The term “supernatural” is often associated with theological or metaphysical claims regarding entities such as deities, spirits, or other non-material agents. This paper does not attempt to prove the existence of any such entity. Instead, it establishes a far more limited and precise conclusion grounded strictly in mathematics and logic.

For the purposes of this paper, the term supernatural will be defined in its most minimal and structural sense:

Supernatural: Any truth, structure, or explanatory necessity that exists beyond the explanatory closure of the natural system itself.

The natural system refers to the physical universe understood as a mathematically describable system governed by consistent laws of physics. Modern physics expresses all natural processes using mathematical relationships, including arithmetic, algebra, and differential equations. Thus, the natural world is describable as a formal mathematical system.

In the early twentieth century, mathematician Kurt Gödel proved his incompleteness theorems, which established a fundamental and mathematically rigorous limit on all formal systems capable of expressing arithmetic. Gödel demonstrated that any such system contains true statements that cannot be proven within the system itself. This result is not philosophical speculation but a proven mathematical theorem.

Because the natural world is describable through mathematical formalism, Gödel’s theorem applies directly to any mathematical system capable of describing physical reality. This has a profound implication: the mathematical structure describing the natural world cannot be fully self-explanatory. There necessarily exist truths that transcend the internal explanatory closure of that system.

This paper presents a formal logical derivation of that conclusion. The argument proceeds using established mathematical principles, definitions, and Gödel’s incompleteness theorem to demonstrate that the natural system cannot be fully self-contained in its explanatory structure.

Under the minimal definition provided above, the existence of truths or explanatory necessities beyond the natural system constitutes the existence of the supernatural in its most basic mathematical sense.

Importantly, this conclusion does not depend on theology, empirical observation, or philosophical assumption beyond the definitions and mathematical theorems presented. The result follows strictly from the logical and mathematical structure of formal systems themselves.

The purpose of this paper is therefore to present, in clear logical steps, the mathematical proof that the natural system is not fully self-explanatory, and that truths necessarily exist beyond its internal formal structure.

Section 1: Definitions

We begin by establishing precise definitions.

Definition 1 (Formal System):
A formal system FFF consists of:

A set of symbols
A set of axioms
A set of inference rules

from which statements can be derived.

Definition 2 (Provability):

A statement SSS is provable in formal system FFF if and only if:

F⊢SF \vdash SF⊢S

meaning SSS can be derived from the axioms of FFF.

Definition 3 (Truth):

A statement SSS is true if it corresponds to objective logical or mathematical reality, regardless of whether it is provable within a given formal system.

Definition 4 (Natural System):

The natural system NNN is defined as the complete set of physical states and laws governing the universe, expressible in mathematical form.

This includes:

physical constants
physical laws
mathematical relationships governing physical interactions

Definition 5 (Explanatory Closure):

The explanatory closure of system NNN, denoted C(N)C(N)C(N), is the set of all truths derivable within NNN:

C(N)={S∣N⊢S}C(N) = \{ S \mid N \vdash S \}C(N)={S∣N⊢S}

Definition 6 (Supernatural):

A truth, structure, or explanatory necessity that exists but is not derivable from within the explanatory closure of the natural system.

Formally:

∃S such that S∉C(N)\exists S \text{ such that } S \notin C(N)∃S such that S∈/C(N)

Section 2: Mathematical Structure of the Natural System

Modern physics describes the natural world entirely using mathematical relationships.

Examples include:

Newton’s law of gravitation:

F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}F=Gr2m1m2

Einstein’s mass-energy equivalence:

E=mc2 E = mc^2 E=mc2

Maxwell’s equations:

∇⋅E=ρε0\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}∇⋅E=ε0ρ

These equations demonstrate that physical reality is describable through mathematical structure.

Arithmetic operations are required for:

measurement
counting
physical calculation

Thus, the natural system contains arithmetic.

Section 3: Gödel’s Incompleteness Theorem

Gödel’s First Incompleteness Theorem states:

Theorem (Gödel, 1931):

For any consistent formal system FFF capable of expressing arithmetic:

∃S such that S is true but F⊬S\exists S \text{ such that } S \text{ is true but } F \nvdash S∃S such that S is true but F⊬S

This theorem is mathematically proven.

It establishes that no sufficiently expressive formal system can prove all true statements within itself.

Section 4: Applicability of Gödel’s Theorem to the Natural System

We have established:

The natural system is describable mathematically.
The natural system contains arithmetic.
Gödel’s theorem applies to all formal systems containing arithmetic.

Therefore, Gödel’s theorem applies to the natural system.

Thus:

∃S such that S is true but N⊬S\exists S \text{ such that } S \text{ is true but } N \nvdash S∃S such that S is true but N⊬S

This means:

There exist true statements not derivable from within the natural system.

Section 5: Logical Derivation

We now derive the conclusion step-by-step.

Premise 1:

The natural system is describable as a formal mathematical system.

Premise 2:

Gödel’s theorem applies to all formal systems containing arithmetic.

Premise 3:

The natural system contains arithmetic.

Therefore:

Gödel’s theorem applies to the natural system.

Thus:

∃S such that S∉C(N)\exists S \text{ such that } S \notin C(N)∃S such that S∈/C(N)

Meaning:

There exist true statements not derivable from within the natural system.

By Definition 6, this satisfies the definition of supernatural.

Section 6: Theorem and Proof

Theorem:

The natural system is not explanatorily complete.

Proof:

Gödel’s incompleteness theorem proves that any formal system containing arithmetic contains true statements that cannot be proven within the system.

The natural system contains arithmetic and is describable mathematically.

Therefore, the natural system contains truths that cannot be derived from within the system.

Therefore, the explanatory closure of the natural system is incomplete.

Thus, truths exist beyond the explanatory closure of the natural system.

By definition, this constitutes the supernatural.

Q.E.D.

Section 7: Implications

This result demonstrates that the natural system cannot fully explain itself.

This conclusion follows strictly from mathematical logic.

This proof does not depend on:

theology
empirical observation
philosophical speculation

It follows directly from Gödel’s theorem and formal system structure.

The proof establishes only that truths exist beyond the explanatory closure of the natural system.

It does not specify the nature of those truths.

Conclusion

Gödel’s incompleteness theorem mathematically proves that any formal system capable of describing arithmetic contains truths that cannot be derived within that system itself.

Because the natural world is describable mathematically and contains arithmetic, it follows that the natural system cannot be fully self-explanatory.

Therefore, truths necessarily exist beyond the explanatory closure of the natural system.

Under the minimal structural definition provided, this constitutes a mathematical proof of the supernatural.

References

Gödel, Kurt (1931)
On formally undecidable propositions of Principia Mathematica and related systems.

Nagel, Ernest and Newman, James (1958)
Gödel’s Proof

Penrose, Roger (1989)
The Emperor’s New Mind

Hofstadter, Douglas (1979)
Gödel, Escher, Bach

Beyond Formal Closure

Gödel, Tarski, and the Necessity of Meta-Level Explanation in Natural Systems

Abstract

This paper examines the structural limits of formal systems as established by Gödel’s incompleteness theorems and Tarski’s undefinability theorem, and considers their implications for mathematically describable natural systems. The argument does not attempt to establish theological conclusions. Rather, it demonstrates that any system capable of expressing arithmetic cannot be fully self-grounding in terms of truth or consistency. If physical reality is describable by formal mathematical structure, then its complete validation necessarily requires meta-level reasoning. This establishes a formally provable boundary to explanatory closure within natural systems.

1. Introduction

Modern physics describes the natural world using formal mathematical structures. Differential equations, algebraic relations, and logical frameworks govern the behavior of matter, energy, and spacetime. This suggests that the natural realm is describable as a structured formal system.

In the early twentieth century, Kurt Gödel and Alfred Tarski established fundamental theorems demonstrating intrinsic limits to formal systems capable of arithmetic. These theorems do not concern theology or metaphysics; they concern provability and definability within formal languages.

The present paper investigates whether those formal limitations imply that mathematically describable systems — including natural law frameworks — cannot be explanatorily complete from within themselves.

The conclusion reached is modest but precise: formal self-containment is mathematically impossible for systems expressive enough to describe arithmetic.

2. Formal Systems and Arithmetic

A formal system FFF consists of:

A formal language LLL
A set of axioms AAA
Rules of inference RRR

A statement SSS is provable in FFF if:

F⊢SF \vdash SF⊢S

Arithmetic is expressible within systems capable of representing natural numbers and their operations. Any mathematical system sufficient to describe physical measurement necessarily includes arithmetic.

Thus, any formal mathematical description of the physical world contains arithmetic structure.

3. Gödel’s First Incompleteness Theorem

Gödel’s First Incompleteness Theorem states:

For any consistent formal system FFF capable of expressing arithmetic, there exists a statement GGG such that:

G is true but F⊬GG \text{ is true but } F \nvdash GG is true but F⊬G

This establishes:

No sufficiently expressive formal system can be both complete and consistent.

The theorem is strictly mathematical and proven within formal logic.

It follows that formal systems cannot internally derive all truths expressible within their own structure.

4. Tarski’s Undefinability Theorem

Tarski’s theorem establishes that:

For any sufficiently expressive formal language LLL, the set of true statements of LLL cannot be defined within LLL itself.

Formally:

If LLL contains arithmetic, then there is no formula within LLL that correctly defines the truth predicate for LLL.

This implies:

Truth for a formal system requires a meta-language.

Truth cannot be internally defined within the same language that expresses arithmetic.

5. Meta-Level Necessity in Formal Systems

From Gödel:

Not all truths are provable within the system.

From Tarski:

Truth itself cannot be defined within the system.

Therefore:

Any formal system expressive enough to contain arithmetic requires meta-level reasoning for:

Truth evaluation
Consistency verification
Completeness analysis

This meta-level reasoning exists outside the system’s formal closure.

6. Application to Mathematically Describable Natural Systems

Modern physical theory is expressed through formal mathematical systems. These systems:

Contain arithmetic
Use formal inference
Operate under axiomatic structures

If a mathematical framework describes the natural world, then that framework is subject to the same structural limitations Gödel and Tarski proved.

Thus:

No mathematical description of the natural world can internally establish:

Its own complete truth
Its own global consistency
Its own total explanatory closure

Meta-level reasoning is required.

7. The Boundary of Explanatory Closure

Define:

Explanatory closure = the ability of a system to account for all truths about itself using only its own internal structure.

Gödel and Tarski jointly demonstrate:

Explanatory closure is impossible for any sufficiently expressive formal system.

Therefore:

Any mathematically describable system — including natural law frameworks — cannot be fully self-grounding.

This is not a theological conclusion.

It is a structural limitation derived from mathematical logic.

8. Clarification of Scope

This paper does not claim:

That Gödel proves metaphysical entities.
That Tarski proves divine agency.
That formal incompleteness implies supernatural beings.

It demonstrates only that:

Formal systems require meta-level structures for truth and validation.

Whether that meta-level corresponds to ontology, metaphysics, or epistemology is a separate philosophical question.

9. Conclusion

Gödel’s incompleteness theorem proves that no formal system capable of expressing arithmetic can prove all truths within that system.

Tarski’s undefinability theorem proves that truth in such systems cannot be defined within the system itself.

Because the natural world is describable through mathematical systems containing arithmetic, it follows that no such description can be fully self-contained in terms of truth and consistency.

Therefore, formal self-grounding is mathematically impossible for sufficiently expressive systems.

This establishes a rigorously demonstrated limit on explanatory closure within mathematically describable systems.

References

Gödel, K. (1931).
On formally undecidable propositions of Principia Mathematica and related systems.

Tarski, A. (1936).
The concept of truth in formalized languages.

Nagel, E., & Newman, J. (1958).
Gödel’s Proof.

Hofstadter, D. (1979).
Gödel, Escher, Bach.

Logical and Epistemological Argument for the Existence of Non-Material Conscious Experience

Introduction to the Paper:

The Author of this paper: Koanic Soul from the website:

http://www.koanicsoul.com/blog/mathematical-proof-that-the-supernatural-exists/may-19th-2012-archive-of-mathematical-proof-that-the-supernatural-exists/

[As of the Aug 26, 2022 I cannot find the author or a reference to the original site so i am putting it here until i can contact the author:]

"Mathematical" Proof That The Supernatural Exists

You should only attempt to read this proof if you have at least read the Wikipedia pages for Descartes’ ―Discourse on Method‖ and ―Meditations on First Philosophy‖, and Kant’s ―Critique of Pure Reason‖ and ―Prolegomena to Any Future Metaphysics‖.

Otherwise, it won’t make any sense – like reading a calculus proof when you only know algebra. The one exception would be if you’re the sort of genius who can intuitively grasp an entire field from a few contextual hints. In this particular case, I estimate such a feat would require a verbal IQ of at least 150, possibly much higher.

The proof for the existence of the supernatural

Without further ado, here is the proof that demonstrates with mathematical certainty that the supernatural exists:

(To see the previous version of this proof, that did not address the possibility of supernatural noumena, click here. Version updated on May 19, 2012.)

Definitions

Definition 1: Noumena – Things as they are in themselves, rather than the human mind’s perception of them.

Definition 2: Phenomena – The perceptions of the human mind, rather than things as they are in themselves. Note that these definitions do not preclude Noumena and Phenomena being identical in any particular case. In fact, any phenomena, considered in itself, would be a noumena.

Definition 3: Material – The objective, physical world. Matter, energy, the spacetime continuum. Physics, chemistry, etc.

Definition 4: Supernatural – That which has real, actual existence, yet is not material. —

Set A:

1a. You cannot be deceived that your subjective experiential conscious awareness is real and actually existing. This is proven in Descartes, and is taken here as given. It is an a posteriori synthetic knowledge based on analysis plus the experience of consciousness.

2a. Your subjective experiential conscious awareness contains only that which you are aware of (phenomena), and nothing more. Purely analytic statement, definitionally true.

3a. Therefore, what you are aware of (phenomena) is real and actually existing.

Law used: Substitution. —

Set B:

1b. You are aware of only phenomena, not noumena, except when noumena and phenomena are identical. Analytically true. Phenomena are what you experience; so the noumena either matches exactly or is something different.

2b. The material world is pure noumena. Purely analytic statement; definitionally true. The material world is objective and physical. (If you disagree, you are abusing the English language and your outlook is no longer properly scientific or materialist anyway.)

3b. Therefore, you are aware of only phenomena, not anything material, except possibly when noumena and phenomena are identical. (―Possibly‖ because the material world is a subset of all noumena. There may also be supernatural noumena. Thus an identical noumena-phenomena pair might be either supernatural

or material.)

Laws used: Substitution, set/subset. —

Set C:

3a. What you are aware of (phenomena) is real and actually existing.

3b. You are aware of only phenomena, not anything material, except possibly when noumena and phenomena are identical.

3c. Therefore, experienced phenomena are real and actually existing, but are not material, except possibly when noumena and phenomena are identical.

Law used: Substitution. —

Set D:

3c. Experienced phenomena are real and actually existing, but are not material, except possibly when noumena and phenomena are identical. (―Possibly‖ because noumena might either be natural or supernatural.)

2d. The phenomena you experience do not resemble the material world as it is in itself (as noumena). Patently obvious. E.g., you see an apple as bright red skin, but not the inner meat, core and seeds, much less atoms or photons or biological vision processes. If you attempt to argue that the material world actually is just as we perceive it, this is no longer scientific materialism, but magical realism or something equally bizarre. See logical expansion section for more.

3d. Experienced phenomena are real and actually existing, but are not material.

4d. If there is a noumena that is identical to a phenomena, then it must be supernatural.

Law used: Substitution. Set/subset. —

Set E

1e. That which is real and actually existing, but is not material, must be supernatural. Definitionally true.

3d. Experienced phenomena are real and actually existing, but are not material.

3e. Experienced phenomena are supernatural.

Law used: Substitution. —

Conclusion:

If one supernatural thing exists, then the supernatural exists. Experienced phenomena exist. Therefore, the supernatural exists.

Note that this is not a proof of the existence of God. For the evidence that Christianity is true, see the next page.

If you disagree with this proof:

Stop. Take a deep breath.

Not a single person unfamiliar with the previously mentioned books has successfully formulated a remotely topical rebuttal to the above proof. They have instead demonstrated incomprehension of its conceptual foundations.

Academic philosophers specialized in this niche can and do discuss concepts related to the above successfully, and I have read their papers and considered their positions. While I strongly disagree with their conclusions, they are at least germane to the subject.

It is EXTREMELY unlikely that you will succeed in bootstrapping yourself to this level of discourse using only the few hints provided in the eight lines above.

At some point, I will expand this page to include an exposition of the Cartesian and Kantian conceptual prerequisites. Until that time, I recommend that you read the aforementioned works before replying. The books are mindblowing and well worth it – as one would expect, since they have shaped philosophical discourse ever since.

Reading order, plus a teaser Begin with Descartes, since he’s much easier. Then read the Prolegomena, then the Critique. Here’s a teaser to whet your appetite. The quotes are taken from top Amazon reviews.

Discourse on Method and Meditations on First Philosophy

―The Foundational Work in Modern Philosophy – 5/5

It’s also a work that I’d recommend to anyone who wants to be introduced to philosophy by reading the work of a great philosopher. And don’t worry: it shouldn’t take you more than an afternoon to read through it.

The Meditations has had an incalculable influence on the history of subsequent philosophical thinking. Indeed, according to nearly every history of philosophy you’re likely to come across, this work is where modern philosophy begins. It’s not that any of Descartes’s arguments are startlingly original–many of them have historical precedents–but that Descartes’s work was compelling enough to initiate two research programs in philosophy, namely British empiricism and continental rationalism, and to place certain issues (e.g. the mind-body problem, the plausibility of and responses to skepticism, the ontological argument for the existence of God, etc.) on the philosophical agenda for a long time to come. Moreover, Descartes was capable of posing questions of great intrinsic interest in prose accessible to everyone.‖

Prolegomena to Any Future Metaphysics

―Simply put, modern philosophy begins with Kant. If anyone wishes to understand the development of philosophy after the 18th century, you must have some grounding in Kant. That said, his works are not easy to read, nor are they well-suited to leisurely reading. While most individuals try a stab at the Critique of Pure Reason, many seem to get lost in his argument.‖

―Kant wrote the Prolegomena to assist readers who were having trouble understanding his Critique of Pure Reason. Nevertheless, the Prolegomena itself is difficult reading. In contrast to much of contemporary philosophy, however, it is worth the effort. One comes away from the Prolegomena with a different world view. This alternative perspective is not something that one need accept or reject, but a point of view that one may consider, part of our conceptual

wherewithal for trying to make some sense of life.

Though commonly cast in the role of a philosophical idealist, Kant emphatically agrees that all knowledge is experientially determined. He parts company with philosophical materialists such as Marx, however, when he posits the existence of mind as organized a priori in a specific though unknowable way. Mind, thus, is not a tabula rasa on which our first experiences are inscribed and then used in making sense of what follows. Mind, instead, shapes all our experiences in terms of its inherent organization.

This leads Kant to the distinction between noumena, things as they actually are, and phenomena, things as we apprehend them upon their encounter with the organization of mind. This means that we can never know the world as it actually is.‖

Critique of Pure Reason

(Note – the Muller translation is the best version, and it’s not available on Amazon. However, you can get it for free online at the above link.)

―The Critique of Pure Reason is the sine qua non of modern thought, as it incorporates the most significant earlier critiques of Plato, Aristotle, Hume, and Descartes, in turn becoming the point of departure (on one hand) for Schopenhauer, and (on the other) for Hegel, Nietzsche, Heidegger, Wittgenstein, and Deleuze–besides its further influence on social and literary criticism (e.g., Marx, Mill, Arnold, Eliot, Adorno, et al.).

Of course the Kritik is a very complex and dry text–(more readable than Hegel and Heidegger; less readable than Schopenhauer and Nietzsche)–which requires much moisture of psychic perspiration.‖

What you’re looking for – tips to get you started

Much of the Wikipedia pages and the primary texts themselves will be irrelevant, tendentious, or outright error.

Below I will highlight some relevant passages from the Wiki pages, to give you an idea of what you should be looking for.

Ignore the filler, but meditate deeply upon the relevant bits:

―The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.‖

The basis of metaphysical/epistemological skepticism.

―Descartes argues that this representational theory disconnects the world from the mind, leading to the need for some sort of bridge to span the separation and provide good reasons to believe that the ideas accurately represent the outside world. ―

More epistemological skepticism.

―Since, then, the receptivity of the subject, its capacity to be affected by objects, must necessarily precede all intuitions of these objects, it can readily be understood how the form of all appearances can be given prior to all actual perceptions, and so exist in the mind a priori‖"

A reason that we do not perceive the material world as it is in itself, but only as perceptions. This proof applies to both the informational-pattern mind and the subjectively-experiencing mind, both of which cannot be material because they do not perceive matter as it is in itself. The former is an abstract construction of convenience, the latter is subject.

I’ll stop there. I’m not going to do the whole reading for you. That’s enough to get you started. Some miscellaneous logical expansions. Since most people are not grasping the givens, I am dealing with objections in the comments.

Some highlights:

Question begging

―You are begging the question of the supernatural by placing ―perceptions‖ outside of the physical world. ―

No. ―Ghosts‖ are by definition supernatural, but do not necessarily exist, and therefore are not begging the question.

―You are begging the question by defining perceptions as non-material, when everyone agrees perceptions actually exist.‖

First, not everyone agrees that perceptions actually exist. Second, it is not question-begging to define the category of x, then prove that x exists, unless you assign it the category ―existing‖.

―Your proof is not syntactically formal because you take certain propositions as given.‖

The goal is to reduce the proof to self-evident propositions, logical transformations, and a necessary conclusion. Nothing more than that. You are asking for a higher standard of formality than I am aiming for, and one that would impede brevity and clarity.

The supplemental section below proves what is taken as given, if the propositions are not already self-evident to you.

You’re abusing the word “mathematical”

No, I’m not:

a. Precise; exact.

b. Absolute; certain.

You’re abusing the word “spiritual” or “material”

No, I’m not: supernatural: of, pertaining to, or being above or beyond what is natural; unexplainable by natural law or phenomena; abnormal.

2.of, pertaining to, characteristic of, or attributed to God or a deity. material: formed or consisting of matter; physical; corporeal: the material world. pertaining to the physical rather than the spiritual or intellectual aspect of things: material comforts.

Higher skepticism

―I do not need to ―know‖ (I am assuming you are, like Kant, priveliging a particular definition of know to mean something along the lines of ―have logical necessity‖, if you would like to taboo the word a different way, please clarify), I merely need to have justified belief that those things exist. ―

This is a philosophical PROOF. We are not talking about practical everyday life. But rather, what we can know for CERTAIN. There is a higher standard in play. Forget your probabilistic skepticism; we are at 100% max industrial strength skepticism.

―Epistimology should lead me to form beliefs that better anticipate experience. ―

No, not necessarily. If a demon feeds you experiential lies, epistemology should still arrive at certain truths. Epistemology presupposes nothing. That’s the whole point. It does not presuppose that experience is truthful. That would break epistemology.

―Unless you have a suggestion of how believing that my brain is not actually existing can help me better anticipate experience.‖

Yes. It can help you know that materialists are incompetent liars, for which copious experiential evidence exists. It can also help you know that the supernatural exists, for which copious experiential evidence exists.

―as they are excluded by Occam’s Razor‖

Occam’s Razor is merely a rule of thumb, not a rule of truth. Otherwise the original model of

physics would be true by virtue of simplicity. We do not get to play by fuzzy rules here. You

either know something 100% or you don’t.

―many are no better than the young earth creationist tactic‖

Absolutely irrelevant example. Elevate yourself to metaphysical discourse. Ditch the mundane.

You are in an alternate dimension. If you cannot find the wormhole, you will never get home.�

Logical vs physical impossibility

―Being able to imagine something, does not make it so. ―

If you can conceive it without logical contradiction, it is by definition logically possible. If you

can’t grasp this, give up philosophy now. But I suspect you can.

―why do you think a mind is possible without some kind of substrate on which to exist? ―

Because I cannot demonstrate that the concept contains an inherent logical contradiction. Same

as I can imagine that a unicorn created the universe in 3 days.

―Your thought experiment does not prove anything other than that human cognitive architecture

can find impossible things ―conceivable‖. ―

There are different kinds of impossible. The two relevant ones here are ―logically impossible‖

and ―practically impossible‖.�

You do not actually know that a mind without physical processes is physically impossible. You

do not even know that your own physical brain exists, or that anyone else is conscious but you.

You therefore flunk epistemology, and your critique of human reason is revealed to be hasty

judgment and emotional preference.�

―I can find many types of perpetual motion machine ―conceivable‖ (My brain can imagine them and insist that they should work as claimed, that doesn’t make them possible.‖

Once again, you do not even know that motion exists, so how can you pretend to know its laws? Different kinds of existence

―2d is wrong. Numbers, ideas, laws, stories, distances, nations are not material, yet they are not called supernatural.‖

You are unfamiliar with this area of philosophy. Numbers are true but don’t exist. ‖ , laws, stories, distances, nations‖ – to the extent they exist, they are material, to the extent they aren’t material, they don’t exist. ‖ ideas‖ – when they are perceptions, they exist but are not material. Exist here is used in the sense of ―actual, real existence‖.

―Let me clarify my sentence here. We have representations of numbers. The representations exist. This 3 is actually a few magnetic dots sitting on a hardrive somewhere.‖ Yes, and in that sense it is not a 3, it is dots. You can’t prove noumenos exists I don’t need noumenos to exist for this proof to work. SOMETHING exists, namely your consciousness. That’s all I need to prove. If the material world doesn’t exist, then obviously we can’t be the substrate of perception

anyway. I have no idea why anyone thinks this hurts the argument.

―If we can’t ever know Noumena, than how can we know that they exist?‖

We infer its existence without being certain of it. Just as we infer the existence of the material world. The informational pattern mind vs the subjective experiencing mind

―The mind is a pattern of information, so in that sense it is distinct from its physical implementation. ... In that sense the information pattern associated with a mind is separate from its physical representation. ―

You are talking about the informational pattern mind. I am talking about the experiential, subjective mind. Totally different. The IP mind is no different than a computer. To the extent it exists, it is material; to the extent it’s not material, it exists only as a convenient human abstraction.

―Why is the experiential, subjective mind distinct from the IP mind?‖

Because IP minds can be conceived of as existing without generating corresponding subjective minds. E.g., a computer.

―You claim that there is something to the mind that is more than its informational pattern. What evidence could you gather from a high-fidelity neuron-by-neuron simulation of a brain that would dis-confirm your hypothesis? ―

No simulation is necessary. You are experiencing one subjective mind. By logical analysis, we demonstrate its non-material nature. Also, the IP mind is different than the material mind. Information flow does not require a material substrate either. If my subjective mind were sufficiently capacious, I could run a simulation of another IP mind inside my own. This mind would not have an independent consciousness. Novel writers do this.

―Also isn’t your criticism of the ES mind equally ―a convenient human abstraction‖? ―

No, because it necessarily has real actual existence according to Descartes’ proof.

―What if the simulation mentioned above allows us to trace the things we lable as the ES mind to particular synaptic junctions, and particular electrical activity.‖

It surely should, since I believe a continuous connection exists between the spiritual and material world.

Phenomena differ from material reality

Anyone who has ever bitten into an apple knows that phenomena differs from noumena. We see the outer red skin of the apple, not the meat, core, and seeds. Thus we perceive the apple, and that perception, or phenomena, is not identical to the apple in itself. The question may be raised: Granted the perception of the apple is not the apple, but the perception itself may be nonetheless composed of material elements; a purely material process.