Why I believe in God, Jesus, and miracles

As I write we approach Easter Sunday, when Christians celebrate the resurrection of Jesus Christ three days after his death by crucifixion. As a Christian I celebrate this holiday. For me this holiday raises many intellectual questions, such as:

  1. Did the resurrection of Christ which Christians celebrate on Easter actually occur?
  2. Did Jesus Christ exist as a historical figure?
  3. Was Jesus Christ involved in miraculous events such as those told in the Gospels of the New Testament?
  4. Does God exist? Is there a loving intelligence with the properties Christians traditionally ascribe to God, such as:
    • omnipotence (absolute power over everything),
    • omnipresence (presence everywhere at all times),
    • and ominscience (total knowledge of everything)?

I answer all four of these questions in basically the same way. As my first step I consider two ways that each question can be made more precise. Each question can be made more precise by considering it as a question about existence, or a question about actuality.

The distinction between existence and actuality is the distinction between the existence of a phenomenon in some world, and the existence of a phenomenon in the actual world we live in.

When these four questions are considered as existence questions, I answer them in the affirmative on a priori grounds based on logic and mysticism. My perspective on logic tells me that all possibilities exist, and that there are no limitations to what is possible (even logically inconsistent phenomena are possible in my view on logic). My perspective on logic is informed and justified both by purely logical considerations, and by mystical experience. From this perspective it follows immediately that Jesus Christ, God, and miracles all exist a priori and certainly.

When these four questions are considered as questions about actuality, I say that the answers to all of them are uncertain to me, but that in my opinion the answers to all four questions are probably still affirmative. I don’t know certainly and empirically whether Jesus Christ existed historically in this time line; I don’t know certainly and empirically whether a miracle has ever occurred in this time line; and I don’t know certainly and empirically whether the universe we live in was caused by an omnipotent, omniscient, ominpresent, loving intelligence. It is my opinion that the true answers to the four questions are probably “yes” when they are considered as questions about actuality.

I will spend the rest of this post laying out my justification for the views just described. I want to begin by clarifying the distinction between existence and actuality, by giving a definition of world.

Definition of “world.”

Many philosophers believe that there exist worlds (universes) other than the world we live in. A world, or universe, is basically a self-contained being. For example, we can define a world as any maximal spatiotemporally connected object.

  • An object x is spatiotemporally connected if and only if for any two parts of x, call them y and z, there is a path in space-time connecting y and z.
    • For instance, if y = z, there is a trivial path in space-time, of length 0, connecting y and z.
    • For instance, if you are reading these words, then there are paths in space-time connecting you and I. In general, if one object affects another within the laws of physics known to mainstream science, then there is a path in space-time connecting the two objects.
  • An object x is maximal spatiotemporally connected if and only if x is spatiotemporally connected, and there is no object y of which x is a proper part, such that y is spatiotemporally connected.
    • A proper part of an object y is an object x such that x is a part of y and x is not y, so that there is a part of y which is not a part of x.

In short, a world (by this definition) is a spatiotemporally connected object such that anything you add to it will make it spatiotemporally disconnected.

The universe as typically conceived by physicists has this property of being a world or a maximal spatiotemporally connected object. The multiverse, on the other hand, is typically not a world in this sense, because things in different universes in the multiverse can’t be connected by paths in space-time, on most conceptions of the multiverse. If you like, you can equate the multiverse with the set of all worlds.

If you don’t like this definition of “world,” you can substitute your own definition of “world,” and the rest of this post should still be intelligible.

Definition of “existent.”

“Existence” is for me a primitive, unanalyzable notion. Everything which exists exists, or in other words, everything exists. This is an uncontroversial opinion for the most part; those who think there are things which don’t exist (i.e., there exist things which don’t exist?) are usually called Meinongians.

On my conception of logic, everything conceivable exists as a matter of logic. To disagree with this is not necessarily to be a Meinongian. Most people don’t believe there are non-existent beings, but they also don’t believe that everything conceivable exists. For instance, most people familiar with the Harry Potter series believe there is no being about which the statements made about Harry Potter in the Harry Potter series are true. This is commonly paraphrased by the statement “Harry Potter does not exist.” The statement “Harry Potter does not exist,” interpreted quite literally, appears to be a Meinongian assertion presupposing the existence of the non-existent being Harry Potter, but most people who assert it would, if pressed, agree that they meant it essentially as a paraphrase of the statement “there is no being about which the statements made about Harry Potter in the Harry Potter series are true.”

So then we have three views on existence in play:

  • my view, that everything conceivable exists,
  • the Meinongian view, that there are non-existent beings,
  • and what I’d call the usual view, that neither my view nor the Meinongian view is correct.

That’s the extent to which I will clarify what I mean by existence. I hope it’s sufficiently clear for you; please let me know in the comments if not.

Definition of “actual.”

“Actual” is easier to define than “existent” for my purposes, because rather than being a primitive notion not definable in terms of other notions, “actual” as I’ll define it is a derivative of the already explained concepts of “world” and “existent.”

“Actual” is a relative notion: it’s relative to a world, implicitly always the world the speaker is in. A being is actual if and only if it is part of the world the speaker is in. When I say George Washington actually existed, I mean that George Washington exists in the past of the world I am in. In other words, I mean that there is a spatiotemporal path (going backwards in time) from me to George Washington.

Why I believe everything conceivable exists

My perspective on logic entails that everything conceivable exists. I believe in my perspective on logic on the basis of reflections and arguments I have presented in a book and two blog posts. I will briefly rehash those reflections and arguments here, with some new elements. For more detailed and careful presentations, see the linked resources.

Justification of a perspective on logic is a difficult problem. Most people, if they have systematically learned anything about logic, are in a position of receiving a view on logic from experts without questioning it. I am an expert on logic; I have published in top logic journals, I peer review papers for top logic journals, and I studied with world renowned experts on logic in the University of Connecticut PhD program. My own perspective on logic is not something I received from other logic experts; I have synthesized this perspective as original research. Therefore I have to face the conceptually difficult problem of justifying my perspective on logic.

This problem is conceptually difficult because logic is foundational to essentially all academic methods of justifying objective claims. The scientific method relies heavily on logic, for example because today the scientific method relies heavily on math, and math is founded on logic. The scientific method can’t by itself justify a perspective on logic if it relies on logic. Futhermore, logic is almost always considered to be a priori; in other words the principles of logic can be established without any empirical investigation of the actual world. If logic is a priori then the scientific method must not be involved in establishing the principles of logic.

If science can’t be used to justify logic, that leaves us with two main tools in the academic toolkit for justifying objective principles: logic itself, and math. Math is founded on logic, so any justification of principles of logic using math will have circularity. And, obviously, any justification of principles of logic using logic will have circularity.

How do we resolve this paradox, that on the face of it there is no way to justify principles of logic, because logic is foundational to all our tools for justifying objective principles?

For starters, I reject the notion that principles of logic are objective knowledge. To me it is obvious that principles of logic are essentially subjective opinions, because they can’t be justified objectively in a non-circular way, and different logicians have different opinions on what principles of logic are correct (witness for example the debate between believers in classical logic and believers in intuitionistic logic).

This view that principles of logic are subjective opinions has the interesting implication that basically all objective learning is grounded in subjective opinion, because basically all methods of objective learning are understood today to be grounded in principles of logic.

I do not believe in the idea that human learning can be built up in a step-wise fashion starting from nothing, the way Descartes attempted to do in his Meditations on First Philosophy. Atheists are amused by the fact that when Descartes attempted to throw out all of his assumptions and build up knowledge from a perfectly blank foundation, he very quickly arrived at the conclusion that the Christian God exists. One could argue that Descartes was not truly able to divorce himself from his own assumptions; even when he thought he did, he didn’t. I think this is a definite possibility. The other possibility I see is that Descartes did not really believe his meditations justified belief in the Christian God, but he lied about this to avoid religious persecution.

I don’t believe that we as humans can divorce ourselves from all of our assumptions. When learning, we never begin from nothing. We always begin from where we are. We can reflect on and question the way we think, but we can only think in a different way by performing transformations on the way we currently think.

My perspective on logic is something I began to arrive at by learning established perspectives on logic, which I was able to do because of my natural cognitive capabilities shaped and developed through my education. My next step was transforming those established perspectives in my mind to arrive at a new perspective which I believe better explains the data I have experienced.

The most relevant experience which my perspective on logic fits is of two types: logical experience, and mystical experience. My logical experience comes from using logic, and particularly using math, logic, and philosophy to study logic. My mystical experience is of entirely different origins which I don’t claim to understand but view as spiritual/divine. My logical experience and mystical experience each reinforce my perspective on logic in different ways.

My relevant logical experience mainly comes from analysis of the phenomenon of logical and mathematical paradoxes. Consider, as a simple example, the sentence “this sentence is false.” This is a perfectly valid English sentence, and if you think about it, you can see that by pure logic, if the sentence is true, then it’s false, and if it’s false, then it’s true. This paradox can be made precise within many systems of formal logic and math, and many variants on this paradox affect many systems of formal logic and math.

Most logicians believe that it’s impossible for a sentence to be both true and false. In other words, there are no true contradictions, and there are no true logical paradoxes. This conviction, and variants on this conviction such as the conviction that not every statement is true, have motivated a vast program of research looking for ways to define logic and math such that logical paradoxes do not arise or such that the paradoxes that arise are in some sense “solved.”

There are ways to define logic and math such that logical paradoxes do not arise or are in some sense “solved.” However, all of these ways involve putting restrictions on what can be expressed or inferred. For example, Zermelo-Fraenkel set theory explains how to define the informal concept of “set” such that logical contradictions do not arise (as far as we know). The “naïve,” informal concept of sets gives rise to Russell’s paradox, which is the paradox of whether the set of all sets which do not contain themselves contains itself. As with the liar paradox, logic tells us that if the statement “the set of all sets which do not contain themselves contains itself” is true, then it’s false, and if it’s false, then it’s true. Zermelo-Fraenkel set theory resolves this paradox by stating axioms (assumptions) about sets which allow math to be developed but do not allow the existence of Russell’s paradoxical set to be proven. At the same time, these axioms rule out the existence of sets such as the set of all sets, the set of all rings, the category of all topological spaces, the category of all categories, and other objects which mathematicians would find it natural to talk about.

Nobody has been able to find a way of defining logic such that everything we can express in English can be expressed, and logical paradoxes do not arise, and all of the rules of logical inference necessary to do math are present. This is true to the best of my awareness, after spending a lot of time looking at the field of logical paradoxes, and extensively discussing this issue with people whose awareness of the field greatly exceeds mine. I believe that in all probability, if such a method existed, then I would have heard about it. In my opinion it is very unlikely that any such method will ever be discovered.

This is my logical justification for believing that true contradictions do exist. I believe there is nothing incorrect about the classical rules of logic and math which give rise to logical paradoxes, because assuming there is something incorrect about those rules leads to a research program which I view as unsuccessful, to revise the rules of logic and math to eliminate or “resolve” logical paradoxes in a satisfactory manner.

The usual rules of classical logic allow us to prove that if any contradiction is true, in other words if any statement is both true and false, then every statement is true. I accept this conclusion. I believe that in the final analysis, every statement is true, and that the common logical arguments which lead to this conclusion are valid, sound arguments.

From a mystical perspective, I justify the belief that every statement is true on the basis of mystical experience. I believe mystical experience has shown me that all is one, which I interpret as meaning that all beings are in the final analysis one and the same as each other. In precise terms, for any beings x and y, x is y. This statement, which I call the Law of One, is logically equivalent to the statement that every statement is true. Of course the statement that every statement is true implies the Law of One. Conversely, the Law of One implies that every statement is true: for example, it implies that the property of truth is the property of falsehood, and since every (precise, objective) statement without the property of truth has the property of falsehood, therefore all statements have the property of truth. This is how through mystical experience I arrive at the same conclusion which I arrived at through purely logical methods explained above.

Why I believe God, Jesus Christ, and miracles exist

From the belief that every statement is true, the belief that everything conceivable exists follows immediately. From the belief that everything conceivable exists, the belief that God, Jesus Christ, and miracles exist follows immediately.

Why I believe God, Jesus Christ, and miracles are probably actual

To say that God, Jesus Christ, and miracles are actual is to make a stronger statement than that they exist. It’s to say that they exist in the world we are in. Of course if every statement is true, then this is true, but only in the trivial sense that applies to all statements. In most contexts I don’t carry the assumption that every statement is true, because this assumption obviates the purpose of thought itself. Without this assumption or anything equivalent to it, can we still conclude that God, Jesus Christ, and miracles are actual?

When I ask whether Jesus Christ is actual, I mean to ask, was there a person in our world of whom most of the statements about Jesus in the Gospels of the New Testament are true, who performed miracles, who died in crucifixon, and who rose from the dead three days later? I am now thinking about this question not from an a priori logical perspective, but from an empirical perspective. I am asking what we can say about this question purely on the basis of historical evidence and inference from it, without drawing on the powerful logical principles I accept which imply that every statement is true.

I believe Jesus Christ probably actually existed. I am no expert on historical Jesus studies. My opinion on this question comes primarily from an argument by Peter J. Williams. Here is a brief version of part of that argument. Why would people who were predominantly monotheistic Jews, who eschewed idol worship, start worshiping Jesus as God, with the energy needed to spread the religion as rapidly as it spread around the first century, under intense persecution, while believing that Jesus performed miracles and was resurrected, unless those facts about Jesus are true and there was a core group of eyewitnesses who got the ball rolling? It’s possible in my mind that as a matter of historical truth, the Gospels are fiction, but in my mind this is a less likely possibility than that they are historically true, because if the Gospels were fiction then it would be more difficult for basic agreed upon facts about the history of Christianity to be true. In the future I would like to publish more analysis of this question, in particular weighing the merits of prominent arguments against the historical existence of Jesus.

Whether a being with the attributes Christian theologians ascribe to God created the universe is another historical question, far more distant than the question of whether the Gospels are true. I do not have any empirical evidence weighing on this question. In my opinion this is the most likely possibility, because that belief coheres well with the rest of what I believe, but of course this question deserves far more analysis than I am giving it here. In all humility I must admit that I view the question of how the universe began as being beyond the capability of human philosophers to clearly resolve in any foreseeable future.

Whether any miracles have occurred is another historical question. I am defining miracles here as roughly any phenomena which defy the laws of physics. I believe miracles are possible and exist in some worlds, on the basis of my views on logic. Whether they have occurred in this world, and whether this can be shown empirically, are additional questions. Many cash prizes are offered by skeptical societies to anybody who can show the existence of paranormal phenomena (basically the same type of phenomena I call miracles). According to Wikipedia, none of those prizes have been claimed. From this we can safely conclude that if miracles exist in the modern world, they are extremely rare and/or hard to reproduce at will and measure empirically.

I have seen some empirical evidence which at least on the surface appears to show the existence of miracles. Most striking is this video of Simone Ravenda which claims to show him bending a fork with the power of his mind. Possibly this video is a mere illusion, as I guess most claimed instances of psychokinetic silverware bending are. However, after significant analysis of this video I haven’t been able to see how it could plausibly be an illusion. In the future I plan to write more about this video.

Here are some scientific studies which appear to show additional independent evidence of the empirical existence of miracles in the modern world:

The PEAR Project: Studies done at Princeton showing that people can use mental intention to bias the output of analog random number generators

Dean I. Radin and Roger D. Nelson. Evidence for Consciousness-Related Anomalies in Random Physical Systems. Foundations of Physics, Vol. 19, No. 12, 1989. A meta-analysis of studies of using mental intention to bias the output of analog random number generators.

Studies showing that large groups of meditating individuals in an area can reduce violent crime in the area

I have reviewed these studies, applying my learning in statistics, research methods, philosophy of science, and epistemology, without finding any problems in their methodology. However I admit the studies could be flawed for reasons I haven’t uncovered, so that I don’t consider them to provide certain evidence of miracles.

My views on logic tell me that miracles are possible and exist, and in light of this preconception, I am not predisposed to reject claimed evidence of miracles without investigation, as many people are. If you are a scientific materialist, then you probably assume that any evidence of miracles is overwhelmingly likely to be unsound, and you may be predisposed for this reason against investigation of any claimed evidence of miracles. I would guess most claimed evidence of miracles is in fact unsound, but when I encounter what appears to me to be high quality evidence of miracles, such as what I have cited above, I am not afraid to say that I think that’s what it is, even while I admit my uncertainty about its actual correctness.

Why I believe humans can commune with God

My views on logic imply that God exists, but if God exists only in some other world we’re not a part of, it doesn’t follow that humans can contact God, as Christians believe we can.

I believe humans can contact, communicate with, and commune with God. Why? Because we are God, as follows from the Law of One. To commune with God is in the final analysis to commune with ourselves and everything that exists, because God is everything that exists. That’s my perspective.

P.S.: This post is not an April fool’s joke. That should be fairly obvious if you’ve read my related writings.

The Earth is spheroid, not flat

Image credit: The Flat Earth Society.

Here is an easy, straightforward method for proving that flat Earthers are incorrect about the geometry of the Earth. Supplies: a computer connected to the Internet, paper and pencil. Prerequisites: some basic skills with math and Internet research.

Earth maps, flat and spheroid alike, can be used to produce predictions about minimum flight times. The fastest way to travel from one place to another is in a straight line. By flying in a straight line, a plane can fly from one place to another in the shortest amount of time possible for its speed.

If you believe, for example, that a given flight from New York City to Paris is traveling no faster than 600 miles per hour, then a spheroid Earth model tells you that the minimum flight time is approximately 6 hours (based on a distance of 3,627 miles). The calculation is to divide the distance by the speed.

Any adequately labeled flat Earth map should enable you to measure the approximate distances between major cities. If you have a flat Earth map displayed on the computer screen, and it has a legend marking out the distances, then you can use that legend to improvise a ruler by holding up paper next to the legend and using a pencil to mark points on the edge of the paper.

A flat Earth model, compared to a spheroid Earth model, will specify different distances between cities in many cases. I conjecture that this is mathematically inevitable. Those distances can be used to estimate minimum flight times between cities. If in any single instance, a plane’s actual flight time was less than the minimum flight time at its maximum speed, as predicted by a flat Earth model, then that example falsifies that flat Earth model.

Note: In reality planes fly in three-dimensional arcs where they ascend and descend, and those arcs are longer than a straight line drawn on the surface of a flat or spheroid Earth. We will ignore this fact for the purposes of this analysis. This simplification does not undermine the integrity of the argument, because it will result in minimum flight time estimates which are lower than the actual minimum flight times. If you underestimate the minimum time for a flight according to a flat Earth model, and you show that the actual time of the flight was less than the estimated minimum, then you’ve falsified that flat Earth model.

Because the Earth is in fact a spheroid, I conjecture that for any labeled flat Earth map, you can find examples where its estimated minimum flight times between cities are greater than actual flight times for some flights, or that if that isn’t true (say because the map was specially concocted to make it false), then some other contradiction between the map’s predictions and reality can be found. My confidence is very high that this conjecture is true. I have found that my conjecture is true in the case of a single flat Earth map which I checked in this way.

I invite you to try this test using whatever adequately labeled flat Earth map is easiest at hand, and using whatever cities you want. Pick some cities, and research flights between pairs of cities, recording their estimated and/or actual flight times. Compare those numbers to the estimated minimum flight times according to the flat Earth model. You can produce those estimates by using the flat Earth model to measure the straight line distance between your two cities, and then dividing that number by some estimate of the maximum speed of the flight. 600mph is a reasonable maximum speed estimate for commercial flights, to the best of my knowledge, and you can calibrate your estimate against actual flight speeds you can research on the Internet.

If you try several pairs of cities, I fully expect you to come across a pair where the estimated minimum flight time on the flat Earth model is greater than the actual reported time of some flight. A single example like that, if the numbers are accurate, proves that that flat Earth model is false. With nothing but a computer and pencil and paper, you can try this test as much as you want, with as many flights and flat Earth maps as you want, and prove to your satisfaction that the Earth is not flat.

If you are able, it could be wonderful to go to Lake Michigan or another large lake. From the Michigan side of Lake Michigan, you would be able to see Chicago with a telescope, if the Earth were flat. Because the Earth is not flat, and is in fact a spheroid, you can’t see Chicago from across Lake Michigan. From the Michigan side, the curvature of the Earth makes Lake Michigan bulge up and cover the tops of the skyscrapers in Chicago. However, sometimes there are mirages of the Chicago skyline which can be seen from the Michigan side; these can be explained while still assuming the Earth is round. You can verify all this with Internet research, or you could go to Lake Michigan yourself to check the facts.

All is one: a logical/mystical explanation

Image by the beautiful, spiritually awake artist Alex Grey.

This post concerns the idea that all is one, that all distinctions are illusory, yet also real. I humbly consider this to be the deepest spiritual and philosophical truth I’m aware of. I believe that mystical experience can reveal this truth to humans, in the sense of providing sense, evidence, and justification for it. I believe this idea, which appears logically absurd, reconciles beautifully and completely with logic, and can in fact be justified using logic alone.

I am presenting the idea from two angles: a mystical angle and a logical angle. The key phenomena being studied are mystical experiences and logical paradoxes.

This post can be motivated from a logical perspective and a mystical perspective.

  1. A logical motivation is to provide an intuitively satisfying explanation of logical paradoxes, to complement and extend the technically and practically adequate solution to logical paradoxes of my previous post, Paradoxes and the rules of logic.
  2. A mystical motivation is to reconcile and marry with logic the proposition that all is one. This proposition is a formulation of nondualism, which is a common species of philosophical idea coming from mysticism.

I’ll explain how I view mystical experience as providing justification for the idea that all is one. I’ll also provide a logical, philosophical argument for the same conclusion, in the section titled “An argument for the Law of One.” That argument is not at all dependent on mysticism; it relies only on logical considerations.

The assumptions and conclusions of this post won’t appeal to everybody. If something about this doesn’t sit right with you, then I advise just leaving it where you found it.

 

The Law of One

In this post I’m concerned with one particular idea which I think can be repeatably supported by mystical experience.

It is the idea of the unity of all things.

It is called the Law of One.

It is called nondualism.

It is called the Tao.

It can be stated as, “all is one.”

It can be rationalized as follows.

Real world systems are highly complex and entangled. Things affect each other in so many ways that to predict the behavior of any part of the universe, you must ultimately be able to predict the behavior of the whole universe. A complete and wholly accurate point of view would have to consider the whole universe as one single and inseparable thing which is not a simple sum of its parts.

The universe is fractally self-similar. If you look throughout nature, you can find similar structures at different levels. A tree’s branches resemble a neuron’s branching dendrites. Some computer-generated pictures of the universe bear a certain resemblance to artistic images of networks of neurons (such as below), and to computer-generated maps of the Internet.

dendrites

Each cell in a human body contains instructions (DNA) for producing another human body. Each human in a society contains an incomplete copy of that society’s body of learning and experience, in the form of language ability, education, socialization, shared memories (history), acquired skills, and so forth.

There are a few examples of how the universe is fractally self-similar. Behind these few and paltry examples, is there a deeper orderliness to the universe that human science has yet to understand? In any case, the idea of the fractal self-similarity of the universe provides a way of illustrating the idea of the unity of all things.

The logical extreme of the idea of the unity of all things states that any two distinct things are in reality identically the same thing. Each part of the universe is one and the same as every other part of the universe. If so, any appearance of separation and distinctness is some form of illusion, and in reality there is only unity.

I believe the truth of the Law of One, the idea of the unity of all things, has been revealed to me in mystical experience. I believe the idea in all forms just described, including the logical extreme of the idea of the Law of One, that any two distinct things are identically the same thing. I believe mystical experience has revealed the truth of these forms to me.

If any two distinct things are identically the same thing, then in my opinion it follows that every statement is true. Consider the following argument. Let A and B be statements, and let A be a true statement. For example, let A be the statement “the sun has energy” and B be the statement “the sun has no energy.” By the assumption that any two distinct things are the same thing, A and B are the same thing. In other words, B is A. Since A is true, and B is A, B is true. That is, the sun has no energy. By the same reasoning pattern one can arrive at the conclusion that every statement is true. I believe this follows from the Law of One and that in the final analysis of reality, every statement is true.

How can I, somebody who has studied the cutting edge in logic and philosophy of logic, believe that every statement is true? How can this square with logic, common sense, or anything? If you believe the Law of One, then it’s a paradox that the Law of One entails every statement. I apply my general method of solving paradoxes to this problem. For more information on how my perspective on logic integrates with my perspective on the Law of One, you can skip to the section titled “An argument for the Law of One.”

 

Epistemic status of this post for me

As stated already, I believe the perspective I’m articulating here. It is what I have arrived at after seeking truth on the relevant topics to the best of my ability for around seven years. I don’t think everybody will share the intuitions that make me believe the perspective. Some people just won’t agree with me, maybe for reasons neither of us can explain.

If you don’t agree with what I’m saying and you can explain why, I’m interested in hearing it.

On the other hand, as far as I can tell after years of thinking about it, the perspective articulated in this post is irrefutable. That doesn’t mean I can prove it; it just means that as far as I can tell, nobody can refute it. I don’t expect people to be able to use words to sway me from the view, and I don’t expect my words will sway everybody towards the view. Yet I remain open to being surprised.

Suppose I’m right that the perspective of this post is irrefutable. In such a situation, the disagreeing parties are likely to feel they have little choice but to agree to disagree. Maybe one or the other is right, or maybe neither is right, but the parties don’t necessarily have any way to resolve the disagreement. I don’t assume this is the case between me and everybody who disagrees with me on this. But I think there are many people with whom I would be in such a philosophical stalemate if we were to discuss this with each other. I rationalize my co-existence with humans of such thoroughly conflicting perspectives by observing that I am fallible, others are fallible, and life is still a great mystery to all of us. We all have our opinions, but none of us know everything, and in my opinion absolute certainty about anything is beyond the ability of humans to attain.

 

Mysticism, mystical experiences, and mystical revelation

Mysticism has various interpretations and aspects. For the purposes of this post I am concerned with mystical experiences, practices intended to create them, and philosophical ideas that grow up around mystical experiences. Those are the aspects of mysticism that will play a role in this post’s discussion.

Mystical experiences are a variety of subjectively powerful experiences. I won’t try to give a definition of “mystical experience.” For examples of the types of experiences people call mystical, see The Mystical Experience Registry.

My first mystical experience occurred the first time I used LSD. I experienced a form of consciousness which felt so deeply, intensely real that by comparison all my prior experiences seemed unreal. I later learned to reproduce similar states of consciousness at will, through meditation and other mystical disciplines. This immediate and subjectively irrefutable sense of touching on a deeper reality is a hallmark of mystical experiences for me.

Mystical experiences are frequently interpreted in religious, spiritual, or philosophical terms. People who have mystical experiences often take the experiences to reveal to them something about themselves, their lives, and/or the world. For example, here is a quote from the Protestant mystic Jacob Boehme, via The Mystical Experience Registry:

The gate was opened to me that in one quarter of an hour I saw and knew more than if I had been many years together at a university…For I saw and knew the being of all beings…I saw in myself all the three worlds, namely the divine…the dark…and the external and visible world..And I saw and knew the whole working essence, in the evil and the good and the original and the existence of each of them…

Can mystical experiences be taken to reveal reality? I think the answer is that certainly they can, at least to the extent any experiences can be taken to reveal reality. Mystical experiences, to me, provide a raw view of reality, at a higher level of concentration than the level of “ordinary,” sober experiences. For me there is a continuity between mystical experiences and “ordinary,” sober experiences. Mystical experiences, for me, are distinguished by the greatest vividness, the greatest density, the greatest intensity and certainty of awareness, and therefore I assume my mystical experiences to constitute particularly rich subjective views into reality.

Everybody who recalls having mystical experiences has the responsibility, if they choose to accept it, to figure out what if anything the experiences tell them about the world.

I think mystical experiences can appropriately be used as evidence to support philosophical conclusions. However, anybody who lacks the type of mystical experience used to support a conclusion is likely to find this type of argument for the conclusion unpersuasive.

The evidence (if any) which mystical experiences provide for conclusions seldom has much influence on people who did not themselves have the relevant experience(s). If I have a mystical experience A which appears to me to support philosophical conclusion X, and you yourself haven’t had an experience like A, does my report of having such an experience as A provide any evidence, for you, for conclusion X? Maybe so, maybe not. I certainly think you are free to conclude that it doesn’t provide evidence for you.

Can mystical experiences form the evidentiary basis for conclusions which transfer from person to person in a repeatable fashion? I think so. I think it requires that people repeatably be able to obtain mystical experiences which support the conclusions in question. That is, it requires chains of people inspiring each other to reach the same conclusions on the basis of reproducible types of experiences. I believe that religious and spiritual memes are often spread by means of processes much like this. Perhaps the same is true of some philosophical memes.

There is no doubt in my mind that sometimes people reach false conclusions on the basis of mystical experience. I assume it’s possible to find examples where different people have reached different, contradictory conclusions on the basis of mystical experience. This is true, for example, if somebody has had a mystical experience which they took to reveal that the Catholic Church teaches the only true religion of God, and somebody else has had a mystical experience which they took to reveal that Sunni Islam teaches the only true religion of God.

The proposition, that mystical experiences can lead people to false conclusions, does not in my view undermine the idea that mystical experiences can be regarded (along with other experiences) as views into the truth. People are able to misinterpret their experiences and overreach their evidence in all kinds of ways to arrive at false conclusions. I don’t think mystical experiences are any different in this regard, and I think this can explain why people arrive at false conclusions on the basis of mystical experiences.

What is harder to explain is how to tell when a mystical experience can reasonably be assumed to provide evidence for a conclusion. Mystical experiences are subjective. They can’t be adequately described in words. Their meaning can’t be analyzed with the machinery of logic. As such, if mystical experiences convey truth, one might assume that that truth can’t be adequately expressed in words or adequately analyzed with the machinery of logic. I think the Law of One is a truth of this nature; as I’ve interpreted the principle, it defies logic and renders words useless by entailing that every statement is true.

When all is said, whether or not a mystical experience supports a conclusion is going to be a matter of subjective judgment and personal opinion.

 

Verifying the Law of One

I believe the reader might arrive at the conclusion that the Law of One is true by producing and observing appropriate mystical experiences. I have met several people who have reached the same or similar conclusions as mine, inspired by mystical experiences of their own.

The quickest and easiest way you might try to get experiential evidence of the Law of One would be to induce a mystical state of consciousness and reflect on questions like, “who am I?” and “what is all this I am aware of?” and “what is that which is witnessing all this?” Contemplate the possible truth of the equations God = I, You = I, Subject = Object. Picture the universe as a single, indivisible object.

If you don’t know how to induce a mystical state of consciousness, the quickest and easiest way may be to take a hallucinogenic drug, such as (for example) LSD, magic mushrooms, nitrous oxide, DXM, or DMT, with an appropriate set and setting, I would do this exercise when you are alone and in a peaceful frame of mind.

This procedure is not perfect. Our sober selves are not necessarily ready to believe the conclusions of our drug-affected selves, and perhaps that skepticism is warranted. Therefore I offer no warranty of suitability for purpose for the quick and dirty method just described for verifying the Law of One.

I would suggest the following steps to a general individual wishing to embark on a laborious and life-encompassing effort of spiritual growth which I hypothesize will probably lead them to experiences confirming the truth of the Law of One, if it is true and the individual wants the truth of the matter. Following these steps entails a commitment to a life of spiritual growth which trends to color all moments. If you faithfully follow these steps and you do not receive confirmation of the Law of One, nonetheless I would suggest the thought that by faithfully following these steps you can hardly avoid receiving great spiritual, emotional, and intellectual rewards in this life (to say nothing of the afterlife). Therefore I suggest it would not be wasted effort even if you do not find my hypothesis to be true in your case.

  1. Take what steps may be needed to be in good physical fitness, as much as practicable.
  2. Shun dishonesty and immorality. As much as practicable, leave any situations you may be in which compel you to be morally corrupt, dishonest, or immoral.
  3. Lead a well-examined life marked by continual and deep self-scrutiny and moral reflection.
  4. Accept and love yourself, and accept and love those in your life, those in your thoughts, and all of existence.
  5. Continually work towards peace, progress, and higher levels of awareness in all aspects of your life.
  6. With faith and determination, practice meditation, concentration, and the deliberate raising of consciousness. Let this practice integrate ever more deeply and pervasively into your life.
  7. Do whatever things inspire the spirit in you.
  8. Let yourself go through life in a natural and unstudied manner.
  9. Reflect seriously and with single-pointed concentration on questions like:
    1. Who am I?
    2. What is all this that I am aware of?
    3. What is that which is witnessing all this?

Each of the steps 1-8 is a type of preparation which I believe will contribute to success in the spiritual exercise listed as step 9. Step 9 is an activity I hope will bring you to realization of the Law of One, if you are open to the possibility, and if the practice of the exercise is in the context of a path of seeking spiritual truth which encompasses and transforms one’s life and being.

The procedure I’m suggesting eventually requires total commitment of the self. Spiritual growth transforms one’s whole being. If it fails to do so, then I expect spiritual growth to be stopped. Spiritual growth transforms the mind and body, and in time it colors all moments.

The length of time the procedure takes to yield success at realizing the Law of One may vary. Such a realization might happen shortly after starting the procedure; or in a matter of months; or in a matter of years; or perhaps not at all.

Unfortunately I can’t guarantee this procedure will cause you to realize the Law of One. I merely predict that it should typically do so, if you’re genuinely interested in the truth of the matter, and you’re prepared and seeking to experience that truth.

Commitment to spiritual growth and practice led me to mystical consciousness which now colors all my experience. Today, by concentration I am able to reproduce at will the intuitions upon which I believe in the Law of One. For me these intuitions are a readily accessible mental proof of the Law of One. The intuitions are a synthesis of years of mystical and intellectual experience around the Law of One, in which I have questioned the idea intensely and from many angles.

Everybody who replicates these subjective insights will come to them by a different path, and I don’t doubt that different people’s subjective insights will always be subjectively different. My path to these insights has been by a spiritual growth process featuring an approximation of total commitment of the self. As awkward as it may be, I cannot prescribe a procedure for reproducing my conclusion which does not resemble the process I myself followed.

I do believe there are other ways of arriving at the conclusion which require less than whole-being commitment to spiritual growth. People may have mystical experiences spontaneously, and through the use of drugs, and as a consequence of difficult emotions, and from many other causes. A single mystical experience might cause somebody to believe in the Law of One. A more convincing kind of evidence is repeated mystical experiences evidencing the Law of One, and the ability to produce at will the intuitions that motivate the belief. Some people might have that type of evidence naturally.

For some readers, it might not be too hard to follow my steps because they are already following most of them. Such readers may already believe the Law of One. Or, they may be in a good position to try out my proposed exercises in step 9, and see if they obtain insight into the Law of One. They might do all this and conclude that the Law of One is false in one or more of the formulations I’ve mentioned.

I believe that the Law of One is a repeatable mystical insight, because the insight appears to have been repeated again and again in variants throughout history, and I have met several people of diverse histories who have had variants of the insight. I have never come across anybody who put the Law of One into words in just the way I have, interpreting it as logically entailing that every statement is true, but I don’t think that means the fundamental insight is new to me. The source which has given me the greatest philosophical inspiration around the Law of One is The Law of One, also known as the Ra material. This text, even if it is a work of fiction, is to me the greatest and most educational philosophical and psychological work I have experienced.

In all of this I see no way of reproducing the conclusion that the Law of One is true, which I can guarantee will work for anybody. I also see no way of falsifying or refuting the Law of One. I can understand the frustration this may cause Law of One skeptics to feel. I am unsure what comfort I can offer such a person. All I can say is that I’m honestly trying to convey reality as I see it, and I recognize in fairness that I may be in error, but if so I don’t and probably won’t recognize my error.

At the end of the day, those who want to believe the Law of One will believe it, and those who want to reject the Law of One will reject it. Whether the Law of One is true is not a question that has been settled by the scientific method. From my current perspective, it is a spiritual and philosophical question, to be decided by individuals, who will base their conclusions on subjective feelings at the end of the day.

I am curious to hear about anybody’s thoughts and experiences around the Law of One and/or mystical revelation.

 

An argument for the Law of One

The rest of this post provides another way of reaching the conclusion that the Law of One is true, by logical analysis and philosophical argumentation instead of by mysticism. The argument I’ll give does not force the reader to accept its conclusion. There are other alternative conclusions the reader can draw. I will present such alternative conclusions. I am not sure how many people will find this philosophical argument for the Law of One compelling in the absence of mystical experience of the Law of One.

I am interested to hear about your reaction to the following argument. I don’t know what to expect people to think about it.

The following argument for the Law of One can alternately be viewed as an explanation of why logical paradoxes happen.

In a nutshell, the perspective of the argument/explanation states: paradoxes allow us to prove the Law of One, and the Law of One explains why we observe paradoxes.

Explaining this requires some background on logic. Here I will present this in simplistic broad strokes. More detail can be found starting from the companion post, Paradoxes and the rules of logic.

 

Background on logic

A “statement” is a piece of language which can be true or false.

An “argument” consists of a series of statements, called premises, intended to support or provide evidence for another statement, the conclusion of the argument.

A “valid” argument is an argument such that it is logically necessary that if its premises are true, then its conclusion is true.

A central question in logic is: what arguments are valid?

The orthodox answer to this question is called classical logic. Classical logic is a species of rules for logic, which allows a wide class of ordinary language and formal language arguments to be analyzed as valid or not.

There are other species of rules for logic, which differently answer the question of what arguments are valid. These are so-called “non-classical logics.” For most non-classical logics, the set of arguments they deem valid is a subset of the set of arguments classical logic deems valid.

Classical logic has a consequence known as the principle of explosion. This is the fact that according to classical logic, from a contradictory set of premises one may validly infer any conclusion.

A contradiction is a statement of the form “P and not P.” For example, “I am alive and I am not alive.” According to classical logic, if a set of premises entails a contradiction, then those premises entail any statement. From the premise “I am alive and not alive,” classical logic says I can infer “the sky is purple.”

The orthodox understanding of this phenomenon is that contradictions cannot ever be true, and so if a set of premises entails a contradiction, then some of those premises are false. Given false premises, logic allows you to infer false conclusions. Garbage in, garbage out.

 

Logical paradoxes

Committing oneself to classical logic and the orthodox understanding of the principle of explosion leads to challenges in dealing with logical paradoxes.

Here is a logical paradox. Consider the statement “this statement is false.” Is it true or false? If it’s true, then it’s false. If it’s false, then it’s false that it’s false, so it’s true. Classical logic says the statement is either true or false, and therefore it’s both true and false, and therefore every statement is true. This argument can be called the liar paradox.

This is a stunningly short argument for the conclusion that every statement is true, phrased in simple English, predicated on the background assumption that classical logic, as straightforwardly applied to English, is correct.

This argument might be taken as demonstrating that something about the background assumptions is wrong. This is the usual way of looking at things in the academic literature I’ve seen. One can say that classical logic is not correct, or that classical logic can’t be straightforwardly applied to English (but perhaps it can be cleverly applied to English in a way that deals with paradoxes).

In Paradoxes and the rules of logic I gave a refinement of the background assumptions which tries to use as little cleverness as possible. In short, I said that we should view the rules of classical logic not as being totally exceptionless, but as having occasional exceptions, in particular in the vicinity of paradoxes. I said these paradox-avoiding exceptions could safely be produced in an ad hoc manner, whenever one encounters contradiction-producing paradoxes such as the liar paradox.

 

Logical paradoxes as proofs of the Law of One

Now I wish to put forward a different way of looking at the meaning of the liar paradox. This is to view the liar paradox as proving that everything is true.

If the Law of One is true, in the extreme formulation which says that any two distinct things are identical, then everything is true. This conditional statement can be reached by a variety of arguments. Here is one. Suppose the Law of One is true. Let A be any statement. Let B be some true statement, e.g., “water contains hydrogen.” By the Law of One, A and B are the same thing. Since B is true, A is true. In other words, every statement is true.

The Law of One (in its logically extreme formulation), and the proposition that every statement is true, are logically interchangeable propositions, in the sense that each entails the other.

Belief in the Law of One, and belief in the liar paradox as a valid argument to the conclusion that every statement is true, cohere with each other. They provide two different routes (one mystical-logical and one purely logical) towards the conclusion that everything is true.

However, if one accepts every statement as true in every context, then it defeats the purpose of language. Statements are part of language. Language exists to serve life. Life has experiences of separateness and partiality. If separateness is an illusion, still it is an inescapable illusion for us.

Any notion of achieving a purpose supposes that there is something which now is not and later could be. Therefore all purposeful action supposes a lack of belief in the necessary future actual existence of some state of affairs.

For those reasons, one can’t always accept the perspective that everything is true. In some contexts, such as contexts where one is trying to achieve some purpose in the material world, it is appropriate not to assume that everything is true, but to assume that for the purposes at hand, only some things are true.

It is in such contexts — including most contexts — that I apply the perspective of Paradoxes and the rules of logic, according to which I reject the arbitrary statements that can be inferred from paradoxes, to retain a context where not everything is considered true.

It is in meditation that I apply the perspective that all is one and everything is true.

The energy of the thought of the unity of all things colors and enlivens my life from moment to moment.

 

Theoretical options

That concludes my explanation of the perspective that logical paradoxes allow us to prove the Law of One, and the Law of One explains why we observe logical paradoxes.

There are many ways to look at the situation other than the one presented here. You can reject the Law of One. You can accept some way of looking at paradoxes that doesn’t involve assuming everything is true. You can ignore the issue of paradoxes.

I don’t claim to be proving this perspective. I’m offering this perspective for consideration. It appears to me to be the most elegant solution I’ve seen for solving and explaining paradoxes. It appears to me to be a successful theoretical integration of mystical intuitions which are very powerful in me, with a logical system of thought which appeared hard to reconcile with those intuitions. This perspective appears to me to be true to the best of my ability to discern truth, but that judgment is subjective.

The perspective of Paradoxes and the rules of logic, with its ad hoc method of rejecting contradictions, is free-standing from the perspective of this post. You can accept that post’s theory without accepting this post’s theory. I think that by taking that route you lose an intuitively grounded story about why we observe paradoxes.

Personally, I favor the perspective of this post because of my mystical intuitions. For me this whole investigation into paradoxes and logic has been motivated by the desire to better understand the Law of One and how it can be reconciled with logic. I have figured out to my own satisfaction how to reconcile the Law of One with logic. Are you satisfied?

I consider this project to have value from a mystical perspective, for bolstering the analytic philosophical defensibility of nondualism. I doubt if my reasoning will convert any skeptics who firmly don’t want to believe in mysticism, but I hope it will provide inspiration and clarity to people who perceive truth in nondualism.

 

Mystical arrogance and chauvinism

To my mind, there is one objection to the perspective I’ve laid out which is the biggest and stickiest. This perspective asserts the primacy of mystical consciousness — the distinctive consciousness which mystics are supposed to experience — as the best source of fundamental metaphysical truth available to humans. This can be viewed as chauvinist and arrogant.

Ayn Rand lays out the objection in the final chapter of Introduction to Objectivist Epistemology:

In the history of philosophy — with some very rare exceptions — epistemological theories have consisted of attempts to escape one or the other of the two fundamental questions which cannot be escaped. Men have been taught either that knowledge is impossible (skepticism) or that it is available without effort (mysticism). These two positions appear to be antagonists, but are, in fact, two variants on the same theme, two sides of the same fraudulent coin: the attempt to escape the responsibility of rational cognition and the absolutism of reality — the attempt to assert the primacy of consciousness over existence.

How do I respond to this objection?

It’s everybody’s choice how they regard mysticism, and how they regard the mystical philosophy I’ve shared in particular. People can choose to perceive the Law of One as true, or to perceive it as untrue. Those who don’t believe in mysticism are free to choose to view mystical philosophy as chauvinist and arrogant. Of course I may feel discouraged if people make this choice, but I don’t begrudge them their freedom.

Do I view mystical philosophy as at all chauvinist or arrogant? I think it easily can be. Perhaps it is always at least a little bit of each.

I have tried to minimize the arrogance and chauvinism of my mystical philosophy. I have spent the past seven years thinking about what I believe on the topic. I have tried to avoid arrogantly rushing to a conclusion. I am an ideologue without a doubt, but I have tried my best to be a stable, reasonable ideologue. I have sincerely and seriously tried to minimize the arrogance and chauvinism of my philosophy. I could have done more, by abandoning mysticism, but that’s not the choice I made. My success is yours to judge.

 

Closing song

My belief in nondualism is fundamentally based on experience, on a type of feeling which feels like evidence. In another attempt to communicate this species of feeling, I want to point the reader to a song which to me conveys the sense of nondualism, in hopes the reader finds a similar perspective on the song.

The song is Joni Mitchell’s “Both Sides Now.” I myself prefer Carly Rae Jepsen’s cover version. Here are the lyrics.

Please enjoy the mystery of existence, and share your thoughts in the comments!

Rothschild trillions

Here’s a simplistic technique for estimating the wealth of the Rothschild family, or for estimating the long term growth in value of any well-managed, diversified investment portfolio. Applying this technique, I suggest that the Rothschild family’s present day wealth is most likely equivalent to trillions of British pounds, and possibly as much as hundreds of trillions of British pounds.

I learned about the rather impressive results of applying this estimation technique to the Rothschilds through SGT Report. Credit for the featured image of Waddeson Manor, above, goes to Colin Park.

Throughout I will use the example of the Rothschilds, but more generally, I’m describing a modeling strategy. This modeling strategy can be used as a general rule of thumb to approximate the growth in value of a diversified, well-managed investment portfolio over a long period of time. Looking at historical performance of such portfolios illustrates that the rule of thumb is often true to some approximation. For an example, take a look at the Growth of 10K charts for American Funds Mutual Funds (for example, AMCAP Fund).

The modeling technique I’m describing starts from a conservative estimate of Rothschild wealth at some point in the past. It assumes that we can reasonably model the change in Rothschild wealth over time by applying a compound interest calculation to the initial wealth estimate.

The model depends on the following parameters: initial wealth date, initial wealth amount, present date, interest rate, and compounding frequency.

For example, let’s choose an initial wealth date of 1815, when Nathan Meyer Rothschild lent 9.8 million pounds to the British government, according to Wikipedia. Let’s choose as our present date, 2018.

Let’s choose an initial wealth amount of, say, 30 million pounds. This conservative estimate assumes that in 1815, Nathan Meyer Rothschild lent a third of the Rothschild family wealth to the British government and its allies. In my opinion, this number greatly underestimates the Rothschild family wealth in 1815. At that time they were an established banking family operating in multiple countries. I would guess they did not lend a third of their family wealth to the British and their allies to fund a war effort. In short:

All of these estimates are low-balling the initial wealth amount. Maybe by a factor of 10 or more.

Working off of the given initial wealth date and initial wealth amount, we can see what estimates the model gives for present day Rothschild wealth, for different values of the two remaining parameters. The two remaining parameters are interest rate and compounding frequency.

You can try out different parameters using a compound interest calculator. Here’s an example calculation:

Compound Interest Calculator(1)

 

In this example we’re assuming the following parameter values:

initial wealth date = 1815

initial wealth amount = 30 million British pounds (equivalent to, 1815 value)

present date = 2018

interest rate = 7%

compounding frequency = 1 per year

 

With these parameters, the model estimates present day Rothschild family wealth as being equivalent to 27 trillion British pounds (2018 value).

The model assumes we can approximate the change in Rothschild family wealth over time by an exponential curve. This curve models the growth of an investment where the investor is receiving compound interest payments and reinvesting their income. This graph shows the curve at various compounding frequencies, assuming a 20% interest rate and a time period of 10 years:

800px-Compound_Interest_with_Varying_Frequencies.svg

This type of model can’t possibly be a perfectly accurate model of the change of the value of a diversified investment portfolio over time. We can assume the Rothschilds have made many investments, which have yielded varying returns. We can assume the Rothschilds have also had expenses, and that they have incurred losses from investments.

The model relies on the hypothesis that the long term changes in the wealth of an old banking family such as the Rothschilds can be modeled reasonably well by one compound interest curve. The hypothesis is that this curve will capture the long term trend of their changes in wealth well enough to provide meaningful and interesting estimates of present day Rothschild wealth.

The hypothesis says, in other words, that if we blur out the complexity of numerous investments with varying returns and losses, and if we factor in expenses, the long term trend of Rothschild wealth change looks a lot like a compound interest curve.

I consider this to be a reasonable hypothesis. It can’t be proven or falsified without access to Rothschild financial records. I think it’s a reasonable hypothesis because the Rothschilds’ situation can be compared to the situation of an investment portfolio manager. A well-managed, diversified investment portfolio will tend to blur out various gains and losses to get something resembling a distorted compound interest curve. I am speaking from my experience working in the investment industry. You can decide for yourself how reasonable you think the hypothesis is. I previously pointed out the American Funds Individual Investments Web site, particularly the Growth of 10K charts for the funds, as a place where you can look at historical changes in some investment portfolios.

Let’s look at what the model gives us for our chosen initial wealth date (1815) and initial wealth amount (30 million British pounds), with varying interest rates and compounding frequencies.

 

10% compounded annually => over 7 quadrillion pounds

8% compounded annually => over 182 trillion pounds

7% compounded annually => over 27 trillion pounds

6% compounded annually => over 4 trillion pounds

5% compounded annually => over 600 billion pounds

4% compounded annually => over 86 billion pounds

 

From these examples you can see that over 203 years, the final result of the calculation is highly sensitive to small changes in the interest rate. An interest rate of 10% provides a model that is very hard to believe, which I would estimate is not accurate. I would estimate that 5% or lower is likely too small to provide a realistic model, because even publicly available mutual funds have historically been able to provide better returns, and without doubt, far better investment opportunities are available to the Rothschilds than to the average small time investor. In addition, we can assume that investors with the wealth and influence of the Rothschilds have access to more and better information than the average investor. Probably they can even influence markets to move in their favor in many cases, especially if they collude with other large investors to do so. In my opinion, interest rates around 5% through 8% provide the most conservative models which are likely to be realistic, after accounting for waste, losses, and expenses.

 

Now let’s look at the effect of changing the rate of compounding.

 

6% compounded annually => over 4 trillion pounds

6% compounded twice annually => over 4 trillion pounds

6% compounded 12 times annually => over 5 trillion pounds

 

8% compounded annually => over 182 trillion pounds

8% compounded twice annually => over 246 trillion pounds

8% compounded 12 times annually => over 321 trillion pounds

 

As these examples illustrate, the final result is not as sensitive to the rate of compounding as it is to the interest rate, but the sensitivity of the result to the rate of compounding appears to increase as you increase the interest rate.

Without access to Rothschild financial records, we don’t know which of these models is most accurate. I’ve hypothesized the models are most likely accurate which assume the Rothschilds had wealth equivalent to at least 30 million British pounds in 1815, and which have interest rates around 5% through 8%. According to most of these models, the Rothschilds presently hold wealth equivalent to trillions of British pounds, and possibly hundreds of trillions of British pounds.

These models make the Rothschild family out to be richer than Jeff Bezos, who is widely reported as the world’s richest man in 2017, with a net worth around $100 billion USD. There is some logic to the idea that a centuries old banking family, with the opportunity to accumulate immense intergenerational wealth, which centuries ago was wealthier than the British government, might today be wealthier than a man who amassed paper wealth through a couple decades of running a successful business.

One reason these models might overestimate Rothschild returns is that it may be that when you have as much money as the Rothschilds do, it’s hard to find enough good investment opportunities to generate good returns on most of that money. Large investment organizations like BlackRock and Capital Group are able to generate good returns on quite large amounts of money; for example, BlackRock manages $5.7 trillion of assets. As another example, the stock market itself generates overall good returns over time for its whole body of investors. Still, if a group controls an amount of money that rivals or exceeds the total volume of global economic activity, then they may well run out of investment opportunities, and the compounding effects of that lack of opportunity would have a large negative impact on their wealth growth, compared to a situation where they don’t lack a sufficient number of good investment opportunities. Shortage of opportunity may well be a limiting factor in Rothschild wealth growth. This consideration suggests against the higher estimates of Rothschild wealth, such as those in the quadrillions of dollars.

I’ve estimated that the Rothschilds have wealth equivalent to trillions of British pounds, and maybe even hundreds of trillions. Personally, I find these estimates of Rothschild wealth to be staggering. I am not certain that they are at all accurate. It’s possible that these models significantly underestimate expenses, poor management, loss, and waste in the Rothschild family finances, so that actually the Rothschilds are far less rich than the models predict. I have tried to present the most honest and clear-eyed estimates that I can. I rather hope the Rothschilds are not as financially successful as I’m guessing they are.

A final observation about elite banking family wealth is that some of those in the financial elite have control over the central banks and banks which create most of the world’s money supply through issuing debt. As the website Illuminati Official says, “Money means nothing to those who print it.” You can form your own opinion as to whether Illuminati Official is the official website of the real Illuminati, or whether it’s a work of fiction. I have no opinion on that question; I don’t feel I have decisive evidence one way or the other. I do think it’s fair to say that those who can create money are unlikely to be wanting for money.

Space aliens have visited Earth

The photo above is copyright Hannah McRoberts and has been analyzed by Richard Haines. Source: Sirius Disclosure Project.

The evidence that space aliens have visited Earth is overwhelming. All of the evidence available to the general public is indirect, and like all indirect evidence, it is subject to uncertainty and to multiple interpretations. However, the indirect evidence is of high quantity and sometimes of high quality, such that it is very improbable that space aliens have never visited Earth. I would be amazed if the evidence for ETs visiting Earth is all correctly interpreted as being something else.

Space aliens are more formally called extraterrestrials, or ETs for short. When I say that space aliens have visited Earth, I mean that ETs have, in the recent past, flown space vehicles in Earth’s atmosphere. I will refer to this possibility as “ET visitation,” for short.

Undoubtedly there is a lot of misinformation and fabrication on the subject of ET visitation. I would not be surprised if most of the available information about ET visitation is false. I assume people often pass around false rumors about ET visitation, and that the causes of these false rumors include unintentional errors in conveying and interpreting information, and also intentional deception.

On the other hand, some of the information about ET visitation seems to have a high degree of credibility, and after studying this evidence with an open mind, it is difficult to deny that there is a very high probability that some of it is a result of ET visitation.

Here’s one bit of evidence. It’s not conclusive by itself. Let’s take it as an appetizer and spend some time analyzing it. The analysis will lead to some conclusions about this piece of evidence, and those conclusions can basically be generalized to all of the evidence.

Jimmy Carter believed in UFOs. He claimed to have seen one. During his campaign to be President of the United States, he promised to disclose everything the US government knew about UFOs. After becoming President, he walked back that promise, citing “defense implications.”

Supporting those claims, Wikipedia says (Aug 30 2017):

During his 1976 election campaign, he is said to have told reporters that, as a result of it, he would institute a policy of openness if he were elected to office, saying:

One thing’s for sure, I’ll never make fun of people who say they’ve seen unidentified objects in the sky. If I become President, I’ll make every piece of information this country has about UFO sightings available to the public and the scientists.[7]

Despite his earlier pledge, once elected, Carter distanced himself from disclosure, citing “defense implications” as being behind his decision.[8]

[7] Good, Timothy (1989) “Above Top Secret: The Worldwide U.F.O. Cover-Up” Quill, ISBN 0-688-09202-0

[8] This day in history – “1973: Carter files report on UFO sighting”, The History Channel

Why would there be defense implications in revealing classified information about UFOs if there was nothing exciting going on with any UFOs?

Is this story about Jimmy Carter conclusive evidence of ET visitation? Not at all. There are a variety of ways of interpreting this evidence which don’t involve postulating ET visitation.

Maybe Jimmy Carter lied when he said there were defense implications in revealing UFO information.

Maybe the facts about Jimmy Carter which I have cited are not true.

Maybe there were defense implications to revealing UFO information because many UFOs were secret government military craft, and revealing all information about UFOs would entail revealing the existence of these secret defense projects.

As I’ve just shown, there is plenty of room for uncertainty about what the cited facts about Jimmy Carter mean. Carter’s comments are open to the interpretation that the US government was aware of ET visitation and keeping it secret; but they are also open to other interpretations. As an isolated piece of information, Carter’s comments are not conclusive evidence of ET visitation.

Carter’s comments are more interesting in the context of the broader picture of the available information about ET visitation. I will paint a version of this picture which I believe. After that I will survey some sources supporting the narrative.

  • There have been cases where ETs visited Earth.
  • The US government and other governments became aware of such cases.
  • The US government and other governments concealed ET visitation from the public.

Let’s get into more evidence. Here are a few more quotes from famous individuals on the subjects of UFOs and ET visitation:

Of course the flying saucers are real, and they are interplanetary.

– Air Chief Marshal Lord Dowding; Head of Royal Air Force during World War II. Quoted in Reuters, August 1954. Sources: Unacknowledged by Steven Greer, Adamski Foundation.

I am convinced that these objects do exist and that they are not manufactured by any nations on earth.

– Air Chief Marshal Lord Dowding. Source: The Telegraph.

My theory is that we have, indeed, been contacted — perhaps even visited — by extraterrestrial beings, and that the U.S. Government, in collusion with other national powers of the Earth, is determined to keep this information from the general public.

– Victor Marchetti, former Special Assistant to the Executive Director of the CIA. Sources: Unacknowledged by Steven Greer, DeclassifiedDocuments.com.

Note: The version of the quote in Unacknowledged does not include the phrase “my theory is.”

“Behind the scenes, high-ranking Air Force officers are soberly concerned about the UFO’s.”

“To hide the facts, the Air Force has silenced its personnel.”

– Roscoe Hillenkoetter, former CIA director

Source: The New York Times, via WantToKnow.info.

Somebody I know personally, through my profession, has told me that she has seen UFOs. She described two occasions. On one occasion, she says, she saw a flying saucer so close up that she could see the windows. On one occasion, she says, she saw a UFO through her bedroom window, so close up that it filled up her whole view of the sky. I am not disclosing the identity of this person. Hearing her story helped me to believe the narrative I’m painting, because it gave me evidence beyond words and pictures on the Internet to. As usual, her claims are not conclusive evidence of anything, and I don’t expect the reader to take them as such.

The Sirius Disclosure Project by Dr. Steven Greer is the best compilation I’ve found of evidence for the narrative I’m painting. It includes, among other evidence:

  • Video of testimony from many people who worked for governments, especially the US government, who claim to have witnessed evidence of ET visitation, with varying degrees of directness, in the course of their duties.
  • Video and photographic evidence of UFOs.
  • Government documents containing evidence of UFOs.
  • Information about the Atacama Humanoid, a strange dead body claimed to be that of an ET.
  • Documentation of an initiative Greer calls CE-5, with the goal of making peaceful contact with ETs. Greer and others have claimed to have received direct evidence of ET visitation by following the CE-5 protocols he formulated.

Here is an example of somebody claiming that the Disclosure Project’s CE-5 protocols helped them to have a UFO sighting. This is a review of the Disclosure Project’s ET Contact Tool app in the Google Play store. This was not the only review of its kind.

Steven Wentworth

5 Stars 10/7/16

It works!

We used Steven Greer’s meditation last night and what we saw none of us can explain. After seeing approx 8 small lights (could have been satellites but changed direction) a very bright circular one descended over us. It was the brightest object in the sky. It moved slowly over us getting brighter before ascending again. Military helicopters even came to check it out too! Can’t wait for next time.

I’ve personally seen two UFOs which I am unable to explain as being any conventional, well-known type of thing.

  1. I was staring at the night sky. Over the course of less than a second, a dot of light popped into my field of vision, rotated in a perfect circle, and popped out of my field of vision.
  2. I was staring at the sunlit sky. I started to see a bright oval of light in the sky. I was amazed by it and wondering what it could be. I thought that, as a conventional explanation, it could be a cloud with sunlight reflecting off it. Shortly after I thought that, the oval disappeared suddenly and completely. To my mind that ruled out the cloud explanation.

From the standpoint of a reader, any of the evidence I’ve cited could be fabricated, hallucinated, misinformed, or otherwise misleading.

I have already pointed out one place where Greer is a little misleading: he omits “my theory is” from the Marchetti quote above. I would say this omission significantly changes the meaning of the quote, and it creates some concerns for me about Greer’s degree of scholarly rigor in interpreting his data.

Edgar Mitchell, one of the Apollo astronauts, has claimed that Steven Greer “began to overreach his data continuously.” and that the Disclosure Project makes “certain claims that simply are not true.” In Unacknowledged, Greer writes, “when the lunar module landed, the rim of the crater was crowded with ETVs (extraterrestrial vehicles).” Mitchell denies seeing “anything in space suggesting UFOs or structures on the moon, etc.” He says “we did it just like we said in the official reports.” So Mitchell can be interpreted as saying that Greer is wrong in saying the Apollo lunar module encountered ET vehicles.

I lend credence to this interpretation of Mitchell, and I accept the likely possibility that Greer is wrong in saying the Apollo lunar module encountered ET vehicles. On the other hand, I also accept the possibility that Greer is correct in making the stated claim, and that Mitchell is lying, possibly because he has been threatened by people in the government. There are other possibilities, such as that the source linked in the last paragraph is fake, and Ed Mitchell never made the quoted statements.

Though Mitchell asserts (in the source linked above from rense.com) that the Disclosure Project is wrong about some things, he asserts in Disclosure Project material that “there have been ET visitations,” and he confirms this belief in the source from rense.com.

Let’s look at more possible examples of inaccuracies in the Disclosure Project.

For a possible example, in the book Unacknowledged, Steven Greer quotes William Colby (a former CIA Director) as saying “The CIA owns everyone of any significance in the major media,” but it has been argued that this quote is made up. As the linked page at metabunk.org notes, William Colby has commented about the CIA’s infiltration of the U.S. mainstream media. though he may have never made that specific statement.

I’m not saying that William Colby definitely did not make the statement Greer quotes him as making. However, the quote does not appear to be well-sourced and may be made up. This is an example of a case where we may doubt the accuracy of Steven Greer’s research.

For another example, it has been argued that the Atacama Humanoid is a human fetus, whereas the Disclosure Project argues that that explanation does not hold much water, citing for example that “the specimen has only 10 ribs, a finding not yet found in humans.” I’ll leave you to decide whose argument is more persuasive here: the UFO/conspiracy theorist’s or the debunker’s.

The Disclosure Project’s witness testimonies are generally credible in terms of who the people claim to be and how they claim to have come across evidence of ET visitation. They include testimonies from people known to the general public.

A good example is Paul Hellyer, a politician who held the positions of Defence Minister and Senior Minister in the Canadian national government.

Paul Hellyer does not claim to have personally had contact with ETs, but Hellyer argues that he has validated the narrative above (and more) on the basis of sources he has seen, his personal background knowledge, and his connections. He has argued this in multiple interviews, and multiple books.

Hellyer cites The Day After Roswell, by William J. Birnes and Lt. Col. Philip Corso, as a source which persuaded him of the truth of ET visitation. Hellyer says he confirmed with the retired United States Air Force general Philip Corso that the claims in the book were true.

What should we make of the Disclosure Project’s video and photographic evidence? It includes photos and videos that don’t look like any usual kind of thing, and look like they could be ETs or ET vehicles.

Video and photographic evidence, generally speaking, can be fabricated in various ways. I am not sure how to tell the difference between accurate and forged photos and videos. Even if a photo or video is accurate, it can still be difficult to determine what it is.

Please comment if you have expertise in the area of photo and video analysis and you’ve applied it to evidence such as that available from the Sirius Disclosure Project, or if you’re aware of research of this type that’s worth looking at. It would be especially interesting if you can provide explanation of the methods of arriving at such conclusions.

At the top of the post is linked an analysis by Richard Haines of one photo sourced by the Sirius Disclosure Project.

The people involved in the Sirius Disclosure Project may possibly have ulterior motives. I believe that in all probability, their primary motives are sharing truth. However, it is possible that the Disclosure Project is a money-making operation based on fabricated evidence, and it is possible that witnesses are motivated by attention-seeking, getting paid, etc. I don’t expect these possibilities are the case, but these are possibilities not strictly ruled out by the evidence I have.

Steven Greer, the leader of the Sirius Diclosure Project, claims to have sustained economic losses by undertaking the project, by giving up a lucrative career as a doctor to work on the project full time, and spending his own money on the project.

Some have called into question Steven Greer’s motives by speculating that he is working with people who are trying to suppress information about ET visitation and related secrets. According to this conspiracy theory, Greer is an operative who is working to control information about ET visitation by exposing some things and not exposing other things which are more critical to hide from the perspective of those who are in control. I do not believe this conspiracy theory, but I acknowledge it is possible.

My belief in ET visitation is not, at the end of the day, based on the assumption that Steven Greer’s sole motives are sharing truth.

The kind of evidence the Sirius Disclosure Project has is not available exclusively through that project. The broad claims of the Sirius Disclosure Project are corroborated by other numerous other sources. To name a handful of others:

  • Paul Hellyer;
  • UFO researcher Grant Cameron;
  • Government whistle-blower William Tompkins;
  • the book The Secret History of Extraterrestrials: Advanced Technology and the Coming New Race by Len Kasten, which was source endorsed by Paul Hellyer in The Money Mafia;
  • the book The UFO Experience: A Scientific Inquiry by J. Allen Hynek. Hynek was a scientist paid by the U.S. Air Force to study the UFO phenomenon.

There is a huge amount of information out there on the subject of ET visitation. It isn’t all true. Therefore researching the topic requires a curious, patient, cautious and skeptical attitude. I have pointed the reader to a relatively small number of sources that I find credible to some important extent.

I am not myself an expert on the literature on ET visitation. I haven’t looked at most of it. I have merely selected out for this post a comparatively small fraction of evidence which, taken together, I find compelling.

Steven Greer, in the Disclosure Project, has provided an extensive body of evidence for ET visitation. Paul Hellyer is a well-known and credible person who corroborates the claim of ET visitation, based on separate evidence which he collected and studied. Other individuals I have quoted corroborate the narrative as well: Apollo astronaut Edgar Mitchell, Air Chief Marshall Lord Downing, Jimmy Carter, Victor Marchetti of the CIA, and CIA Director Roscoe Hillenkoetter.

The evidence I’ve pointed to is ambiguous and uncertain. What was really behind Jimmy Carter’s comments? Is the Sirius Disclosure Project mostly true information, or is Sirius Disclosure a fake news operation motivated by money or power politics? What about Paul Hellyer? Is he misinformed or correct in his opinions? And so on and so forth. One may question the credibility of every source I’ve put forward.

I could add more evidence to the pile, but basically it would all have the same ambiguities and uncertainties that are present in the evidence that’s already on the table. I’m going to assume I’ve put enough evidence on the table to support my argument. The question, which every reader can answer for themselves, is whether this evidence is sufficient, considering the degrees of uncertainty present in it.

What makes the evidence convincing for me, despite the uncertainties, is the following philosophical reflections.

What we have in essence are a large number of signals appearing to convey the message, ETs have visited Earth. Strictly speaking, we don’t know where the signals came from. There are multiple possible explanations of how the signals reached us. If ET visitation has not occurred, then all the messages testifying to ET visitation are misrepresentations. If some are not misrepresentations, then ET visitation has occurred. How probable is it that none of the signals which appear to be indicative of ET visitation are in fact consequences of ET visitation?

These signals are indirect evidence. All indirect evidence is subject in some way to the kinds of uncertainties I’ve pointed to in interpreting the ET visitation evidence on the table.

It is true as an exceptionless rule that there are multiple different possibilities consistent with a finite set of observations. No matter how much information you have, there are multiple different ways the world could be that are consistent with your information.

In the case of indirect evidence such as testimonies and reports, there are always sources of uncertainty resulting from the indirectness.

Even so called direct evidence of one’s own senses is only trustworthy to the extent one can trust one’s perceptions. Hallucinations occur. To use perceptions as evidence one needs to recall them through memory, but memory is fallible, and it is possible to have memories of things that did not happen. The trustworthiness of one’s own sensory perceptions is not absolute.

If I personally talked with an ET, then I would be more confident than I am that ET contact with humans has occurred. There would be fewer degrees of uncertainty in the evidence on which I base that conclusion. And, evaluating the evidence would be much simpler.

Evaluating the ET evidence which I have put on the table requires processing a lot of information and then trying to look at it holistically to form an overall judgment about what can be concluded from it.

Each piece of information is subject to sources of uncertainty. The question is, how likely is it that at least some of the evidence is a consequence of real ET visitation? As said, my judgment is that it’s highly likely. In other words, it’s highly unlikely that all of the available evidence for ET visitation is fabricated, misinformed, or otherwise fake.

In general I am happy to accept that things occurred on the basis of much less evidence than what I have for the proposition that ET visitation occurred. Usually, to believe that something occurred I just need to hear a report or two of it.

In the case of ET visitation, I have seen reports from numerous sources of apparent character and distinction, and I have seen a variety of other evidence.

Extraordinary claims require extraordinary evidence. The claim that ETs have visited Earth is extraordinary, and the evidence for it is extraordinary.

It’s your responsibility, if you choose to accept it, to decide what you think. Let me know what you think in the comments, if you want.

You believe in conspiracy theories

I’m a conspiracy theorist. What is a conspiracy theorist? Is it good or bad to be a conspiracy theorist?

Here are some definitions, one from Google and the others from me:

  1. conspiracy is a secret plan by a group to do something unlawful or harmful. (Google)
  2. conspiracy theory is any hypothesis or theory which postulates the existence of a conspiracy.
  3. conspiracy theorist is one who studies conspiracy theories and who believes that conspiracies exist.

Do conspiracies exist? Yes. The Holocaust, the mass imprisonment and killing of undesirable people by the Nazis in WWII, is an example of a conspiracy. The Holocaust was a secret operation, but the defeat of the Nazis blew the lid off the secrecy.

If you believe the Holocaust didn’t happen, then you still believe in conspiracies, because you believe there is a massive conspiracy to fabricate the Holocaust.

If you’re not sure whether the Holocaust happened, then you can still see by logic that either the Holocaust happened, or there was a massive conspiracy to fabricate the Holocaust, and therefore one conspiracy or the other happened.

So in any case, you, the reader, believe there has existed at least one massive conspiracy in the history of the world.

“The Holocaust happened” is a conspiracy theory. It’s a theory which postulates a conspiracy. If you’ve studied the Holocaust, then you’ve done conspiracy theory (at least a little bit of it).

In at least a small sense, you, the reader, are a conspiracy theorist. You’re a conspiracy theorist in the sense that you’ve studied and believe in the Holocaust — unless you doubt the official story of the Holocaust, in which case you’re a conspiracy theorist for that.

The only readers who might not be conspiracy theorists are any readers who have never studied the Holocaust. In that case, you’ve taken an interestingly unique path of education, and you should go learn about the Holocaust, because it teaches some important lessons about humanity.

Basically, then, anybody reading this is a conspiracy theorist, at least to a small extent.

Is it good or bad to be a conspiracy theorist?

Studying true conspiracies is good if you believe the truth is generally good for us.

Studying untrue (non-real) conspiracies is basically a waste of time. It can be entertaining and/or a good learning experience. It can also cause a lot of unnecessary fear, anger, and sense of alienation.

Unfortunately, to tell whether a conspiracy theory is true or not, you have to study it.

Most people choose not to gamble their time on learning about conspiracy theories that might or might not be true. However, some conspiracy theories are true. Conspiracies really occur, and they can have major consequences for society and individuals. So it’s important that people are looking into conspiracies.

Being a conspiracy theorist can be good or bad, depending on what kind of impact it has on you and the people around you. Being a conspiracy theorist has good and bad consequences.

Personally, I value learning about conspiracies. I value the truth, and I have taken it upon myself to try to figure out what’s going on, to the extent that my resources and competing priorities allow. I believe that conspiracy theories are important to study if you aspire to some approximation of an accurate big picture of what’s going on on Earth right now. I think there are probably very interesting conspiracies out there whose existence is not accepted by mainstream thinking.

Scientific materialism is arrogant and laughable (or vacuous)

Scientific materialism, more accurately called metaphysical naturalism, “is a philosophical worldview, which holds that there is nothing but natural elements, principles, and relations of the kind studied by the natural sciences.” (Quoted from Wikipedia.)

I will henceforth use materialism as a shorthand for scientific materialism, i.e. metaphysical naturalism.

In other words, materialists hold that the world is the elements, principles, and relations posited by science. By “the world,” I mean everything that exists. Elements may include things such as electrons and stars. Principles may include laws such as the law of gravity. Relations may include, for example, the relation of gravitational attraction between the Earth and the Moon.

Different materialists differ about what elements, principles and relations are real and constitute the world. For example, some materialists say that the only elements that really exist are the smallest elements, such as subatomic particles. Other materialists say that macroscopic objects, such as chairs and giraffes, also exist.

Here is a dilemma for materialists. Are the elements, principles, and relations which constitute the world, those of today’s science, or those of a hypothetical future science?

If you think the world is the elements, principles, and relations of today’s science, then you think our current understanding of the universe is very close to finalized. That’s arrogant to assume. I find it laughable to assume that.

The history of science has been characterized by periodic “revolutions,” where established theories are found to be wrong in some cases or are otherwise overturned. If not arrogance, why assume that revolutions in fundamental science are basically in the rear-view mirror for humans today?

Fundamental science is not even one coherent idea today. Physicists use conflicting paradigms which they have trouble reconciling with each other: in particular, quantum physics and relativity. If you think today’s science describes reality, what is today’s science? What are the elements and relations that exist in the universe according to physics? What principles apply to them? To the best of my understanding, physicists don’t agree to any one theory answering these questions over all scenarios.

Suppose, on the other hand, that you’re a materialist and you think the world is the elements, principles, and relations of some hypothetical completed science of the future.

How far in the future do you suppose the theoretical fundamentals of science will be completed? It’s arrogant to assume that science will be completed soon. It’s arrogant to assume that a completed science would fundamentally resemble the science of today. For example, perhaps a completed science would be well beyond human intelligence to comprehend even in its fundamentals or the basic underpinnings of its fundamentals.

I don’t assume that there is such a thing as a completed science. It’s possible that there is an actually infinite amount of theory required to completely explain the world, and that this infinite theory can’t be compressed into any kind of finite representation.

A direct philosophical interpretation of Gödel’s first incompleteness theorem says that an actually infinite set of axioms is required to entail all truths about the natural numbers, and that these infinite axioms can’t be compressed into any kind of finite representation. The set of statements which are true of the natural numbers is a complete and consistent set of statements including the axioms of Peano arithmetic, and therefore by Gödel’s first incompleteness theorem, this set cannot be effectively generated, i.e. it is not recursively enumerable. By the same reasoning, the same is true of any set of axioms sufficient to prove all true statements about natural numbers.

To simplify the language, you can’t write a computer program that would (in theory, if it could run forever) list out all the statements that are true about natural numbers. Nor can a program list out a set of true statements (axioms) about natural numbers which is sufficient to prove (logically entail) all statements true of natural numbers.

To simplify further, Gödel’s first incompleteness theorem as interpreted says that you will never get a complete description of the fundamentals of math, unless you have infinite time.

This interpretation rests on the assumption that we can coherently speak of the set of all true statements about natural numbers (in some formal language such as the language of Peano arithmetic). In short the assumption is that statements about natural numbers are all objectively true or false.

What if science is infinite in the way this interpretation says math is? What if a completed science would be infinitely complex in its fundamentals and not possible to finitely describe? If so, then a completed science would certainly never be comprehensible, even in its fundamentals, to a being such as a human. In this scenario, only an infinite being of godlike intelligence could fully comprehend a completed science.

To me it’s arrogant and laughable to reject the possibility that a completed science would be very different from today’s science, beyond human comprehension, and even infinitely complicated. On the other hand, if materialists accept this possibility, then they admit that in no meaningful sense do they comprehend what their view says about the world. In that case their view says nothing and is vacuous.

Thus, in all the possibilities I have envisioned, scientific materialism is arrogant and laughable, or else vacuous and devoid of content.

What exactly is the substance of my accusation? I’ve said that philosophy may be inherently arrogant. If all philosophy is arrogant, then it’s not interesting to say that scientific materialism is arrogant, because scientific materialism is a philosophical hypothesis.

The substance of my accusation is that scientific materialism is arrogant specifically in its neglect of the possible greatness of the gap between human understanding of physical reality and a completed understanding of physical reality. Scientific materialists whose views are non-vacuous are assuming there is not a significant possibility that a correct and complete understanding of the fundamental principles of physical reality would be beyond the comprehension of humans and would bear little resemblance to the theories of today’s physics. I describe the unwarranted assumption — that we are close to understanding the physical world — as an example of intellectual arrogance.

To put the point differently, I am observing that scientific materialists who endorse contentful versions of scientific materialism must assume that certain possibilities do not exist or are not significantly likely. A reasonable person can reject that assumption of contentful scientific materialism.

I’m interested in pointing out that scientific materialism can be doubted, because I want to clear space for other metaphysical views to compete with scientific materialism. This is necessary for me, because of my intellectual history in American academia, where scientific materialism is the prevailing metaphysical view. In my background, scientific materialism has been held in elevated prestige compared to other views, well beyond what it deserves in my opinion, so that I feel the desire to mock it with justified accusations.

Let me know what you think. Is there a form of scientific materialism against which my accusations are unsuccessful?

Subjective and objective philosophy

By subjective philosophy, I mean philosophy which sees itself as basically engaged in a project of thinking about people and their experiences. In other words, subjective philosophy self-consciously reflects and portrays the self-perceived nature of people, and inevitably the self-perceived nature of the philosophers themselves.

By objective philosophy, I mean philosophy which sees itself as basically engaged in a project of describing how the world really is, and (optionally) how people really are.

In the term subjectivism, I mean to include all schools of philosophical thought which are biased towards subjective philosophy.

In the term objectivism, I mean to include all schools of philosophical thought which are biased towards objective philosophy.

Philosophy can be both objective and subjective. The two categories are not mutually exclusive. Furthermore, I’m not saying that all philosophy falls into at least one of the two categories; maybe there’s philosophy which is neither objective nor subjective.

Metaphysical naturalism, a.k.a. scientific materialism, is an objectivist school of philosophical thought which is popular among the academically schooled humans of Earth in 2017. Metaphysical naturalism purports that the things that really exist are the things which figure in the theories of natural science. These theories are either the theories of the natural science of today, or the theories of some hypothetical completed natural science.

Ayn Rand is a prime example of an objectivist philosopher. She originally coined the term Objectivism. I don’t think that Ayn Rand meant the term “Objectivism” in the same sense I define the term “objectivism.”

Existentialism is a school of largely subjective philosophical thought which is popular among the academically schooled humans of Earth in 2017. Existentialists are often concerned with examining how humans look at themselves, their lives, others, and the world. This includes how our environments and our choices affect our concepts of self, life, others, and world. Existentialists commonly believe that life has no inherent meaning but humans can choose what their lives mean to them.

Postmodernism is a school of subjectivist philosophical thought which is popular among the academically schooled humans of Earth in 2017. Postmodernist philosophers (not all of them, I assume) seek to explain human ideas by explaining how those ideas arise in the context of humans’ psychologies and social lives, and considering what purposes the ideas serve for the humans who hold them. This type of project has sought to undermine the claim to objectivity of ideas in fields such as science and history. For example, see Michel Foucault in The Archaeology of Knowledge.

One can find simpler examples of subjective philosophy throughout culture. For example, consider the idea that it is wrong to say things which make people feel uncomfortable. This is a subjective ethical principle, because it bases ethical judgments on people’s subjective feelings of discomfort.

Immanuel Kant is an interesting example to look at. Kant (e.g., in his Critique of Pure Reason) is a skeptic about objective reality. Kant doesn’t think humans can ascertain how things in themselves are. He says that’s because our contact with objective reality is always mediated by perceptions, which are mental constructs.

Kant’s skepticism about objective reality is interestingly combined with what can appear to be a rather naive objectivism when it comes to his own psychological theories. The Critique of Pure Reason is mostly a treatise on psychology, describing the structure and features of the human mind. The theory is quite detailed. It looks to me Kant thinks his theory is objectively true for all humans and perhaps for all minds. For example, Kant writes:

For there is no other function or faculty existing in the understanding besides those enumerated in that table.

Source: Critique of Pure Reason. Translated by J.M.D. Meiklejohn (1784). Published by Barnes & Noble, Inc. (2004). Part II, §6, p. 37.

My reading of Kant is that he thought of his psychological theories as objective and true for all humans. Let me know if you have evidence against that reading.

Ludwig Wittgenstein’s Tractatus Logico-Philosophicus is an example of a text with major subjective and objective concerns. In it Wittgenstein is concerned with describing how language depicts the world: an investigation of how subjects relate to objects by studying the objective intermediary of language. Wittgenstein is also concerned in the Tractatus with demonstrating the distinction between that which can and can’t be expressed. In the Tractatus, that which can’t be expressed includes “the mystical,” which is of course subjective. Quoting Wittgenstein in the Tractatus:

6.51. 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.

6.52 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.

6.521 The solution of the problem of life is seen in the vanishing of this problem.

(Is not this the reason why men to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?)

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

Objectivist and subjectivist philosophers have had a lot of division. For example, see Ayn Rand’s attack on subjectivism in the final chapter of Introduction to Objectivist Epistemology. There she writes:

The crass skepticism and epistemological cynicism of Kant’s influence have been seeping from the universities to the arts, the sciences, the industries, the legislatures, saturating our culture, decomposing language and thought.

In the history of philosophy — with some very rare exceptions — epistemological theories have consisted of attempts to escape one or the other of the two fundamental questions which cannot be escaped. Men have been taught either that knowledge is impossible (skepticism) or that it is available without effort (mysticism). These two positions appear to be antagonists, but are, in fact, two variants on the same theme, two sides of the same fraudulent coin: the attempt to escape the responsibility of rational cognition and the absolutism of reality — the attempt to assert the primacy of consciousness over existence.

To speak in generalizations, objectivism (in my sense, not the Randian sense) and subjectivism have the following dynamics.

  • Objectivism accuses subjectivism of arrogance, narcissism, or romantic weak-mindedness, for placing the self at the center of philosophy.
  • Objectivism holds itself superior for its focus on reality and its practical successes.
  • Subjectivism rasies skeptical challenges to objectivism. Subjectivism accuses objectivism of arrogance, for claiming too much insight into the real world.
  • Subjectivism accuses objectivism of being unconscious of the self’s degree of influence on philosophy.

These generalizations of course do not apply at all times or to all subjectivist or objectivist philosophies.

To put it simply, objectivism looks down on subjectivism for its self-conscious indulgence of humanness, whereas subjectivism accuses objectivism of being unconscious of its own indulgence of humanness.

“Objectivism vs. subjectivism” is not a war to be won by one side. There is no single issue at stake in the dynamics between objectivism and subjectivism. I can’t envision what a comprehensive answer to the “objectivism vs. subjectivism” question would be. I don’t think there’s just one question.

My philosophy has often been about bringing together objective and subjective philosophical threads in some coherent way. For example, I have for about seven years been concerned with the problem of reconciling rationality and mysticism. I have shared thoughts about this problem in my books Eh na? and Winning Arguments, and in my posts on neosocratic.net.

Rationality is first and foremost an objective philosophical paradigm, whereas mystical philosophy is a highly subjective philosophical paradigm. It is hard to make rationality and mysticism play nicely together. I would like to be able to point you to a nice overview of how I make them work together in my thinking, but it doesn’t exist yet. Stay tuned.

Objectivism was the prevailing philosophical mentality in my formal education. My professors were mostly just concerned with describing reality as it actually is independent of human sentiment and opinion. Even when studying humans, as in my Psychology courses at Arizona State University, my professors focused on objective studies, facts, and figures, most of the time studiously neglecting anything subjective.

This struck me as a backwards way to approach studying ourselves. To me it’s clear that much more can be learned about humans by thinking and talking, as opposed to studying human behavior in artificially limited experimental circumstances which are usually designed to demonstrate a pre-determined conclusion via statistical methods that are often flawed. Of course there are highly informative experiments in psychology, but in my opinion they are the exceptions, not the rule.

I think my experience with the Arizona State University Psychology Department exemplifies the extreme degree of intellectual aversion to the subjective which is prevalent in much of academia.

It has been personally challenging for me to publicly advocate unpopular subjective philosophical ideas, as I have done and am preparing to do further. A lot of my challenges have been caused by cognitive dissonance from the clash between subjective thinking and the ways of thinking I developed from my objectivist academic education.

I am interested in subjective philosophy centrally because I believe that it is very beneficial for us to exercise judgment in how we think about ourselves, how we think about others, and how we think about ourselves in relation to each other and the world, I think a great deal of human potential can be unlocked by thinking about these topics in more constructive ways. We humans are relying on numerous failing patterns of thought, feeling, and mentation, particularly in the areas of self and other. It is important to consider that we can choose how we think around these topics, and that the choices we make have effects on our personal and social realities.

In short, some of the most important philosophical issues are deeply personal and subjective in nature. I think it’s essential for philosophy as a whole to embrace the mysteries of subjectivity deeply and completely as possible. Equally, I think it’s essential for philosophy as a whole to embrace the mysteries of objective reality deeply and completely as possible.

Mystical philosophy is an especially problematic form of subjective philosophy. It can be accused of asserting the primacy of consciousness over existence, as Ayn Rand did. More sharply, one can accuse mysticism of asserting the primary of mystical consciousness over other forms of consciousness and existence, when it comes to discerning truth. Basically, mystical philosophy can be viewed as being supremacist, in a bad way, putting some forms of consciousness over others. That thought has been a source of a lot of cognitive dissonance for me. Here’s what I say about it.

Truth can be perceived and talked about. Generally, conscious perception of a truth precedes talking about it.

It is undeniable that some forms of consciousness are more likely than others to be correlates of true perceptions of a given kind of truth.

For example, the consciousness of a sober, sane, awake adult human will yield perceptions of their immediate physical surroundings which are reliably true. Humans make errors in perception, but our sensory perceptions are typically accurate to reality.

On the other hand, schizophrenic psychosis frequently involves hallucinations and delusions: highly convincing perceptions of phenomena that are not real. (If the phenomena are real, then the diagnosis of hallucination or delusion is mistaken.)

Unlike the consciousness of a sober, sane, awake adult human, the consciousness of a schizophrenic is not a reliable correlate of true perceptions.

To give another example, the consciousness of a professional mathematician is a far better tool for discerning mathematical truths than the consciousness of somebody with no training in math.

It is not necessarily an attractive reality that some forms of consciousness are better than others as correlates of true perceptions. It is, however, a reality.

Whereas I think the examples of the schizophrenic and the mathematician will arouse little controversy, there is much more basis for controversy about whether mystical consciousness is a usual correlate of true perceptions. This is a matter of opinion. People are free to reject the point of view that mysticism is a source of truth, and I’m not aware of any general way to talk people out of the point of view that mystical consciousness is a variety of true perception.

Nonetheless, I believe that mystical philosophy has the potential to help people to unlock their inner potentials. I believe I have witnessed how mysticism has helped to bring depth and energy to my consciousness. I have attempted to demonstrate this energy and depth in my philosophy (to what success, the reader to judge). I feel an urgency from a service to others perspective to create new and useful mystical philosophy to share with others.

To balance these conflicting concerns, I think it’s useful to say that anybody who isn’t interested in mystical philosophy should ignore it. I also think it’s useful to say that the recognition of truth in mystical philosophy is rooted in subjective perception. Therefore if an idea in mystical philosophy doesn’t resonate with you, let it be, leave it behind.

I think this idea can be extended to subjective philosophy in general. The standards of evaluation are generally subjective. People’s perceptions of subjective philosophy are informed by their personal biases. Depending on people’s biases they will resonate differently with different subjective philosophies. A philosophy that is healthy food for one person might be harmful food for another.

With objective ideas, there is the hope that expert consensus can cause true ideas to spread throughout the population. This dynamic makes most participants passive consumers of truth, with the responsibility for discerning truth resting with experts.

Especially with subjective philosophy, in my opinion there is the need for the responsibility for discerning and finding truth to rest more with each individual. Everybody will resonate differently with different ideas, and there are a lot of different ideas to choose from, so that we only have time for a small fraction of them. We can derive many different kinds of value from ideas, we all want different things, and there is room for all of us to make our choices.

The most informed and intellectually responsible people about a topic think for themselves about the topic. The idea of thinking for oneself can be opposed to the idea of trusting experts and authorities. Trusting experts is generally a better tactic when one is relatively uninformed and appropriate experts exist. On some subjects, such as various philosophical subjects, one may contend there are no experts. Where there are no experts, intellectual responsibility necessarily devolves to each of us.

I think that mysticism is one of the areas where there are no experts. Or, more modestly, unthinkingly trusting experts won’t take you on a very informative journey with mysticism, because a non-expert in mysticism has no real hope (in my opinion) of discerning who might be an expert in mysticism vs. who is a mere performer or a mere academic without deep experiential understanding of mysticism.

I think the same goes for subjective philosophy more generally. There are no experts on it. Or, more modestly, expertise in subjective philosophy is in the eye of the beholder. It’s an open playing field. The game is whatever you want it to be.

Are philosophers arrogant?

Is it inherently arrogant to be a philosopher? I think maybe so. I think arrogance is a tendency philosophers should push back against in themselves, but I suspect it is inherent in the activity of philosophy anyway.

Maybe it’s inherently arrogant to think you can say something true, new, and useful about topics which have confounded humans and remained mysterious for all of recorded history.

Let’s analyze more carefully. For starters, what do I mean by “philosopher,” and what do I mean by “arrogant?”

In the past, people (e.g. Isaac Newton) did not draw clear distinctions between philosophy, science, and magic; these concepts were somewhat rolled together into one.

Historically, “philosophy” encompassed any body of knowledge.

In the 19th century, the growth of modern research universities led academic philosophy and other disciplines to professionalize and specialize.

Wikipedia

With the rise of the modern university system, there was a shift in the meaning of “philosophy.” The term went from referring to intellectual studies in general, to referring to a specific area of study, the area studied by philosophy departments in universities.

Basically, it seems to me that the department of philosophy in a university is the department which studies all the questions which aren’t the kind of question addressed by any other department.

Academic philosophers don’t answer questions of physics, biology, history, etc. Academic philosophers study a “miscellaneous” category of questions, which includes most of humanity’s deepest and most intractable intellectual mysteries. The category includes many questions which people have asked for all of recorded history without arriving at any agreed upon answers.

For this post I’ll assume that philosophers are people who ask and try to answer big questions, which can’t be answered by any established methodology in academia, and which relate to perennial intellectual mysteries. Is it inherently arrogant to engage in such activity?

What do I mean by “arrogant?” Here are some dictionary definitions I looked up:

  1. having or revealing an exaggerated sense of one’s own importance or abilities.” (Google)
  2. “exaggerating or disposed to exaggerate one’s own worth or importance often by an overbearing manner” (Merriam-Webster)
  3. “Someone who is arrogant behaves in a proud, unpleasant way toward other people because they believe that they are more important than others.” (Collins Dictionary)

Do philosophers necessarily meet any of these definitions?

I’ll set up a case which tries to maximize the likelihood of not meeting these definitions. Let’s consider a philosopher who says something like this:

I am interested in big questions which have confounded humans as long as we can remember. I don’t believe that I myself can answer these questions definitively, but I believe that humanity as a whole can deepen our understanding around these questions. I believe that I can build on the work of past philosophers, and perhaps help out future philosophers, towards furthering humanity’s progress around these questions.

This philosopher’s assumptions could be questioned. Maybe philosophy does not progress in the way the philosopher says it does. Maybe philosophers across history wander from opinion to opinion in an overall aimless way, always arrogantly viewing the opinions of the day as the pinnacle of human understanding.

Though the premise can be doubted, I would say it’s not arrogant to believe that humanity deepens its philosophical understanding over time, because this is a belief about humanity, not about oneself in particular.

Is it arrogant to believe that one can potentially help with humanity’s philosophical progress? If you accept the premise that many people have already done so, I would say not. It may be arrogant to think you can help with humanity’s philosophical progress if you’ve put no effort into training yourself as a philosopher (such as by studying what philosophers have said in the past). But somebody who has trained as a philosopher is not necessarily arrogant to suppose they may be in a position to contribute to humanity’s philosophical progress.

It might seem, then, that the statements above could be the statements of a non-arrogant philosopher. Of course a philosopher could say these things and still be arrogant. Yet there seems to be nothing inherently arrogant about this philosopher’s expressed attitude towards philosophy.

Let’s examine further, though. Maybe philosophers are necessarily arrogant whenever they stake claims. The complexities in philosophy are such that it is fundamentally hard to tell when a claim is justified. Perhaps, then, making any kind of general statement in philosophy is always hazarding a guess, and always implies the arrogance of jumping to a conclusion. Yet a philosopher who never staked any claims would arguably not be much of a philosopher. Perhaps for this reason doing philosophy is inherently arrogant.

It would be arrogant of me to assert positively that there can never exist a non-arrogant philosopher. I believe it would be arrogant of me to deny that I myself am an arrogant philosopher. I am not familiar with any philosophers who I am satisfied to call non-arrogant. I am inclined to accept the generalization, “philosophers are arrogant.”

I believe that arrogance is an important tendency for philosophers to push back against in ourselves. Jumping to conclusions is a good way to be wrong. Much of the challenge and reward of philosophy is found in unpacking the subtle moving pieces of our thoughts, teasing apart distinctions, and uncovering fallacies which we have unconsciously passed over.

The principal antidote for intellectual arrogance is intellectual humility. Intellectual humility, in my opinion, requires acknowledging that my perspective has deficiencies I’m not yet aware of, and others’ perspectives basically always have at least some merit.

For me, intellectual humility entails that if I am going to make positive assertions, then first I must take apart my thoughts and rigorously look for defects, and I must hear others’ points of view on the questions I’m asking. These steps are important counter-measures against the negative consequences of intellectual arrogance.

Yet, even if I take these counter-measures, it doesn’t obviate my worry that I am arrogant or can be viewed as arrogant in virtue of doing philosophy. I do still suspect that arrogance is the perennial condition of a human philosopher. Maybe the time we have in life is too limited to think issues through to the extent that our philosophical statements can be considered so cautious that it is not arrogant to hazard making them.

I see great value in doing philosophy. I think it is very important for the future of humanity. Because I love philosophy more than I love having a squeaky clean public image, I am willing to expose myself to ridicule by publicly exhibiting arrogance for the sake of philosophy. Those who don’t like what I’m doing are entitled to ridicule me for it. I’m writing, with the hazard of attracting ridicule, for the sake of people who may find what I’m doing helps them with their projects and problems.

Still, you might ask, if doing philosophy is arrogant, and arrogance is wrong, then how can it be a good idea to do philosophy? As far as I can see, this question only arises if you assume a perfectionist attitude about morals. A perfectionist attitude about morals would say that behavior must be free of moral flaws in order to be moral. This is not a realistic perspective on morals.

So, maybe the activity of philosophy has embedded in it an inherent moral flaw, arrogance. If so, that does not mean that philosophy is not a morally good activity to engage in. It means that philosophy is a morally imperfect activity. In a world where moral imperfection is ubiquitous, if not universal, this is hardly much of an argument against philosophy, at least if you think that philosophy has enough positive value to counter-balance its moral imperfections.

Paradoxes and the rules of logic

Consider the statement “this statement is false.” Is it true or false? Some reflection will show that if it’s true, then it’s false, and if it’s false, then it’s true. What should we make of that? Is it both true and false? Or else what’s going on?

This is a classic logical problem known as the “liar paradox.” The liar paradox, and paradoxes like it, have been subject to immense philosophical attention stretching back thousands of years.

In this post I’m going to present a solution to this classic problem. In a nutshell, I say, ignore it, like almost everybody does. The length of the post is spent in making this solution rigorous and explaining the basis of my opinion that this is the best way of solving the liar paradox and similar paradoxes, for most purposes.

The workings of the solution lead to a picture of logic which is potentially surprising and new to people. In this picture, the rules of logic have exceptions, the rules of logic are subject to legitimate subjective differences of opinion, and the rules of logic are not completely rigorous and formal, but are made up as we go along to at least some extent. In the course of the work I hope to convey a deeper explanation of this picture.

I’m not trying to provide a full picture of how the practice of logic should work under the assumption that the rules of logic are not completely rigorous and formal. I’m providing a solution to paradoxes which exploits that assumption. I hope for other work which builds out a bigger picture of how logic can work when it’s not completely rigorous and formal. I have sketched only a little fragment of what I imagine to be a big space of potentially interesting problems and solutions.

 

The problem

In this post, by “paradox” I will mean, “an argument which proceeds from apparently true premises to a contradictory conclusion.” A contradictory conclusion is a statement of the form (P and (not P)), asserting that a statement P is both true and false.

Here is an example of a paradox: the liar paradox. Consider the statement “this statement is false.” I’ll refer to this statement as L. If L is true, then L is false. If L is false, then L is true. L is either true or false. Therefore L is true and L is false, or in other words, (L and (not L)) is true. The preceding argument, which I call the liar paradox, has a contradictory conclusion, so it is a paradox.

Other examples of paradoxes include Russell’s paradox and the Sorites paradox. In this post I will focus mainly on the liar paradox as a chosen example of a paradox.

This post explains a general method of solving paradoxes.

What does it mean to solve a paradox? Every paradox presents a problem: it appears to imply that something false is true, which is impossible, at least on a traditional understanding of logic. Nothing impossible can occur, but paradoxes appear to be cases where something impossible occurs. In that sense, paradoxes are intellectual, theoretical problems. To solve a paradox is to solve this problem, for example by pointing out which of the paradox’s premises are not true, or by explaining why its conclusion does not follow from its premises.

 

This theory, this post, and their history

I don’t claim the theory I’m giving is fundamentally new. I think it is basically a technical extrapolation of the common way of responding to paradoxes like the liar paradox, according to which these paradoxes can safely be ignored.

I didn’t base this theory on anybody else’s work.

I first described this post’s method of solving paradoxes in my book Winning Arguments. This post aims to describe the method in a quicker and more surveyable way, putting together thoughts that are scattered throughout a wide span of text in Winning Arguments.

This post is aimed at a general philosophical audience. It is not very technical and it doesn’t engage deeply with the scholarly literature on paradoxes. There are over 2,000 scholarly works about the liar paradox cited on PhilPapers. This post talks about one solution to the liar paradox, which is in competition with a huge number of solutions discussed in the weighty corpus of paradox research. I have kept the comparison with competing solutions brief and superficial, relative to the extent of the literature.

I studied the topic of paradoxes in the University of Connecticut Philosophy PhD program, where I learned about paradoxes among lovely and intelligent philosophers including, for example, world paradox experts Jc Beall and David Ripley. I published research related to paradoxes in two of the top journals related to the topic: the Journal of Philosophical Logic and the Review of Symbolic Logic.

The solution to paradoxes which I’m describing in this post is something I began conceiving around 2011, during my undergraduate studies at Arizona State University. I have been developing the idea since then. By the time I left UConn in 2015, I had all the pieces of the theory conceived. It took me until 2017 to put the pieces together, to believe the resulting theory, and to put it down in writing.

This post does not provide my full theory of paradoxes. It only provides the first piece of the theory. This piece of theory is called the ad hoc method of rejecting incorrigible paradoxes, or the ad hoc method, for short.

The ad hoc method deals only with the technical aspect of solving paradoxes. The other part of the theory, to come in a later post, deals with the more philosophical question of why paradoxes happen and how we can explain them.

 

Summary of the ad hoc method of rejecting incorrigible paradoxes

Some arguments have apparently true premises and contradictory conclusions, but some of their premises, though apparently true, are false. An appropriate method of solving such paradoxes is to identify which of the premises are false.

In contrast, this post is mainly concerned with incorrigible paradoxes. An incorrigible paradox, by definition, is an argument which leads from true premises to a contradictory conclusion via correct rules of deductive logical inference.

The notion of an incorrigible paradox is implicitly relative to: (a) some language in which arguments can be formulated, (b) some opinion about what rules of deductive logical inference are correct, and (c) some opinion about what statements are true. You will get different, sometimes irreconciliable notions of what constitutes an incorrigible paradox by starting from different choices of (a), (b), and (c).

If a paradox is not incorrigible, then either it has at least one false premise, or its conclusion does not follow logically from its premises, and solving the paradox is a matter of finding a false premise or using logical methods to demonstrate that the conclusion doesn’t follow from the premises.

If a paradox is incorrigible, then the ad hoc method of rejecting incorrigible paradoxes recommends rejecting the conclusion of the paradox and all further inferences from it, understanding this rejection to be an ad hoc modification/exception to the rules of logic one employs.

 

Assumptions

The notion of an incorrigible paradox is implicitly relative to some language, some opinion about what rules of logical inference are correct, and some opinion about what statements are true.

In this post, I’m going to choose English as the language in which arguments can be formulated.

I’m going to assume that the rules of classical logic, as described for example by the system LK, are correct rules of deductive logical inference.

I’m going to assume a lot of common sense about what’s true. I will assume that the following statements, which I construe as premises of the liar paradox, are true:

  1. The statement L = “This statement is false” is an English statement.
  2. If L is true, then L is false.
  3. If L is false, then L is true.

From these premises it follows by the rules of classical logic that L is true and L is false, and that (L and (not L)) is true.

The rules of classical logic are always described relative to some formal language, such as the language of first-order logic used in the system LK. In this post I’m assuming the rules of classical logic can be construed as rules governing use of the English language.

Since English isn’t based on a set of precise rules that cover all cases, it is practically impossible to give a precise description of the rules of classical logic as they apply to English.

When logicians apply the rules of classical logic to English, they generally rely on a precise understanding of the rules of classical logic as understood through some formal description such as the system LK, and on a more artistic understanding of how to translate between English and a formal language such as first-order logic. This mapping between English and the formal language yields an imprecise method for applying the rules of classical logic to English. This imprecise method is precise enough to be unproblematic for typical purposes, and for our purposes.

According to the assumptions of this post, an incorrigible paradox is an English-language argument whose premises are true and whose conclusion follows from the premises by the rules of classical logic. By assumptions, the liar paradox is an example of an incorrigible paradox.

The solution to paradoxes of this post will work for basically any choice of language, rules of logic, and concept of truth. The assumptions of this post, as described in this section, are primarily for the purpose of making the discussion concrete. If you dislike the assumptions chosen in this section, you can still use the solution to paradoxes I’m describing, replacing English with your language of choice, replacing classical logic with your logic of choice, and using your choice of assumptions about what statements are true.

 

The ad hoc method of rejecting incorrigible paradoxes

To solve any paradox by the method this theory prescribes, you start by determining whether or not the paradox is incorrigible. This requires answering two questions: whether the premises are true, and whether the conclusion follows logically from the premises. Answering whether the conclusion of an argument follows from the premises by the rules of classical logic is basically a routine process if you are familiar with appropriate techniques. Answering whether the premises are true is in general more complex, and I don’t provide any general method for doing that.

If you show that a paradox is not incorrigible, then you’ve solved the paradox. Either you’ve shown that its premises or not all true, or you’ve shown that the conclusion doesn’t follow logically from the premises. Either way, you’ve shown that there is no problem.

If your analysis concludes that a paradox is incorrigible, then the next step of the method is to reject the conclusion of the argument. One makes the stipulation that the paradoxical argument is to be rejected, even though its premises are true and its logical inferences are valid. This is an ad hoc modification/exception to the rules of logic which one employs.

One ends up having not only positive rules of logic, according to which certain inferences are correct, but also negative rules of logic, which supersede the positive rules by stating that inferences which are valid in general are invalid in some particular cases (the cases of incorrigible paradoxes).

This method leaves the rules of logic one employs perpetually incomplete. If you employ this method, then the rules of logic you follow are unlike (for example) the rules of the system LK in that you lack a precise and complete description of the rules of logic you follow. If you employ this method, then you have the expectation that if you encounter new incorrigible paradoxes in the future, then you will need to extend the rules of logic you employ, by adopting new negative rules to block the new incorrigible paradoxes.

In classical logic, it is possible to infer any statement from a contradiction. If you can infer a statement of the form (P and (not P)) from a given set of premises, then you can infer any statement whatsoever from those premises. This is called the principle of explosion.

Because of the principle of explosion, the ad hoc method of rejecting incorrigible paradoxes also involves rejecting any variants on a paradoxical argument which can (in other variations) be used to prove any statement. For every argument whose conclusion is a contradiction, there are many variations with conclusions including all statements. All such variants are rejected, in the method.

People may arrive at differing results by this method. Differences on what constitutes an incorrigible paradox may arise from different opinions on what rules of logic are correct, different opinions on what statements are true, and different judgments about what constitutes a variation on an incorrigible paradox, among other possible sources of differences. Different judgments about what constitutes a variation on an incorrigible paradox may arise because I don’t offer any general method for making such judgments; rather, I assume there to be some ineliminable element of artistry involved in making such judgments. This assumption is justified later.

These sources of potential variability in people’s results from this method may be viewed as a consideration against the use of this method. Of course, people arrive at different results in reasoning due to all kinds of causes. I view the mentioned consideration against this method as a valid one, to be weighed against other considerations (and of course I believe this method has considerations in its favor that outweigh the considerations against, for general purposes).

According to the ad hoc method of rejecting incorrigible paradoxes, one augments the rules of logic one follows on an ad hoc basis by adding negative rules which exclude the inferences to the conclusions of incorrigible paradoxes. One does this as needed. One also rejects all variations on incorrigible paradoxes which can be used (in further variations) to prove arbitrary statements. I don’t provide strict rules on how to draw the line between such variations on incorrigible paradoxes, and other arguments; I assume there is an ineliminable element of artistry in drawing the line. In other words, I assume that the technique of drawing the line can’t be made completely formal.

Some appropriate questions:

  1. How does the ad hoc method of rejecting incorrigible paradoxes compare to other ways of solving paradoxes? Why use this method over competing methods?
  2. What’s the reason for the assumption that there is an ineliminable element of artistry in identifying variations on incorrigible paradoxes which can be used (in further variations) to prove arbitrary statements?
  3. What are the risks involved in using the ad hoc method of rejecting incorrigible paradoxes?
  4. Is there any intuitive picture that explains why this method is correct?

Subsequent sections will speak to these questions. Here is a summary of the subsequent sections.

 

Non-classical logic and its successes and limitations with paradoxes reviews some of the successes and limitations of some competing approaches to solving paradoxes, which are based on restricting the rules of classical logic in some formally defined way, in the form of a so-called non-classical logic. This section looks (in a very high level way) at the pros and cons of approaches using non-classical logic, as compared to the ad hoc method of rejecting incorrigible paradoxes. This section speaks to questions 1, 2, and 3.

Implications for reasoning talks at a high level about how this approach to paradoxes works in the context of everyday practical reasoning. This section speaks to question 3.

Implications for math talks at a high level about how this approach to paradoxes works in the context of math. This section speaks to question 3.

I will speak to question 4 in a subsequent post.

 

Non-classical logic and its successes and limitations with paradoxes

Classical logic is the prevailing perspective on logic. Classical logic is a system of rules of inference, which exists in many variants, and which is used, taught, and studied far more often than any other paradigm of rules of logic.

A non-classical logic is any system of rules for logical reasoning which is not a form of classical logic. Non-classical logics are a huge and diverse category. PhilPapers cites over 6,000 works on non-classical logics.

An early and important type of non-classical logic is intuitionistic logic. Roughly, this is the logic you get by removing from classical logic the principle that every statement is either true or false.

Another important type of non-classical logic is relevance logic. Systems of logic known as relevance logics aim to disallow inferences known as “paradoxes of relevance,” such as the inference (valid in classical logic) from the premise “the sky is blue” to the conclusion “if the sky is red then the sky is blue.”

Neither intuitionistic logic, nor most relevance logics, solve the liar paradox and similar paradoxes.

I’ll focus on two categories of non-classical logics which get traction in solving paradoxes such as the liar paradox. These are paraconsistent/paracomplete logics, and substructural logics.

As far as I’m aware, these are the best studied categories of paradox-solving logics, with no competing categories of comparable prominence in the academic literature. Each of these categories includes many different formal systems of logic, and the literature around each of them is extensive and technical. I’ll only provide a very high-level survey of what is going on in these subfields of logic, without going into technical details about any of the systems.

For a more detailed survey of the topic of non-classical logics, I would recommend Graham Priest’s An Introduction to Non-Classical Logic. That book does not discuss substructural logics. For an entry point into the field of substructural logics, I would recommend Greg Restall’s article in the Stanford Encyclopedia of Philosophy. Now I’ll proceed to my nutshell survey of these fields.

A paraconsistent logic is a system of logic in which some statements can be both true and false, without every statement being true, and without every statement being false.

An example of a paraconsistent logic is LP, the Logic of Paradox. LP is a system of logic in which there are three possible “truth values:” true, false, and paradoxical (meaning both true and false). Every statement is either true, false, or paradoxical.

LP provides simple rules for determining the truth value of any statement as a function of the truth values of the sub-statements that make it up, provided one knows the truth values of the smallest sub-statements. For example, a sentence of the form “A or B” is has the following truth value:

  • “True,” if A is true and B is true.
  • “False,” if at least one of A or B is false and neither is paradoxical.
  • “Paradoxical,” if at least one of A or B is paradoxical.

Notice that these three possibilities cover all the possibilities, so that the truth value of “A or B” is always determined by the truth value of A, the truth value of B, and the given rules.

LP is similar in design to classical logic, but in LP, you can let some statements be both true and false, without all statements being so. LP allows this by having rules that are less restrictive than those of classical logic; they let you infer less from the same premises, so that in particular the principle of explosion is not valid in LP.

A major problem with LP is that its rules are too weak to allow the development of math in the usual manner of proving theorems from a limited set of axioms. I have proven facts about LP which illustrate this general phenomenon. That LP is too weak to allow the development of math in the usual manner is such a broad and imprecise statement that I doubt it can be stated completely and precisely, much less proven.

LP is an example of a paraconsistent logic, meaning it allows for true contradictions without every statement being true.

Moving on to another type of non-classical logic: a paracomplete logic is a logic in which some statements can be neither true nor false.

K3, or Kleene 3-valued logic, is an example of a paracomplete logic. In K3, there are three possible truth values: true, false, and neither. K3 has simple rules, exactly parallel to LP’s, for determining the truth value of any statement from the truth value of the statements making it up, provided one is given the truth values of the smallest statements.

Kripke’s “Outline of a theory of truth” is an example of applying K3 to solve paradoxes like the liar paradox. Kripke’s solution works as far as it goes, but it doesn’t go as far as giving an operational explanation of how to reason in the presence of paradoxes, and it’s not clear how to extend it to work for paradoxes of set theory such as Russell’s paradox.

In any case, K3 is an example of a paracomplete logic, one which allows for statements which are neither true nor false.

Some logics are both paraconsistent and paracomplete. FDE, or First-Degree Entailment, is a simple example. It has four truth values: true, false, both, and neither. It works like a fusion of LP and K3.

Substructural logics are another class of non-classical logics, usually defined in the form of a sequent calculus. A sequent calculus is a manner of defining a system of rules of logical inference. It is based on patterns called “sequents.”

A sequent is a pattern of the form “A1,…,An entails B1,…,Bm,” where A1,…,An is a sequence of zero or more statements, and B1,…,Bm is another sequence of zero or more statements.  Usually the word “entails” is written as a turnstile. A basic way of reading the sequent “A1,…,An entails B1,…,Bm” is as saying “if A1,…,An are all true, then at least one of B1,…,Bm is true.”

A sequent calculus tells you how to produce all sequents that are “valid,” by repeatedly applying a small set of rules. The system LK is an example of a sequent calculus, one which defines the rules of classical logic.

The system LK tells you what arguments are valid according to classical logic, if you can translate the arguments into the language of first-order logic. Take an argument to consist of one or premises A1,…,An, and a single conclusion B, with the claim being that the premises are true and B follows from them. Suppose A1,…,An and B are written in the language of first-order logic. Then the argument in question is valid according to classical logic, meaning its conclusion follows logically from its premises, if and only if “A1,…,An entails B” is a valid sequent in the sense that it can be produced according to the rules of the system LK.

Sequent calculi have rules known as “structural rules.” In the system LK, there are the following structural rules:

  • Weakening: If you add statements to the premise or conclusion side of a valid sequent, then you get another valid sequent.
  • Contraction: If a statement occurs repeatedly on the premise side or conclusion side of a valid sequent, then you can drop extra occurrences and still have a valid sequent.
  • Permutation: You can change the order of the premises and conclusions in a valid sequent, and get a valid sequent.

There is also the rule of cut, which is not always classified as a structural rule. It is harder to summarize, but you can look at it in Wikipedia’s presentation of LK.

Substructural logics are logics which relax/weaken some of the structural rules of a sequent calculus, with the system LK being a prototypical starting point.

One reason some people are interested in substructural logics is that some people see them as a promising avenue for solving paradoxes.

One example of an approach to paradoxes based on substructural logic is an approach advanced by Dave Ripley and others, articulated for example in Ripley’s paper Paradoxes and failures of cut. This approach starts with an LK-like sequent calculus, and removes the rule of cut.

This approach avoids the problem seen in the case of LP, that the weakening of logic makes too many things unprovable, so you can’t get things like math off the ground. It avoids the problem because the rule of cut is not necessary for the completeness of the system LK. One can remove the rule of cut from the system LK and exactly the same sequents are valid (derivable) in the resulting system. This is Gentzen’s cut elimination theorem. The catch is that sequent derivations not using the cut rule may need to be much longer than derivations of the same sequent using the cut rule.

The interesting observation is that by starting with this cut-free sequent calculus, one can add a concept of truth which gives rise to the liar paradox, without causing the system to explode the way that classical logic does. Ripley’s theory shows how to reason in the presence of the liar paradox, in a way that works and is operationally understandable.

Ripley has also applied his approach to other types of paradox, including paradoxes of vagueness and paradoxes of set theory. Perhaps it can be deemed a generally successful approach to paradoxes. In my opinion, the only part of Ripley’s approach that is not evidently successful is the approach to the paradoxes of set theory. It remains to be seen how capable Ripley’s set theory is of proving the usual theorems of math. Many failures and difficulties have been encountered in this area. Similarities between Ripley’s set theory and LP set theory may be a warning sign of limitations similar to those found in LP set theory. However, as far as I’m aware, it remains to be seen either way whether or not this set theory can be used effectively as a foundation for math. Resolving this uncertainty would shed light on how generally Ripley’s cut-free approach can be applied to solve paradoxes. Does it work on all the hardest paradoxes, or does it fail to apply to some of the hardest paradoxes?

I have discussed only a small and biased selection of approaches to solving paradoxes using non-classical logic. I have discussed each approach only to a superficial extent. We have only skimmed the surface of this subject. I, personally, have not read most of the academic literature on paradoxes. I am limited by the desire to keep this post’s length reasonable and this section not overly laborious or time-consuming for the reader.

Now I will make some general comments on how the ad hoc method of rejecting incorrigible paradoxes compares to approaches to solving paradoxes based on non-classical logic.

I am not aware of any approach to paradoxes based on non-classical logic which solves all of the hardest paradoxes, including the liar paradox, the Russell paradox, etc., which approach is uniform across such paradoxes, and which approach results in a method that is practically usable. I do not rule out the possibility that such an approach can be constructed. However, my own suspicion is that it won’t happen. My own suspicion is that the paradoxes are an intellectual trick of God which no finite system can completely contain or address. I have no proof of that opinion. My opinion is that the opinion can’t be proven, it can’t be proven that it can’t be proven, and so forth.

All currently existing non-classical logic solutions to paradoxes that I’m aware of, insofar as they are successful, are successful in a limited area. On the other hand, the method I’ve proposed can be applied uniformly to all paradoxes. I’m not aware of a non-classical logic approach to paradoxes which can claim the same.

All non-classical logic approaches to paradoxes involve the complexity inherent in non-classical logic. Learning how to apply the full formal rules of classical logic, as expressed e.g. through the system LK, is a lot to ask of people. Non-classical logics provide more stuff to learn, and they are usually more complex and/or less intuitive and/or harder to apply than classical logic. In most non-classical logic solutions to paradoxes I have seen, there is no clear idea of how to operationalize and apply the ideas. In the cases I’ve seen and can recall, when there is an idea of how to operationalize the solution in principle, there is still not a fleshed out idea of how to do it practically.

In contrast, the method I’ve proposed is easy to apply. Indeed, I think the ad hoc method of rejecting incorrigible paradoxes is the method which most people instinctively apply when presented with the liar paradox. The method is so easy to execute that it doesn’t even need to be taught.

Considering these things, I think it’s fair to say that from a practical perspective, the method I’ve proposed has distinctive advantages over non-classical logic approaches to paradoxes. I think most people will probably be sympathetic to my assessment that at least at this time, the method I’ve proposed is more suitable for most practical purposes, compared to non-classical logic approaches.

Where the non-classical logic approaches are better than the ad hoc method of rejecting incorrigible paradoxes is mainly in the theoretical qualities of exactness, formality, and certainty. The non-classical logic approaches provide systems of rules that are not ad hoc, but in principle handle all cases, in their domains of applicability. Meta-logical theorems can provide assurances that certain undesired outcomes will not result from applying the rules.

On the other hand, the method I’ve proposed is inherently inexact, and there is the possibility that applying it will fail to protect one from falsehoods that can be inferred from paradoxes, if one somehow unintentionally invokes a paradox in one’s reasoning. This is an area where non-classical logic approaches have the advantages.

In summary, the ad hoc method of rejecting incorrigible paradoxes has the advantages that it is easy to learn and apply and it works uniformly across all cases, whereas the non-classical logic approaches have the advantages of exactness, formality, and certainty.

The question becomes, which considerations are more important? This depends what is important to you.

If your interest in paradoxes is theoretical, and an exact solution to the problems is simply what you want, then you’ll deem that more important than ease of learning and having a general, easily usable solution on the table.

If you’re interested in this topic for some extrinsic reason, e.g. because you want to understand how to reason in general for all purposes, then you will likely favor the ad hoc approach I’ve presented, because you can apply it today to all your paradoxes. Naturally, it’s up to you how you approach these problems, and how much time you spend thinking about them. I would not discourage you from taking whatever approach to paradoxes seems to you to suit your goals.

In my view, the approaches to paradoxes based on non-classical logic have had such tough going because they are going against a general principle, one I call the law of no perfect system.

In general, the law of no perfect system is that there is no perfect system for doing anything. Whatever your problem is, if it’s above a certain level of complexity, then there is no finite and exact set of rules which solves the problem optimally in all cases.

As applied to this case, there is no perfect set of rules for logic which has everything it can correctly have and nothing else, defined formally and finitely.

Gödel’s first incompleteness theorem can be construed as the law of no perfect system as applied to axioms for math. It implies that there is no set of axioms for math, which can be listed by a computer program, which prove everything true and nothing false about math.

The law of no perfect system, as a general rule of thumb, tells you that it is proper for rules to have exceptions. Because no system of rules is able to handle everything, each particular situation should be considered as a particular situation where exceptions to rules might properly apply.

I think the general law of no perfect system is fairly common sense, but as applied to logic, it goes against the grain of the academic literature. I’m not aware of other defenses, besides the present one, of the law of no perfect system as applied to logic. Please let me know of any you’re aware of.

 

Implications for reasoning

What does the ad hoc method of rejecting incorrigible paradoxes have to tell us about general reasoning for practical purposes?

As far as I can tell, the theory has virtually no implications in this area. For practical purposes, people already reason as if they were following the ad hoc method of rejecting incorrigible paradoxes.

By using the ad hoc method, one accepts the possibility that one will be led from truth to falsehood by following the rules of logic, by stumbling across some unseen paradox. I’m not aware of cases like this, but it is a theoretical possibility that this will happen to somebody and that it will matter for their purposes.

One accepts a certain level of risk and uncertainty around one’s use of logic by using the ad hoc method. To put it in perspective, most people carry a much higher level of risk and uncertainty around their use of logic, because they probably haven’t learned any set of rules for logic, and they probably don’t subscribe to any theory about how to solve paradoxes.

 

Implications for math

The ad hoc method of rejecting incorrigible paradoxes, or for short the ad hoc method, has some practical implications for some theoretical math.

Using the ad hoc method has consequences for set theory. The method lets you do math using naive set theory, in which every set you can describe exists, avoiding the need to use a set theory like ZFC whose paradox-avoiding mechanisms introduce complications and limitations.

Using the ad hoc method has consequences for category theory. Category theory has conventionally used paradox-avoiding mechanisms of varying levels of complexity in rigorous presentations. The ad hoc method tells us that there is no need to do this. Paradoxes arise naturally from category theory, but they can be handled by the usual ad hoc method, without a need for paradox-avoiding restrictions. Category theory’s paradox avoiding restrictions usually limit what categories you can talk about, preventing you from talking about sensible categories such as the category of all sets, the category of all groups, or the category of all categories. It’s nice to do away with the paradox avoiding restrictions.

Using the ad hoc method has consequences for type theory. For example, the original impredicative formulation of intuitionistic type theory gave rise to a paradox, Girard’s paradox. Subsequent systems introduced paradox avoiding restrictions which reduced the expressive flexibility of the systems. As in other cases, these paradox avoiding restrictions can be done away with if one is comfortable with the ad hoc method of rejecting incorrigible paradoxes.

This method can even be applied to dependent type theory as applied to software development. People already use logical methods in this context which bear some resemblance-like relation to the ad hoc method of rejecting incorrigible paradoxes.

For example, Idris is a computer programming language based on dependent type theory. In Idris, you can prove theorems in your code, and in particular you can apply this capability to prove that your software has desired properties. In Idris, you can prove any statement. Yet, this is unlikely to happen by accident. Arguably, Idris’ ability to prove any statement is an outcome of overall-desirable design tradeoffs. Normally you wouldn’t use that ability, and the fact that it’s there does not prevent you from drawing confidence from the proofs which you write and Idris verifies. From such a proof, formulated in a normal fashion free of prove-anything back-doors, you can draw practical certainty that the statement proven is true.

Although it can prove any statement, Idris contains paradox avoiding restrictions (a hierarchy of nested type universes). As far as I can see, those paradox avoiding restrictions are not necessary. They’re not necessary to keep the system from proving arbitrary statements, because Idris developers have built the capability to prove any statement into the system anyway. Probably there is approximately nothing to lose from dropping the paradox avoiding restrictions and including the axiom Type : Type which allows paradoxes to be proven. This modification would (arguably) make the system simpler and nicer to use.

Please comment if you’re aware of paradox theories similar to the one laid out here, and to share any paradox research that you think I might find interesting.