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
(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.)
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
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.
1a. You cannot be deceived that your subjective experiential conscious awareness is real and
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.
1b. You are aware of only phenomena, not noumena, except when noumena and phenomena are
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
Laws used: Substitution, set/subset.
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.
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
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.
1e. That which is real and actually existing, but is not material, must be supernatural.
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
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
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.
―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
―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
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
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
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
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
―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
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.