two_laws.md

title
The Two Laws of Love

The Two Laws of Love

Consider the following two laws:

For people $$A$$, $$B$$, and $$C$$,

1. Law of Symmetry: If $$A$$ loves $$B$$, then $$B$$ loves $$A$$.
2. Law of Transitivity: If $$A$$ loves $$B$$ and $$B$$ loves $$C$$, then $$A$$ loves $$C$$.

These laws probably seem patently false. Please withhold your disbelief until you see how they are used. Just like laws in the sciences, they are part of a system that governs how and when to apply them, and they cannot be evaluated apart from that system.

Here are some rationales for the law of symmetry:

• $$B$$ is grateful for $$A$$'s love, so they love $$A$$ in return.
• $$A$$'s kinetic love has helped $$B$$, so $$B$$ kinetically loves $$A$$ to aid them in continuing to help $$B$$.

And some rationales for the law of transitivity:

• Since $$A$$ loves $$B$$ potentially, $$A$$ wants $$B$$'s desires to be fulfilled. One of $$B$$'s desires is for $$C$$ to be supported (kinetically loved). Thus $$A$$ also wants $$C$$ to be supported.
• One of the things that $$B$$ does with their time is help $$C$$. $$A$$ loves $$B$$ in part by helping $$B$$ help $$C$$.

Notation

It will be useful to introduce some symbols. Here is how the law of symmetry looks with these symbols:

$$A\heart B \vdash B \heart A$$

Here we have used the symbol "$$\heart$$" instead of the word "loves", and we have used the symbol "$$\vdash$$" instead of the words "If...then".

A tangent about why I chose the symbol $$\vdash$$:

The symbol $$\vdash$$ is called a "turnstile" and it is used in formal logic for inferences, i.e. $$P\vdash Q$$ means that we infer $$Q$$ from $$P$$ according to some agreed-upon "rules of inference". We use it here because the law of symmetry is somewhat like an inference: we are inferring that $$B\heart A$$ from prior knowledge that $$A\heart B$$. Of course, a better way to look at it is that $$B\heart A$$ is an event which happens because of the event $$A\heart B$$. But since mathematicians usually concern themselves with ideas and not material reality, there is no symbol for causality. I decided to use the turnstile for causality because I think of it as the material version of inference. While inference brings one belief in my mind to another, causality brings one event in the material world to another. In keeping with this conceit, I will also use the word "inference" to describe causations such as that from $$A\heart B$$ to $$B\heart A$$. Marx and Engels similarly reappropriated idealist language for material reality, as in their use of the word "dialectic". [insert link explaining this last point]

And the law of transitivity:

$$A\heart B,B \heart C \vdash A\heart C$$

So the two events $$A\heart B$$ and $$B\heart C$$ together cause $$A\heart C$$. We separate these events with a comma "$$,$$".

Communities

In their current state, these laws don't explain very much. But one thing they do explain is the division of society into commuunities. To see this, let us draw a graph representing the society. Dots will represent people, and we will draw an arrow from one dot to another to indicate that the person represented by the first dot loves the person represented by the second dot.

{% include svg/diagrams/community1.svg %}

BTW, what we have just drawn is a mathematical object called a directed graph. A graph consists of dots and lines connecting them. The word "directed" indicates that the lines are actually arrows, i.e. they have direction.

Notice that this diagram obeys both laws. It obeys symmetry because whenever there is an arrow from a dot $$A$$ to a dot $$B$$, there is also an arrow going back from dot $$B$$ to dot $$A$$. It obeys transitivity because whenever there are arrows from $$A$$ to $$B$$ and from $$B$$ to $$C$$, there is also an arrow from $$A$$ to $$C$$.

In this diagram, we can see that people are partitioned into separate communities, and everybody in a community loves everybody else in that community and nobody in a different community. If two people $$A$$ and $$B$$ were in separate communities and $$A\heart B$$, then everybody in $$A$$'s community would also love $$B$$ through transitivity, and again by transitivity all these people in $$A$$'s community would love everybody in $$B$$'s community too, so $$A$$ and $$B$$ would actually end up being in the same community after all.

Also notice that everybody who is in a community loves themself, but people who are not in communities sometimes love themself and sometimes don't. In fact, the two laws of love ensure that people in communities will love themself, but carry no such assurance for people who are not in communities. We will talk more about this in the later section Genesis of Self-Love.

So at the current stage of our development, society is partitioned into communities. These communities don't overlap, and not everybody is in one.

The Four Caveats

To make these laws seem less reductive, we introduce the following four caveats:

1. Fuzziness: Love is a fuzzy relation. This means that a person $$A$$ doesn't just love or not-love a person $$B$$, there are degrees of loving. $$A$$ can love $$B$$ more or less. The statement $$A\heart B$$ isn't simply true or false, there are degrees of truth. {% include svg/diagrams/fuzzy.svg %}

{:start="2"} 2. Delay: The two laws of love have delays built in. If $$A$$ loves $$B$$, then $$B$$ will love $$A$$ later. If $$A$$ loves $$B$$ and $$B$$ loves $$C$$, then $$A$$ will love $$C$$ later. 3. Lossiness: There is a loss involved with each of the above laws. If $$A$$ loves $$B$$, then later $$B$$ will love $$A$$ less (than how much $$A$$ loves $$B$$). If $$A$$ loves $$B$$ and $$B$$ loves $$C$$, then later $$A$$ will love $$C$$ less. 4. Normativity: The conclusions of the above laws is merely normative. So if $$A$$ loves $$B$$, then after a delay $$B$$ will feel a normative force to love $$A$$ (to a lesser degree than $$A$$ loves $$B$$). Similarly, if $$A$$ loves $$B$$ and $$B$$ loves $$C$$, then sometime later $$A$$ will experience a normative force to love $$C$$.

This still probably seems preposterous. What does it mean for there to be a delay? Love does not happen at a single moment, it is a continuous process. And why must there be a loss? That sounds sad. Can't $$B$$ love $$A$$ as much as $$A$$ loves $$B$$? These questions will be addressed soon when we talk about maintaining love. For now, consider the following rationales:

• Rationale for delay of symmetry law: $$A$$ loves $$B$$, but $$B$$ doesn't notice right away. When $$B$$ notices, they then normatively love $$A$$ back. Delay is the time it takes takes for ostensive love to be noticed.
• Rationale for lossiness of transitivity law: Suppose $$A$$ loves $$B$$ and $$B$$ loves $$C$$. $$A$$ won't love $$C$$ as much as $$B$$ does, because there is more separation. They probably don't even know $$C$$ as well. They also won't love $$C$$ as much as they love $$B$$. Right now they only care about $$C$$ because $$B$$ does, $$C$$ doesn't matter much to them in $$C$$'s own right.

How do these caveats impact the communities that form? Well, since love is fuzzy, the communities also become fuzzy. Their boundaries become weaker, and they now can overlap. The delayed nature of the laws means that the boundaries of the communities can shift over time as new arrows between dots arise. The normativity means that within a community, not every arrow need be actual love, some arrows may be merely normative. Now we have a much better picture of reality!

The genesis of self-love

People in our theory do not automatically love themselves. It does not violate either law for someone to not love themselves. However, the laws do explain the circumstances whereby someone might come to love themself. Let us tell a parable about where self-love comes from.

Suppose $$A$$ is isolated, i.e. they are not part of any community, so they don't love anyone, no one loves them, and they don't love themself.

{% include svg/diagrams/selfLove1.svg %}

$$A$$ will acquire self-love in three steps.

Step 1: Another person $$B$$ begins to love $$A$$.

{% include svg/diagrams/selfLove2.svg %}

Step 2: By symmetry, $$A$$ begins to love $$B$$.

{% include svg/diagrams/selfLove3.svg %}

Step 3: By transitivity, since $$A\heart B$$ and $$B\heart A$$, $$A\heart A$$.

{% include svg/diagrams/selfLove4.svg %}

So that is how $$A$$'s self-love originates. In fact, it is the only way it could originate from the two laws of love.

A good way to think about this parable is to suppose that $$A$$ is a newborn baby and $$B$$ is $$A$$'s caretaker. Since a newborn baby is not generally isolated, we can say that step 1 occurs before birth. At some point, the baby will reciprocate and love their caretaker back (step 2). Since they are lovable in the eyes of their caretaker whom they love, they will also begin to love themself (step 3).

We can apply the rationales for transitivity given above to better understand this last step. We will write them again here, but in place of $$A$$ and $$C$$ we will refer to the baby, and in place of $$B$$ we will refer to the caretaker of the baby.

• Since the baby loves the caretaker potentially, the baby wants the caretaker's desires to be fulfilled. One of the caretaker's desires is for the baby to be supported (kinetically loved). Thus the baby also wants themself to be supported, i.e. they love themself.
• One of the things that the caretaker does with their time is kinetically love the baby. The baby loves their caretaker in part by helping the caretaker kinetically love the baby, so the baby kinetically loves themself.

I think that this process is necessary for people to love themselves. I don't think that people just automatically love themselves. The love of other people (whom I love) is the reason for me to love myself --- without it I have no reason to.

This is especially clear in the case in which $$A$$ is a newborn baby. If a newborn baby never had any caretaker who loved them kinetically, they would die quickly. Then need someone else to love them kinetically before they can acquire the means to love themself kinetically.

Even when someone is no longer a baby, this process must be reinforced for them to maintain their love for themself. Thus we are led to a slight modification of our previous model: we now say that love decays over time. For self-love, or really any kind of love, to maintain, it must be replenished by repeated applications of symmetry and transitivity. This answers our previous question about lossiness. The inferences are lossy, but repeated applications will combine to counter the loss.

The Replenishing of Self-Love

There are three ways that self-love can be replenished.

1. $$A\heart B,B\heart A \vdash A\heart A$$. This is what we just described. In addition to replenishing self-love, it is the origin of self-love. In general this inference is more effective if there are many different $$B$$'s through which it happens, and even more if these $$B$$s know each other, i.e. if $$A$$ is in a community.

2. $$A\heart A\vdash A\heart A$$, by symmetry. $$A$$ is grateful for the love of themself, so they reciprocate by loving themself. Alternatively, they apprciate the love that they get from themself, so they support themself, that this love may continue.

3. $$A \heart A, A\heart A \vdash A\heart A$$, by transitivity. Since I love myself, I will help myself do the things that "myself" wants to do. One of these things is to help myself. So I will help myself help myself, i.e. I will help myself.

I think that all three of these mechanisms are necessary for self-love to be maintained. The second and third ways are very tautological, and they happen very fast, since they take place within a single mind. The repeated applications of them give a fractal structure to self-love, and they help it stay alive in the short-term. However, for long term maintainance the first way is needed, i.e. you have to actually be part of a community.

Self-Love: What could go wrong

If a person $$A$$ doesn't love themself very much, then part of this process has to be deficient. There are 4 possibilities for what could be deficient:

• There could be no person $$B$$ who loves $$A$$. This is genuine isolation.

• $$A$$ could be insufficiently reactive to the normative force of the inference $$B\heart A \vdash A\heart B$$ that occurs in step 2 of the "genesis of self-love" parable above. In other words, something prevents $$A$$ from reciprocating their love to $$B$$.

• $$A$$ could be insufficiently reactive to the normative force of the inference $$A\heart B, B\heart A\vdash A\heart A$$ that occurs in step 3 of this parable. In other words, something prevents $$A$$ from caring about people that people they love care about. even when they love $$B$$.

• There could be obstacles in $$A$$'s thought to the self-maintaince of their self-love through the second and third mechanisms shown above.

Interests

Here is a way of looking at love. Needless to say, I don't think it's the only way.

Suppose each person has a set of "interests". I don't mean "interests" in the sense of "I'm interested in math", I mean interests in the sense of "it is in my best interest to eat well". My set of interests is the set of all things that are in my interest.

Now consider the following interpretation of love:

"$$A$$ loves $$B$$" means that all of $$B$$'s interests are also $$A$$'s interests.

or alternatively,

that $$A$$'s interests include $$B$$'s interests.

If $$I(A)$$ is the set of all $$A$$'s interests and $$I(B)$$ is the set of all $$B$$'s interests, then this interpretation says:

$$A\heart B$$ means that $$I(B)\subseteq I(A)$$

The idea is that if $$A$$ loves $$B$$, then whatever is good for $$B$$ if it happens is also good for $$A$$ if it happens. It's in $$B$$'s interest to eat well? Then it's also in $$A$$'s interest for $$B$$ to eat well. It's in $$B$$'s interest for $$C$$ to lose his bicycle? Then it's also in $$A$$'s interest for $$C$$ to lose his bicycle.

This interpretation of love gives a great explanation of the law of transitivity. If the interests of $$A$$ include those of $$B$$ and the interests of $$B$$ include those of $$C$$, then those of $$A$$ will include those of $$C$$.

{% include svg/diagrams/interestsEuler.svg %}

Now the law of symmetry, with the caveats, says broadly that if $$A$$'s interests include $$B$$'s, there will be a tendency for $$B$$'s interests to start to include $$A$$'s. Thus the law of symmetry is revealed as a general tendency for the interests of people in communities to converge.

This interpretation can also be modified to account for fuzziness. $$I(A)$$ might include all, most, some, very little, etc. of $$I(B)$$ and we can interpret these degrees of inclusion as degrees to which $$A\heart B$$.

We can also identify a person with their interests. Who I am, my identity, is in a sense, the things that I do or attempt to do, i.e. my interests. Under this identification, when I love someone they become part of me since all their interests are also my interests. When two people love each other, they become in a sense the same person. When the interests of people in a community converge, the community becomes in a sense a single organism, with a single common set of interests.

Empathy

We can look at transitivity through the concept of empathy. When $$A$$ loves $$B$$, $$A$$ empathizes with $$B$$ to feel $$B$$'s feelings as their own. If $$B\heart C$$, then $$A$$ empathizes with $$B$$ to feel $$B$$'s love for $$C$$ --- hence $$A\heart C$$.

Here is one inference that this way of looking at transitivity clarifies. Suppose $$A\heart B$$ and $$C\heart B$$.

{% include svg/diagrams/empathy1.svg %}

Suppose that for whatever reason, $$B$$ is not very reactive to the normative force of the inference $$C\heart B \vdash B\heart C$$, so that $$B\heart C$$ stays purely normative. Since $$B\heart C$$ lacks actual reality, I use a dashed line for the arrow from $$B$$ to $$C$$.

{% include svg/diagrams/empathy2.svg %}

So $$B$$ feels a normative force to love $$C$$. Since $$A\heart B$$, $$A$$ empathizes with $$B$$ and thus also feels this force. Thus $$A\heart C$$ normatively.

{% include svg/diagrams/empathy3.svg %}

Now $$A$$ and $$B$$ both feel normative forces to love $$C$$. $$A$$'s normative force is weaker than $$B$$'s, because of the loss associated with the $$A\heart B,B\heart C\vdash A\heart C$$ inference. But $$A$$ and $$B$$ have different reactivities to normative forces, because the other things in their life are different. We have stipulated the $$B$$ has a low reactivity to the normative force to love $$C$$, and thus doesn't actually love $$C$$. However, it is possible for $$A$$'s reactivity to the normative force to love $$C$$ to be strong enough that $$A$$ begins to actually love $$C$$ in spite of the weaker normative force.

{% include svg/diagrams/empathy4.svg %}

What is going on, in more usual language, is something like this. $$A$$ loves $$B$$ and sees that $$C$$ is helping $$B$$. $$B$$ for whatever reason doesn't reciprocate the love of $$B$$, even though they feel they should. $$A$$, on the other hand, thankful to $$C$$ for loving $$B$$, steps in and assists $$C$$ in their efforts to love $$B$$, as well as loving $$C$$ in general.

If we look at people as their interests, as described in the end of the previous section, then when $$A\heart B$$, $$B$$ is a part of $$A$$. Then, when $$C$$ helps $$B$$, they help a part of $$A$$, so $$A\heart C$$ according to a simple application of the law of symmetry: $$C\heart A\vdash A\heart C$$.

Communities Built Around A Common Love

One application of the previous section is that in which $$B$$ is not a person, but rather some activity that $$A$$ and $$C$$ both like doing, a project they both like working on, or even a non-existent being such as God that they both purport to love.

We can indeed incorporate non-living and even non-existent entities into our model. They can be loved, but sadly they cannot kinetically or potentially love. They can, on the other hand, ostensively love (it does seem to some people that God loves). It is useful to speak of a non-living or non-existent entity normatively loving, even though they can't act on the normative force to actually love.

For sake of illustration, suppose that $$B$$ is (some conception of) God. We now go through the same narrative as in the previous section. We start with both $$A$$ and $$C$$ loving God:

{% include svg/diagrams/empathy1.svg %}

Then $$\textrm{God}\heart C$$ by symmetry. But since God is non-existent and can't actually love $$C$$, this love is merely normative and ostensive. It is normative because God should love $$C$$ given all $$C$$ has done for God, and it is ostensive because it appears that $$\textrm{God}\heart C$$.

{% include svg/diagrams/empathy2.svg %}

$$\textrm{God}\heart C$$ ostensively with respect to $$A$$, i.e. it seems to $$A$$ like $$\textrm{God}\heart C$$. From $$A$$'s perspective, $$A\heart \textrm{God}$$ and $$\textrm{God}\heart C$$ --- thus $$A$$ begins to love $$C$$.

{% include svg/diagrams/empathy4.svg %}

$$A$$ also begins to love $$C$$ because of the logic discussed in the previous section: $$A$$ empathizes with God, by virtue of $$A$$'s love for God. Since $$A$$ perceives that $$C$$ has gained favor in God's eyes, and that God should want to help $$C$$ in return, $$A$$ takes this task upon themself, and begins to love $$C$$.

This is the logic by which religious communities and other communities built upon a common love form. A bunch of people who all love God will start to love each other, just as $$A$$ and $$C$$, united by a common love of God, begin to love each other. As stated above, $$B$$ actually doesn't have to be God per se, but could be a mission or activity. Then the resulting community is not a religious community, but rather a community built around that mission or activity.

We can also view the formation of communities in this way with the interpretation of love in terms of interests. If a whole bunch of people all love $$B$$, then their interests all include the interests of $$B$$. Thus their interests all overlap. We have previously analyzed the law of symmetry and found that it is a general tendency for interests that overlap to start to overlap even more. This implies that the interests of these people will begin to overlap more, i.e. they will begin to love each other.

Maintaining Relationships

We have looked at how self-love is maintained. Now we look at how love for another person is maintained. Here are three inferences that reinforce $$A$$'s love for $$B$$:

1. $$B\heart A\vdash A\heart B$$ (symmetry). In other words, if $$A$$'s love is reciprocated, it is easier to maintain.

2. $$A\heart C,C\heart B\vdash A\heart B$$ (transitivity). If $$A$$ also loves someone else who loves $$B$$, that can reinforce $$A\heart B$$.

3. $$A\heart A,A\heart B\vdash A\heart B$$ (transitivity). Since $$A$$ cares about themself, they care about the things they care about --- and one of those things is $$B$$.

4. $$A\heart B, B\heart B \vdash A\heart B$$ (transitivity). Since $$A$$ loves $$B$$, they want $$B$$'s desires to be fulfilled. One of these desires is for $$B$$'s desires to be fulfilled. Thus $$A$$ wants $$B$$'s desires to be fulfilled.

Inference 3 is of special note. It is the only inference of those listed which does not rely on other people than $$A$$. Through inference 3, $$A$$ can just decide, independently of everything else, that they are going to maintain their love for $$B$$ and that is that.

Inference 2 is also important because it does not rely on the person being loved.

Now suppose $$A$$ is tasked with taking care of someone, $$B$$, who isn't capable of reciprocating, and doesn't love themself very much either. This is a position that a social worker or doctor might find themselves in, if they are tasked with taking care of a very unlikable person. Then inferences 1 and 4 are not possible mechanisms for reinforcing $$A\heart B$$. So $$A$$ must maintain their love for $$B$$ through inferences 2 and 3 alone. Inference 2 is the force of will, integrity, and self-love, and inference 3 is the support of people $$C$$ in the community. If $$A$$ is a social worker caring for a very depressed person, $$C$$ is a person in the community whom $$A$$ respects (i.e. $$A\heart C$$) and who approves of the idea that $$B$$ should be cared for (i.e. $$C\heart B$$). Thus, it takes a lot of self-love (3) and community support (2) to love someone who doesn't reciprocate or love themself.

On the other hand, if $$A$$ lacks self-love, inference 3 is not a possible mechanism for reinforcing their love of $$B$$. Lacking inference 3 makes it very difficult to maintain love. Thus inference 2 will also be difficult, because it will be hard to find people $$C$$ that $$A$$ loves. The only mechanisms available for $$A$$ to use to maintain their love for $$B$$ are inferences 1 and 4, which are both provided by characteristics of $$B$$ (namely, $$B$$'s self-love and $$B$$'s love for $$A$$). These characteristics are what the archetypical social worker (now called $$B$$) of the previous example provide to $$A$$, the depressed patient. $$A$$ can maintain their love for $$B$$ because $$B$$ has the self-love and community support necessary to maintain their love for $$A$$ (inference 1), and because $$A$$ sees that $$B$$ loves themself a lot and concludes that loving $$B$$ must be a good idea (inference 4). Thus we get to another way of saying the same thing as the previous paragraph: for someone who lacks self-love to maintain their love for someone, that someone must love themselves a lot and reciprocate a lot.

[I used a bit of semi-circular logic in the previous paragraph. I should talk about how really the solution is community.]

Love as a Quiver

Now we give our model another upgrade.

We have been representing $$A\heart B$$ with an arrow from $$A$$ to $$B$$. This arrow decays with time, and must be replenished by a steady supply of new inferences.

Now we say that there can be multiple arrows from $$A$$ to $$B$$. These multiple arrows represent different ways that $$A$$ loves $$B$$. They can also represent ways that $$A$$ hates $$B$$, or any other manifestation of intimacy (we will talk about hate in the later section). Each arrow is an event that takes place at a particular time, and it will never be repeated. These arrows decay, and eventually vanish. Love is maintained by replenishing them with a steady supply of new arrows. New arrows are generated by new inferences, which will never generate an arrow that has already been generated in the past.

We call this model a quiver, because a quiver (aka multigraph) is the mathematical object which is like a graph but where there can be multiple arrows between nodes.

This upgrade improves our model so that it captures

• That $$A$$ can love $$B$$ in multiple ways.

• That love evolves and changes in quality with time.

• That $$A$$ can simultaneously love and hate $$B$$. There is no contradiction here because love and hate are simply two different arrows from $$A$$ to $$B$$ that both occur at the same time. This is particularly important to keep in mind when reading the next couple sections about hate. Also important to keep in mind is that there can be multiple "hate" arrows from $$A$$ to $$B$$ representing different ways that $$A$$ hates $$B$$.

The Laws of Hate

Hate has all the same types/aspects as love: we can talk about kinetic hate (actually hurting someone), potential hate (having potential to hurt someone), normative hate (feeling compelled to hurt someone), and ostensive hate (seeming like you hate someone). Just like love is not just a feeling and is primarily about the action of helping someone, hate is also not just a feeling: it is primarily about the action of hurting someone.

We write hate with an upside down heart: $$A \butt B$$ is taken to mean that $$A$$ hates $$B$$.

Now we write the laws of hate.

1. Symmetry: $$A\butt B\vdash B\butt A$$. If $$A$$ hates $$B$$, then $$B$$ hates $$A$$. This makes sense. Basically, if $$A$$ does a bad thing to $$B$$ then $$B$$ hates $$A$$.

2. Transitivity: $$A\heart B, B\butt C\vdash A\butt C$$. If $$B$$ has an interest in hurting $$C$$ and $$A$$ loves $$B$$, then $$A$$ also has an interest in hurting $$C$$. In short, the enemy of my friend is my enemy.

3. Transitivity: $$A\butt B, B\heart C\vdash A\butt C$$. If $$A$$ hates $$B$$, then they want $$B$$'s desires to not be fulfilled. One of these desires is for $$C$$ to be free from harm. Thus $$A$$ wants $$C$$ not to be free from harm, i.e. $$A$$ hates $$C$$. In short, the friend of my enemy is my enemy as well.

4. Transitivity: $$A\butt B, B\butt C\vdash A\heart C$$. If $$B$$ hates $$C$$, then $$B$$ wants to hurt $$C$$. If $$A$$ hates $$B$$, then $$A$$ wants to hurt $$B$$ by thwarting their plans to hurt $$C$$, i.e. $$A$$ wants to help $$C$$. Thus $$A\heart C$$. In short, as the saying goes, "the enemy of my enemy is my friend".

Notice that these are just the same as the laws of love, except that $$\heart$$s are at times replaced by $$\butt$$s. The transitivity laws follow the same pattern as multiplying positive and negative numbers. Just as a positive times a negative is a negative, a $$\heart$$ and a $$\butt$$ produce a $$\butt$$. And just as a negative times a negative is a positive, two $$\butt$$s make a $$\heart$$. Thus we can speak of hate as negative love.

A Brief Recap of Our Changing Logic

Before continuing to talk about hate, I will recap the stages through which our logic has traveled so far.

1. (starting point) $$A$$ either loves $$B$$ or doesn't. In other words, $$A\heart B$$ is either true or false.

2. (the "fuzzy" caveat) There are degrees of love. $$A\heart B$$ can be more or less true. There is a continuous spectrum of truth, with "False" at one extreme and "True" at the other. {% include svg/diagrams/fuzzy.svg %}

{:start="3"} 3. (love as a quiver) Love is multifaceted. $$A$$ can love $$B$$ in multiple ways at the same time. Now $$A\heart B$$ looks like this: {% include svg/diagrams/multifaceted.svg %}

{:style="list-style-type: none;"} 100. Each arrow represents a different aspect of $$A$$'s love for $$B$$, and each arrow's truth lies somewhere on the spectrum from True to False.

{:start="4"} 4. (introduction of hate) Love can be negative, and this negative love is called hate. Now we have the same diagram as stage 3, except the truth of the arrows lies on a scale from $$-$$True to False to True. {% include svg/diagrams/bifuzzy.svg %}

The Genesis of Self-Hate

How does someone begin to hate themself? There are two possible mechanisms:

1. $$A\heart B, B\butt A \vdash A\butt A$$. This is the case where $$A$$ loves someone, $$B$$, who hates them. $$B$$ is perhaps an abusive parent of $$A$$, who kinetically hates $$A$$ although $$A$$ loves them. In this situation, $$A$$ starts to see themself through $$B$$'s eyes, and thus starts to hate themself as $$B$$ hates them.

2. $$A\butt B, B\heart A \vdash A\butt A$$. This is the case where $$A$$ hates someone, $$B$$, who loves them. Perhaps $$A$$ is now the abusive parent, and they kinetically hate their child, $$B$$, who loves them. Since $$B\heart A$$, $$B$$ is involved in helping $$A$$. Thus when $$A\butt B$$, $$A$$ damages something which helps themself, and thus $$A$$ hurts themself. Another instance of this is where $$A$$ is a traitor and $$B$$ is the community they have betrayed. Since their community benefits them, they have actually hurt themself through their act of betrayal, since they have sabotaged something that was benefiting them.

Both of these cimcumstances are abusive relationships. In the first, $$A$$ is the victim; in the second, $$A$$ is the abuser. Both roles engender self-hate.

It is not always bad to hate oneself. There are some aspects of me (for instance) that should be hated, and it is healthy for me to hate them and try to overcome them. There is a popular misconception that hating these aspects of myself is antithetical to my overcoming them, since I will just feel guilty and not get to the root of the problem. However, this is only a characteristic of ineffective hate. If I effectively hate the right parts of myself and I support myself in the effort to hate them, I do have a chance at overcoming them.

This benign self-hate can be generated with the same mechanisms as shown above, but the examples must be reinterpreted:

1. $$A\heart B, B\butt A\vdash A\butt A$$. $$B$$ is training $$A$$ in some sport, musical instrument, or other skill. In addition to helping $$A$$ learn things related to this skill, $$B$$ must also help $$A$$ unlearn things that impede this skill, such as bad habits $$A$$ got from school. $$B$$ kinetically hates the parts of $$A$$ that have these bad habits by advising and helping $$A$$ to get rid of them. Since $$A\heart B$$, $$B$$'s advice is accepted, and $$A$$ starts to kinetically hate these parts of themself as well. In this example, $$B$$ has actually loved $$A$$ by hating them and helping them hate themself.

2. $$A\butt B, B\heart A\vdash A\butt A$$. Suppose $$A$$ hurts $$B$$ (who loves $$A$$), and they feel guilty, as in the previous example. It is ethical and healthy for $$A$$ to hate themself, or at least the part of them which hurt $$B$$.

How Hate Can Unite a Community

Interestingly, the laws of hate have given us another means for the genesis of self-love. Suppose we start again with an isolated $$A$$.

{% include svg/diagrams/selfLove1.svg %}

Then $$B$$ comes along and hates $$A$$. I will denote hate with a red arrow.

{% include svg/diagrams/selfLoveHate2.svg %}

By the symmetry of hate, $$A$$ hates $$B$$ in return.

{% include svg/diagrams/selfLoveHate3.svg %}

Since $$A\butt B$$ and $$B\butt A$$, the transitivity of hate tells us that $$A\heart A$$.

{% include svg/diagrams/selfLoveHate4.svg %}

What has happened is that $$A$$ has united with themself against a common enemy, $$B$$. This makes a lot of sense in the case where $$A$$ is a community, and $$B$$ is a threat to the commuunity. The community $$A$$ unites and loves itself because through doing this it thrwarts the plans of the enemy $$B$$, who aims to hurt $$A$$.

The Consequences of Self-Hate

Now suppose $$A\butt A$$. How does it affect $$A$$'s relationships? We have 4 inferences:

1. $$A\butt A, A\heart B\vdash A\butt B$$. A self-hating person will hate those they love, because they can hurt themself by hurting those they love.

2. $$A\butt A, A\heart B\vdash A\butt B$$. A self-hating person will help their enemies, as by doing so they can hurt themself.

3. $$B\heart A,A\butt A\vdash B\butt A$$. If $$B$$ loves a self-hating person $$A$$, then $$B$$ might by hoodwinked into actually hating $$A$$, as they assist $$A$$ in hurting themself. This is enabling.

4. $$B\butt A,A\butt A\vdash B\heart A$$. If $$B$$ hates a self-hating person $$A$$, then $$B$$ might decide to help $$A$$, that $$A$$ may better hurt themself. Thus $$B\heart A$$.

Inferences 3 and 4 could be benign, if we take $$B$$ to be the trainer from the previous section. Since the trainer loves $$A$$, they will help $$A$$ hate certain parts of themself, i.e. they will hate $$A$$. And since the trainer $$B$$ hates these parts of $$A$$, $$B$$ will support $$A$$ in their efforts to hate them too, i.e. $$B$$ will love $$A$$.

In addition to describing some instances of depression, inferences 1 and 2 could descibe someone in the process of great change, who chooses to switch sides in a war, for instance. They hate who they used to be, which is themself, thus they hate themself. Out of hate for themself, they push away those who used to be on their side, and embrace those who used to be the enemy.

The Replenishing of Self-Hate

How is $$A$$'s self-hate mainatined? There are five possible mechanisms:

1. $$A\butt A\vdash A\butt A$$. A self-hating person hates themself in retaliation for the harm they have inflicted on themself. In other words, a self-hating person hates themself for being a self-hating person.

2. $$A\heart B, B\butt A\vdash A\butt A$$.

3. $$A\butt A, B\heart A\vdash A\butt A$$. These two inferences are identical to those in the section on the genesis of self-hate. They infer self-hate from an abusive relationship. But since every relationship that a self-hating person has is abusive, all reiationships that they have will reinforce their self-hate.

4. $$A\heart A, A\butt A\vdash A\butt A$$. $$A$$ loves themself, so they help themself hurt themself. Thus self-love also reinforces self-hate.

5. $$A\butt A, A\heart A\vdash A\butt A$$. $$A$$ hates themself, so they thwart their own efforts to love themself by hating themself.

Self-Hate Begets Self-Love

Consider this inference: $$A\butt A,A\butt A\vdash A\heart A$$. In other words, if $$A$$ hates themself, then they are the enemy of their enemy, so they are their friend! Thus self-hate begets self-love.

Let's think more about what this means. $$A$$ hates themself, so we can think of $$A$$ as divided against itself in two parts which hate each other.

{% include svg/diagrams/divided1.svg %}

Each part unites with itself against a common enemy, as descrbed in the section titled "How Hate Can Unite a Community".

{% include svg/diagrams/divided2.svg %}

This really happens. When someone hates themself, they unite with themself against themself, and the resulting self-love can be very powerful. People go to great lengths to hate themselves.

So both self-hate and self-love beget self-love, and any form of love or hate from another person begets self-love. The only person who would lack any semblance of self-love is the person who is completely isolated, such as the "isolated nodes" in the graph above.

Further Work

Here are some things that should be done:

• I think that the rule $$A\heart B, C\heart B \vdash A\heart C$$ may be more fundamental than transitivity, but I'm not sure. This should be thought about.

• I consistently conflate loving $$A$$ and loving a part or aspect of $$A$$. This conflation should be deconstructed.

• The structure of self-love, self-hate, love between two people, love in a community, etc. should be more comprehensively analyzed. If the laws of love keep being applied to generate new arrows from old, what is the general progression of the quiver?

• A lot of the concepts of this were initially from Erich Fromm's The Art of Loving. This book should be read in more detail and its insights applied.

• This theory should be developed by applying it to literature, biography, and history, where much more complex situations than my little examples arise. Also a good source of these examples of Adam Smith's The Theory of Moral Sentiments.

• It seems to me that saying $$A\heart B$$ is very similar to saying that $$B$$ is an interest of $$A$$. Thus $$I(A)$$ is the set of all entities that $$A$$ loves. These entities don't have to be people. But then $$I(A)$$ is not just a set, because it has lots of structure now. This gives a direct social manifestation of the Yoneda Lemma, and should be worked out in more detail.

• An analysis of dominance, submission, oppression, and liberation is sorely lacking. This needs to be added.

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• Write this feature for staticman so I will feel comfortable using it for comments!