Uncategories and empty categories




What does "savory" mean when talking about food? Merriam-Webster says:

  • having a pleasant taste or smell
  • having a spicy or salty quality without being sweet
  • pleasing to the sense of taste especially by reason of effective seasoning
  • pungently flavorful without sweetness

Macmillan says:

  • a small piece of food that tastes of salt or spices and is not sweet

But when found in the wild, "savory" is usually contrasted with sweet, and is either freed from the "salt or spices" requirement, or used in a context that already implies "salty, spicy, or sweet." As this debate on chowhounds shows, plenty of cooks think "savory" means "not sweet." It is then not a category, but an uncategory, defined by what it is not.

Spirit as uncategory

Recently I had a conversation with a woman who wanted to know whether I really believed only in material things. I said, no; I also believed in magnetic fields and gravity, for instance.

She said those didn't count, because magnetic fields and gravity fields are explained by particle interactions. I said, maybe they are, but I still believed in them after I stopped believing in the soul, but before anybody told me they were mediated by particles.

She said gravity and magnetism are deterministic. I said I also believed in quantum mechanics. She said that didn't count as belief in something non-material either, because the things we see quantum-mechanical effects in aren't intelligent.

I was confused: What did being intelligent have to do with being material? She said that non-material things were spirits, and spirits were intelligent.

I should have immediately realized where this was going, but I pressed on. I said I was willing to believe that one could use gravitational forces to build a (very very large) computer, with a quantum-mechanical random number generator, and then implement an intelligent program on it, and would that count as a spirit?

By this time she was getting a little upset with me, and said, approximately, that a spirit is an intelligent being, not composed of analyzable simpler parts, whose interactions with our world are not subject to any physical laws or statistical regularities, yet which can perceive our actions and cause things to happen in our world.

That meant if she found something she called a spirit, and I found that it had a mind containing information about our world, that would prove there were statistical regularities in its interaction with our world, and a configuration of parts to store the information, and it would by definition no longer be a spirit.

She'd begun with the postulate that intelligence was unexplainable, perhaps because that was what she needed God for. So she defined a category that meant "intelligent beings that have no parts and no information and cannot be observed in our universe" and used it to explain human intelligence.

This category combined two important categories of uncategories: impossible uncategories defined not to be anything that exists, and inaccessible uncategories defined not to be anything that can be observed. Both are empty categories, defined so that you can't find any members.

There turn out to be a lot of these! Platonic forms, magic, soul, essence...

God as the ultimate empty category

Suppose you want your tribe to obey a set of rules. So you tell them the rules were made by an old man called God.

Pretty soon the tribe is tired of these rules, and they ask where God is, so they can argue with him. Well, you can't say he's three valleys over, or they might go there and look. You have to say he isn't anywhere they can go. God is an inaccessible uncategory.

Try this experiment on a religious friend: Tell him you think you might believe in God. Then ask him to list the qualities that define God. Argue with anything using the word "perfect", like "a perfect being, perfectly just, perfectly loving," etc. (Anything that requires perfection is an uncategory, but they aren't helpful just now.)

If you can get him to settle for a list of sufficient conditions like "created the universe," "can know anything in the universe," "has power over everything in the universe," etc., then tell him that, yes, you now believe in God. After he's finished congratulating you, explain that you have decided that it's almost certain, based on your priors, that we live in a simulation, and the being who runs this simulation is God. You call Him Fred. Most likely He's the super(universe) equivalent of a grad student.

Your religious friend may say that isn't believing in God. Go over the list of God's attributes he just made, and ask which one Fred doesn't have.

(Pro tip: Avoid trying this experiment on family members.)

Fred seems too real. Many difficulties with any given monotheistic religion have been pushed into the God concept and dismissed by adding another impossible quality to God. You could call God the ultimate uncategory, the node in a religious GUT where nonsense accretes. A God who exists might not have all those qualities. So the concept of God has been constructed and connotated to make sure anybody who exists can't be Him.

People seldom start religions by saying they're God. They say they're God's messenger, or maybe God's son. But not God. Then God would be this guy you saw stub his toe, and he'd end up like that guy in "The Man Who Would Be King."2

Empty categories protect false beliefs

Rarely, such uncategories may be created deliberately, such as Russell's "the set of all sets that do not contain themselves." But there's no need to suppose most were made deliberately.

Most new theories are bad theories. A bad theory whose parts are all open to inspection can be easily dismissed. But a bad theory that postulates an entity or category that has a definition that sounds satisfiable, but is not, is harder to dismiss. All the difficulties in the theory can be pushed into the empty category, where they are safe from attack, since no one can find an instance of the class. If the postulated entity is an agent (spirits, God, a homunculus), any qualities needed by the theory (absolute goodness, infallibility, oracular computational power) can be attributed to it without fear of disproof. So theories with empty categories are selected for and accumulate in religion, psychology, philosophy, and ethics, where people have beliefs that (A) are stated in terms of vague, abstract concepts, and that (B) they care about deeply enough to tolerate the phrase "it is obvious that" in a proof.

Empty categories like spirit and God are easy to catch. But there are more subtle empty categories.

Free Will

To ask if a mental process is made under free will, you start by observing how its inputs determine its distribution of outcomes. If the distribution has a single value, you say that it's deterministic. If it's random, you say that randomness isn't free will. If it has a probability distribution, you say it is a mix of determinism and randomness. If you can't define its inputs or outputs, you can't call it a process and can't ask whether free will was involved.

The only way you could decide someone had free will was if you found a homunculus inside them making their choices. "Free will" is an uncategory that defends the belief that humans are special and not made out of parts.

(I could be wrong. Consciousness is still mysterious.)

Non-computational consciousness

See John Searle's Chinese room argument. Or don't. It defines consciousness as an impossible uncategory, arguing that anything that can be understood obviously can't be conscious.


Note I did not say "virtue." "Virtue" is a category; societies list the behaviors they want out of people. Even if the list just says "Men: Violent. Women: Chaste," those are behaviors that can be observed. When the Greeks, who believed in fate, spoke of virtue, they didn't get so worked up over the "merit" aspect of it. Great warriors had virtue, even if they merely inherited it by being the son of a god, and even if, like Achilles, they didn't want to act heroically.

Christians, who believed in free will and an eternal destination dependent on it, came to think more in terms of merit. A person forced to do something gains no merit from it; neither does a person who did it accidentally. Merit exists only where free will does.

Because we believe in free will, we try to make social rules and laws give people what they "merit" rather than maximize social utility. Instead of making sure to imprison the criminal who has a brain injury that makes him violent, we set him free, because it isn't his fault. Instead of giving scholarships to students who score high on tests, to invest in our future, we give them to students who score high relative to their demographically-predicted scores.

But if you investigate the "merit" of any actual human, you'll find an endless regress of circumstances which all of the blame or credit eventually accumulates to.

Human terminal values

Humans are genes' way of reproducing themselves. Human behavior implements a utility function all of whose terminal values are statements about gene allele frequencies. As humans were not even aware of allele frequencies until recently, anything a human thinks it values cannot be a terminal value of a human utility function. As the terminal values of different alleles are at odds with each other, nearly all the values of any given human's utility functions are competing in zero sum games with the values of other humans.

A human society's values are ultimately stated in terms of the gene alleles common in that society. These tend to be the values we think of as human values, because they often supervene on rationality and must be expressed explicitly. But, again, they benefit genes, not humans.

Most of the time, this is fine with us. We get hungry; we eat. We're cold; we put on a jacket. Our interests are largely aligned with those of our genes. But if for some reason you want to know what "human terminal values" are, and collect them into a set of non-contradictory values, ethics gets untenable, because your terminal values benefit alleles, not humans, and play zero-sum games, not games with benefits to trade or compromise.

There are two schools of thought current now in psychology regarding human values. One says that evolution encodes human values directly, and so we're stuck today with values that evolved in the Stone Age. People from this school of thought often say that racism, xenophobia, homophobia, and/or rape are human values, and attempts to mitigate them go against human nature. (For example, [3], [4], [5], [6].)

The other school of thought says that evolution encodes the computational ability to choose behaviors that implement human values in the particular environment [7]. Hence, men may have preferred women with narrow waists a hundred years ago, but (they argue) have changed in some modern societies since the sexual revolution in the 1970s to prefer women with wider waists. People subconsciously compute that they no longer want to be racist and xenophobic in an era in which trading with other cultures is more beneficial to our genes than killing them.

Neither school of thought would allow that many things we think of as human values really are. Consider the reactions of a mother and father on finding out their son is gay. They may be able to accept this and value their son's happiness above social pressure. But all current scientific theories of human behavior would say that parents are programmed to want their children not to be gay. Parents who tolerate homosexuality in a child have overwritten their terminal genetic values with instrumental human values, period.

Neither school would propose that human terminal values contain anything we, as modern humans, value. Either we are Stone Age machines programmed to hate, rape, and kill, or we are computers subconsciously optimizing our reproductive efficiency, that will switch from toleration, liberalism, and rationality to racism, conservatism, and religion as soon as conditions change.

There is a school of thought that has tried to develop a consistent set of human terminal values that could be programmed into a symbolic logic. They first assume that there exists a finite set of concepts with which you can represent the world in a context-insensitive manner, as is required for symbolic logic. Then they have looked for a consistent minimal set of terminal values behind existing expressed human values. They resolve conflicts between values by prioritizing the values in this set, and have successfully come up with a set of values that, as you might predict, in many ways optimizes the genetic fitness of people who observe them. They take the genes' side in most reproductive issues, including homosexuality, incest, birth control, and abortion. We call this school of thought the Catholic Church.

ADDED: If you don't believe that humans, human preferences, and your feelings, were produced by evolution, this is not the place to have that argument.

2. If they do claim to have some sort of personal godhood, or not to be dictating the thoughts of some higher being, they'll speak in aphorisms and parables, or invent their own vocabularies, so that you can't argue with them (Jesus, Buddha, Hegel).

3. Thornhill & Palmer (2000). A Natural History of Rape. Cambridge, MA: MIT Press.

4. Santos, Meyer-Lindenberg, Deruelle (2010). Absence of racial, but not gender, stereotyping in Williams syndrome children. Current Biology 20(7):R307-308.

5. Edward Wilson (1975). Sociobiology. Cambridge, MA: Harvard University Press.

6. Steven Pinker (2002). The Blank Slate. NYC: Viking.

7. David Buller (2006). Adapting Minds: Evolutionary Psychology and the Persistent Quest for Human Nature. Cambridge, MA: MIT Press.