What can first-order logic do for your self-esteem?

Whereas nerds stand to benefit, even more than normal people, from becoming more assertive, outgoing, optimistic, obamalike in temperament, and all those other good things,

Whereas the fundamental problem with nerds is that they’re constantly overthinking everything,

Whereas this means nerds are regularly beaten in life by people who think less than they do,

Whereas it also means that nerds can’t read self-help books without coming up with dozens of (generally sound) reasons why everything they’re reading is a load of crap,

Whereas there’s therefore a large unmet need for self-esteem-boosting, personality-improving materials that would somehow fly under nerds’ radar, disarming the rational skeptical parts of their brains,

This holiday season, as my present to all my nerd readers, I’ve decided to start an occasional series entitled Nerd Self-Help.

Today’s installment: What should you do when you find yourself asking whether you have any “right to exist”?

Pondering the problem this morning, I hit upon a solution: Ask yourself whether the integer 8 has any right to exist.

In first-order logic, existence is not even a property that can be predicated of objects.  Given a universe of objects, you can ask about properties of those objects: for example, is there a perfect cube which is one less than a perfect square?  But it’s simply assumed that when you use a phrase like “is there,” you’re quantifying over everything that exists.  (As many of you know, this was the basic insight behind Kant’s refutation of Anselm’s ontological proof of the existence of God: the notion of “a being that wouldn’t be perfect without the added perfection of existence,” said Kant, is gobbledygook.)

Similarly, I claim that if you were to formulate a theory of human rights in first-order logic in any “natural” way, then whether you have a right to exist is not even a question that would arise within that theory.  Such a theory might include your right to not be murdered, to get a fair trial, to engage in consensual sexual activities, to own property, etc., but not your “right to exist”: that “right,” to the extent it even made sense, would simply be presupposed by your being part of the universe of persons that the theory of rights was quantifying over.  In other words, the sequence of words “do I have the right to exist?” seems to me to dissolve on analysis, an ill-formed non-question.

Now, I don’t doubt that there are plenty of logical, metaphysical, and legal objections that might be raised against the above argument.  But here’s the key: don’t think about it too much!  Just trust that there’s a rational-sounding argument for why you shouldn’t doubt your right to exist, and be happy.

Merry Christmas, everyone!

41 Responses to “What can first-order logic do for your self-esteem?”

  1. Carl Says:

    Would you say this is of a piece with your general skepticism about anthropic arguments?

  2. Scott Says:

    Carl, depressed people worry about the rightness of their existence, whereas anthropicists merely worry about its probability. 🙂 Still, I guess it’s of a piece with my general skepticism about all philosophical questions.

    (Note that among scientists, this seems to put me in an extreme pro-philosophy fringe; many scientists don’t even think about philosophical questions enough to reject them as meaningless.)

  3. Or Says:

    Does this mean that the question of abortions is undecidable in any theory of human rights that is formulated in higher-order logic (since we can not reason about whether unborn babies have right to exist)? 🙂

    It actually sounds plausible…

  4. Or Says:

    There was a typo in the last message: I meant to ask about theories formulated in first-order logic, of course.

  5. Scott Says:

    Or, I’d phrase that and related debates in terms of a “right to not be killed,” which I think of as subtly but crucially different from the “right to exist.” Even depressed people who brood about their not having any right to take up space on the earth, would probably run for their lives if a man with an ax were chasing them.

  6. michael vassar Says:

    I don’t think that overthinking is the fundamental problem, but I have written about this in Overcoming Bias.

    I think that a “rights” framework is very nerdy and is pathological to overdo however. Fortunately, it’s lacking in good intellectual foundations as well, so it’s easy to discard in a nerdy logical way.

  7. Jair Says:

    Scott, I’ve read this post over a couple times and I think I understand what you’re getting at: It’s not very helpful to assign a predicate E(x) to mean “x exists”, since you are forced to conclude ∀x E(x). After all ~∀x E(x) is equivalent to ∃x ~E(x), a contradiction. But I don’t see any logical problems with R(x) meaning “x has a right to exist”. After all, I’m pretty sure 3 has a right to exist, but I’m not at all sure whether, say, Chaitin’s constant or a well-ordering of the real numbers have a right to exist. I don’t trust ’em.
    I look forward to your next nerd self-help blog. You could discuss game-theoretical advantages of optimism and assertiveness.

  8. Bruce Says:

    There is a well-developed field called “free logic” in which existence is treated as a predicate, within a first-order framework. I don’t know whether this falls within your restriction of “natural”, but it is definitely an approach that has been studied extensively by many logicians over the past fifty years. Also, Lesniewski’s formal theories of ontology and mereology definitely deal with existence, although in a logical framework that doesn’t look like modern first-order logic (later formulations of mereology have been given as first order theories, or in more exotic systems like free logic or plural quantification systems.) Of course it is easy to object that none of these systems correspond to “first-order” logic as we typically think of it, but I’m assuming that you were trying to make a philosophical point and not just a definitional one.

  9. Joe G. Says:

    This seems pretty patronizing, especially the last paragraph. Your solution to nerds overthinking everything is: “don’t think about it too much! Just trust that there’s a rational-sounding argument”

  10. M. F. Mokbel Says:

    A more ill-formed non-question would be: Do I have a choice to exist or not?

    And it’s not that nerds only always overthinking everything, it is how we trained ourselves over time to think “correctly” in a simple and coherent way so as to reason about things in an elegant communicative form. Some nerds like to complicate things to understand how it works, and they found it more enjoyable than a straightforward answers, which might seems nonsense for them because it does not involve any sort of “long term thinking”. After all the truth is there, so either way will lead to the same conclusion. As Einstein said: “Everything should be made as simple as possible, but not simpler”.

  11. John Moeller Says:

    Joe G.:

    Isn’t self-help always patronizing? 🙂

  12. Jonathan Vos Post Says:

    Back when Philosophy departments were dominated by Moral Philosophy professors and and Theology professors, Clive Staples Lewis [29 November 1898 – 22 November 1963, the date of death being the same as that of John F. Kennedy], known to his friends including J. R. R. Tolkien as “Jack,” known to this generation primarily as the C. S. Lewis who wrote those Narnia books adapted into these movies) distinguished between debates about a “right to not be killed,” as subtly but crucially different from the “right to exist.”

    His example used an axiom of Angelology (really, Google that word) that Angels, being immortal, can’t be killed, even by God.

    Hence he asked the nuanced question: “can an Angel who exists be caused by God retroactively not to have existed?”

    He gave Old Testament and New Testament citations, some of which support “Yes” as an answer and some of which support “No.”

    He then sidestepped the Angelology and asked if Rome could be caused not to have been built.

    All this was to answer a snailmail from a lady (this being during World War I) who wanted to know if it was theologically reasonable for her to pray that her son, who had been in a battle and was thus either alive or dead, but the news of the outcome of the battle had not reached her, could be alive. That is, although God knew if he was alive or dead right now, could she expect God to respond to her prayer that the son be alive, whether or not in some tense not in English he had been dead but would be not having been dead?

    Clive Staples Lewis, not using Propositional nor Predicate nor Modal Logic, answered that he believed that God could, being omnipotent, undo causality. But, he suggested, God chose NOT to break His own laws, for essentially Aesthetic reasons, consistency being Beautiful.

    So far as I know, when Godel gave an axiomatization of the Ontological Argument, he did not factor in a sub-theory of God’s aesthetics.

    Philosophy departments have changed rather substantially. Whether Logic is taught at any given university by the Math department, the Philosophy Department, the Computer Science department, or the Electrical Engineering department is mostly a matter of historical accident. I was denied the right to teach Logic once when I was a Math professor, because the Dean of Arts and Sciences did not consider Logic to be Math!

  13. John Sidles Says:

    Speaking as the son of a Iowan Methodist Sunday-School teacher … who grew up to marry a Jewish/Hungarian writer … a woman who has just finished a (deeply personal) book that (in its foundations) is about happiness.

    My wife Constance found considerable virtues in Hava Tirosh-Samuelson’s weighty historical review Happiness in Pre-Modern Judaism: Virtue, Knowledge, and Well-Being.

    The preface can be found on Google Books, and it is well worth reading. From my Iowa farm-boy perspective, Prof. Tirosh-Samuelson’s work reads like a scholarly Judaic version of Dale Carnegie’s How to Stop Worrying and Start Living! (maybe an example of convergent evolution?)

    Happy holidays to all! 🙂

  14. math idiot Says:


    I hope your Nerd Self-help can discuss “the meaning of my existence”, a long thought problem without a solution to me, next time. Thanks.

  15. Scott Says:

    Joe G: It might be patronizing, if I weren’t hard at work on the not-thinking problem myself!

  16. snarles Says:

    Overthinking isn’t the problem; the problem is thinking about the wrong things.

    That said, I don’t know why anyone would question their right to exist. Morals are simply a way of defeating Prisoners’ Dillemas–the system of morals you should try to enforce is whatever system of morals best helps achieve a society you prefer.

  17. Cody Says:

    First, it seemed a little odd that you question your right to exist—I had never considered this, (though I should be a qualified nerd).

    Then it seemed strange that when faced with the question, “whether the integer 8 has any right to exist”, it is existence that breaks the question, rather than rights. Personally, I can only make sense of ‘good’ and ‘bad’ and ‘perfection’ and ‘rights’, within some specified context, (i.e. with respect to me, or you, or America, or vertebrates).
    Though my first order logic is certainly rusty, and you may be expressing something that conflicts with my stance.

    In either case, I hope everyone enjoys the season!

  18. Jonathan Vos Post Says:

    Since Cody mentions the season, I should add a comment on the appropriateness of that thought. As film reviewer/historian James Berardinelli points out, a famous novel and a famous film (about the same Christian holiday) explore the same narrative solution to the problem posed by Scott Aaronson.

    As wikipedia summarizes: Charles Dickens’s tale “A Christmas Carol” parallels “It’s a Wonderful Life” (1946), an American film produced and directed by Frank Capra and loosely based on the short story “The Greatest Gift” written by Philip Van Doren Stern (November 1939). “In both stories, a man revisits his life and potential death (or non-existence) with the help of supernatural agents, in the end experiencing a joyous epiphany and a renewed view of his life.”

    Death, as a halting state, is not identical to nonexistence, because it is reached by a different trajectory from life. Hence, in Fantasy literature at least (where we have no computational problem with Closed Timelike Curves), life has history variables as well as state variables. Whether this can be embedded in Quantum Mechanics and General Relativity or not, it would not be trivial to axiomatize.

  19. wolfgang Says:


    once you think about whether you over-think a problem then you have reached Nerd Level 2 imho.
    And writing a self-help blog post on how to avoid this dilemma should qualify you for Nerd Level 3.

    PS: I really like comment #7 which shows that you could have written your blog post in 2 lines.

  20. snarles Says:

    I like the “Nerd Levels.”

    Relatedly, suppose you had two skynet-type AI programs (each with access to networked robot factories) that had destroyed humanity, and were now dedicated to destroying each other. Suppose each side is about evenly matched. Now each AI has to figure out how many computer cycles to spend on gaining more processing power, building drones, building factories, developing new technologies, reconnaissance, hit-and-run attacks–but also how many computer cycles it can afford to spend on /optimizing/ these problems. But getting an estimate of how much CPU should be spent on strategy requires processing as well–how much time should each AI devote to figuring out how much time it should spend thinking about everything else? And as you can see, answering this question requires still more cycles… and ad infinitum. Therefore, maybe the best best for each AI is to simply randomly decide which how much time it should spend on each meta-level. (e.g. I’ll devote 100 cycles to thinking about thinking about thinking, 10000 to thinking about thinking, 10000000 on thinking, and 1000000000 on actually executing my plans.)

  21. MattF Says:

    What about a right to not be the empty set?

  22. Harrison Says:

    Q: Do I have a right to exist?

    A: Does 8?

    It’s very Zen; I like it. On that note, I suppose, Zen in general tends to place a heavy emphasis on “not overthinking it,” which is probably one of the reasons it’s attractive to me (and plenty of other nerdly types), if not as a philosophy, then as something interesting to learn about.

    And Merry Christmas and happy holidays, everyone!

  23. John Preskill Says:

    Damn! This blog is *weird*.

  24. Perry E. Metzger Says:

    The problem here is that higher order logics are too tempting.

  25. Cyril Says:

    “Even depressed people who brood about their not having any right to take up space on the earth, would probably run for their lives if a man with an ax were chasing them.”

    This is not about rights, this is about fears and wishes. Consider a depressed man who claims that there is no reason for him to live, staying at the edge of the roof. He will probably not jump and commit suicide, despite his claims. Was he lying indeed?

    Consider another man, quite happy and having a lot of reasons to live, staying at the edge of the roof. But now the building is in fire, and he will be roasted alive in a few minutes. On the other hand, there is a safety net above ground, so jumping is near safe, much safer that not jumping. Does he necessary jump? There was a lot of real cases when people doesn’t and was roasted alive, just because they have an uncontrollable fear of falling from high.

    So, maybe, the first man does really want not to live, just fears falling from high?

  26. Scott Says:

    Damn! This blog is *weird*.

    Thanks, John! I try. 🙂

  27. John Armstrong Says:

    wolfgang: clearly by considering this spectrum of Nerd Level 1, Nerd Level 2, and so on, you’ve placed yourself in Nerd Level $\omega$ (Scott plz fix LaTeX kthx).

    And then I’m in Nerd Level $\omega+1$.

    What we need is to find someone in Nerd Level $\epsilon_0$.

  28. matt Says:

    Scott, if you really want to not worry, just go do all the stuff you urge people not to do in scottaaronson.com/blog/?p=355 though be careful and build up slow. I’m serious about all three suggestions in that sentence.

    On the other hand, I totally disagree about one thing-8 does not exist in the same sense that we, the readers, exist. We’re all conscious beings. We actually exist. Hmm, there isn’t a good way to explain the difference. Penrose would say that we’ve got some reality that mathematical concepts lack. Turing probably wouldn’t. The basic distinction is that some people think a program can’t be conscious in the same way that we are and some think it can. It’s easy to be accused of mysticism for holding to the first belief, but it’s just as much mysticism to say that a program can be conscious like we are (and if you don’t think you’re conscious, that’s really a problem!).

  29. Leopold Says:

    8 doesn’t exist. Not in the sense we do, in this universe. 8 exists as mathematical object – in a world that has little to do with our own. We know the axioms of Formalia (we made them), and they don’t talk about “rights”. We don’t know our own morals – we know some, but not the whole deal – and we don’t know everything about the universe, and wouldn’t even if we were logically omniscient. Morality is meaningless in the world of math – not in this one. So do, you can’t dodge the question like that.

    Also, your “don’t think too much about it” advice sounds disturbingly like what you’ve written previously: http://www.scottaaronson.com/writings/selfdelusion.html
    I’ve installed gut reactions to block that. I’m not sure if I should, but I get confused otherwise.

  30. Rafee Kamouna Says:

    Dearest Scott,

    All answers are definitely (forcibly) TRUE, since ZFC is inconsistent!


    Keep it between you and me; don’t inform anybody.


    Rafee Kamouna.

  31. Jonathan Vos Post Says:

    Executive summary of a prior too-long submission:

    “8 does not exist in the same sense that we, the readers, exist.”

    That’s the oldest known metaphysical debate in Mathematics, or at least on ontological status of mathematical objects, with at least 8 or 9 factions:

    (1) Platonists (Transcendent Realists): 8 and triangles and
    aleph-null exist, if anything, MORE than humans do.

    (2) Logicists: all mathematical statements are necessary logical truths.

    (3) Formalists: mathematical statements are equivalent to statements about the consequences of certain string manipulation rules. (includes machine-readable proposal, the QED project, which might later become the basis for machine-generated proofs of fundamental Mathematical theorems, a.k.a. “Mapping the Genome of Mathematics.”)

    (4) Intuitionists:: “there are no non-experienced mathematical truths” [L.E.J. Brouwer].

    (5) Constructivists: only mathematical objects which can be finitely and explicitly constructed in a specific sense properly belong to mathematical discourse.

    (6) Fictionalists: reject or reverse Quine’s argument on indispensability.

    (7) Embodied Mind Theorists: mathematical thought is a natural outgrowth of the evolved human cognitive machinery embedded in our physical universe in efficacious ways that benefit Darwinian fitness.

    (8) Social Constructivists (Social Realists): mathematics is a social/cultural construct, akin to English Common Law, or the game of Chess, and are ultimately a political
    struggle of mathematicians seeking sex, money, or power.

    (9) Quasi-Empiricists

    There are also Linguistic theorists and Aesthetic theorists of
    the ontology of Mathematics. And I’m probably missing whole schools of thought. Bottom line: we oversimplify this ancient, subtle, and multi-polar debate at peril to our scholarship, if not our right to exist.

  32. Cody Says:

    Jonathan Vos Post, which one of those defines existence in a way that allows for both the abstract existence of mathematics and the physical existence of atoms, while preserving the stance of physicalism and rejecting all notions of supernaturalism?

  33. Lewis Powell Says:

    I recommend Aristotle’s Nicomachean Ethics as some more substantive nerd self-help.

    The basic idea is that our purpose in life is to be happy, and we can do that by habituating ourselves to moderation.


  34. math idiot Says:

    I am trying to answer my own question:”What is the meaning of my existence?” based on Scott’s logic:

    Today’s installment: What should you do when you find yourself asking whether you have any “meaning to exist”?

    Pondering the problem this morning, I hit upon a solution: Ask yourself whether an ant has any meaning to exist.

    My answer is:it is either none or for survival only.

  35. John Sidles Says:

    Those skilled philosophers at The Onion have presented a cogent analysis of Scott’s question in their recent Pre-Game Coin Toss Makes Jacksonville Jaguars Realize Randomness Of Life.

    As the coin-toss was in the air, [Jacksonville Jaguars running back Fred Taylor] was apparently struck by an existential epiphany, and asked the ref “What meaning can life have, if the future can be dictated by the random chance of this coin? Existence is a vulgar absurdity.”

    Coach Del Rio chewed Taylor out, telling him to “Quit pondering the inconsequence of being, in a universe governed by chaos, and just play some football!”

    The above is the beginning of a lengthy and exceedingly funny overview of philosophical conceptions of meaning, from the early Greeks and the premodern Jews and Christians, through 20th century existentialism.

    The Onion concludes with a one-line summary of the modern view of “meaning” as grounded in sociobiology, cognitive science, and game theory:

    Bad news for Jacksonville fans is good news for the rest of the AFC South!

    I stand in awe. Who are these folks at The Onion?

  36. matt Says:

    JVP said I wrote a “too long” submission. Does that win a prize or something? In any event, my post had nothing to do with the (non)existence of 8 and everything to do with the existence of conscious readers, so the whole ontology of math was kind of irrelevant.

  37. Niel Says:

    I would go one step further than Scott, and ask what a “right” is. This ultimately leads to the same conclusion as Scott does, but it can hardly be seen as shying away from thinking about things too much.

    My view here is similar to my view about questions about whether free will is compatible with the view that the universe is governed physics. Rarely does someone ask what exactly “will” is, and what it is supposed to be “free” of, which should be the very first questions in such a discussion! Either that, or — if you are morally inclined rather than materially — to ask what “the laws of physics” can mean in a world-view dominated by personal choices.

    With a little consideration, it is easy to see that such questions are a confusion between two different kinds of ontology — one which has material principles, and one which has moral principles. You need to know what you’re talking about and *how* you are talking about it to avoid pitfalls.

    I concur with those who say that the problem is not with over-thinking, but rather with thinking about the wrong — which in this case is to say, poorly defined — things. One ought to define the terms that one is worrying about: at the very least, this provides a good short-term treatment for extistential angst complicated by mental-compulsion, and also leads to longer term therapies.

  38. Vijay Krishnan Says:

    ># Scott Says:
    >Comment #2 December 24th, 2008 at 6:06 pm

    > Carl, depressed people worry about the rightness of their
    > existence, whereas anthropicists merely worry about its
    > probability. 🙂 Still, I guess it’s of a piece with my general
    > skepticism about all philosophical questions.

    I think the following post on overcomingbias is a nice read.

    It argues that the true reason for depression due to “existential angst” (which seems close to “worry about the rightness of one’s existence”), is very likely one of the known things that causes us to get depressed, such as financial problems, relationship problems, boring job etc.

  39. John Sidles Says:

    My wife gave me a copy of The Guide for the Perplexed for the holidays … and I have to say … this guy Maimonedes has no detectable sense of humor at all.

    Fortunately, Google revealed the “Philosophers Jokes” site. Here’s one by Raymond Smullyan:

    A philosopher went into a closet for ten years to contemplate the question, What is life? When he came out, he went into the street and met an old colleague, who asked him where in heaven’s name he had been all those years.

    “In a closet,” he repied. “I wanted to know what life really is.”

    “And have you found an answer?”

    “Yes,” he replied. “I think it can best be expressed by saying that life is like a bridge.”

    “That’s all well and good,” replied the colleage, “but can you be a little more explicit? Can you tell me how life is like a bridge?”

    “Oh,” replied the philosopher after some thought, “maybe you’re right; perhaps life is not like a bridge.”

  40. Pat Cahalan Says:

    @ Neil

    You’re thinking about it too much, thus breaking the boundary conditions of the question.

  41. John Sidles Says:

    Upon consulting the Real-World Superhero Registry (best … website … ever!), it’s apparent that there is an unfilled superhero niche for Predicate Man … or Predicate Gal … hmmmm … perhaps The Predicator would be best.

    Being The Predicator would be all about just showing up, and reminding everyone that they have a right to exist, and that there’s no need to over-think everything, and helping folks with their homework and tax returns and other logical challenges, and in general helping everyone chill out and get in touch with the “better angels of their nature.”

    Come to think of it, there would be no need for The Predicator even to wear a costume, or let people know that they had been helped by a superhero.