2. The epistemic argument from loose lips

According to Keeley's epistemic argument, BS conspiracy theories are prima facie unwarranted because there are too many ways for the relevant conspiracies to be exposed. As he puts it,

To be clear, when Keeley says that an explosive secret could not be closeted, he doesn't mean that this is metaphysically impossible (Reference Keeley and Coady2006: 111). Rather, he means that it's out of step with how we understand the world today to think that a group of conspirators is capable of keeping an explosive secret closeted (Reference Keeley1999: 123–4). The former claim is about metaphysical necessity. Meanwhile, the latter claim is epistemic, not metaphysical: Keeley intends to make a point about the epistemology of BS conspiracy theories rather than about their truth value (1999: 111). Moreover, the latter claim is about capabilities (i.e., what someone has the ability to do), not necessity: Talk of capabilities is weaker, since the fact that I am not capable of doing a backflip doesn't entail that it's metaphysically impossible for me to do a backflip.

Having clarified that Keeley's argument makes an epistemic claim about conspirators’ capabilities, we can state it as follows:

The motivation for (E1) is that its negation is absurd. Suppose (E1) is false. Then, one could be prima facie warranted in believing that there is a BS conspiracy without being prima facie warranted in believing that a large group of people is capable of working together in secret. This implies that one could be prima facie warranted in believing that people are doing x without being prima facie warranted in believing that people are capable of doing x. But no one can be prima facie warranted in believing the former but not the latter. Therefore, (E1) is true.Footnote ⁵

To see why (E2) is plausible, suppose an arbitrary agent knows that any BS conspiracy would face many internal and external threats of exposure. Internal threats of exposure include sloppy conspirators who leave behind evidence, morally outraged conspirators who blow the whistle, conspirators who discuss the conspiracy for a book deal or as part of a plea deal, etc. (Keeley Reference Keeley1999: 124). Meanwhile, external threats of exposure could come from the press, investigative government agencies, observant people with relevant knowledge, etc. (Keeley Reference Keeley1999: 122). But seemingly if one knows that a BS conspiracy could be exposed in all these different ways, then one is at least prima facie unwarranted in believing that a large group of people is capable of working together in secret. Since the agent is arbitrary, what goes for this agent goes for everyone. Therefore, anyone who knows that a BS conspiracy would face many internal and external threats of exposure is prima facie unwarranted in believing that a large group of people is capable of working together in secret.

3. The alethic argument from loose lips

Similar considerations can be used to motivate the alethic argument. According to this argument, BS conspiracies theories are false, not just unwarranted:

To see that (A1) is true, suppose any big conspiracy would have been exposed by now. Then, every theory that posits a big conspiracy that has not been exposed is false. But, by definition, a big conspiracy that has not been exposed just is a BS conspiracy. And, by definition, a theory that posits a BS conspiracy just is a BS conspiracy theory. It follows that every BS conspiracy theory is false. Therefore, if any big conspiracy would have been exposed by now, then every BS conspiracy theory is false.

The motivation for (A2) mirrors the motivation for (E2). If there were any big conspiracies, then there would be a conspiracy consisting of many knowing conspirators who have different worldviews and different agendas. Such a conspiracy would face many threats of exposure inside and out. But seemingly a conspiracy that faced so many threats of exposure would have been exposed by now. Therefore, any big conspiracy would have been exposed by now.

4. The statistical argument from loose lips

Grimes’ (2016) statistical argument uses the Poisson probability mass function to calculate the probability that there would be at least one leak sufficient to expose a conspiracy. The Poisson probability mass function is as follows:

$$P( x ) = \displaystyle{{\lambda ^xe^{-\lambda }} \over {x!}}\;{\rm for}\;x = 0, \;\;1, \;\;2, \;\ldots $$

Here, x is the number of times the target event occurs, λ is rate at which the target events occur, e is Euler's number ≈ 2.71828, and ! is the factorial function.

To calculate the probability that there will be at least one leak, L, we find the probability that there will be less than one leak (in which case, x = 0) and subtract from one:

$$L( {x = 0} ) = 1-\;\displaystyle{{\lambda ^0e^{-\lambda }} \over {0!}}$$

Since λ ⁰ = 1 and 0! = 1, we can simplify the formula as follows:

$$L( {x = 0} ) = 1-e^{-\lambda }$$

Grimes says that λ = tϕ, where t is the number of years the conspiracy has been going on and ϕ is the mean expected number of leaks per year (2016: 4). Then,

$$L( {x = 0} ) = 1-e^{{-}t\phi }$$

To calculate the probability of a leak, we need to know what ϕ is. Grimes says that ϕ can be understood in terms of p and N(t), where p is the probability that a given conspirator will leak the conspiracy per year, and N(t) is the number of conspirators at any given time (2016: 4). If the conspiracy consists of two people, then the probability that it will remain secret in a given year is (1 − p)². If three people, then (1 − p)³. More generally, the probability that a conspiracy will remain secret per year is (1 − p)^N(t). And if the probability that a conspiracy will remain secret per year is (1 − p)^N(t), then the probability that it will be leaked (i.e., not remain secret) per year is 1 −  (1 − p)^N(t). Hence,

$$\phi = 1-\;( {1-p} ) ^{N( t ) }$$

Thus, the probability that there will be at least one leak sufficient to expose a conspiracy can be expressed as follows:

$$L( {x = 0} ) = 1-e^{{-}t( {1-\;{( {1-p} ) }^{N( t ) }} ) }$$

Grimes’ main question is: How many years and how many conspirators would it take for the probability of a leak to exceed 95%? Put this way, it's natural to rewrite the Poisson probability mass function as a function whose inputs are time and the number of conspirators:

$$L( {t; \;N( t ) } ) = 1-e^{{-}t( {1-\;{( {1-p} ) }^{N( t ) }} ) }\;$$

Before we put this formula to work, there are two empirical parameters that need to be estimated to solve for L: namely, p and N(t). Grimes estimates p (the probability that a conspirator will leak the conspiracy in a given year) based on considerations relating to the exposure of the NSA PRISM program, the FBI's use of pseudoscience in criminal trials, and the Tuskegee syphilis experiment (Reference Grimes2016: 6–7). Of these three examples, the value for p is lowest for people involved with the NSA PRISM program at 4.09×10⁻⁶, or approximately one in a quarter-million. Since Grimes wants to be generous to the conspiracy theorist in the way he assigns probabilities, he sets p to 4.09×10⁻⁶ when calculating the probability that other conspiracies would be leaked (2016: 8).

Next, Grimes considers the value of N(t) (the number of conspirators at any given time) for four conspiracy theories: the moon landing conspiracy theory, the antivaxxer conspiracy theory, the climate change conspiracy theory, and the cancer cure conspiracy theory. He estimates that:

These estimates are based on data concerning the size of various organizations that would have to be involved if the relevant conspiracy theory were true. For example, the estimate for the number of conspirators who would be involved in faking the moon landing is based on the reported peak NASA employment in 1965, and the estimate for the number of conspirators who would be involved in the antivaxxer conspiracy is the sum of the number of people employed by the CDC (15,000 people) and the WHO (7000 people) (Grimes Reference Grimes2016: 8). Notably, Grimes assumes that everyone employed by these organizations would be a conspirator; he doesn't entertain the possibility that the conspiracies might be limited to small groups within these organizations.

Based on these estimates for p and N(t), Grimes calculates the amount of time it would take for the probability of a leak to exceed 95%. The probability that the faking of the moon landing would be leaked is calculated to exceed 95% after 3.68 years. The probability that the suppression of a cure for cancer would be leaked is calculated to exceed 95% after 3.17 years. Depending on the number of conspirators, the probability that the suppression of a vaccine-autism link would be leaked is calculated to exceed 95% after either 3.15 years or 34.78 years. Last, depending on the number of conspirators, the probability that deceit about climate change would be leaked is calculated to exceed 95% after either 3.7 years or 26.77 years (Grimes Reference Grimes2016: 11).

Strictly speaking, Grimes’ calculations are only aimed at these four conspiracy theories. Therefore, his calculations don't constitute a fully general objection to BS conspiracy theories. Nevertheless, Grimes’ methodology, if cogent, can be applied to other BS conspiracy theories on a case-by-case basis. Once we select some BS conspiracy theory, we simply calculate the number of years until exposure by keeping the estimation of p at 4.09×10⁻⁶ and estimating N(t) on empirical grounds.

5. New conspiracy theories

Having clarified the argument from loose lips, I will discuss some of its limitations. The first limitation concerns whether it can be applied to the wave of new conspiracy theories that keep coming up on the news and online. The answer is that it depends on which version of the argument we use. Consideration of new conspiracy theories shows that (E2) of the epistemic argument and (A2) of the alethic argument are unjustified unless they are restricted so that they do not apply to new conspiracy theories.Footnote ⁶ However, the statistical argument can be used to object to at least some new conspiracy theories assuming that it's otherwise cogent.

A new conspiracy is a conspiracy that has been around for only a short time, and a new conspiracy theory is a theory that posits a new conspiracy. For example, the following conspiracy theories apparently posit new conspiracies:

New conspiracies confront the epistemic argument with a dilemma. According to (E2), anyone who knows that a BS conspiracy would face many internal and external threats of exposure is prima facie unwarranted in believing that a large group of people is capable of working together in secret. But the belief that is supposed to be prima facie unwarranted can be interpreted in two ways:

If (E2) is about the former, then the epistemic argument doesn't rule out new conspiracy theories, since no new conspiracies have been around for a long time. Meanwhile, if (E2) is about the latter, then (E2) is unjustified: The premise that a BS conspiracy would face many internal and external threats of exposure doesn't support the conclusion that the relevant conspiracy would be exposed in a short time. Internal threats of exposure might take a long time to leak the conspiracy because conspirators would have incentives to keep the conspiracy secret, making them reluctant to leak the conspiracy deliberately and careful to avoid leaking it accidentally. Meanwhile, external threats of exposure might take a long time to cause the conspiracy to be exposed because investigations often take a long time. Thus, since the latter reading of (E2) is unjustified, it's better to restrict it so that it doesn't make a claim about new conspiracies.Footnote ⁷

New conspiracies also make trouble for the alethic argument. According to (A2), any big conspiracy would have been exposed by now. When (A2) is instantiated with respect to a new big conspiracy, “by now” refers to a short time, since new conspiracies have only been around for a short time. Therefore, (A2) entails that any new big conspiracy would be exposed in a short time. However, the reason given for (A2) is that a big conspiracy would face many internal and external threats of exposure, and this doesn't show that exposure would only take a short time. As with the epistemic argument, this reason doesn't rule out the possibility that the conspirators could be slow to leak the conspiracy or that an investigation could take a long time. Even if we were to concede that this reason supports the conclusion that any big conspiracy would be exposed eventually, it doesn't suggest that exposure will be quick enough to rule out new conspiracy theories. To avoid this problem, (A2) should be reformulated so that it doesn't make a claim about new conspiracies.

Unlike the epistemic and alethic arguments, the statistical argument can be applied to new conspiracies. In a follow-up to his initial article, Grimes argues against various conspiracy theories about COVID-19: e.g., that the COVID-19 pandemic is a hoax, that SARS-CoV-2 was created and released deliberately, and that COVID-19 is caused by 5G radiation. He estimates that the number of people who would need to be involved in these conspiracies is so high that the relevant conspiracies would have been exposed in a matter of weeks. For example, he calculates that if there were a conspiracy among drug companies, public health bodies, and researchers to cover up the fact that the COVID-19 pandemic is a hoax, then there is a 95% chance that this conspiracy would be exposed in 40 weeks (Grimes Reference Grimes2021: 10). Thus, if the statistical argument is otherwise cogent, then it can be used to rule out some new conspiracies. This is not to say that the statistical argument always works against new conspiracies, since there could be new conspiracy theories that posit few enough conspirators that the statistical argument cannot rule them out in a timely manner. Rather, my point is that the statistical argument is better equipped to handle new conspiracies, whereas the epistemic and alethic arguments lack a clear basis for maintaining that new conspiracies would have already been exposed.

6. Small conspiracies

Another limitation of the argument from loose lips concerns small conspiracies. Some views that are ordinarily labelled as “conspiracy theories” only need to posit small initial conspiracies that have no need to add further conspirators later on. But the argument from loose lips only applies to conspiracy theories that posit big conspiracies. Therefore, the argument is not general enough to rule out all the views that are ordinarily labelled as “conspiracy theories.”

There are several well-known conspiracy theories that do not need to posit big conspiracies. For example,

First, some versions of the JFK conspiracy theory posit a small conspiracy. For example, consider a version involving the CIA:

We can divide this conspiracy into two parts: an initial conspiracy to assassinate Kennedy and a later conspiracy to cover up the CIA's involvement. The initial conspiracy need not have involved more than a few people. In fact, the conspiracy would be more likely to succeed if it were kept small. Likewise, the cover-up need not have involved more than a few people. According to this theory, the CIA was able to cover its tracks because Allen Dulles helped guide the Warren Commission to the conclusion that Oswald acted alone. In which case, it would not be necessary to posit a vast conspiracy involving various government agencies or the press.Footnote ¹⁰

We can also state a version of the Oklahoma City bombing conspiracy theory that posits a small conspiracy. Here is an example:

This theory doesn't implicate the press or government agencies other than the ATF. It doesn't even implicate all of the ATF – just some of its agents. And as long as the original conspirators within the ATF kept quiet, there is no clear reason why this theory would require positing any further conspirators.

Last, there are versions of the 9/11 conspiracy theory that can avoid positing big conspiracies. Consider the following:

According to this theory, the conspiracy consisted of Bush, some of his most trusted associates, and probably some members of the CIA. If this small group of people could remain quiet and cover up their involvement, there would be no need to involve anyone else.

One objection to my point about small conspiracies is that the views ordinarily labelled as “conspiracy theories” must posit further conspirators to explain why no external investigators have uncovered the conspiracy.Footnote ¹¹ For example, Keeley writes:

According to Keeley, the views that are ordinarily labelled as “conspiracy theories” must explain why the relevant conspiracy has not been exposed, and often the only feasible explanation is that the people who are tasked with investigating the conspiracy are in on it. This has the effect of swelling the estimated number of conspirators. If this pattern applies to conspiracy theories about Kennedy's assassination, the Oklahoma City bombing, and the 9/11 attacks, then my examples are not problematic for the argument from loose lips.

However, my examples show how this objection can be answered. Instead of constantly expanding the conspiracy, the conspirators could take steps to avoid detection by investigators, circumventing the need to bring the investigators into the conspiracy and allowing the conspiracy to remain small. Allen Dulles could have deliberately misled the Warren Commission. Members of the ATF could have covered up their involvement well enough that no one had sufficient evidence to accuse them. Bush and others could have avoided exposure because there was no way for investigators to prove their involvement provided the conspirators all remained silent.

Another objection is that even if some conspiracies could be kept small, this won't work for all conspiracies. For example, it's plausible that the conspiracies posited by the following conspiracy theories could not be kept small:

When we look at these conspiracies on case-by-case basis, it's hard to see how they could avoid involving a large group of knowing conspirators.

Consider the climate change conspiracy theory. Approximately 150,000 climate scientists have published on climate change from 1991 to 2015 (Powell n.d.). Meanwhile, between 97% and 99.94% of published articles about climate change agree that anthropogenic climate change is occurring (Cook et al. Reference Cook, Nuccitelli, Green, Richardson, Winkler, Painting, Way, Jacobs and Skuce2013; Powell Reference Powell2016).Footnote ¹² As Grimes says, it seems that nearly every published climate scientist would have to be part of the climate change conspiracy (Reference Grimes2016: 11). After all, it's unlikely that such widespread data manipulation would happen without most of the co-authors being aware. And even if only half of the co-authors on these papers were in on the conspiracy, the conspiracy would still consist of approximately 75,000 climate scientists. But if approximately 75,000 people are part of the conspiracy, then it's big by any standard.

There is also reason to think that the flat Earth conspiracy theory must posit a big conspiracy. This is because there is an extremely broad base of testimony that speaks against the claim that the Earth is flat, which is difficult for flat-Earthers to explain without saying that such testimony comes from conspirators trying to mislead the public.Footnote ¹³ For example, the flat Earth conspiracy would need to involve a variety of physicists, astronomers, cosmologists, and government agencies (e.g., NASA) across the globe. Moreover, the fact that no government in the world contradicts the view that the Earth is round makes it likely that many governments would have to be involved in the conspiracy, especially the governments that have space programs. I cannot give a precise estimate of the number of conspirators who would have to be involved. Nevertheless, the fact that the flat Earth conspiracy theory is committed to the existence of an international conspiracy among physicists, astronomers, cosmologists, public officials, and government workers suggests that it must posit a big conspiracy.Footnote ¹⁴

Likewise, there is reason to think that the Holocaust denial conspiracy would need to involve a large group. The USC Shoah Foundation (2021) has recorded over 50,000 interviews in which people (mostly Jewish survivors) describe their experiences of the Holocaust.Footnote ¹⁵ Moreover, this conspiracy would apparently have to include all four government bodies (those of the US, the UK, France, and the USSR) that worked together to prosecute Nazi war criminals during the Nuremberg trials. Additionally, the Holocaust denial conspiracy theory must posit further conspirators to explain the existence of incriminating Nazi documents, photographs and videos of Nazi atrocities, archeological evidence of mass graves, and statistical data that point to a huge decrease in the Jewish population of Europe. Given the broad range of evidence that would need to be faked, the conspiracy would probably have to be a big one.

Based on these considerations, I grant that some of the views ordinarily labelled as “conspiracy theories” would probably need to posit big conspiracies. Nevertheless, this objection doesn't fully nullify the problem presented by small conspiracies. Assume that conspiracy theories about climate change, the Earth being flat, and the Holocaust must posit big conspiracies. But this doesn't show that conspiracy theories about Kennedy's assassination, the Oklahoma City bombing, and the 9/11 attacks would have to posit big conspiracies. Therefore, consideration of small conspiracies serves its stated purpose: It shows that the argument from loose lips fails to rule out some important conspiracy theories that it was meant to rule out.

Small conspiracies are problematic for all three versions of the argument from loose lips. Due to the vagueness of “big,” the epistemic argument and the alethic argument only work when the relevant conspiracy is obviously big by any reasonable standard. But the aforementioned conspiracy theories about Kennedy's assassination, the Oklahoma City bombing, and the 9/11 attacks do not posit obviously big conspiracies. Meanwhile, the statistical argument only works if our calculations show that there is a high probability that a given conspiracy would have been exposed by now. The problem is that each of the conspiracies I described would involve very few people. Even if we assume that 100 people would be involved in each conspiracy, the probability that they would be leaked doesn't reach 95% until after approximately 7327 years according to Grimes’ methodology.Footnote ¹⁶ Moreover, even if we waited 100 years after Kennedy's death, Grimes’ methodology says that there is only about a 4% chance that a conspiracy of 100 people would be exposed.Footnote ¹⁷ Since the Oklahoma City bombing conspiracy theory and the 9/11 conspiracy theory posit newer conspiracies, Grimes’ methodology entails that the probability of their being leaked in the same amount of time is even lower (assuming they did not involve more than 100 conspirators).

7. Alleged evidence for BS conspiracy theories

A third limitation of the argument from loose lips concerns its dialectical efficacy (i.e., whether its premises provide BS conspiracy theorists with a non-question-begging reason to change their minds). The argument from loose lips doesn't address the alleged evidence cited in support of BS conspiracy theories. But the argument isn't dialectically efficacious if it doesn't address this alleged evidence. Therefore, the argument is not dialectically efficacious.