Chats both online and in person seem to consist of confident claims which are either extreme absolute statements (“vaccines don’t work at all”, “you will never catch a cold if you take this supplement”, “artificial sweeteners cause cancer”) or profess no knowledge (“damned if I know”, “we will never know the truth”), sometimes blaming the lack of knowledge on external forces (“of course they don’t tell us the real reason”, “the security services are keeping those studies secret, of course”, “big business is hiding the truth”). Moderate statements that something may or may not be true, especially off the center of all-possibilities-equal, and expressions of personal uncertainty (“I have not studied this enough to form an opinion”, “I have not thought this through”) are almost absent. Other than in research and official reports, I seldom encounter statements of the form “these are the arguments in this direction and those are the arguments in that direction. This direction is somewhat stronger.” or “the balance of the evidence suggests x” or “x seems more likely than not-x”. In opinion pieces in various forms of media, the author may give arguments for both sides, but in that case, concludes something like “we cannot rule out this and we cannot rule out that”, “prediction is difficult, especially now in a rapidly changing world”, “anything may happen”. The conclusion of the opinion piece does not recommend a moderate course of action supported by the balance of moderate-quality evidence.

The same person confidently claims knowledge of an extreme statement on one topic and professes certainty of no knowledge at all on another. What could be the goal of making both extreme and no-knowledge statements confidently? If the person wanted to pretend to be well-informed, then confidence helps with that, but claiming no knowledge would be counterproductive. Blaming the lack of knowledge on external forces and claiming that the truth is unknowable or will never be discovered helps excuse one’s lack of knowledge. The person can then pretend to be informed to the best extent possible (a constrained maximum of knowledge) or at least know more than others (a relative maximum).

Extreme statements suggest to an approximately Bayesian audience that the claimer has received many precise signals in the direction of the extreme statement and as a result has updated the belief far from the average prior belief in society. Confident statements also suggest many precise signals to Bayesians. The audience does not need to be Bayesian to form these interpretations – updating in some way towards the signal is sufficient, as is behavioural believing that confidence or extreme claims demonstrate the quality of the claimer’s information. A precisely estimated zero, such as confidently saying both x and not-x are equally likely, also signals good information. Similarly, being confident that the truth is unknowable.

Being perceived as having precise information helps influence others. If people believe that the claimer is well-informed and has interests more aligned than opposed to theirs, then it is rational to follow the claimer’s recommendation. Having influence is generally profitable. This explains the lack of moderate-confidence statements and claims of personal but not collective uncertainty.

A question that remains is why confident moderate statements are almost absent. Why not claim with certainty that 60% of the time, the drug works and 40% of the time, it doesn’t? Or confidently state that a third of the wage gap/racial bias/country development is explained by discrimination, a third by statistical discrimination or measurement error and a third by unknown factors that need further research? Confidence should still suggest precise information no matter what the statement is about.

Of course, if fools are confident and researchers honestly state their uncertainty, then the certainty of a statement shows the foolishness of the speaker. If confidence makes the audience believe the speaker is well-informed, then either the audience is irrational in a particular way or believes that the speaker’s confidence is correlated with the precision of the information in the particular dimension being talked about. If the audience has a long history of communication with the speaker, then they may have experience that the speaker is generally truthful, acts similarly across situations and expresses the correct level of confidence on unemotional topics. The audience may fail to notice when the speaker becomes a spreader of conspiracies or becomes emotionally involved in a topic and therefore is trying to persuade, not inform. If the audience is still relatively confident in the speaker’s honesty, then the speaker sways them more by confidence and extreme positions than by admitting uncertainty or a moderate viewpoint.

The communication described above may be modelled as the claimer conveying three-dimensional information with two two-dimensional signals. One dimension of the information is the extent to which the statement is true. For example, how beneficial is a drug or how harmful an additive. A second dimension is how uncertain the truth value of the statement is – whether the drug helps exactly 55% of patients or may help anywhere between 20 and 90%, between which all percentages are equally likely. A third dimension is the minimal attainable level of uncertainty – how much the truth is knowable in this question. This is related to whether some agency is actively hiding the truth or researchers have determined it and are trying to educate the population about it. The second and third dimensions are correlated. The lower is the lowest possible uncertainty, the more certain the truth value of the statement can be. It cannot be more certain than the laws of physics allow.

The two dimensions of one signal (the message of the claimer) are the extent to which the statement is true and how certain the claimer is of the truth value. Confidence emphasises that the claimer is certain about the truth value, regardless of whether this value is true or false. The claim itself is the first dimension of the signal. The reason the third dimension of the information is not part of the first signal is that the claim that the truth is unknowable is itself a second claim about the world, i.e. a second two-dimensional signal saying how much some agency is hiding or publicising the truth and how certain the speaker is of the direction and extent of the agency’s activity.

Opinion expressers in (social) media usually choose an extreme value for both dimensions of both signals. They claim some statement about the world is either the ultimate truth or completely false or unknowable and exactly in the middle, not a moderate distance to one side. In the second dimension of both signals, the opinionated people express complete certainty. If the first signal says the statement is true or false, then the second signal is not sent and is not needed, because if there is complete certainty of the truth value of the statement, then the statement must be perfectly knowable. If the first signal says the statement is fifty-fifty (the speaker does not know whether true or false), then in the second signal, the speaker claims that the truth is absolutely not knowable. This excuses the speaker’s claimed lack of knowledge as due to an objective impossibility, instead of the speaker’s limited data and understanding.