Why Known Liars Making a Claim Actually Reduces Its Probability: A Bayesian Explanation
The Intuition
Most people think that if someone makes a claim, it should at least slightly increase our belief that the claim is true - after all, why would they say it if it weren't true? But Bayes' theorem shows us something counterintuitive: if the person making the claim is a known liar, their assertion can actually make the claim less likely to be true than it was before they opened their mouth.
A Quick Refresher on Bayes' Theorem
Bayes' theorem tells us how to update our beliefs when we receive new evidence:
P(A|B) = P(B|A) * P(A) / P(B)
Where:
- P(A|B) is the probability of A being true, given that we observed B
- P(B|A) is the probability of observing B if A were true
- P(A) is our prior probability of A being true
- P(B) is the overall probability of observing B
Setting Up the Problem
Let's say there's a claim C, and a known liar L asserts that C is true.
We need to figure out:
- P(C) - our prior belief that C is true before the liar speaks. Let's say 50% (we have no idea).
- P(L says C | C is true) - the probability the liar would assert C if C were actually true.
- P(L says C | C is false) - the probability the liar would assert C if C were actually false.
Here's the key insight: a known liar is someone who is more likely to say things that are false than things that are true. So:
- P(L says C | C is true) = 0.2 (a liar rarely tells the truth)
- P(L says C | C is false) = 0.8 (a liar usually lies)
Running the Numbers
We want P(C is true | L says C).
First, compute P(L says C):
P(L says C) = P(L says C | C is true) * P(C) + P(L says C | C is false) * P(not C)
= 0.2 * 0.5 + 0.8 * 0.5
= 0.1 + 0.4
= 0.5
Now apply Bayes' theorem:
P(C is true | L says C) = P(L says C | C is true) * P(C) / P(L says C)
= 0.2 * 0.5 / 0.5
= 0.2
We started with a 50% belief that C was true. After the known liar asserted C, our belief dropped to 20%. The liar's endorsement is actually evidence against the claim.
Why This Matters
This result has profound real-world implications:
Propaganda and Disinformation
When a source with an established track record of lying makes a claim, rational observers should treat that claim with more skepticism than they had before, not less. The claim is tainted by its source. This is not an ad hominem fallacy - it is correct probabilistic reasoning.
The Inverse is Equally Useful
If a known liar denies something, that denial is actually evidence for the thing being true. If an authoritarian regime denies committing atrocities, and that regime has a strong track record of lying, the denial should increase your belief that the atrocities occurred.
Stacking Liars Does Not Help
If multiple known liars independently assert the same claim, each additional liar's assertion further reduces the probability. Ten liars all saying the same thing is not reinforcement - it is ten pieces of evidence pointing away from the claim. This assumes their assertions are independent; if they're coordinating, it's essentially one assertion from one source.
Religious Texts and Religious Claims
This reasoning applies directly to religious texts and claims made by religious figures. Religious texts such as the Bible, the Quran, and others contain numerous claims that have been demonstrably shown to be false: the age of the earth, the global flood, the creation narrative, the sun standing still, and many more. These texts have, by any empirical standard, an extremely poor track record of making true claims about the physical world.
Now consider what happens when these same texts make unfalsifiable claims - the existence of God, an afterlife, a soul, divine purpose, or miracles that conveniently left no trace. A naive observer might say "well, we can't disprove those claims." But Bayes' theorem tells us something stronger: the very fact that a source with such a poor track record is the one making these claims is evidence against them. If the Bible gets geology, biology, cosmology, and history wrong repeatedly, its assertions about metaphysics deserve less credence, not a free pass simply because they are unfalsifiable.
The same applies to religious authorities. A priest, rabbi, or imam who makes verifiably false claims - about history, science, or even the contents of their own texts - establishes themselves as an unreliable source. When that same person then asserts the existence of God or the truth of their theology, Bayes' theorem tells us their assertion should lower our posterior probability, not raise it. The more such unreliable sources pile on to the same claim, the worse it gets - as we saw with stacking liars above.
This is not a proof that God does not exist. It is a mathematical observation that the primary sources making the claim have disqualified themselves as evidence for that claim. If your best witnesses are known liars, calling them to the stand hurts your case.
Trust is Information-Theoretic
This analysis shows that trust is not just a social nicety - it has rigorous mathematical consequences. A source's reliability directly determines whether their statements function as evidence for or against their claims. A perfectly reliable source's assertions would push your belief toward 100%. A perfectly unreliable source's assertions push your belief toward 0%. And a source that is right exactly half the time? Their statements carry zero information - you can ignore them entirely.
The Takeaway
Bayes' theorem formalizes what many people intuitively sense but struggle to articulate: the credibility of a source matters just as much as the content of their claim. Known liars asserting something is true is, mathematically speaking, evidence that it is false. The next time someone with a track record of dishonesty makes a bold claim, remember: their very act of claiming it has made it less likely to be true.
















