A Logical Definition of Love

Logic and Love

We can all see patterns of behavior, but that is not to say that behavior follows patterns. This paper is to define a pattern that I have found in the ideas and actions which mankind has used the word love to describe. Any axioms and assumptions I make must be accepted as true for the majority of society.

This paper is most certainly not a rigorous proof, however I still want to follow a logical flow, so I need a solid foundation to work from. My chosen axioms are based on what would seem to me, as traits shared by our society as a whole. Traits so common, I’d say they’re ubiquitous and can support the rest of my contention. To state this axiom I must stereotype our culture, as must be done to discuss any large collection of things as a whole. Thus my coming argument can only be valid for the stereotyped portion of society which this axiom applies to.

With that said, I will use this as my pedestal…

 Axiom 1 - People want what they do not have.

Seems pretty straight forward. It’s a very widely used phrase which has given birth to many idioms and philosophical quotes – “The grass is always greener on the other side of the fence”, “Have one’s cake and eat it too”, etc.

I’m using this declaration in more of a metaphysical sense however. The word ‘have’ in my usage refers to a sense of intellectual ownership. To completely and thoroughly ‘understand’ a given topic (if that is even possible) instills a sense of possession, a custody of the intellectual property. Let’s say I have been taking derivatives since I was a fetus and now I ‘understand’ everything there is to know about derivatives and rates of change. Then in my mind I feel I can do with derivatives anything I please, just as I can do anything I please with this dead fish I’m holding in my hands. I ‘understand’ derivatives, just as much as I ‘have’ this fish.

So from here on I’m replacing the word ‘have’ with the word ‘understand’. I know this next claim may ruffle some feathers initially, but give me a moment to justify it.

 Axiom 2 - People want what they do not understand

This may seem off the wall at first, but it’s true. A colloquy might go as follows…

hooplehead - "A lot of people don't understand physics, and the lot of them
              hate it!"
mathnathan - "What do they hate?"
hooplehead - "Well, all of it! It's just confusing math, and Greek symbols."
mathnathan - "Do they hate televisions, and airplanes, and satellites?"
hooplehead - "Well no, of course not. But those aren't physics."
mathnathan - "Then what are they?"
hooplehead - "It's just technology, stuff that we use. Physics is the math
              and the equations behind it."
mathnathan - "Would you disagree with me if I said everything comes from
hooplehead - "Well no. I see where you're going with this though, you
              think that because this technology came from physics, it
              is physics?"
mathnathan - "Not at all. I'm sure you'd agree however, that just as in
              religions and in our families, the creator, or those which
              make things possible deserve high reverence and
              respect, no?"
hooplehead - "Yes, that is true. Religions promote worship of their
              gods for giving them life, and children are taught to respect
              their parents and elders for making their lives possible
              as well. I see what you mean."
mathnathan - "Then you'd agree that people at least respect physics."
hooplehead - "Hmmm... Yes, this I agree with."
mathnathan - "Why do you suppose that is?"
hooplehead - "They respect what it can do."
mathnathan - "Physics has made a lot of things possible, it's quite powerful
              is it not?"
hooplehead - "It is..."
mathnathan - "Would you disagree that people as a whole, yearn for power?
              Whether for selfish, or righteous gains?"
hooplehead - "Hmmm, that may be debatable."
mathnathan - "Power brings possibility, and that can bring necessities.
              Even if indirectly or on a small scale people yearn for
              power to make things happen, for the betterment of
              society, or for the betterment of themselves.
              Either way, people do yearn for power."
hooplehead - "Okay, I'll give you that one."
mathnathan - "So if people want power, and physics is power, then people
              want to have physics."
hooplehead - "Well you can't have physics."
mathnathan - "Then they would want to be able to use it's power, so they
              would want to understand physics."
hooplehead - "I suppose they would..."

What happens if people do understand something then? (2) has a truth value so I can apply some laws of propositional logic to it.

Since (2) is actually an implication, or the “if-then” logic structure it can be written as follows…

 Axiom 2 - If people do not understand it, then they want it.

Notice this says nothing about what happens if people do understand something. This states if they don’t understand it, they want it. That is all it says. so I need another axiom.

Again I chose to look at the world around me to find another trait riddled in our personalities, and characters.

Music… Everyone has a favorite song. We’ll listen to the song over and over and over. Eventually though, we know every word. We can hum every chord progression. We know the life story of the musicians. We heard the song performed live… And eventually we move onto a new song.

Books… Stories are an excellent example. There is so much mystery in the plot twists, or there is so much drama in the love triangles that we can’t put the books down. However, after reading the book 5 times, the appeal begins to die. We know exactly what is going to happen to the Sally if she opens that door…

Movies… Plays… Art… After it is wholesomely digested we move on to something else.

Once we know something entirely, inside and out, then our desire to ‘have’, or ‘understand’ it dies. Which lead me to my 3rd axiom.

 Axiom 3 - If people do understand it, then they do not want it.

I hope all of my pure mathematicians reading this noticed that (3) is the inverse implication of (2). Of course the irrational behavior of humans would satisfy this…

There are occasions which may look like exceptions. Humphrey likes this painting so much, that no matter how many times he looks at it, it fills him with euphoria. No matter how many times Gretchen listens to this song it still gives her chills. My theory can explain these anomalies, and I’ll touch on them again at the end.

Why did our interest in these physical things die? Their existence, and their complexities are finite. A book is a book is a book. We see a new book that intrigues us, and by (2) we’ve got to have that book. The book can not change though, and once our minds have mastered it’s existence, by (3) we move on to another book. Our desires for things in the physical world follow a cyclical path. Our cycle from (2) -> (3) -> (2) -> (3) continues to spin, we just introduce new infatuations from the physical world to accommodate it.

People are not books… Nor are they songs, or movies, or sculptures. Though some people may look like they were sculpted out of stone, fortunately for us they were not. People have a constant ability to grow and learn and their inner complexities can become more and more complex with experience and knowledge. So let’s say we see a person who looks as if they were sculpted from stone and they appeal to us. Just as in finding an intriguing book, by (2) we want this person! We get close to this person, and begin to learn about them. The more we learn about them, the more they learn about us. They become more and more sophisticated with what we’ve contributed to them, and our contributions become more and more sophisticated with that they contribute to us. THIS cycle breaks our previous cycle, and (3) is never reached.

From the perspective of an entire planet the life of a living thing lasts no longer than the blink of an eye, and this cycle throughout our history has claimed the majority of many lives. We are no longer interested in trying to understand anything else. This struggle to understand someone matches the ideas and actions that our culture defines with the word love.

Which brings me to my definition of love.

 Theorem 1 - Love is the unending attempt to understand someone.

What about when people say they ‘love’ things, or ideas? This theorem leads to an intuitive corollary which can answer those as well.

Corollary 1 - To love something unchanging is the self-reflection of your
              changes due to that thing, leading to the unending attempt to
              understand yourself.

Corollary 1 encapsulates the idea of loving yourself. If you were in a moment wildly memorable, and a particular song was played, that song will stick with you for a long time. You’ll listen to it later on and remember the moment and the feelings that came along with it. Let’s say however that this moment was so impacting that it changed your life. This is like a semi-circle of the cycle of love. This moment contributed to the growth and development of you, so when reliving the moment, over and over, the change that this moment brought to you meets who you are now. So you can “relive” the change and this song will constantly be changing you. With that foundation, I say that through this self reflection you’re constantly trying to understand yourself.

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9 Responses to A Logical Definition of Love

  1. John says:

    Nathan, this is a very interesting way to define “love”…and very mathematical too. I can tell you really worked hard on it, and that what you wrote is what you really feel about “love.” It’s a very extensive piece, but I feel that you have done justice in attempting to portray to your readers how you view the topic as something serious and not trivial. Superb.

  2. Lugh says:

    You have a hiccup in your logic, specifically surrounding Axiom 1. It becomes increasingly obvious later in your argument as you define around it.

    It is not as simple as “People want what they do not have.” For instance, I do not have malaria, and I do not want malaria. Even your example of physics betrays a personal bias. There are people who do not want physics. They may want the results of physics. They almost certainly want someone else to want physics. But they do not want the physics themselves.

    Later in your argument, this subtle bias crops up again and again. You refer to people “who appeal to us.” Or an “intriguing” book. It is clear that you understand that “not having” is a necessary but not sufficient condition for “wanting.” There must be at least one other quality involved, that quality that creates “appeal.”

    That quality is also necessary to avoid the obvious flaw exposed by extending the argument to the extreme. No person can ever completely understand another person. If you understand some portion of a person, but not all of that person, then, by your argument, you should fall into the loop of loving that person. Consequently, we should all love each and every person we meet. However, this is patently not the case.

    We need to add another condition. But, it cannot be as simple as “appeal.” That causes the entire argument to collapse into “People want what they want.” However, I think we can manage this without getting too far down into the weeds.

    Because we are talking about wants, we can safely hedge out needs. We are talking gastronomic delights here, not survival rations. Romantic love, not procreation and furtherance of the species. So we cannot explain it on the basis of physical urges. One common thread is certainly sensual pleasure. But, that does not explain love, either of a good woman or a good book. I do not think we can fall back on some Platonic ideal of “good,” as that would mean that we should all love the same things.

    For the sake of this argument, let’s simply say, “People want things that will make their lives better.” That could be a sensual pleasure that improves your environment, an intellectual pleasure that engages your brain, or an emotional pleasure that soothes your soul. It’s still a bit circular, but I think it will do for now.

    When you add this as an “AND” condition everywhere you discuss “understanding,” you can end up with a much more powerful and robust final theorem: “Love is the unending attempt to understand someone who makes your life better.”

    (As a note, please do not take this excessively long comment as an indication that I do not like your post. Indeed, it is an indication that I like it very much. I just wanted to shore up your argument a bit. I would be very interested in seeing where you take it from here.)

  3. Nathan Crock says:

    Lugh: Your criticism is invaluable! I am both humbled and flattered that you’d take the time to contribute such well constructed ideas to my own. I see exactly your point, and I’m looking forward to tweaking this and making it a persuasive argument. Thank you for your input!

  4. Lemontree says:

    Amazing (You + Lugh). Thanks for sharing.

  5. Dubs says:

    I think one analogy (ignoring Lugh’s wonderful addition) is that the first cycle [(2) --> (3) --> (2) --> (3)] is like Z, infinite and unending. On the other hand, the “love” cycle is an infinite and never ending attempt to reach the concrete goal (3); in this way, the cycle is like ℝ ∈ [0,1]. This set is infinite and unending, but it is also a much larger set than Z, or more precisely, ℝ ∈ [0,1] is uncountably large. (And that’s with the limit [0,1].) In this way, love is something that is much more… worthwhile? it has uncountable possibilities, unlike material desires, and yet the cycle maintains a concrete goal.

    I think it makes sense, but I can’t be sure.
    (I suppose Lugh’s addition could be included without really changing what I’m saying.)

  6. Hey Nathan… fun to find your post. Love your logic (‘spose you’ll take that to mean that I don’t fully understand it :)

    And, I’ll bite and throw in another viewpoint… The love that you have defined as an ‘attempt to understand’ intimates a ‘taking’ sort of love, a looking/seeking experience, a romantic looking to be fulfilled sort of love. Romantic love, and love, are often two very different creatures. As you’ll see the Theorem I propose seems somewhat opposite to yours.

    I’d like to offer the beginnings for a proposal on a logic for love that can be applied to anyone, not just a romantic partner.
    Here you go… hope you can have some fun with it:
    Axiom 1 – People fear the unknown in other people.
    Axiom 2 – People fear what they do not understand/accept in others.
    – If people do not understand/accept other people, they fear them.
    Axiom 3 – If people do understand/accept others, then they do not fear them.
    Theorem 1 – Love is the ability to offer understanding/acceptance to others.

  7. Nathan Crock says:


    I appreciate that you read my post, and I’m glad my ‘logic’ had a positive impact on you, haha. When it comes to metaphysical things as complex and intricate as love I don’t think there is one correct way to define it, just a way that makes sense to you. I wrote this post as a way to share my perspective on love and how it makes sense to me. I hope that it may enlighten someone somewhere.

    Thank you for taking the time to share your thoughts on love, it seems to me that you’ve put much more time into exploring it than I. I do plan to rewrite this one day and the input that you, Dubs, and Lugh have provided will form an excellent foundation for a more persuasive and robust theory.

  8. Lanora says:

    As a Newbie, I am always searching online for articles that can

    be of assistance to me. Thank you

  9. MichaelBrew says:

    Love as used in a romantic relationship is the extent to which one satisfies a certain group of needs of the other.it can be a need to belong,family,happiness,time,security,finance,stability,sex,shared ambition etc.The hypothesis is that the choice of person you “love” is defined by the extent to which that person cateres to those needs & most crucial in what ratio distribution according to the reciever’s priorities.A new love connection can be attributed to a factor of 1,when disatisfaction arises the factor drops to a lower tolerance value below which minimum to 0 love can exist.This hypothesis defines a soul mate as an ununique person who posseses qualities that satisfies receivers needs naturally in close proximity to desired priority ratio distribution & giving a factor of 1.The probability of meeting a soul mate in a giving lifetime is equal to 1 divided by world population which is 0,nth 0
    therefor A wife/husband is a derivative of this soul mate and can be defined as the person with the maximum factor closest to 1 out of all people a person has met.

    Michael S Brew

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