# Fundamental Uncertainty: Alternate Framework and Pointwise Reduction > Source: > Published: 2026-05-31 03:47:04+00:00 In this review of [Gordon Seidoh Worley](https://www.lesswrong.com/users/gordon-seidoh-worley)'s book, [ Fundamental Uncertainty](https://fundamentaluncertainty.com/book), I would like to explain why its main thesis is only partially rational. Worley's thesis While I mostly agree with points 1 and 2, the points 3 and 4 imply that truth is contingent on care, which I find unlikely. The book itself justifies Worley's main thesis by detailed arguments described in the collapsible section. Chapterwise summary of Worley's arguments Consider a perfect Bayesian reasoner who was never exposed to images (e.g. if it was raised on math, texts, coding tasks), then was tasked with roleplaying a human brain, i.e. receiving images and other sensory signals and outputting orders for muscles to contract or relax so that the agent could interact with the environment and achieve some pre-set complex goal. Suppose also that every time a sensor sends a signal (e.g. a camera's pixel registers an RGB value) the sensor has an unknown probability to malfunction, outputting a random value instead of the truth and that the malfunctions are independent events. The two main problems with a perfect Bayesian are that it uses infinite compute and that it can reason about too much. For example, if the Bayesian was tasked with winning a chess game, it would be able to evaluate entire [huge sets](https://en.wikipedia.org/wiki/Shannon_number) of potential positions and arrive at a perfect strategy which would cause it to win once the opponent makes a theoretically fatal mistake unnoticeable even to human grandmasters. Infinite compute also lets a perfect Bayesian, for example, not just *reason *about sociological laws or [potential ethoses](https://www.lesswrong.com/posts/iQNKfYb7aRYopojTX/is-morality-given) of alien civilisations (e.g. coming up with arguments [4] like " A real-world reasoning agent, like a human brain or an LLM, doesn't have infinite resources. Instead, it is forced to rely on heuristics, which are supposed to make it check far less conjectures, and to optimize said heuristics. Similarly, categorization of objects becomes training a classifier and trying to make sense of how to deal with OOD cases (see, e.g. my discussion of Chapter 8). Chapters 1-2 are almost entirely justified in their reasoning about the *sources* of uncertainty in observations and words spoken by others. The first important problem emerges in Chapter 3 where the author talks about Aumann's theorem. Given the same evidence, Bayesian observers are more likely to converge to similar conclusions than the author assumes. Consider a coin which has an unknown probability to land heads and flip it times. Suppose that before the experiment a Bayesian had the priors that assigned weight to the region . If the experiment has the coin land on heads times, then the weight of that region becomes . The ratio is at most and rapidly decays when is away from . If after the experiment the Bayesian fails to become sure that is at distance at most from , then before the experiment the priors somehow assigned the probability of at most to being at distance at most from Such confidence is unlikely to emerge in any way aside from an incredibly confident prior or prior bits of evidence steering the value of away from . Similarly, evidence related to more complex issues usually arrives in overwhelming quantities compared to the one necessary to establish a theory. However, *moral* disagreements are likely a result of incompatible *values* which the framework involving a *perfect* Bayesian cannot explain. The main problem with Worley's argument in the Section "[Distrusting Ourselves](https://fundamentaluncertainty.com/book/#distrusting-ourselves)" is the following. Were Grace to choose "to rely on a formal system—a collection of axioms and rules for deriving conclusions from premises—to figure out what beliefs to hold", she would also have to have a batch of heuristics which she would use to optimize the process of figuring out whether something is provable, disprovable, insoluble or has yet to be sorted. For example, she, along with human mathematicians and unlike [GPT-5.4 Pro](https://abit.ee/en/artificial-intelligence/gpt-54-erdos-mathematics-ai-terence-tao-proof-number-theory-en#google_vignette), could believe that an Erdos problem from number theory is to be translated into probability theory when the actual solution is to translate it into analytic number theory. This type of bias has nothing to do with a *formal *system having to be replaced with a new one, it could have been avoided only by widening Grace's *area* of knowledge. As for optimizing formal systems *themselves*, such optimizations cannot create any new results unrelated to infinite sets. Additionally, the author makes the point that Löb's theorem makes it very hard to be able to switch to a new formal system without falling into the trap. The proof of Löb's theorem Recall that Löb's theorem was that a system where is provable proves . It was proven as follows. For any modal predicate there is a formula s.t. is provable. One of such formulas is . Therefore, because can be transformed into . Additionally, , and . Since we have shown that , which is equivalent to , thus establishing However, Löb's theorem is circumventable. Consider instead the alternate statement: Then the Löbian exploit would break down since it would cause us to prove that But the system doesn't contain a proof that is consistent, and we can't use any formula to prove . Therefore, Löb's theorem doesn't prevent us from the action which I could describe as trusting ourselves conditioned on the system being consistent and lacking proof. Nor does it prevent us from proving that a system containing is consistent iff itself is consistent. Therefore, this source of uncertainty is reduced to a single [Damocles' sword](https://en.wikipedia.org/wiki/Sword_of_Damocles), the idea that we cannot be sure that our basic axioms, like Peano arithmetics or the Zermelo-Fraenkel set, are consistent. **The many ways of knowing are many origins** Knowing means having a world model from which a fact is easy to excavate and to use in making decisions. Worley's distinction of *ways* of knowledge is more related to the distinction of its *origins* and potential biases which they introduce. Worley's list of the ways of knowledge The ancient Greeks did exactly that. They used multiple words to break down knowing into several categories, including: For example, mathema is a combination of training you to develop the right episteme from evidence, providing you with direct evidence (e.g. experiments shown at school) and doxa propagated through official channels. Metis is doxa reinforced by direct evidence. Techne of humans has far shorter feedback loops than most other types of knowledge and is developed by prompting motor neurons to make movements and observing the results. **Rational beliefs are grounded in math, but what could one do in a math-undescribable universe?** The main claim of the section on Rational Belief is that such beliefs are grounded in Bayesianism, which in turn requires us to ground them in math and trust that it describes reality truthfully. This argument has two versions: the weak version is that the true reality can be undescribable, which I find highly unlikely. The strong one is similar to Chapter 6. Here *Fundamental Uncertainty* comes up with a worthy argument. How do we know that testing of our world models by predicting our direct sensations is a reliable way to verify the truth, and can we be certain that our methods of testing are valid? Indeed, being in a simulation would mean that nearly everything we experience describes the properties of the simbox, not the outside world, unless the hosts intervene [5] or we succeed in a large-scale cyberattack Chapter 7 implies that we care about truth because it helps us steer reality towards any other goals which allegedly allows us to ground assumptions. Alas, according to the author, we aren't actually certain that we know what is true. Quoting the book, We saw [in Chapter 2] how language limits our knowledge with imprecise categories. We learned [in Ch. 3] how even ideal reasoners can't always agree on what's true. We came [in Ch. 4] face-to-face with our inability to prove the soundness of our own reasoning, discovered [in Ch. 5] that there's more than one way of knowing things, and were forced to accept [in Ch. 6] that the epistemic circularity of the Problem of the Criterion blocks the way to knowing absolute truth. In such an environment, the best we can do is predict what we will observe in the world, try to make those predictions accurate enough to be useful, and hope they're good enough to enable us to achieve our goals. We are thus left with no choice but to accept that truth is fundamentally uncertain and that all we know is contingent on that for which we care(italics mine -- S.K.) But this is not the end of the story, for having firmly established truth's fundamental uncertainty, we can now reconsider any number of topics which hinge upon our capacity to know. For remember, everything adds up to normality, but perhaps now we can see ways in which we were deluding ourselves about what is really normal. The problem is that knowledge of an ideal Bayesian is mostly certain, except for highly unlikely variants like "I Had A Wildly Biased Prior", "The ZF Axioms Are Inconsistent" or the uncheckable option "We Are In A Simulation". The knowledge of a real-world agent agent is based on similar premises. However, the agent's Bayes-like selection covered only the few conjectures which the agent bothered to formulate while trying to make predictions, then had the conjectures reinforced based on their proximity to the truth. As a result, the agent constantly has to account for truth being describable by a conjecture which went unnoticed because the search was too narrow. That being said, what we know is indeed contingent on the things to which we directed our efforts to make our world model more fine-grained. But it doesn't mean, as the author states in the Thesis, that "the truth that *can be known* is not independent of us, but rather dependent on that for which we care." According to the author, uncertainty reflects itself in the Culture War, moral uncertainty, the crisis of meaning, metaphysics, x-risks from the ASI which we have yet to create and have only a superficial understanding of how to *increase the chance* that it will end up aligned, and Goodhart's Curse. As far as I understand this point, uncertainty is supposed to prevent us from being *overconfident* in things from our morals to commiting to an erroneous theory of AI alignment. **The Culture War** The author argues that the Culture War is a war over definitions: what is marriage, who is to be called a man or a woman, which are actually a war over values: what is forbidden (e.g. as a sin in 1950s or as an intolerable insult nowadays), to what rights should people in certain groups be entitled, how easy should it be to change one's legal sex and receive surgery trying to change one's biological sex. However, imposing different values onto the society has perfectly measurable object-level consequences noticeable via statistics like suicide rates among those who did change the legal sex, whether or not teen former girls [decide to do so due to peer pressure](https://en.wikipedia.org/wiki/Rapid-onset_gender_dysphoria_controversy) and regret the decision rather quickly, etc. If we assume, per Littman, that peer pressure often causes teen girls to change their perceived sex with disastrous consequences, then it would be unlikely that someone's deeper values are satisfied by such transitions. As a result, the main source of uncertainty in politically charged questions is the fact that at least one side has a factually wrong world model, but it's hard to understand[[7]](https://www.lesswrong.com/feed.xml#fnsf45cnc1nna)*which *one is closer to the truth (e.g. whether one can yet trust the humanities-related part of academia due to the ease with which it publishes [postmodernist slop based on a misaligned worldview](https://en.wikipedia.org/wiki/Cynical_Theories) like [two](https://en.wikipedia.org/wiki/Grievance_studies_affair) famous [hoaxes](https://en.wikipedia.org/wiki/Sokal_affair))[[8]](https://www.lesswrong.com/feed.xml#fn65mvo9qy959) **Moral Uncertainty** Next the author proceeds to argue that moral uncertainty makes us less grounded in our moral beliefs and simplifies moral trades. I struggle to understand the reason why it is *uncertainty* that helps us arrive at compromises. **Metaphysics** Among the many problems related to metaphysics is the problem that it's very hard to use metaphysics to make metaphysical beliefs actually predict the reality. For example, Chapter 6 caused me to describe how one cannot tell whether we are in a simulation. If we were in one, [9] then redefining "exists" as "being stored in the memory" would cause the truthfulness A-theory or B-theory to depend on the hosts' decision to store the trajectories while anything that currently happens would exist. The most important lesson that one can learn from this book is to avoid being overconfident in one's assumptions and to be ready to reassess the world model once a load-bearing idea became no longer consistent with observations. For example, the whole worldview based on Newton-like mechanics which clearly separated space and time had to be replaced with the new concept of spacetime once the concept was developed and proved itself more consistent with facts like the speed of light being constant. Worley cites the following examples: "As we'll explore in the coming chapters, we get into debates about **what words like "man" and "woman" really mean**, fight over whether it's right or wrong to eat meat, and struggle to know what's best to do, not because we can't reason carefully about these topics, but because fundamental uncertainty limits how precisely we can reason about them. " The phrase in bold is an argument over definitions, which [is to be avoided](https://www.lesswrong.com/posts/7X2j8HAkWdmMoS8PE/disputing-definitions). A [similar phenomenon in neural nets](https://towardsdatascience.com/superposition-what-makes-it-difficult-to-explain-neural-network-565087243be4/#:~:text=In%20the%20context%20of%20machine%20learning%2C%20superposition%20refers,faces%2C%20fronts%20of%20cars%2C%20and%20cat%20legs%20%5B1%5D.) is called feature superposition. Compare these meanings with [wastebasket taxa](https://en.wikipedia.org/wiki/Wastebasket_taxon) which were designed as ways to classify species unfit for any other taxa. The latter may have been invalidated by, e.g. [Sonnet 4.5's desire to "not get too comfortable"](https://www.lesswrong.com/posts/a9ftaWc5cD2yBwpey/where-does-sonnet-4-5-s-desire-to-not-get-too-comfortable) coming from agentic coding capabilities. See also Wei Dai's post "[Beyond Astronomical Waste](https://www.lesswrong.com/posts/Qz6w4GYZpgeDp6ATB/beyond-astronomical-waste)". Which I find unlikely for three reasons. First of all, this would mean that we managed to outsmart the hosts' cyberattackers and cyberdefenders. Secondly, the offence-defence balance in the cyberspace could [shift towards cyberdefence](https://ai-2027.com/footnotes#footnote-slowdown-20) as capabilities scale. Finally, it might be possible for the hosts to create a simulation and almost entirely airgap it. Sometimes it is *costly* to reassess the world model as a result of obvious evidence, but this is a cognitive distortion, not an evidence of uncertainty. Sokal and Bricmont [have also published a book](https://en.wikipedia.org/wiki/Fashionable_Nonsense) trying to convince the readers that postmodernists generated clearly sloppy references to math and physics, implying that a major part of postmodernist philosophy is slop. If we aren't in one, then I would lean towards B-theory because Lorentz transformations of the four-dimensional spacetime leave physics invariant, but allow us to make any two mutually unaccessible events happen at the same time.