare its fundamental concepts unquestionable.
It can say:
"In the current theory, we temporarily start here."
But it should not say:
"This needs no explanation and should not be questioned."
The former is scientific method.
The latter approaches dogmatic structure.
7.2 Constraint on New Systems
Likewise, no new system is exempt.
If a new system proposes new first principles, such as:
nothing;
being;
one;
binary states;
spatial fissures;
background fields;
manifestation mechanisms;
structural source terms;
then it must also explain:
Why these concepts are necessary;
How they are generated;
How they avoid arbitrary assumptions;
How they are compatible with or demarcated from existing knowledge;
What new explanations they can derive;
What testable differences they can produce;
Under what conditions they would be falsified or discarded.
Therefore, this paper does not use the Principle of Origin Proof to unilaterally attack old systems.
Instead, it explicitly declares:
The Principle of Origin Proof is first and foremost a universal discipline.
It constrains old theories and also constrains new theories.
No system enjoys first-principle immunity.
VIII. Falsifiability Section: How Can This Principle Turn Back and Examine This Paper Itself?
If this paper only criticized modern science's first-principle immunity without explaining how it itself can be examined, then it would fall into the same double standard.
Therefore, this section specifically explains:
The Principle of Origin Proof proposed in this paper must be able to turn back and examine this paper itself.
8.1 This Paper Is Not an Irrefutable Positional Manifesto
This paper does not propose an irrefutable slogan:
"All first principles must be proved in the manner I recognize."
That would become a new dogmatism.
What it proposes is a meta-methodological requirement:
When a concept is placed at a theoretical starting point, it must explain its own mode of defense; if it cannot be proved temporarily, it must acknowledge explanatory debt rather than disguise that debt as an endpoint.
This principle itself can be refuted.
For example, if someone can prove:
Some first principles need no meta-level defense to acquire ontological legitimacy;
Axioms, as long as formally valid, automatically complete origin explanation;
Operational definitions can completely replace ontological explanations;
Predictive success necessarily entails ontological completeness;
Questioning first principles is logically necessarily meaningless;
then the principle of this paper would need revision or abandonment.
8.2 Minimum Falsification Criteria for This Paper
This paper is at least weakened or falsified in the following cases.
Case 1: First-principle immunity is proved not to be a double standard
If it can be proved that a theory's demand that external systems prove first principles while exempting its own first principles does not constitute methodological asymmetry, then this paper's "double standard" critique fails.
Case 2: Formal effectiveness is proved equivalent to origin explanation
If it can be proved that a theory, as long as formally effective and predictively successful, automatically completes ontological explanation, then this paper's "explanatory debt" concept loses necessity.
Case 3: Origin questioning is proved necessarily meaningless
If it can be proved that all questioning of first-principle sources, generative mechanisms, and non-arbitrariness are only linguistic illusions or category errors, then this paper's "Principle of Origin Proof" would need retraction.
Case 4: The new system cannot provide any explanatory gain
If a new system claims to surpass established science but cannot provide gains in the following:
Fewer arbitrary assumptions;
Stronger structural unity;
Deeper generative explanations;
Compatibility with existing facts;
Production of new predictions;
Allowance for falsification;
then it cannot gain legitimacy by borrowing this paper's critique of old systems' gaps.
This point is especially important.
Because this paper opposes immunity itself, not seeking immunity for some new system.
8.3 Falsifiability Requirements for New Systems
Any system claiming to supplement first principles must at least accept four types of tests.
First, logical tests
Its first-principle concepts must not be mutually contradictory, cannot rely on metaphors instead of derivations, and cannot use vague wording to evade definition.
Minimum requirements:
Concepts are distinguishable;
Levels are arrangeable;
Derivations are not circular;
Starting points are not arbitrary;
Conclusions do not equivocate.
Second, explanatory tests
It must explain problems that the old system cannot explain, or explains insufficiently.
For example:
How the unit is established;
Why constants are non-arbitrary;
How structures are generated;
Why quantum objects show dual readouts;
Why chemical stability has spatial configuration.
If it merely restates old problems with a new set of terms, without explanatory gain, it does not hold.
Third, compatibility tests
It cannot arbitrarily negate facts that have been extensively verified.
If the new system explains light, mass, space, numbers, chemical bonds, or quantum phenomena, it must explain:
Why the old theory is valid in its domain of applicability;
At which boundaries the new theory corrects the old theory;
How the old theory is retained as an approximation, projection, or local model.
It cannot simply say "old theory is all wrong."
Fourth, predictive tests
It must give at least some testable predictions that differ from existing theory.
These predictions can be:
New experimental phenomena;
New parameter relations for old phenomena;
Low-cost verifiable differences;
High-risk discriminant experiments;
Reparameterized explanations of known anomalies.
If there are no testable differences, it can only serve as a philosophical interpretation, not a scientific theory.
8.4 This Paper Allows Its Own Failure
This paper explicitly allows the following conclusion:
If the Principle of Origin Proof cannot produce stronger explanatory power, cannot promote better theoretical construction, and cannot establish falsifiable research lines, then it is an ineffective philosophical requirement.
This must be stated clearly.
Because the true scientific attitude is not:
"I demand that others accept."
But:
"I give a principle, and I also give the conditions under which it may fail."
Thus, the difference between this paper and dogmatized systems is:
This paper does not demand unconditional belief;
This paper does not sanctify its starting points;
This paper acknowledges that its own principles can be challenged;
This paper requires that old and new systems be subject to the same review;
This paper marks what cannot be proven as explanatory debt, not as an endpoint disguised.
IX. Responses to Possible Objections
9.1 Objection 1: All systems need axioms; infinite proof is impossible
This is the most common and most powerful objection.
Indeed, any formal system needs certain starting points. If every starting point had to be proved within the same system, it would lead to circularity or infinite regress.
But this paper does not demand that.
What it demands is:
Axioms can be working starting points, but cannot thereby obtain ontological immunity.
In other words:
Axioms need not be internally proved in a formal system;
But when axioms are asserted as ontological claims, they need meta-level defense;
If defense is temporarily impossible, it should be acknowledged as explanatory debt;
"We temporarily start here" must not be surreptitiously replaced by "this need never be explained."
Therefore, this paper opposes not the axiomatic method, but the sanctification of axioms.
9.2 Objection 2: Mathematics only studies formal structures, not responsible for ontological explanation
If mathematics only claims to be a symbolic game within formal systems, then this paper's critique of mathematical ontology would indeed not directly apply.
But in reality, mathematics is not always like that.
Mathematics is often used as:
Scientific language;
Model of world structure;
Foundation of physical theories;
Highest standard of logical rigor;
Structural tool in ontological discussions.
Once mathematics assumes these roles, it cannot fully retreat to the safe zone of "I am just a formal game."
Therefore, this paper distinguishes two kinds of mathematics:
Mathematical stanceThis paper's attitude
Purely formalist mathematicsMay temporarily not bear ontological explanation
Mathematics as language of world structureMust face origin explanatory debt
9.3 Objection 3: Physics only cares about measurable quantities, not ontology
This is a typical operationalist stance.
It has its reasonableness.
Science must certainly respect measurement and cannot replace experiment with untestable ontological imagination.
But the problem is:
Not caring about ontology is a methodological choice, not proof that ontological questions do not exist.
Physics can temporarily say:
"We only deal with measurable relations."
But it cannot thereby infer:
"All ontological questions are meaningless."
Because historically, many questions once thought metaphysical or unaskable later became scientific questions. For example:
Whether atoms are real;
Whether the speed of light is finite;
Whether space is curved;
Whether time is absolute;
Whether vacuum has structure;
Whether mass can be converted to energy.
Thus, operational success cannot shut down origin questioning.
9.4 Objection 4: Your new system also has first principles; why is it exempt?
It is not exempt.
This is the most crucial response of this paper.
Any new system proposing new first principles must also submit to the same review.
If it says "one has structure," it must explain how the structure of "one" is established.
If it says "light is a fissure in space," it must explain the definition, mechanism, mathematical expression, and testable differences of the fissure.
If it says "the complete first principle is not one, but a deeper non-evident choice of being," it must explain:
That "non" is not an empty word;
That "evident" is not a metaphor;
That "choice" is not arbitrary will;
That "being" is not a circular definition;
How from that first principle one derives unit, difference, structure, and the empirical world;
Where the system might fail.
This paper does not unfold the complete system here; it gives only the minimal interface:
If there exists a deeper first principle than "one," it must be able to explain how "one" is generated, rather than treating "one" directly as a structureless starting point.
This is the connection point between this paper and the complete system.
But within this paper's scope, only the methodological requirement is proposed, not the full ontology.
9.5 Objection 5: Is this dragging science back to metaphysics?
No.
This paper does not ask science to abandon experiments and return to empty metaphysical speculation.
What it asks is:
Bring first-principle issues back into the scope of defensible, constructible, falsifiable, and gainful research.
The real question is not "whether it is metaphysical," but:
Whether it is clear;
Whether it is self-consistent;
Whether it has explanatory gain;
Whether it is compatible with existing facts;
Whether it produces testable differences;
Whether it acknowledges its own failure conditions.
If an origin theory satisfies these conditions, it is not empty metaphysics, but frontier work between philosophy of science and foundational science.
X. Minimal Interface with the New System: Open the Door, Do Not Dump
The main task of this paper is not to fully unfold the new system, but to establish an entry point.
This entry point is:
First principles have no immunity.
Once this principle holds, both old and new systems face the same question:
How is your starting point established?
For established science, this means:
The origin conditions of the natural number unit still need explanation;
The non-arbitrariness of fundamental constants still needs explanation;
The ontological structure of quantum objects still needs explanation;
The ultimate structural status of chemical models still needs explanation.
For new systems, this means:
Cannot only criticize old theories;
Cannot only propose new terms;
Cannot rely only on intuition;
Cannot replace proof with grand narratives;
Must produce generative chains, explanatory gains, and falsification conditions.
Therefore, this paper only lightly indicates a direction:
If "one" already contains minimal distinguishable structure, then "one" may not be the highest first principle.
A deeper first principle must be able to explain the generative process from "no distinction to distinction," "from non-manifest to manifestation," "from non-countable to unit establishment."
This direction may be provisionally called:
non-evident choice of being→difference→boundary→one→many→structurenon-evident choice of being→difference→boundary→one→many→structure
But this paper does not force it out as a completed proof.
In this paper, it serves only a seed function:
To illustrate that the Principle of Origin Proof not only destroys old systems, but can also demand and promote new systems to give deeper generative explanations.
XI. From Effective Science to Origin Science
The development of science is not a simple replacement from error to truth, but a progressive process from lower explanatory power to higher explanatory power, from local effectiveness to greater unity, from empirical fitting to structural generation.
Newtonian mechanics is not useless.
It remains effective under low-speed, weak-gravity conditions.
Classical electromagnetism is not useless.
It remains effective in macroscopic continuous field regimes.
Chemical bonding models are not useless.
They remain effective in reaction prediction, materials design, and molecular structure analysis.
The problem is not whether old theories are useful, but:
Does usefulness equal finality?
The answer is no.
The direction advocated by this paper can be called:
From effective science to origin science.
Effective science focuses on:
How to compute;
How to predict;
How to classify;
How to control;
How to model.
Origin science further asks:
Why the starting point holds;
How the unit is generated;
Why constants are non-arbitrary;
Why structure appears;
How boundaries form;
Why laws have this form.
The two are not enemies.
Truly complete science should simultaneously possess:
effective prediction+origin explanationeffective prediction+origin explanationformal rigor+generative self-consistencyformal rigor+generative self-consistencyexperimental test+first-principle defenseexperimental test+first-principle defense
If there is only effective prediction without origin explanation, science becomes a powerful technological system, but leaves first-principle voids.
If there is only origin narrative without experimental test, the theory slides into empty speculation.
Therefore, this paper's claim is not to replace effective science with origin science, but to demand:
Effective science must acknowledge explanatory debt;
Origin science must accept falsification discipline.
XII. Conclusion: Science Is Not Afraid of the Unknown; It Is Afraid of Declaring the Unknown a Forbidden Zone
This paper has proposed and argued a core judgment:
Modern science and modern mathematics are extremely rigorous on intermediate-level problems, but often exhibit immunity mechanisms on first-principle issues.
This immunity mechanism does not invalidate science, but creates a methodological double standard:
Demanding that external theories prove their starting points;
Yet treating its own starting points as axioms, definitions, constants, or operational conventions;
Extremely strict at the complex level;
Stopping questioning at the origin level.
This paper calls this phenomenon "first-principle immunity."
The danger of first-principle immunity is that it disguises scientific temporary methodological starting points as ontological endpoints.
Therefore, this paper proposes the "Principle of Origin Proof":
Whatever is taken by a theory as a first principle, primitive term, fundamental unit, or an unquestionable starting point cannot obtain ontological immunity solely through formal effectiveness; it must be constructed, generated, derived, proven non-arbitrary, or explicitly marked as an unpaid explanatory debt.
At the same time, this paper emphasizes:
This principle must also constrain any new system.
A new system cannot automatically gain legitimacy merely by pointing out old systems' explanatory debts. It must provide stronger generative explanations, structural self-consistency, empirical compatibility, and falsifiable predictions.
Thus, this paper is ultimately not anti-science, but anti-scientistic immunity.
What makes science truly powerful is not that it has no starting points, but that it allows questioning of starting points.
What makes science truly dangerous is not that it has unknowns, but that it disguises unknowns as unquestionable endpoints.
If a system demands that people "don't ask, just believe," then in the real world it is closer to a creed than to science.
Science can temporarily not know, but it cannot canonize "not knowing" as "not allowed to ask."
The final conclusion of this paper is:
First principles have no absolute immunity.
Axioms can be starting points, but cannot masquerade as endpoints.
Effectiveness can prove usefulness, but cannot prove completeness.
Truly thorough science must be able to both explain complexity and dare to face the most superficial, most fundamental, and most origin-level questions.
References and Further Reading Notes
Note: This V1 is a theoretical framework draft. The following references are used to support discussions on the axiomatic method, philosophy of science, physical interpretation, foundations of mathematics, and effective theory. The formal publication version will require further verification and standardization according to the target journal's format.
Hilbert, D. (1899). Grundlagen der Geometrie.
Classic source of Hilbert's axiomatic method.
Zermelo, E. (1908). Untersuchungen über die Grundlagen der Mengenlehre I. Mathematische Annalen.
One of the foundational documents of modern set theory.
Fraenkel, A. A. (1922). Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre. Mathematische Annalen.
Related to the development of ZF set theory.
Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik.
Core document on the boundaries of formal systems.
Tarski, A. (1936). Der Wahrheitsbegriff in den formalisierten Sprachen.
Important document on truth definition and formal languages.
Quine, W. V. O. (1951). Two Dogmas of Empiricism. The Philosophical Review.
Critique of the analytic/synthetic distinction and empiricist foundations.
Kuhn, T. S. (1962). The Structure of Scientific Revolutions.
Discussion of paradigms, normal science, and scientific revolutions.
Popper, K. (1959). The Logic of Scientific Discovery.
Falsifiability and the demarcation problem.
Lakatos, I. (1970). Falsification and the Methodology of Scientific Research Programmes.
Methodology of scientific research programs.
Feyerabend, P. (1975). Against Method.
Critique of a single scientific methodology.
Carnap, R. (1950). Empiricism, Semantics, and Ontology. Revue Internationale de Philosophie.
Discussion of internal and external questions within frameworks.
van Fraassen, B. C. (1980). The Scientific Image.
Constructive empiricism and the realism debate.
Hempel, C. G. (1965). Aspects of Scientific Explanation.
Models of scientific explanation.
Weinberg, S. (1992). Dreams of a Final Theory.
Background on ultimate theories and fundamental constants.
Feynman, R. P. (1965). The Character of Physical Law.
Popular classic on the nature of physical laws and explanation.
Dirac, P. A. M. (1930). The Principles of Quantum Mechanics.
Classic text on the formal system of quantum mechanics.
Bohr, N. (1934). Atomic Theory and the Description of Nature.
Quantum interpretation and complementarity.
Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Fizika.
Core document on quantum foundations and hidden variables.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review.
Classic document on the completeness of quantum theory.
Schrödinger, E. (1935). Die gegenwärtige Situation in der Quantenmechanik.
Source of quantum superposition and Schrödinger's cat discussion.
Ball, P. (2011). Beyond Weird.
Modern popular discussion of quantum interpretation issues.
Pauling, L. (1939). The Nature of the Chemical Bond.
Classic work on chemical bond theory.
Atkins, P., & Friedman, R. (2011). Molecular Quantum Mechanics.
Foundations of molecular quantum theory and chemical models.
Bunge, M. (1967). Scientific Research.
Discussion of models, explanation, and ontology in philosophy of science.
Suppes, P. (1960). A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences.
Important document on the relationship between mathematical and empirical science models.
Appendix A: Condensed Version of Core Propositions of This Paper
Scientific success does not equal completion of first principles.
Formal proof does not equal origin proof.
Axioms can be working starting points, but cannot automatically become ontological endpoints.
Fundamental constants can be used, but may still carry explanatory debt.
Effective models can predict phenomena, but do not equal ultimate structure.
Demanding first-principle proof from external theories while exempting one's own first principles is methodological double standard.
First principles must be constructed, generated, derived, proven non-arbitrary, or marked as explanatory debt.
This principle also constrains new systems.
New systems must provide logical self-consistency, explanatory gain, empirical compatibility, and falsifiable predictions.
Truly thorough science does not refuse first-principle questioning, but brings such questioning under rigorous discipline.
Appendix B: One-Sentence Version
Science is not afraid of temporarily not knowing; it is afraid of packaging "not knowing" as "not allowed to ask"; axioms can be starting points, but cannot obtain permanent immunity by virtue of their status as starting points.
References and System Sources
Note: This V1 is a theoretical framework draft. This paper contains two categories of references:
The first category is "system source documents," used to mark the new system interfaces, terminology directions, and bases for subsequent development in this paper;
The second category is "public academic literature," used to support public discussions on the axiomatic method, philosophy of science, foundations of mathematics, physical interpretation, chemical models, and falsifiability.
Among these, the system source documents are internal system drafts and have not yet undergone community review as public academic publications. Therefore, this paper does not use them as authoritative evidence that external readers must accept, but only as source notes for the new system interfaces and as research clues for subsequent development. The "Principle of Origin Proof" proposed in this paper likewise applies to these internal system drafts.
1. System Source Documents
Luo Xiaomao (Luo Han). Non-Evident Choice Philosophical Matrix. Internal system draft, 2026.
Source for the first-principle direction of "non-evident choice," from non-manifest to manifestation, from indistinction to difference generation, etc., involved in this paper.
Luo Xiaomao (Luo Han). Non-Evident Choice Physical Public Source. Internal system draft, 2026.
Source for the origin generation, existential structure, physical interfaces, space and manifestation relations, etc., involved in this paper.
Luo Xiaomao (Luo Han). Non-Evident Choice Law Source Mathematics. Internal system draft, 2026.
Source for the issues of units, numbers, structure, laws, formal interfaces, and mathematical foundations involved in this paper.
Luo Xiaomao (Luo Han). Tri-Source System: Philosophical Matrix · Physical Public Source · Mathematical Law Source. Internal comprehensive system draft, 2026.
Source for the three-layer linkage of philosophy, physics, and mathematics, and the complete system structure involved in this paper.
2. Public Academic Literature and Further Reading
2.1. Axiomatic Method, Foundations of Mathematics, and Formal Systems
Hilbert, D. (1899). Grundlagen der Geometrie.
Classic source of Hilbert's axiomatic method.
Zermelo, E. (1908). Untersuchungen über die Grundlagen der Mengenlehre I. Mathematische Annalen.
One of the foundational documents of modern set theory.
Fraenkel, A. A. (1922). Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre. Mathematische Annalen.
Related to the development of ZF set theory.
von Neumann, J. (1923). Zur Einführung der transfiniten Zahlen. Acta Scientiarum Mathematicarum.
Related to von Neumann's construction of natural numbers and set-theoretic concepts of number.
Dedekind, R. (1888). Was sind und was sollen die Zahlen?
Classic on natural numbers, the nature of numbers, and the foundations of arithmetic.
Peano, G. (1889). Arithmetices principia, nova methodo exposita.
Classic source of Peano's arithmetic axioms.
Frege, G. (1884). Die Grundlagen der Arithmetik.
Important text on number, concept, logicism, and the foundations of arithmetic.
Russell, B., & Whitehead, A. N. (1910–1913). Principia Mathematica.
Important attempt at logicist foundations of mathematics.
Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik.
Core document on the boundaries of formal systems, incompleteness, and provability limits.
Tarski, A. (1936). Der Wahrheitsbegriff in den formalisierten Sprachen.
Important document on truth definition, formal languages, and metalanguage distinctions.
Boolos, G. S., Burgess, J. P., & Jeffrey, R. C. (2007). Computability and Logic. Cambridge University Press.
Modern textbook on logic, computability, formal systems, and metamathematical issues.
2.2. Philosophy of Science, Explanatory Debt, and Theory Boundaries
Popper, K. (1959). The Logic of Scientific Discovery.
Classic on falsifiability, demarcation, and empirical testing.
Kuhn, T. S. (1962). The Structure of Scientific Revolutions.
Discussion of paradigms, normal science, anomaly accumulation, and scientific revolutions.
Lakatos, I. (1970). Falsification and the Methodology of Scientific Research Programmes.
On research programs, protective belts, hard core, and theoretical progress/regression.
Feyerabend, P. (1975). Against Method.
Critique of a single scientific methodology, useful as background for methodological pluralism.
Carnap, R. (1950). Empiricism, Semantics, and Ontology. Revue Internationale de Philosophie.
Classic discussion of linguistic frameworks, internal and external questions.
Quine, W. V. O. (1951). Two Dogmas of Empiricism. The Philosophical Review.
Classic critique of the analytic/synthetic distinction and empiricist foundations.
Hempel, C. G. (1965). Aspects of Scientific Explanation.
Models of scientific explanation, covering-law explanation, and explanatory structure.
van Fraassen, B. C. (1980). The Scientific Image.
Constructive empiricism, scientific realism, and status of theoretical entities.
Bunge, M. (1967). Scientific Research.
Systematic discussion of scientific research, models, explanation, ontology, and methodology.
Suppes, P. (1960). A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences.
Important document on the relationship between mathematical models and empirical science models.
2.3. Physical Foundations, Quantum Interpretation, and Constants
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review.
Classic on the completeness of quantum theory.
Bohr, N. (1934). Atomic Theory and the Description of Nature.
Important source on quantum interpretation, complementarity, and experimental language.
Schrödinger, E. (1935). Die gegenwärtige Situation in der Quantenmechanik.
Source of quantum superposition, measurement problem, and Schrödinger's cat.
Dirac, P. A. M. (1930). The Principles of Quantum Mechanics.
Classic text on the formal system of quantum mechanics.
Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Fizika.
Core document on Bell's theorem, hidden variables, and quantum nonlocality.
Feynman, R. P. (1965). The Character of Physical Law.
Classic popular lectures on physical laws, explanation, and the structure of natural laws.
Weinberg, S. (1992). Dreams of a Final Theory.
Discussion of ultimate theories, fundamental constants, unification, and boundaries of physical explanation.
Penrose, R. (2004). The Road to Reality.
Large-scale text on mathematics, physical foundations, space-time, quantum theory, and reality.
Rovelli, C. (1996). Relational Quantum Mechanics. International Journal of Theoretical Physics.
Important document on the relational interpretation of quantum mechanics.
Bohm, D. (1952). A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. Physical Review.
Important document on de Broglie–Bohm theory and hidden variable interpretation.
Everett, H. (1957). "Relative State" Formulation of Quantum Mechanics. Reviews of Modern Physics.
Original document of the many-worlds interpretation.
Ball, P. (2018). Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different.
Modern popular discussion of quantum interpretation issues.
2.4. Chemical Models, Chemical Bonds, and Effective Theory
Pauling, L. (1939). The Nature of the Chemical Bond.
Classic work on chemical bond theory.
Atkins, P., & Friedman, R. (2011). Molecular Quantum Mechanics.
Foundations of molecular quantum theory, orbitals, bonding, and chemical models.
Hoffmann, R. (1995). The Same and Not the Same.
Philosophical discussion of chemical structure, models, similarity, and explanation.
Nye, M. J. (1993). From Chemical Philosophy to Theoretical Chemistry.
Study of the history of chemical theory, model replacement, and chemical foundations.
Bader, R. F. W. (1990). Atoms in Molecules: A Quantum Theory.
Theory of atoms in molecules, involving chemical structure and electron density interpretation.
Jensen, W. B. (1998). Logic, History, and the Chemistry Textbook. Journal of Chemical Education.
On chemical teaching models, historical narratives, and conceptual structures.
2.5. Scientific Realism, Model Realism, and Ontological Extensions
Psillos, S. (1999). Scientific Realism: How Science Tracks Truth.
Important modern text on scientific realism.
Chakravartty, A. (2007). A Metaphysics for Scientific Realism.
Discussion of scientific realism, ontological structure, and metaphysical foundations.
Ladyman, J., Ross, D., Spurrett, D., & Collier, J. (2007). Every Thing Must Go: Metaphysics Naturalized.
Important text on structural realism and naturalized metaphysics.
French, S. (2014). The Structure of the World: Metaphysics and Representation.
Discussion of structural realism, mathematical structure, and physical reality.
Worrall, J. (1989). Structural Realism: The Best of Both Worlds? Dialectica.
Classic paper on structural realism.
3. Citation Notes
This paper cites the internal documents of the "Non-Evident Choice" system, which does not mean that readers are required to accept that system unconditionally. On the contrary, the "Principle of Origin Proof" proposed in this paper also constrains these system drafts in reverse.
Therefore, the citation of internal system literature in this paper has a threefold nature:
Source attribution: to indicate that the new system interfaces, terminology, and directions in this paper are not ad hoc, but originate from an already formed internal system draft;
Research entry point: to provide literature references for subsequent unfolding of the philosophical, physical, and mathematical layers of the "Non-Evident Choice" system;
Self-constraint: to make explicit that this system must also submit to the review of origin proof, explanatory gain, empirical compatibility, and falsifiability.
In other words:
This paper does not use internal system drafts to gain immunity;
rather, it places internal system drafts under the same review rules.
If established science cannot be exempt from first-principle questioning, then new systems likewise cannot be exempt.
If old theories must repay explanatory debt, new systems must also demonstrate actual ability to repay.
If science opposes "don't ask, just believe," then new systems cannot demand that others "don't ask, just believe."
This is the fundamental difference between this paper and dogmatized systems.