Archive for category Physical and Nonphysical

Subjective and Objective Truth

I am better understanding the “dark night of the soul” that mathematics has been for me.

I think that truth needs to involve an element of fantasy. That sounds like a paradox; but I think that our fantasies are true.

If I visualize something so vividly that it feels at least as real to me as physical reality, what grounds do I say that physical reality is real, and the visualization is unreal?

Well, one ground would be that other people can’t see the visualization; but I’ll address that issue later.

Try it. Visualize a red triangle. Visualize it so strongly that it becomes as real as your own hand. Then visualize it so strongly that it’s more real than your hand. It can be done.

People regularly achieve this sort of transcendence of physical reality on the wings of pure faith. Think of the ascetics who deprive and punish their bodies for the sake of a belief. Think of the feminists, who have managed to make widely accepted a truth that has no evidence other than what people’s hearts tell them. Think of the mathematicians, who study a vast paradise of nonexistent and impossible objects. Think of the fiction writers, who live in an imaginary world of their own creation.

Fantasy, the truth that comes from inside us, is subjective truth. The truth that comes from examining the outside world, is objective truth.

Subjective truth is considered by many to be nonexistent. And indeed, I cannot assert the existence of subjective truth in the same way that I can assert that 2+2=4. The reason is that subjective truth is subjectively true; whereas objective truth is objectively true. But subjective truth is not objectively true. Similarly, objective truth is not subjectively true.

Objective truth can only be determined through the methods of empiricism. For subjective truth, the method is this: whatever you wish to be true, is true.

The nature of our experience at this nexus places great emphasis on objective truth. We are, in the ordinary course of things, absorbed in the shuffle of the physical world and its necessities. And this same emphasis on objectivity is reflected in our intellectual climate.

Subjective truth is hard to find, hard to notice, hard to hold onto. But it is better and more important than objective truth.

People have different subjective truths. I can see my own visualizations; you cannot. My passions are not your passions. My ideals are not your ideals.

There is therefore great paradox in trying to share one’s subjective truth. Subjective truth is not objectively true. What is true for me, may not be true for you. For the most part, therefore, we must have our own truth and let others have theirs. The problem of sharing truths is a hard one.

I cannot wish to share my truth with another, if for them it is falsehood. I can only wish to share it with them, if for them it is truth.

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The Mind and the Brain

If the mind is not the brain, then we need to say that there is an additional thing out there, which is the mind. It will be a very mysterious thing.

That thing needs to interact with the brain somehow. We know, from experimental psychology, that many psychological functions are functions of the brain — the brain is implicated in memory, learning, sensory and motor functions, executive functions, language, etc.

So we need to say that the mind and the brain bear some sort of relationship to each other, and both contribute in their own ways to psychological functioning.

It makes sense to me to say that the brain serves functions which are more “mechanical,” lower-level, than the functions served by the mind. The mind, then, would serve higher-level functions. Under this view, we would say things such as these:

* My brain is the thing that computes sums, but my mind is the thing that enjoys doing math.
* When I compose music in my head, my temporal lobes contain a representation of the music, but my mind is the thing that is performing the creative act of composition.
* When I feel pain, there is a chain of signaling proceeding from my peripheral neurons, and eventually into my brain, but that which feels the pain qualia is my mind.

These examples give a rough idea of the sort of division of functions I am hypothesizing. I can make the idea more concrete with a metaphor.

Imagine that my body is a giant robot, like the robots in Gundam Wing, and my mind is the pilot of this robot. The brain is the set of instruments, in the cockpit, with which the pilot interacts with the world.

* The occipital lobe is a video display.
* The temporal lobe is a sound system.
* The motor cortex is a control panel, with joysticks, buttons, etc.
* The frontal lobe is a sort of digital assistant, which automatically performs various helpful tasks. Among other things, it has a pocket calculator, a calendar, and software that gives me important reminders from time to time.
* The brain also has a filesystem which stores all of my memories.

This crude analogy is intended to illustrate the sort of relationship that the mind and the brain might bear to each other. A finished theory would give precise descriptions of the respective functions of the mind and the brain; but I do not have that information.

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Reductionism II

I said previously that objective reality is not a mathematical structure. The question arises, what then is the objective reality?

Rather than answering this question, I prefer to dissolve it. The subjective/objective distinction is a confusing one; so I prefer to say that it is a confusion.

By “objective reality,” we mean something which is forever beyond our experience. But we also mean something which, through our experience, we can know everything about. Appearances are all subjective; and objective reality is not an appearance. To take this perspective to the peak of its absurdity, we may consider the final appearance — the appearance which contains all possible knowledge of objective reality, which unites all possible appearances into one. We have to say that the final appearance is distinct from the objective reality. But what is the difference? We have, on the one hand, the experience of everything, and, on the other hand, everything. The two contain the same information; they are isomorphic; but one is visible and unreal, and the other is invisible and real. Why is the visible unreal, and the real invisible, if there is nothing about the real which cannot be rendered visible?

Let us dissolve the subjective/objective confusion. At a given moment, we see some things, and we do not see others. Right now I see a table; but if I turn my head to the left, I will no longer see a table. The table is still there, but I am not looking at it.

What about the distinction between the table and the appearance of the table? What about the fact that the table is made of molecules, whereas this fact isn’t expressed in my visual impression of the table? We resolve the problem in the same way. The molecules are there, but I can’t see them, in the same that way that when I look at a beach from inside an airplane, I can’t see the individual grains of sand.

We have no need for a distinction between subjective and objective. Reductionists need to postulate such a distinction in order to make sense of their philosophy that mathematical structure is all that really exists. They need to say that, for instance, the qualitative “redness” of red is a subjective illusion. But we do not say anything like this; for us, all of the features of our experience are equally real. The appearances are the reality.

The rationalist has become fascinated by a particular aspect of their experience: its mathematical structure. They have become so enamored with it that they want to say that it is everything. It is quite true that mathematical structure is everywhere; but it is not true that it is everything.

What about the lawfulness of the universe? Is it true that everything follows the laws of physics, without ever deviating from them to the slightest degree? It is imaginable that the world could fail to be a mathematical structure, and yet never violate the laws of physics.

Only there is some discomfort in saying this. It feels more right to say either that the world is a mathematical structure, or that it sometimes violates the laws of physics. The middle position feels awkward. And yet, it also feels awkward to say that the world does not follow the laws of physics; because it is clear that usually and for the most part, it does follow the laws of physics. What are we to do about this?

Let us recall that quantum physics is probabilistic. We cannot say, in a quantum physics experiment, exactly what we will observe in a given instant. We can only give statistical patterns that our observations follow. So at the lowest level, the universe does not strictly follow its laws. The “laws of physics” are more accurately called “trends of physics.”

We can expect this quality to propagate up to the larger levels of reality. We can expect atoms and molecules not to strictly follow the laws of chemistry, and organisms not to strictly follow the laws of biology.

As far as I know, this is consistent with experimental observations. As far as I know, experiments in chemistry are usually done with large numbers of atoms and molecules, and the observations are observations of the aggregate behavior of the substances involved. And, as far as I know, every experiment has some degree of experimental error. The usual assumption is that if the experiment were “perfectly performed,” there would be no experimental error; but what if this is wrong? What if the experimental error is a feature of reality?

As for biology, we don’t even have a set of rules which can predict in general the behavior of biological organisms. We don’t understand life.

We can re-interpret the laws of nature as trends of nature. They are not absolute rules, but patterns that things tend to conform to. But it makes little sense to say that there is a single, fixed set of laws, and things always randomly deviate a little bit from those laws without ever deviating radically from them.

But maybe we want to say that things do sometimes deviate radically from those laws.

Supernatural phenomena (telepathy, telekinesis, etc.) would be an example of this. We can also say that the behavior of the higher levels of reality is not reducible to the behavior of the lower levels: it follows additional laws. In particular we want to say this with living organisms: that living organisms follow laws that atoms do not follow.

We want to say this because of our intuition that living organisms are special: that they are somehow different from dead matter. Scientists have installed a bias against this intuition; but we want to take down this bias, and notice the obvious, that living organisms seem special.

We also want to say that humans follow laws that other living organisms do not follow. The same line of thinking justifies this. It is intuitively obvious that humans are special.

Many sets of laws can co-exist, because they fit within each others’ margins of error. Since every set of laws is fuzzy, they can avoid coming into conflict with each other. Note that not every possible combination of law-sets would do this; but we want to say that the laws of our universe do this.

For our view to be complete, we need to offer an answer to the question, why have rationalists not interpreted reality in this way? If reality is not really sharp and rigid, why have rationalists interpreted reality as being sharp and rigid?

I think that some people have an aesthetic taste for simple, precise, and rigid rules, and when they look at the universe, they are interested in finding this. I think that it is not the way the universe is, but the taste for simplicity, precision, and rigidity, that has led rationalists to see the universe’s laws as simple, precise, and rigid.

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My year-long struggle with materialism may finally be ended.

I shall summarize the problem. For a long time I objected to materialism without knowing why. Eventually I made a concerted attempt to articulate my problems with it.

It turns out that my strongest ethical intuition is that whatever happens is good and acceptable. There is no true wrongness in existence. Ethics consists of following the way of the universe, without fighting for or against anything. My inability to believe in badness constrains my worldview significantly.

Every sufficiently developed metaphysics implies an ethics, and every sufficiently developed ethics implies a metaphysics. For instance, Christianity has both a metaphyics (God exists, Jesus is his son sent to save humanity, we go to heaven or hell when we die) and an ethical theory (be a good Christian). The metaphysics and the ethics do not make sense without each other. If the metaphysics is false, then it makes no sense to follow the ethics. If the metaphysics is true, then the ethics are the only ethics that it makes sense to follow. We may make similar comments about every religion. Each religion gives us a metaphysics and an ethics which cannot be separated from each other.

Materialism is a metaphysics, so under our theory it must imply an ethics. What ethics does it imply? Precisely this: that nothing objectively matters, and we can choose to hold whatever value system we care to hold. Note carefully that under many metaphysics, this is not true.

For a long time I rejected materialism because I did not agree with the ethics that it implied. To me, materialism was a despairing worldview. The chief problem I had was that materialism does not place inherent value on humanity or enlightenment. The most serious problem was the idea that we die with our bodies. It seemed wrong to me that human existence should be limited and finite, and that it should be possible for this thing, the only thing of value, to be destroyed by unconscious, amoral, and random forces.

I felt that the world existed for the sake of humans, and humans existed for the sake of God. The goal of the natural world was to become human, and the goal of humans was to become God. This ethics necessarily implies a metaphysics. It requires us to postulate the existence of God, postulate reincarnation, and in doing so reject materialism.

An additional aspect of my problem was my inability to believe in true badness. I cannot believe in hopeless situations. It could conceivably be the case that humans are what matter, and that human existence is limited, finite, and subject to arbitrary annihilation. But under this worldview, evil exists. So I cannot hold this view.

At this point the only solution I saw was to reject materialism. But this was difficult for me to do, because I felt that I might be deceiving myself. There is no observable evidence to the effect that materialism is false. Materialism is, if not definitely true, certainly a possibility that is not ruled out by the evidence. The only thing that ruled it out was my ethics. Being a logical person, I was not comfortable with this.

A couple nights ago I came to a resolution of this problem, and possibly the end of my long struggle with materialism. I came to believe in the possibility — though not the certainty — that materialism is true. In order to do this I had to become emotionally OK with the possibility.

The dam broke when I realized that dying and permanently ceasing to be conscious could be like enlightenment. I thought, maybe humanity and consciousness is a cosmic accident that has no bearing on anything, and the universe as it is, dead and amoral and unconscious, is just fine without it. I was able to believe this, and be OK with it.

In part I was able to believe it because it lined up well with things I already felt. I already saw humanity as a piece of gum on a giant cosmic shoe. I already felt that the way of the universe was askew from human concerns, and that really our existence was subordinate to the existence of another force unimaginably vaster and grander than ourselves.

These were never propositions of despair for me, because I always saw the higher force as good. I always wanted to be on its side. Thus, my only ethics was to follow the way of the universe. Whatever the higher force wants, I want. If this isn’t true, then I just need to change what I want until it is in conformity with the way of the universe.

So I translated the foregoing ideas into the context of materialism. Under materialism, the universe doesn’t care about humanity. OK, then; if materialism is true, then I don’t care about humanity. If it’s possible for me to die, then I am OK with dying. If it’s possible for the whole human race to be gobbled up by nanobots in the next ten minutes, then I can accept that as a good outcome.

I’m OK with the idea that a human is not a more valuable form of existence than say, a star or a squirrel or a rock. I’m OK with the idea that consciousness is not more valuable than unconsciousness, that intelligence is not more valuable than unintelligence. If that’s true, then when we die we just change to a different form which is neither better nor worse.

My impulse to believe in universal goodness is, apparently, so strong that I am more ready to stop caring about humanity than I am to stop having faith in the way of the universe.

I am not at all depressed any more by the idea that materialism is true. Actually, it has broken down the walls between myself and nature. I used to be caught in the Enlightenment idea that humans are superior to nature and that it exists for us. Now I feel that we are one with nature and not superior to it. All physical things appear more wonderful to me now that I see them as being as valuable as I am.

Under materialism, nothing matters. But this does not have to be a proposition of despair. If nothing matters, then by virtue of this everything is beautiful and acceptable.


Physicalism and Mathematicalism

Under physicalism, existence consists of mathematical patterns. Everything that exists is a mathematical object as described by whatever physical theory is a true description of the universe.

If physicalism is true, then everything that exists is isomorphic to some mathematical construct. A mathematical construct is something such as a natural number, a set, a graph, etc.

If physicalism is false, it can still be the case that existence consists of mathematical patterns. Let us call this view “mathematicalism.”

Mathematicalism. Everything that exists is isomorphic to some mathematical construct.

If physicalism is true, then mathematicalism is true. But mathematicalism can still be true if physicalism is false. Thus, for instance, things such as souls, angels, and demons may exist, and be mathematical patterns. It might be that the mind is an entity distinct from the brain, but nonetheless a mathematical pattern like the brain.

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Why We Believe

Why do we believe what we believe? I suggest three factors.

Experience coherency. It is clear that our beliefs are founded upon our experiences. I am unlikely to accept a belief that does not cohere with my experiences, and I am less likely to reject a belief which strongly coheres with my experiences.

Just as our experiences shape our beliefs, our beliefs also shape our experiences. This is obvious with the case of spiritual intelligences. I believe in spiritual intelligences, and I seem to experience contact with spiritual intelligences. The more strongly I hold this belief, the more frequent and vivid these experiences are. In times when I do not hold this belief, I do not have these experiences.

There seems to be a kind of feedback loop: the more I see it, the more I believe it, the more I see it, the more I believe it… It works the other way as well: the less I see it, the less I believe it, the less I see it, the less I believe it…

I suggest that such a feedback loop between belief and experience is a common feature of beliefs in general, and not peculiar to this case. What we experience determines what we believe, and what we believe determines what we experience.

In the case of propositions about objects in physical world, beliefs seem to have less of an effect on experience. It is indeed possible to deny the evidence of one’s senses if this is strongly enough in conflict with a strongly held belief. But this rarely happens. On the other hand, with beliefs that are not propositions about physical or mathematical objects, it is easy to believe that it constantly happens that what we believe shapes how we see the world. It is easy to believe that to some extent “seeing is believing” with beliefs that are not propositions about physical or mathematical objects.

Belief coherency. One factor determining whether we accept or reject a belief is its coherency with our experience. Another factor is its coherency with the other things that we believe.

I am more likely to believe something if it coheres with what I already believe. I am less likely to believe something if it does not cohere with what I already believe.

It is possible to undergo a “paradigm shift,” in a which a whole set of interdependent beliefs are replaced with another set of interdependent beliefs which is inconsistent with the old set. Thomas Kuhn described this phenomenon in the history of science. One can also see it for instance when a person accepts or rejects a religion.

I suggest that paradigm shifts occur because it is very difficult to “sit between two stools” (as Gurdjieff put it). To have inconsistencies in one’s belief system is stressful, requires cognitive effort, and generates cognitive dissonance. Therefore, when one is torn between two belief systems, it is likely that eventually one will reject one of the systems wholesale and embrace the other one wholesale.

Social coherency. We believe things that other people believe. All of us have a many-tiered circle of trust. We have groups of people whom we trust and mistrust to greater and lesser degrees. If a belief is not held by people in our circle of trust, then we are less likely to believe it. If a belief is held by people in our circle of trust, then we are more likely to believe it. The size of the effect is in proportion to the closeness of the people in question to the center of our circle of trust.

I suggest that social coherency is an incorporation of others’ beliefs and experiences into our determination of our beliefs. In other words, we believe things that cohere with our experiences (experience coherency) and beliefs (belief coherency), and we also believe things that cohere with others’ experiences and beliefs.


Let us analyze how these tools explain why we believe the things that we believe.

Arguments are a major factor in determining our beliefs. We are more likely to accept a belief if somebody can provide a convincing argument for it. I suggest that an argument is a means of revealing belief coherency. An argument proceeds from premises to conclusion. It has no effect if the listener does not believe the premises. If they do believe the premises, and the argument is internally strong, then they will believe the conclusion. They believe the conclusion because the argument has demonstrated to them that the conclusion coheres with things that they already believe (namely, the premises).

Arguments are the foundation for mathematics and philosophy. Evidence and arguments are the foundation for science. Evidence is, in essence, a process of sharing experience within a circle of trust (namely, scientists). A scientist says, “we experienced x as the outcome of our experiment,” and the rest of the scientific community takes it as a datum that this experience occurred.

Our available evidence and arguments together are not sufficient to account for our beliefs. Our beliefs are underdetermined by the available evidence and arguments. If we were all familiar with exactly the same body of evidence and arguments, it would still be possible (probably easy) to hold differing beliefs. The duality between physicalism and anoological non-physicalism is an example of a place where our beliefs are underdetermined.

What accounts for the portion of what we believe that is not fixed by the evidence and arguments? I suggest that belief coherency is an important factor. Since our beliefs are underdetermined, we simply adopt the belief system which is the simplest account of the data. The desire for coherency probably plays a significant role in forming our beliefs when these beliefs surpass the data, but I am not yet willing to state that it is the whole story.

What accounts for religious beliefs? After scientific and mathematical beliefs, these are the most prominent and highly developed belief systems in human society. Religious beliefs are not primarily based on arguments or evidence. Why do people believe them?

I suggest that social coherency is a factor: that people hold religious beliefs in part because the people around them hold religious beliefs. This alone can account fairly well for the people who are religious only in a casual manner, who are not passionate about religion but believe in it in a passive way without ascribing great importance to it.

This, however, does not explain how people originally came to hold religious beliefs. I suggest the following hypothesis, which however does not so much answer the question as narrow the domain of inquiry:

(H.1) One or more great individuals are the first cause of every religion’s existence.

(H.1) states that Christianity exists because Christ existed, Islam exists because Mohammed existed, Buddhism exists because the Buddha existed, Taoism exists because Lao Tzu existed, and Hinduism exists because the various Indian gurus (e.g. Gaudapada, Adi Shankara) existed. (H.1) need not mean that these figures were the only figures instrumental in bringing about any religion; it may be the case that there were many other important figures in each case.

Furthermore, I suggest the following:

(H.2) People who are passionately religious hold religious beliefs because they have religious experiences.

“People who are passionately religious” would include the great individuals of (H.1). If (H.2) is true then experience coherency plays an important role in deciding peoples’ religious beliefs.

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The Anoological Hypothesis

I am going to give an improved formulation of some of the concepts explored in the previous post. First I present the following hypothesis:

The Anoological Hypothesis. It is impossible to arrive at reasoned consensus regarding the truth-value of any proposition about non-physical non-mathematical entities. In particular, it is impossible to prove any non-tautological proposition about non-physical non-mathematical entities.

“Anoological” is composed of the Greek words “nous” (mind or spirit) and “logos” (reason). Put simply, therefore, the anoological hypothesis is the hypothesis that we do not have rational knowledge of anything mental or spiritual. Put more precisely, we only have well-defined and widely agreed upon propositions about physical and mathematical entities, and we have no well-defined or widely agreed upon propositions about non-physical non-mathematical entities. Let us further explore the meaning of this hypothesis and the reasons for believing it.

Firstly, what is meant by “non-physical non-mathematical entity?” It is any entity that is not describable by the physical sciences or by mathematics. Such entities include God, souls, angels, demons, heaven, hell, Cartesian egos, astral planes, brahman, Platonic forms, etc. They also include thoughts, feelings, sensations, intentions, consciousness, etc., if these entities are not describable by the physical sciences.

We will divide the entities just mentioned into two further roughly defined categories, for convenience. “Psychological entities” are those entities which are features of the human mind, such as thoughts, feelings, sensations, intentions, and consciousness. “Spiritual entities” are God, souls, angels, etc. Psychological entities may or may not be non-physical non-mathematical entities. Spiritual entities definitely are. These categories are not intended to be precisely defined, or necessarily exhaustive of the category of non-physical non-mathematical entities.

The three categories “physical entities,” “mathematical entities,” and “non-physical non-mathematical entities” are intended to be exhaustive of all entities that are discussed by human beings. The inclusion of mathematical entities as a category is necessitated by the clear fact that mathematical entities are not physical entities, and nonetheless are the objects of our most firmly established knowledge. Here we must leave aside the debates about whether or not mathematical entities exist, and what they are if they do exist.

What is meant in the anoological hypothesis by “reasoned consensus?” Firstly, by “consensus” I mean the kind of consensus that mathematical and scientific propositions frequently obtain, where almost all people with knowledge on the subject agree upon a single truth-value for the proposition in question. Consensus is a measure of the level of agreement in informed peoples’ beliefs.

That non-tautological propositions about non-physical non-mathematical entities rarely have such consensus is readily apparent. Certain propositions about psychological entities have consensus, such as “pain hurts” and “pleasure feels good.” It is not clear, however, that any of these consensus-bearing propositions are non-tautological.

It is clear at any rate that there is no non-tautological proposition about any spiritual entity about which there is consensus. According to physicalists, spiritual entities do not exist, and therefore all non-tautological propositions except for “x does not exist” are false of spiritual entities. This proposition does not have consensus, because many people believe that spiritual entities do exist. Physicalists and believers in spiritual entities together assure that there is no non-tautological proposition about spiritual entities which has consensus, because physicalists deny all of the propositions which believers in spiritual entities affirm, and vice versa.

There have been, and are, groups of people in which non-tautological propositions about non-physical non-mathematical entities had or have consensus. The present entire world population is not such a group of people, but we can cite examples of other such groups. In Medieval Europe it was the consensus that heaven and hell existed. In much of India it is the consensus that people live through a series of incarnations. Among physicalists it is the consensus that spiritual entities do not exist.

When examining groups other than the present entire world population, it is sometimes the case that there is consensus about propositions about non-physical non-mathematical entities. However, in none of these cases (except possibly the case of physicalism) is this “reasoned consensus.”

“Reasoned consensus” means, consensus due to the fact that the propositions upon which there is consensus have been proven. “Proof” means the kind of justification provided for mathematical theorems or scientific hypotheses. It does not necessarily mean mathematical proof; there is the possibility of admitting much that is informal and uncertain in the kind of proof under discussion. It is conceivable that we could stretch the notion of “proof” to include some justifications for believing in physicalism. Though I myself do not believe that this is the case, I do think it is possible to argue it and so I do not assert positively that consensus about physicalism is never reasoned consensus. At least all consensus besides physicalism that has existed in human history regarding propositions about non-physical non-mathematical entities has not been reasoned consensus.

It is difficult to say precisely what proof consists of. What modes of reasoning are admissible? What types of evidence are admissible? What premises are admissible? Such problems are complex. One useful measure (but not a final definition) of proof is its ability to produce consensus. This would appear to create a circle in definition between “reasoned consensus” and “proof,” but it does not. Consensus can be produced through means other than proof, such as charisma, duress, or brainwashing. “Reasoned consensus” excludes all means of producing consensus other than proof.

That is all for the meaning of the anoological hypothesis. Let us now consider the grounds for believing it. These are chiefly empirical in the informal sense. Put simply, a great many propositions about physical and mathematical entities have been proven. No proposition about a non-physical non-mathematical entity has ever been proven. Even such valiant attempts as Descartes’ ontological argument have failed to produce consensus. That this has consistently been the case after many, many attempts to prove such propositions, is strong evidence for the proposition that it cannot be done. This proposition is the anoological hypothesis.

The anoological hypothesis, if true, has large implications. Specifically, it implies that all ontologies must be consistent with exactly one of two hypotheses:

Physicalism. Non-physical non-mathematical entities do not exist.

Anoological non-physicalism. Non-physical non-mathematical entities exist, and it is impossible to prove that they exist.

Physicalism is the usual choice in philosophy today. Anoological non-physicalism is a little-considered alternative, and also the only conceivable alternative to physicalism if the anoological hypothesis is true.

Furthermore, if the anoological hypothesis is true, it is impossible to prove either physicalism or anoological non-physicalism. This is so because physicalism and anoological non-physicalism are both propositions about non-physical non-mathematical entities, and under the anoological hypothesis such propositions cannot be proven. If the anoological hypothesis is true, then we are stuck with these two ontological alternatives, and no means to establish one over the other.

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Materialism and the Veil of Unknowing

I identify three positions which we may take with regard to the epistemological status of religious propositions.

The Nonreligious Case. We may posit that all religious propositions are false.

We will restrict the notion of “religious propositions” to pointedly exclude those claims that would also be likely to be believed by somebody who disbelieved all religion. For instance, if some religion claimed that eating a particular type of seafood led to sickness, and it did so, this would not count for our purposes as a religious claim. Similarly, for our purposes, “killing is wrong” would probably not count as a religious claim.

Either we posit the Nonreligious Case, or we posit that some religious propositions are true. Here there are two possibilities:

The True Belief Case. We posit that the propositions of one religion are true, and the propositions of all other religions are false.

The Syncretic Case. We posit that some propositions of many religions are true. We posit that some religious propositions are true, some religious propositions are false, and no religion has a monopoly on the truth.

The Nonreligious Case, the True Belief Case, and the Syncretic Case are the three main ways that we may treat the propositions of religion, and all of them are problematic. Let us examine the problems with each of these cases.

One may gather from the data at that roughly 90% of people believe in religious propositions. 84% of people belong to some religion, and about half of the remaining 16% are “theistic.” This gives us the conservative estimate that 90% of people believe in religious propositions.

This means that in the Nonreligious Case, we posit that 90% of people have a basically erroneous worldview.

In the True Belief Case, we posit that at least 46% of people have a basically erroneous worldview. The largest religion is Christianity, and so if we believe in Christianity then we say that 66% of the world has an erroneous worldview. This would be the smallest number of people whose worldviews we would reject in the True Belief Case if not for the fact that Islam, the second largest religion at 21% of the world, accepts most of the propositions of Christianity and Judaism. In Islam therefore one shares many of one’s propositions with Christianity and Judaism, and together these religions constitute about 54% of the world. Therefore if we believe in Islam, we reject the worldviews of 46% of the world.

In the Syncretic Case, we posit that a minimum of 0% of people have a basically erroneous worldview, and we also posit that every person’s worldview contains substantial errors. We cannot accept all of the propositions of all religions, because this would lead to absurdity and logical contradiction. In the Syncretic Case we must accept only some religious propositions, and reject other religious propositions. We are also able to adopt an attitutude of fallibility and say that we do not know for sure that we have made the correct assessment of any given religious proposition.

All three of these cases are reasonably popular things to believe. From’s estimates we may infer that somewhere in the region of 8% of the world posits the Nonreligious Case. Many certainly posit the True Belief Case: at a minimum, almost every Christian and Muslim posits this case, giving us a minimum figure around 54% of the world. Many of the remaining 38% posit the Syncretic Case; this is popular in regions including India, China, and Japan. In India there is a great diversity of religion but a general acceptance of these diverse religions as different ways of approaching the same thing. In China and Japan the religious atmosphere is one of a melting-pot-like blending of different traditions.

If we accept the Syncretic Case, it becomes important to ask, “what religious propositions are true?” We will see later that there are fundamental difficulties with answering this question. However, a good initial heuristic is that we ought to take more seriously those propositions which a larger proportion of people hold, and less seriously those propositions which fewer people hold.

Religions differ in the claims they make, and there are certain commonalities in the claims they make. Consider, for instance, the following four concepts:

1. The Christian concept of salvation.
2. The Muslim concept of the Day of Judgment.
3. The Hindu concept of samsara and moksha.
4. The Buddhist concept of samsara and Nirvana.

These are five different concepts which have some commonalities. All of them posit the following propositions:

1. There is an afterlife.
2. In this afterlife one is rewarded or punished for one’s moral qualities in this life.
3. One possibility is to spend eternity in a place of infinite positive value.

The position that in this case all of these religions are saying the same thing is absurd. The position that they are saying things that have nothing in common is also absurd. We may draw a Venn diagram in which each circle represents the meaning of these religious concepts:

Since the common propositions are what interest us, the greatest area of interest is the area marked in red. We will call this area the concept of “liberation/salvation.” Liberation/salvation means everything common to these concepts, as captured in the three propositions given above.

Of secondary interest are the area marked in blue, which we may term “liberation,” and the area marked in green, which we may term “salvation.”

We may perform an analysis such as the preceding one for many different religious concepts and eventually arrive at a picture of the world’s most common religious beliefs. By taking the intersection of all religious beliefs we will arrive at a picture of the propositions most worth our consideration.

I propose that this process will be eased by first grouping the major world religions thematically. I propose three categories:

1. The Abrahamic religions. These are Christianity, Islam, and Judaism.

2. The Eastern religions. These are Hinduism, Buddhism, Sikhism, and Jainism.

3. Animistic religions. These are primarily tribal religions (but also encompassing Chinese folk religion and Shintoism) which we will define by their positing of various “spirits,” and a general lack of distinction between the spiritual world and the material world.

These three categories will encompass the religious beliefs of about 80% of people. The first two categories will encompass the religious beliefs of about 75% of people.

We could also potentially add Chinese religion to this list, which is a mixture of Confucianism, Taoism, Buddhism, and Chinese folk religion. I choose to exclude it because of its overlap with both Eastern religions (with Buddhism) and animistic religions (with Chinese folk religion).

The following table compares Eastern and Abrahamic religions.

Abrahamic Eastern
Christianity Islam Hinduism Buddhism
God Allah Ishvara
Soul Atman
Heaven Jannah Higher Lokas Higher Realms
Hell Jahannam Lower Lokas Narakas
Angels Angels Devas Devas
Demons Demons Asuras Asuras
Satan Shaitan
Salvation Salvation
Moksha Nirvana
Sin Sin Karma Karma
Grace Samadhi Jhana
Prophets Prophets Gurus Bodhisattvas

Some concepts which appear consistently through all of these religions are those of heaven, hell, angels, demons, sin/karma, guru/prophets, and liberation/salvation. Furthermore we may add grace/enlightenment, for although Islam does not have a handy term for this concept, it is certainly a notion familiar to Sufism.

The general message we obtain, if we take these religions as telling us the truth, is along these lines:

1. There is a vast spiritual world beyond our physical world, some parts characterized by great joy and bliss, and other parts characterized by great suffering.

2. This world is peopled by spiritual entities, some more evolved/intelligent/powerful than us. Some of these entities are good and some are evil.

3. We will live after death, and whether the place of our future living is characterized by joy/bliss or suffering will depend upon how we live in this life, including the sin/karma that we accumulate.

4. The occasional guru/prophet comes to save and enlighten the human race.

5. The ultimate goal of life is liberation/salvation, which is characterized by union with or closeness to God, or in atheistic systems by a freedom from suffering or karma/action.

If we wish to take animistic as well as Abrahamic/Eastern religions into account, then we may posit considerably less. Taking the intersection of these three categories of religion, we obtain roughly the following: “there are spiritual entities.”

Most of the religious propositions that we have examined depend upon the proposition that nonphysical, i.e. mental/spiritual, entities exist. Such entities include God, souls, angels, demons, heaven, and hell. To accept the existence of any of these entities is to reject materialism, and therefore to posit materialism is to reject most of the claims of religion. Our critical “hinge question” therefore becomes: do mental/spiritual entities exist?

It is clear at any rate that it seems to be impossible to prove propositions about mental/spiritual entities. All of our rigorously established knowledge is about physical entities and mathematical entities. Let us attempt to further explicate this difference.

Many propositions have been put forth by humans about physical, mathematical, and mental/spiritual entities. In every culture these entities are discussed and propositions are made about them. Some of the propositions that have been put forth by humans have been rigorously justified and backed up with various kinds of evidence. Some of these propositions have not.

The only propositions which have ever been rigorously justified are propositions about physical and mathematical entities. No proposition about a mental/spiritual entity has ever been rigorously justified. There is strong empirical evidence that the only propositions that can be rigorously justified are propositions about physical and mathematical entities.

Therefore, one of two things is the case.

Materialism. No proposition about mental/spiritual entities is true.

The Veil of Unknowing Hypothesis. Some propositions about mental/spiritual entities are true, but none of these propositions can be rigorously justified.

That these are the only two likely cases can be seen from the empirical fact that no proposition about a mental/spiritual entity has ever been rigorously justified.

The Veil Hypothesis is so named to suggest the metaphor of a veil covering up mental/spiritual entities so that we are not able to have adequate rational knowledge of them. One thing in particular that is true under the Veil Hypothesis is that mental/spiritual entities exist, but we cannot rigorously justify the proposition that they do exist.

Is it a priori plausible that there could be propositions that are true but not provable? An analogy from Gödel’s first incompleteness theorem will suggest to us that this is, at least, not a priori implausible.

Gödel’s first incompleteness theorem. There are mathematical facts that are true but not provable.

This result, here given in simplified form, is a mathematical fact that was established by Kurt Gödel in 1931. Let us consider a philosophical conclusion that might tentatively be drawn from it:

The Strong Incompleteness Hypothesis. There are facts about the world that are true but not provable.

Gödel’s incompleteness theorem does not strictly entail the Strong Incompleteness Hypothesis. The former is a mathematical theorem, and the latter is a philosophical conclusion which may follow intuitively from Gödel’s incompleteness theorem. The Strong Incompleteness Hypothesis is a priori plausible. Moreover, I suggest that the a priori plausibility of the Strong Incompleteness Hypothesis makes it easier to believe that the Veil Hypothesis is not a priori implausible.

As previously stated, either:

(a) materialism is true, or
(b) the Veil Hypothesis is true.

Either of these cases would be interesting. In the former case we are interested to know why it is that 90% of people hold these false religious beliefs. In the latter case we are interested to know more about mental/spiritual entities, and why our knowledge of them is limited in this way.


Mathematics and Ontology

If we accept materialism, then we say that every part of existence can be described by mathematics. This is so because physical laws consist of mathematical equations, and according to materialism existence is described by physical laws. We therefore say that under materialism, existence is mathematical.

If we reject materialism, we must nonetheless acknowledge that some of existence is material and is described by science. We may reject materialism and nonetheless maintain that all of existence is mathematical. If we reject this as well, then we are forced to conclude that some of existence is mathematical, and some of it is not. It cannot be that none of existence is mathematical, because some of existence is described by science.

This leaves us with two theories of existence. Either it is wholly mathematical, or it is part mathematical and part unmathematical. In the latter case we need not posit that there is a sharp distinction between the two; there could be room for a fuzzy border.

Let us call these views the Mathematical View, and the Divided View.

If we accept materialism, then we accept the Mathematical View. We only accept the Divided View in a case in which we reject materialism. Here we will take “rejecting materialism” to mean “including nonphysical categories in our ontology.” This is the only act which we may seriously call a rejection of materialism. To the category “physical entities” we add, for instance, the category “mental entities,” or the category “spiritual entities.”

It is odd to notice that these three categories seem to be exhaustive for almost any ontology, and even more strongly seem to be exhaustive for the entities which we directly experience. We experience physical entities such as tables and chairs. We experience mental entities such as thoughts and feelings. We experience spiritual entities such as moments of grace/enlightenment. There does not seem to be a fourth category. Put differently, there do not seem to be any entities which do not readily fall into at least one of these three categories.

Some ontologies, of course, use only one of these categories. We have materialism, in which we posit that all entities are really physical entities. We have idealism, in which we posit that all entities are really mental entities. We may also imagine some kind of spiritual monism in which we posit that all entities are really spiritual entities; Advaitism may be such a philosophy. Furthermore it is easy to imagine ontologies using only two of these categories, or consolidating two categories into one (e.g. merging “mental” and “spiritual”). But the odd fact remains that there does not seem to be a fourth category.

I draw the following tentative conclusions. Every ontology will have to posit some combination of these three categories (either including all three, reducing the number by exclusion and/or merging, or increasing the number by splitting). Furthermore, each category will be either wholly mathematical, wholly unmathematical, or somewhere in between.

No monistic ontology can have its one category be wholly unmathematical, because the parts of the world described by science are mathematical, and those parts of the world will be contained in the one category of any monistic ontology.

Furthermore, any ontology which contains the category “physical” will probably have that category be wholly mathematical. (This conclusion could only be altered upon very detailed philosophical inquiry.)

It is difficult to imagine that the category “spiritual” could be wholly mathematical, and so any ontology which contains the category “spiritual” will probably have that category not wholly mathematical. Most likely it will be wholly unmathematical.

What are likely or obvious candidates for ontologies?

1. The materialist ontology, in which there is one category, “physical,” and it is wholly mathematical.

2. The idealist ontology, in which there is one category, “mental,” and it is partially (perhaps wholly) mathematical.

3. An ontology in which all three categories are present, “physical” is wholly mathematical, “mental” is partially mathematical, and “spiritual” is wholly unmathematical. Let us call this a “physical-mental-spiritual ontology.”

One thing that these inquiries show is the great philosophical difficulty that arises in rejecting materialism. If we take the claims of religions seriously then we almost certainly do reject materialism, but in doing this we cast ourselves out into very confusing and uncertain territory.

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I thought I would attempt to articulate my religious beliefs. Lately these have coalesced into something fairly definite, and since I am not aware of a word for these beliefs I thought I would coin one. I am an atheologist.

“Theos” means “God.” “Logos” means “speech.” An “atheologist” is one who believes that God cannot be discussed. To an atheologist, all statements regarding the nature of God, or regarding God’s existence or non-existence, are neither true nor false, but simply nonsensical. They are nonsensical to the atheologist because they are attempts to discuss something that cannot be discussed.

I am not the first atheologist. Bodhidharma, the founder of Zen Buddhism, also held this position. So did Ludwig Wittgenstein and U.G. Krishnamurti. Atheologism can be placed alongside atheism, monotheism, polytheism, pantheism, etc., as another belief that it is possible to have about God.

How did I arrive at this position? From the beginning of the year through the summer, I was practicing meditation and Yoga very intensively, according to the system set forth by Aleister Crowley and the Indian mystics. These people had claimed, as it is common to claim, that by meditating I could obtain direct contact with God and experience the reality of God for myself. I worked very hard to obtain such experiences.

In the summer my efforts began to pay off richly. I began to have vivid and overwhelming experiences which lined up very well with what was described in the books on the subject. By careful analysis of my experiences, and careful analysis of the descriptions given in the books of what it was supposed to be like to have “oneness with God” or whatever you care to call it, I concluded that I was having these experiences.

It would follow, I concluded, that I had touched upon the true nature of reality and this was now directly accessible to me and laid before my awareness.

It became a matter of great importance to me that I figure out whether or not this was so. Was this the truth? Was this reality? I became extraordinarily skeptical and subjected these experiences to the most intense scrutiny and criticism, trying to find any way that I could doubt that they were reality. All of my efforts crumbled feebly before their towering irreducibility. I finally concluded that I had found the truth, that I had found reality, and that it was totally immune to any conceivable philosophical criticism.

The next matter, then, was to lay down what I had discovered. I tried to do this for a long time. I tried to subject my experiences to rigorous analysis and explain exactly what it was that they were. I always failed. Though I had found the truth, I was not able to make any positive statement that sounded true even to me. Valiantly I continued my attempts.

Things went on like this until sometime last semester I read Wittgenstein’s Tractatus Logico-Philosophicus. The bulk of this text is a highly esoteric analysis of the logical structure of language, which attempts to investigate the nature of meaning in order to draw a demarcation between what can be discussed and what cannot be discussed. The book then ends by veering off suddenly from its highly technical logical investigations into religious, ethical, and aesthetic considerations, ultimately concluding that the subject matter of religion is beyond language and beyond logic.

His conclusions shook me to the core, because he had expressed in a very clear way something that I had been painfully discovering for myself over the past few months. I was led to the massively counterintuitive conclusion that I had found the truth, and I could not talk about it.

This also made it clear to me why it was immune to philosophical criticism. Philosophical criticism is necessarily in the sphere of words, and this was outside of the sphere of words. It was like trying to grab space. Logic couldn’t refute it because it couldn’t even get a grip on it.

I have gradually gotten used to this. It is still somewhat upsetting. My current theory is that it needs to be this way, that somehow for the cosmos to accomplish what it’s trying to accomplish it needs to be the case that we can only find the truth by our own efforts, and not by others’ efforts. The theory goes that if upon finding the truth we could share it with everybody, this would somehow spoil the great cosmic game.

Though this explanation is highly speculatory, the facts stand firm independent of it. I still cannot doubt that what I found this summer is reality. I still cannot say anything about it that sounds true even to me. That the truth is inexpressible has become an irreducible datum for me, as concrete and factual as the couch I’m sitting on. Repeated and persistent experiment has shown it to be so. I invite all others to try and replicate my experiment; the methods are all given in Part I of Liber ABA by Aleister Crowley, among other places. If anybody more competent than I succeeds in expressing the truth, then I will joyfully recant my position. Until then, I am an atheologist.

I will end by quoting at length the final passage of the Tractatus, the closest thing I have to a holy text. (“The closest thing,” because an atheologist having a real holy text would be absurd.)

“How the world is, is completely indifferent for what is higher. God does not reveal himself in the world.

The facts all belong only to the task and not to its performance.

Not how the world is, is the mystical, but that it is.

The contemplation of the world sub specie aeterni is its contemplation as a limited whole. The feeling of the world as a limited whole is the mystical feeling.

For an answer which cannot be expressed the question too cannot be expressed. The riddle does not exist. If a question can be put at all, then it can also be answered.

Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked. For doubt can only exist where there is a question; a question only where there is an answer; and this only where something can be said.

We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer.

The solution to the problem of life is seen in the vanishing of this problem. (Is this not the reason why men to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?)

There is indeed the inexpressible. This shows itself; it is the mystical.

The right method of philosophy would be this: To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other — he would not have the feeling that we were teaching him philosophy — but it would be the only strictly correct method.

My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)

He must surmount these propositions; then he sees the world rightly.

Whereof one cannot speak, thereof one must be silent.”

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