Subjective and Objective Truth

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Four Unreasonable Poems

1.
Hey guys, look at all this truth I brought for you!
Oh, you don’t want any of it?
…Not a word?

2.
I shouldn’t need
to dress up my intuitions in math
to make them acceptable to you.

But I’ll do it,
if it means you’ll finally listen.

3.
First I believed everything I was told.
That’s what you do when you’re a child.

As a teenager I began to know things for myself,
and they told me I was wrong.

I was epistemically torn, and beaten, and battered
and bruised until finally I believed
that whoever has the power
is the one who’s right.

I fell for that ancient ruse,
like a rock off a cliff.

I played the game.
I believed only what I could force others to believe.
Damn could I play.

And I took all of this and began calling it “truth.”

But y’know, truth sort of has a different melody
than the one we’re singin’ in school.

4.
I am sick of conspiring
in my own downfall because it’s easier
than standing up.

The Academician

The academician does not see the truth.
He does not open his ears to the warbling sound of his inner teacher,
who speaks of the brightest of noons and the darkest of sunsets,
the highest of foothills and the lowest of mountains.

He does not set his gaze on the soft, caressing glow of truth,
but fades out that glorious sunset
with his Kodak monochrome image capturing software,
the tool of those great census bureau workers of the universe, reason.

The academician speaks the truth about all things outside,
but he omits the truth about himself,
and in this omission all of his words are reduced to so much dust,
so many files and records of tiny bits of data.
In his quest to know everything he finally knew nothing,
and in this miserable not-knowing he might finally learn to hear himself.
Let us hope!

Why I do math, II

Earlier tonight I was walking back from a meditation session, and I concluded that math was nothing but a giant power trip, something people use to control other people and the natural world. So in my mind I renounced math, with that little nagging voice saying that there was no way I was done with it.

Later this evening I found myself reading about sheaves, and ejaculating wild screams of ecstasy as if I were a woman in orgasm. What a deep conundrum this is! What other human could possibly empathize with my soul’s dilemma?

Proof vs. Listening

Most of the time, we don’t have the option of formally proving our ideas. It’s really only in math and science that we can do this. But most intellectual problems in the real world don’t fit that paradigm. Most real-world intellectual problems are decision problems. You have a group of people who are trying to decide something (a workplace, a family, a country, a group of friends, a romantic partnership). They need to share ideas with each other, and eventually they need to agree on something. But they need to do this without the use of formal proof, because almost always, you can’t prove that your idea for what to do is the best one.

The situation is the same in philosophy and religion. We don’t have the luxury of formal proof in these disciplines, but we still need to think about things together and eventually agree about something.

We want to hold philosophical and religious beliefs, but it’s sort of meaningless to do so unless other people agree with us. I’ve tried being a lone believer who has his own perspective on reality that nobody else shares. But I can’t shake this feeling that I’ve regressed into solipsism when I do that. If my beliefs are unproven and held only by me, by what metric are they tested? How do I know that they’re right? How could I possibly distinguish between a private true belief, and a private delusion?

“Proof” can take many forms. There’s formal proof, which is the best kind. But you can also know something just through having experienced it. It is in this sense which I know, for instance, that my happiness is mostly a function of my inner state, rather than a function of what’s going on in my life. I’ve ascertained that experientially, though I can’t prove it to somebody else.

And a further kind of proof, I think, comes from a lot of people adopting a belief. We’ve never had any formal proof that democracy is a good idea; but the fact that a lot of people believe in it constitutes a strong argument for it. Similarly, the very fact that most people believe in God constitutes an argument in favor of God’s existence.

Now, if I have an idea, and I share it with other people, two things can happen. Other people can think the idea is good and adopt it; which boosts my confidence that the idea is right. Or other people can say, “hmm, I don’t think that’s such a good idea;” which lowers my confidence that the idea is right.

People act as a sounding board for each other’s ideas. You put an idea out there, and if it echoes throughout the social matrix, resounding again and again, then it’s a good idea. If it dies soon after it leaves its maker, then it’s not a good idea; so the theory goes.

The problem is that our social matrix doesn’t seem to be a very efficient sounding board. I’ve probably written up hundreds of philosophical ideas, but the number of these ideas that gained traction among my peers is close to zero. I spent years making music, but nobody really listened to my music.

Am I to conclude, from these facts, that I’m a bad philosopher and a bad musician? That seems false. More like, people aren’t listening to me. But I can’t just blame other people: maybe I’m not listening to other people either. We’re not listening to each other.

I think this is what stymies philosophy and metaphysics. To do philosophy, you really need the sounding board effect, because it’s basically all you’ve got. The social sounding board needs to be sensitive and of high quality. People need to be able to give you honest and sympathetic feedback based on genuine listening to your idea.

We don’t have that for philosophy. Even philosophy departments aren’t that. If you tell your idea to a philosophy professor, they’ll probably say it’s wrong. Everybody thinks everybody else is wrong in philosophy departments. That doesn’t get you anywhere; being told you’re always wrong teaches you nothing.

I think science has flourished over philosophy, religion, art, music, etc., in large part because science has the advantage of formal proof. With science, you can have ideas getting widespread traction, without people, y’know, actually having to listen deeply and sympathetically to each other. We don’t know how to listen, so we like science.

Skepticism? Skepticism!

For a long time I’ve been puzzled by skepticism. Skepticism is the perfectly rational idea that you should only believe something if it so captures you with its undeniable truth that you have no choice.

The problem is that it seems like a lot of religion breaks down under skepticism. But maybe a lot of religion is actually something I want to believe. So maybe I should be a little merciful with my doubting?

As of tonight’s experience, this no longer worries me. Skepticism is the correct position, and insofar as it really is certain, religion can defeat skepticism.

A true mystical experience cannot be doubted. The skeptic need only be willing to test the hypothesis that “if you use this mental technique, then you will be struck down by a Thing so fantastically brilliant and real that there will be no atom left in your body capable of denying it; and then you will be a believer.”

If the skeptic is a talented mystic, then after they do the experiment, they will be a believer: without having had to sacrifice an iota of their skepticism.

Faith! Faith?

I am absolutely bewildered by the word “faith.”

When I hear the word “faith,” I think of that inexplicable gusto that the mystics have, that tireless devotion and unswerving ‘inner certainty’ that lets them turn the Earth without guns or tanks, but only pure love and pure will.

But when I hear the word “faith,” I think of the act of believing in something without proof — i.e., something that you should never do.

Let me try to make you sympathetic to this idea. In science we go to outrageous lengths to make sure that we are right. We use these tedious, miserable things called “mathematics” and “formal reasoning” to try to rule out all possibility of error. We spend a lot of time caring about tiny, trivial things, just to avoid being wrong.

And you know what? Half the time, we’re still wrong. Turns out it’s really, really hard to be reliably correct, correct without error, not merely thinking that you’re correct but actually, truly correct.

No matter how intuitively appealing your idea is, sometimes you do the math and find out it’s wrong. Not just partially wrong, not just reduced to a matter of opinion — but flat out wrong. And sometimes you even do the math, and it all checks out and looks perfect, but then you find that you flipped a negative sign in one single, miserable equation and it makes the whole thing wrong. And if you’re a good scientist, you see that flipped negative sign and you throw out your beautiful idea and don’t look back.

You don’t struggle to salvage it, you don’t cling to it, and you sure as hell don’t start doing fuzzy epistemology like “oh you know, some things are a matter of opinion; let’s just agree to disagree; reason has its limits after all; you scientists think you know everything, but there’s a lot of mystery in the universe.” No. You just throw the idea in the garbage bin. Because hey, it might be beautiful, but it’s not true.

So: faith? Believing in something without proof? Without any proof at all? Hell to the no, not if you want to be right. If one flipped negative sign can destroy a brilliant scientist’s beautiful, meticulously constructed theory in its entirety, what the hell makes you think you can believe something without proof?

Now Euthypro in the audience pipes up. “OK, I get it, we’re wrong a lot, and so if we want to be sure we’re right we need proof. But surely you can’t do this all the time? You yourself pointed out that life is too complicated to scientifically study every aspect of it before we do anything. That’s not feasible. Our informally drawn conclusions are the best we’ve got; and sometimes, most of the time even, we’ve just got to go with them for the decisions we make.”

Yes, I agree. I have opinions. I have beliefs that I haven’t proven. But there are different degrees of belief. There’s the “I’ll still say the same thing if you ask me tomorrow” degree of belief. There’s the “I’ll make logical deductions from it” degree of belief. And then there’s the “I’ll tell the whole damn world and mercilessly shoot down anybody who disagrees with me” degree of belief.

This final degree of belief, you may informatively note, is almost exclusively found in scientists, politicians, and the religious.

The scientists? They deserve it. They really are right. The politicians? The religious? It’s entirely less clear that they deserve it. Not because scientists are some special, privileged group. But because it’s entirely less clear that the politicians and the religious, regarding the claim that sets them so afire, really are right.

Now let’s take an informative example: creationism. There are people who teach this in public schools, for crying out loud. That is surely the final, ultimate level of dominance that any belief can obtain. And creationism, at least in its more naive forms, is false.

In general, religious people are entirely willing to get up on the pulpit and preach their beliefs, as truth, without proof, while absolutely oozing that pompous air of authority. As a lover of the truth, this bothers me. I’m all for religion. But I’m also all for, well, actually being right before you get up on that pulpit. And I’ve seen how hard it is to achieve that.

Now we return to why I am perplexed by the word “faith.” This word surely denotes the highest and purest religious attitude, the most desirable quality that a person could have. And yet it also denotes believing something without proof. Which is something that you should never do. What am I to think about this?

Now Euthyphro says, “OK, so just invent two words. One of them can mean the highest, purest religious attitude, and the other one can mean believing something without proof. No more conflict.”

But I feel like they have something to do with each other.

I don’t really have any answers here. I just want to point out that I am confused as hell about this word. I think we philosophers don’t do enough admitting when we’re confused.

Three Seekers of Truth

Meet Warren. Warren is a physicist. He loves understanding things. He gets excited about calculus. He thinks that black holes are the coolest things ever. He thinks that they’re even cooler once you know the physics. To Warren, a rainbow doesn’t lose any of its beauty after you understand how it works. What Warren wants to do with his life is use science to make the world better, and share his love for the truth with other people.

Now meet Alexander. Alexander is a lot like Warren. He, too, loves understanding things. He, too, loves the truth. But unlike Warren, Alexander believes in God. He had a conversion experience as a teenager, where God revealed Himself to him, and his life was changed forever. Now Alexander studies philosophy, theology, metaphysics. He sees himself as a privileged witness to a great, hidden truth. He sees himself as a light-bringer, one who was sent to bring knowledge of the spirit to the world.

Now meet Ram. Ram is a lot like Alexander. He, too, has experienced enlightenment. He, too, feels himself to have been a witness to a deep, eternal truth. But Ram rarely talks about it. Maybe he’s a monk living in the forest; maybe he’s homeless; maybe he’s bagging groceries at the store near your house; maybe he’s teaching math at a local high school. Ram is enlightened, but his response to that fact was just to keep living his life. He’s the Zen master on the corner; he’s the Buddha begging for change; he is an enlightened man disguised as an ordinary person.

Warren is the rationalist. Alexander is the metaphysician. Ram is the mystic. These three have an intimate, tangled relationship with each other. I have seen the archetypal conflicts of that relationship played out in my life over and over again: between me and my friends, between public figures and other public figures, and most especially, between me and myself.

I pointed out that Alexander is a lot like Ram. But Warren is a little like Ram, too. Warren’s wonder at the beauty and order of the universe can approach the same sort of stupefying ecstasy whose momentary occurrence shapes and defines the lives of Ram and Alexander. Warren’s steadfast conviction of the worth of knowing, the vow he made in his heart to follow the truth wherever it leads, is rather akin to the religious conviction that captivates and consumes Ram and Alexander.

Warren has strong beliefs about reality. He believes that science is the only way to seek the truth. He believes that materialism is true; reductionism is true; the mind is the brain; God does not exist; we do not have souls; everything follows the laws of physics. To Warren all of these things are basic and obvious.

Alexander, too, has strong beliefs about reality. He believes that God is real, and the purpose of human life is to seek union with Him. Alexander believes that we live forever. He believes in a metaphysical realm beyond the physical universe and the means of human observation. Unlike Warren, who believes that truth comes only through reasoning and empirical observation, Alexander believes that truth can come through gnosis, through “inner knowing.”

Warren and Alexander have an ongoing drama. They each have their philosophical convictions, and each feels that these are important points that everybody needs to appreciate. Each feels not only that their beliefs are *true*, but that the world would be a better place if everybody accepted them. But they don’t agree with each other, and so they get into interminable arguments.

What a complex relationship these two have! How many layers there are to their social dynamic! Each feels superior to the other. Each feels like he is enlightened one, and the other is lost and off the path. Each wants to convince the other.

Why? Partly as a demonstration of dominance. Partly out of a sincere desire to help the other, by sharing with the other what was so valuable to the self. And partly out of a sense of insecurity, a buried fear that maybe you are right and I am wrong.

And funnily enough, each feels, deep down, that the other has something to offer them. They might never admit it. But this is part of the perversity of their relationship, that each is rather attracted to the other’s philosophy. If only subconsciously, they want to learn it.

If you are skeptical of this claim, consider this. When I am totally sure that somebody else is wrong, and I don’t expect to change their minds, then I just ignore them. To feel the impulse to argue, I need a little fear. Cranks don’t scare me. What scares me is when I think somebody’s wrong, but I have the feeling of truth pulling me toward their view, and yet I can’t stand the thought that it really is true. That is when I will start trying to refute them.

Warren is scared of Alexander, and Alexander is scared of Warren. Neither will admit it. Warren admires Alexander, and Alexander admires Warren. Neither will admit it. This is the secret, buried aspect of their relationship. Neither will admit that the other affects them.

That is the social aspect of Warren and Alexander’s relationship. But they see their problem as an intellectual one. For them, it is not a matter of how you make me feel and how I make you feel. Rather, it is a question of whether or not God really exists, whether or not the mind really is the brain, and so forth. It is purely a question of what is really true, and not about the people talking about it. That is how they feel.

To a great extent, they obscure their social problems from themselves by thinking that there is only an intellectual problem. Of course, let us not make the opposite mistake, of thinking that there is only a social problem, and ignoring the intellectual problem. It is clear that there is a genuine intellectual problem being discussed. But this intellectual aspect is almost overly clear; it is so naked and so thoroughly examined that it seems like there is almost nothing more to gain from analyzing it further. On the other hand the social aspect of the problem is quite obscured, quite ignored, quite neglected. Mightn’t making new intellectual progress depend upon first making new social progress? Mightn’t having a productive discussion depend upon finding a new *way* of discussing?

So that is Warren and Alexander. There is another complex relationship that we must examine: that between Alexander and Ram.

Ram is quite obviously the entire source of Alexander’s inspiration. Alexander can be himself only insofar as he can approximate being like Ram. His metaphysical knowledge is an empty and worthless shell indeed without the pure, experiential mysticism that Ram lives so fully; and Alexander *knows* this, if not in every moment.

Alexander’s entire game can be described like this. Having imperfectly grasped, through the veil of the intellect, the wisdom that Ram lives, Alexander practices a mysticism that is always distorted by his continual attempts to employ logic in areas where it is not helpful. (The concept of “areas where logic is not helpful” amuses Warren immensely!) Sometimes Alexander is oblivious to his own folly; other times he is aware of it but doesn’t know what to do about it. He doesn’t know *how* he would live other than through his intellect.

Ram’s attitude towards Alexander is very simple. For Ram, Alexander is exactly as beautiful and insignificant as the flowers he passes on his morning walk. But Alexander has a very complex attitude towards Ram. He is allured, bewildered, mystified, humbled, belitted by Ram. And, at the same time, he routinely utterly fails to notice when Ram passes him by on the street. He routinely fails to hear Ram’s worldless teachings because he drowns them out by all his talking.

That is Ram and Alexander. Our final pairing is Warren and Ram, who barely know each other at all. Warren doesn’t know what mysticism is, and even if he did, he would have no problem with it. Warren doesn’t have anywhere to disagree with Ram, because Ram never says anything. On the other hand, Ram has heard of science, and he finds it as beautiful and insignificant as the flowers he passes on his morning walk.

A corrollary of this fact is that, for Ram, there is no problem of reconciling rationality and mysticism. Ram never saw any conflict to begin with.

Mysterious Words

Bob and Elaine are scientists who live in a two-dimensional world called Finlandia. The people of Finlandia have a culture much like our own, including elaborately developed physics and mathematics. All of their physics and mathematics are in two dimensions. Everything they experience is in two dimensions.

One day, Bob has a vision of a three-dimensional sphere. He tries to explain his revelation to Elaine.

Bob: “I saw something grand and marvelous! Something unlike anything I’ve ever seen before!”
Elaine: “What was it?”
Bob: “Uh… It was this amazing thing! The most profound revelation I’ve ever had!”
Elaine: “Cool, but what was it?”
Bob: “It’s hard to explain. I think it might have been like the thing discussed in that old sacred text, ‘The Revelations of Thoth.’ I’m thinking of the passage that goes, ‘…and it shall be a form beyond form, a substance beyond substance, outside the world, without the limits of corporeal existence, and all men shall wonder at it.'”
Elaine: “But modern science has thoroughly falsified the Revelations of Thoth. Only the uneducated and superstitious believe in that any more. Are you slipping out of common sense, Bob?”
Bob: “Look, I know it doesn’t fit with science, but I saw it! It was right there in front of my eyes!”
Elaine: “Well, I’d like to see it for myself. Do you know how I can do that?”
Bob: “No, I have no idea. The vision just came to me.”
Elaine: “That’s no good. Well if I can’t see it for myself, can you at least explain clearly what you saw?”
Bob: “Yeah, the Revelations of Thoth explains it perfectly clearly.”
Elaine: “Hmm, well I don’t really understand it. I’m not sure that what Thoth is saying even makes logical sense. Can you try to explain it more clearly?”
Bob: “Sure, let me give it a try.”
[thinks for a few moments]
Bob: “I guess I saw outside space. I transcended space.”
Elaine: “What would that mean?”
Bob: “Uhh, there was this thing. It was like a circle, but it wasn’t anything like an ordinary circle. It was a super-circle.”
Elaine: “What is a super-circle? I mean, I know what a circle is, but what was ‘super’ about this circle?”
Bob: “It was outside space.”
Elaine: “That sounds like nonsense.”
Bob: “I’m telling you, it was outside space!”
Elaine: “What would that even mean?”
Bob: “Hmm, this isn’t working. I need to think more, and then I’ll get back to you.”
[the next day]
Bob: “OK, maybe now I can explain. So we have a circle, of radius r. Except that the circle is also every size smaller than r, and it repeats itself infinitely in super-space, without ever becoming more than one thing.”
Elaine: “Well that’s starting to look more like an explanation. But it’s full of contradictions and undefined terms. How could a circle be more than one size? How could something be repeated infinitely while only being one thing? And what the heck is super-space? You’re not even using your terms consistently. Before you said that thing was outside space; now you say that it’s in super-space. Which is it? And what would either of those even mean?”
Bob: “Well they really mean the same thing, you see. But you have a good point. I’m really bothered by my inability to explain this thing clearly. Let me try again and get back to you.”
[the next day]
Bob: “OK, I’ve got it now. Imagine a point, which expands to become a circle, and then shrinks back down to a point. Except this process is timeless. It is in every state at once, in an eternal state of superposition.”
Elaine: “Hmm… Here’s the thing, Bob. Your explanations sound sensible and scientific on the surface, but if you look more closely, they don’t really make sense. Like, what you said has a formal, mathematical flavor to it, but it can’t actually correspond to a coherent idea. What would it mean for a process to be timeless? How could a circle be more than one radius at once? And what do you mean by ‘superposition?’ I mean, I know what that word normally means in the context of physics, but you’ve appropriated it in a way that doesn’t make sense. I’m starting to lose faith in you, Bob. I think you’re just spouting pseudoscientific nonsense.”
Bob: “Huh! [storms off angrily]”
[a few days later]
Bob: “Elaine, I think I figured out why I can’t explain the super-circle to you. It’s beyond math, beyond physics, beyond language, even beyond thought. We can’t understand it with the intellect. It breaks logic. That’s why it can’t be explained in language. The only way to understand it is through direct experience. Anybody who hasn’t had a vision of a super-circle can’t make sense of discourse about it.”
Elaine: “…I don’t know what to say to that. I think you’ve lost it.”

Bob was not the first person to have a vision of a sphere. The person who wrote the Revelations of Thoth had also had such a vision; as had many Finlandian mystics. Even some Finlandian mathematicians had had visions of three-dimensional objects, but they generally kept the visions to themselves, for fear of being thought insane. So occasionally conversations like the one between Bob and Elaine would happen; but the concept of three-dimensional objects never gained wide acceptance in the scientific community.

This was true until several hundred years after Bob lived, when a mathematician laid down the theoretical framework which could generalize to arbitrary numbers of dimensions. This was harder for Finlandians to think of than it was for us, because they only had two data points from which to notice the pattern of N dimensions, whereas we had three.

Initially there was a great deal of controversy about the theory of higher dimensions. But it eventually became accepted, because it helped to resolve some obscure problems in physics and higher mathematics.

A lot of people regarded the theory of higher dimensions as nothing more than a meaningless formal device. Of course, the mathematician who formulated the theory was working from his direct experience of higher dimensions; and other mathematicians had such experiences, or intuited the possibility of such experiences. So there was an ongoing debate between the higher-dimensional formalists, and the higher-dimensional realists.

Why was Bob unable to speak clearly about spheres? I think the basic reason was that they were outside of “consensus reality.” Since there was no analogy to spheres in ordinary Finlandian experience, there was not even adequate language to talk about them.

At first Bob simply spoke in vast, empty superlatives: “super,” “transcendent,” etc. When pushed to make his ideas more logically precise, he ended up with things that half made sense, but were full of undefined terms and logical contradictions. It is understandable that he finally concluded that spheres were indescribable and ineffable, beyond the limits of thought.

Bob and Elaine’s dialogue is intended as an allegory about mysticism. Bob’s discourse is very similar to mystical discourse about God, the Tao, Brahman, etc.

“Tao” is a word much like “super-circle.” We know that we mean something by it, but we don’t know exactly what. “Tao” is a placeholder for “this mysterious thing that we have some vague ideas about but don’t understand well enough to talk about clearly.”

The further analogy between the Tao and the super-circle is that both of them refer to things which only some people experience. Somebody sees a sphere and then goes around talking about it, making no sense to the people who haven’t seen a sphere. That is also how it is for the Tao.

The person who has experienced the Tao thinks, rightly, that they will not make sense to anybody who has not experienced the Tao. But there is an additional level on which they don’t make sense even to themselves.

Nobody has a firm grasp on the Tao, in the way that we have a firm grasp on, say, trigonometry. The Tao is something that is mysterious unto us. So when we talk about the Tao, we are talking about something of which we have a very shaky understanding.

Philosophy is full of mysterious words like this. “Mind,” “consciousness,” “qualia,” “idea,” “existence,” “a priori,” “truth,” “probability,” “property,” “should,” etc. We know that we mean something by these words; but we don’t know exactly what.

Philosophy is almost exclusively a discipline of thinking about things that are mysterious unto us. This can account for many facts about philosophy. It can account for its lack of rigor, relative to math and science; for the lack of consensus among philosophers; for the way that problems go unsolved for thousands of years. These are all things that we would expect to see in a discipline of thinking about mysterious questions.

I do not think that an idea’s being mysterious, vague, or speculative is reason to refrain from talking about it. Surely there is use in talking about consciousness, thoughts, ethics — and yes, the Tao — even though we don’t really know what any of these things are.

Reductionism II

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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