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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Materialism

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.

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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.

Discussion

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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