Abandoning statistical world-models for wishful thinking
How preferential thinking underlies both rationality and self-delusion
There’s an inconvenient aspect of human thinking that we’ve all encountered at some point in time. Our vanity makes us more likely to spot it in other people, but occasionally you might catch a glimpse of it in yourself. It can be summarized by the following well-known adage:
People believe what they want to believe.
This all-too-human tendency has long been a thorn in the side of empiricist theories of belief. Such theories try to explain belief formation exclusively as the act of building internal representations of real-world experiences. Modern AI research has generally adopted this philosophy of mind, and Machine Learning algorithms are almost uniformly designed to create world models that predict statistical patterns of experience as accurately as possible:
According to [predictive coding] theory, such a mental model is used to predict input signals from the senses that are then compared with the actual input signals from those senses. — Predictive coding
Improving the model components of a model-based agent so that they conform better with reality is almost always a good idea, regardless of the external performance standard. — Sutton, AI: A Modern Approach (4th Ed)
Naturally, theories of mind that frame belief as accurate, statistical world-modelling struggle when confronted with observations of actual human psychology. They are ill-equipped to answer such questions as:
Where does someone go when they are “hiding from the truth”?
How can your mind remove “uncomfortable thoughts”? Why does it try?
When someone has to “face reality”, what were they doing before then?
How can someone who is “living in dreamland” ever leave that place?
Clearly our everyday lived experience is at odds with any theory of statistical world-modelling. When it really matters, such as with political beliefs, religious convictions, or life decisions, we find people everywhere throughout time prefer to take solace in wishful or motivated thinking. They routinely talk about what they want to be true as though it were actually true, and genuinely believe it too. Uncomfortable as it may be, this is an indelible aspect of how humans form their sincerest beliefs. Wishful thinking governs a significant portion of social interactions, self-understanding, and financial decisions, to the point that rational, statistics-based belief formation may only account for a small fraction of the overall total.
When people notice this trend, they are likely to shrug and say that people sometimes think rationally and at other times engage in wishful thinking, hoping to end the discussion there. But that raises the obvious question of how and why a brain would switch between the two, and why it would abandon rational calculation for indulgent fantasy. Every proposed explanation, like stress, lack of information, being short on time, or the absence of conscious deliberation, admits of too many exceptions to account for the observed behaviour. It is hard even to clearly distinguish the two sides, as what seems rational to one person appears delusional to another who doesn’t share their circumstances.
Parallel to this, we find that training one’s mind in critical thinking tends to refine their reasoning faculties. This suggests that “rationality” is actually a complex network of learned, circumstantial skills. So the two sides are actually on a continuum: rationality and wishful thinking are merely inflections of one underlying, general mode of thinking. Such a hypothesis may be difficult to accept since the two seem so incompatible. They represent the difference between belief in the sense of Bayesian belief networks, and belief in the sense of religious faith. Yet even though they arise in the mind in different ways, ultimately their effect on your thinking is the same — both are how you represent the world to yourself.
The focus of this post will be on uniting the two under a single mode of thought. Since the rational side has been so thoroughly expounded and its praises so loudly sung there is little need to go over its many definitions here. If the two sides are in fact on a spectrum, then finding a “true” definition of rationality is largely unimportant compared to understanding the foundation that underpins them both. Wishful thinking, on the other hand, seems closer to our default mode of thinking. Unlike rational thought, which needs to be inculcated through education and training, even a child can believe what they want to believe.
Despite how naturally it arises in the mind, wishful thinking has been little studied, perhaps because it lacks the gravitas and philosophical pedigree of rationality. It is no secret which side of this dichotomy people generally prefer to identify themselves with, especially in the academic world. Thus I don’t believe anyone has done an honest, sympathetic dive into wishful thinking as a mode of belief formation. Its analysis has been reduced to a catalogue of intellectual failures, like one might peruse in a museum of oddities, to regard condescendingly or to openly deride. This post, in contrast, will try to clearly define what it means for people to “believe what they want to believe”; specifically, what it means to equate what is true with what you prefer to be true.
Our first clue that the mind naturally unifies preference and truth under a common function is reflected in the simple word “yes”. “Yes” can be used to mean both “that is true” and “I’d like that”. It is not just that the same word has two meanings; both uses of “yes” are about accepting some thought or experience, albeit in different contexts. They even intuitively feel like connected concepts. The same can be said for the word “no”, which you use to reject both a fact and also an undesirable state of affairs.
There are many English words that demonstrate this same pattern. The words “right” and “wrong” refer to both truth — e.g. that answer is wrong — and preference — e.g. killing is wrong. “Positive” and “negative”, follow the same pattern — e.g. I’m feeling positive today, vs that’s positively true. “Good” and “bad” are also used this way — e.g. you’re getting bad information vs bad dog. Even the words “true” and “ideal” often mean the same thing — e.g. a true circle and an ideal circle both designate a mathematically correct, perfect circle (other examples listed in footnote 1).
Surely this is no coincidence. The linguistic overlap between what people value and what they deem true seems to demand an explanation. One possibility is that humans are drawn to, and strive for, positive truth; this is the rationalist perspective. Another — or perhaps the same? — explanation is that we only believe something to be true if it is appealing or valuable to us somehow; this is sometimes labelled “wishful thinking”. It’s also possible that the trend isn’t psychologically significant; it may merely be an observation that humans tend to unite truth with their ideals as part of a socially-encouraged trend towards optimism, one that ensures pessimists don’t rock the communal boat.
This post, however, will argue that this tendency is actually built into the nature of cognition itself, and indeed that it is foundational to all thinking.
To set the stage, consider a quote from 18th century philosopher David Hume:
The imagination has the command over all its ideas, and can join, and mix, and vary them in all the ways possible. It may conceive objects with all the circumstances of place and time. — Hume, Treatise of Human Nature
Hume asserts that the imagination is free to compose thoughts in any way chooses. Let’s investigate how true this is by trying the following thought experiment:
Imagine yourself holding a wooden ball, tossing it up and down, and then finally have it come to rest in your hand. Seems simple enough. Now imagine the same set of actions, except now the ball is a white-hot piece of iron. Calmly toss it up and down in your mind. Imagine it landing in your hand, and the piercing heat on your palm. Are you able to let it come to rest in your hand? Unlikely. It is more likely you will do one of three things:
- You will imagine yourself flinching and dropping the ball.
- You will imagine the ball avoiding your hand through some other method
- You will re-imagine the white-hot iron ball as a sort of cool, glowing ball of light, which makes it safe to hold.
It seems that your imagination is not free to calmly and objectively visualize any possibility you choose. Given that most people have never held a hot ball of iron, the above phenomenon can’t be explained as the result of habit, as having experienced something so often your mind can’t diverge from it. It’s simply that your mind can’t settle on thoughts that it deems to be outright unpleasant. The appeal or repulsiveness of various thoughts drive your imagination to become conscious of new thoughts. You can do the same exercise using embarrassing or uncomfortable images, or regretful memories from your past. It seems when such thoughts appear, there are automatic systems within your psyche that immediately try to imagine a resolution, to either make it comfortable (like the ball of light), or to drop it like a piece of burning iron².
This is the universal situation for all thinking humans, at all times. It also means that in a steady state, all your thoughts will be of solutions, and none will cause any mental tensions. The mind never comes to rest an uncomfortable thought. “Yes, indiscriminate crime happens…” you may think, but then add “…however, I take extra precautions which other people don’t”. Or “it is guaranteed that I will get old and die…but I feel healthy now, and who knows what technology will exist in the future”. This explains why people tend towards “hope” in their beliefs; that is, towards an optimistic perspective of the future. Whenever a miserable, horrific, or depressing possibility presents itself the mind automatically tries explain it away, avoid it, resolve it, or paper it over; and it does so as reliably as it withdraws your hand from a burning stove.
This reflex should not be taken as a psychological weakness to be overcome. As an automatic psychic mechanism it is undoubtedly useful, since it helps you plan actions that extricate yourself from bad situations. Focusing on solutions, or on avoiding problems, is a useful step on the way to actually implementing such behaviour in practice. Otherwise you would complacently step into danger and accident, unprepared to find a way out.
More importantly, we have found the missing link between so-called wishful thinking and rationality: namely utility. Thinking of dropping the iron ball is undoubtedly useful, but it is also a variety of wishful thinking. Your mind refuses to accept a painful thought, and replaces it with a positive one. This is not about truth, it is about the version of truth that is useful to you. Beliefs are not in themselves equal to reality, they are at most a representation of it. So truth is exclusively a feature of how an explanation benefits you. A belief that doesn’t represent something useful to your goals is not useful to have at all³.
For example, the “elegance” of a novel mathematical theorem which, to many mathematicians, makes it feel more credible, simply reflects that it is easier to work with. It has fewer variables, and uses terms which intuitively match the goals of the domain. It may even give you a new insight or perspective that changes your way of interacting with the problem for the better. Your peers are therefore more open to accepting it because of its greater practical utility to their needs.
The popular truism that “desires cloud rational thought” is an old misunderstanding. You know from experience that your mind more easily learns and retains knowledge if it is interesting or useful to your immediate needs. And every act of reasoning, even solving a math problem, is done for a reason, a motive⁴; perhaps to show off, or to help address a broader problem. Our cultural tendency to purge motives from beliefs and reasoning, to keep the latter somehow “pure” and objective, is based on the recognition that very often competing motives can skew reasoning in unproductive ways, especially across a many individuals. Still, the desire for objectivity remains simply another desire, one which generally aims at aligning the needs of a group for the purpose of collaboration. To frame rationality as “the desire to suppress desire” reveals an obvious self-contradiction. There is only a war between desires.
Pure rationality is an attractive human fiction, an aspirational ideal. And to give this ideal the space it needs to breathe, we tend to separate rational world-modelling, an intellectual activity, from learning more practical, i.e. motivated actions and skills. But there is really no reason to exclude beliefs from also being driven by motivations. Just as you do what it is useful to do, you think what it is useful to think.
And if you are more willing to take in some facts than others, this must inevitably skew your knowledge, and ultimately your beliefs. When we say that some person or another “doesn’t want to hear about that topic” we are putting the lie to any theory of the mind as an ideal, rational information-gatherer. Similarly the phrase “I want to believe” would be nonsensical unless you felt you could influence your beliefs beyond what you strictly experienced through your senses.
So where can one find examples of truly neutral beliefs, unbiased by motives, where the mind simply reflects the statistical patterns of experiences, without introducing anything of its own will? Even pure curiosity is driven by the desire to make things familiar, or comforting. When your curiosity identifies something new, the act of identification always fits the novel experience into a known — and therefore useful — concept. For example, when you explain someone’s unusual or erratic behaviour by concluding they must be hungry, you are fitting an unknown experience into a known one you can address. Should they deny it, you might still persist, saying “I choose to believe they were just hungry”.
And here we finally circle back to the topic of wishful thinking, and the quotes that began this post. “Living in dreamland”, “hiding from the truth”, and the “inability to face reality” are all methods of avoiding thoughts that are too unpleasant, but for which your mind has no other solution except to ignore them, and push them out of mind. People tend to denigrate wishful thinking since its most blatant cases are relatively rare. But wishful thinking is not fundamentally different from rational contemplation. Both aim for thoughts or beliefs that relieve the prevailing mental tension. By refusing to give rationality a privileged position in the mind, we can finally combine all modes of thinking under one common rubric, without leaving anything out.
Making this argument is an uphill battle. In general people prefer to adhere to an invented ideal of the rational man and ignore, or rationalize away, wishful thinking as an exception, one that will likely be explained at some point within the rational model itself. When David Hume confidently asserted that sensory experiences were the only forces that made people believe, the obvious failures of this explanation required that he shift the blame to human “imperfection”:
If the mind suggests not always these ideas upon occasion, it proceeds from some imperfection in its faculties; and such a one as is often the source of false reasoning and sophistry. — Hume, Treatise of Human Nature
John Locke was also confused and frustrated that people didn’t actually believe the way he thought they ought to believe:
To check this precipitancy, our understanding and reason were given us, if we will make a right use of them, to search and see, and then judge thereupon. How much sloth and negligence, heat and passion, the prevalency of fashion or acquired indispositions do severally contribute, on occasion, to these wrong judgments, I shall not here further inquire. — Locke, Essay Concerning Human Understanding
In both their writings the authors alternate, without realizing it, between claiming to describe what people actually do, and what people should do but don’t. They seem unaware of the irony of doing so. They confuse their ideal image of the human mind as a rational evaluator of experiences with what is actually true, and seem angry at the inevitable contradictions.
Nor are they exceptional cases. The theory that the human intellect forms its beliefs by calmly weighing statistical evidence is certainly a tempting one. It feels like a safe, solid ground on which to build intelligence. It is useful, both as a foundational theory, and in practice — and therefore it must be true. In contrast, the theory that belief is based on what is perceived to be useful to your needs, is itself not as useful. This has been the cause of many an epistemological paradox.
Within societies, individuals want to believe that their peers’ beliefs will be driven by objective experiences. This makes the latter more reliable, predictable, and above all reasonable. “Reasonable” here applies to both definitions — following logical patterns, and also aligned on motives. If someone then says “people believe what they want to believe, regardless of what is statistically evident”, that is uncomfortable since it seems to throw out all possibility of social coordination. So we push the thought out of mind like a lump of hot iron, and replace it with a calm, cool, glowing ball of pure light: the ideal, rational man.
¹ Other examples include: “correct” (correct answer vs correct posture), “perfect” (perfect square vs perfect meal), “real” (real event vs really pretty), “sound” (sound logic vs sound body), “dubious” (dubious facts vs dubious character).
² Some beliefs people hold may seem negative or pessimistic, such as the belief that “I am suffering because I have no money”. Although suffering is a problem, the words themselves, including the word “suffering”, you are thinking of are the correct way to express your problem to others in English, and to get their help or attention. The problem is suffering, and a solution is the expression of the words “I’m suffering”. Context also matters: seeing a fire that might spread to something you love causes tension; seeing a fire that you are safely away from is a relief.
³ You may have noticed a small equivocation between a thought being useful, and a thought containing something useful. Though it would take too long to explain here, other parts of this post, combined with footnote 2 makes the point that a thought is only useful if it represents something that resolves a tension.
⁴ Note: The word “reason” can refer to a real, logical cause — e.g. the reason the stock market dropped — and a driving motivation or justification — e.g. my reasons for disliking him.
