A priori vs false witness statement

Question

John tells Linda the following false statement to trick her into believing that UFO:s exist.

Yesterday when I was walking in the forest I saw a UFO for 5 seconds and then it disappeared, you have to believe me because:

1. You were not there to observe the same thing as I did.
2. No other person was around to refute my observation.
3. The UFO told me something I did not know before about you having a cat when you were younger named "Tom", if I did not encounter the UFO and get this information, how can I know that you've had a cat?

How can Linda refute believing Johns statement and expose it as being false? She was not there to observe the UFO and the statement about the cat is true.

Can she use a priori knowledge to counter Johns proposed a posteriori knowledge?

My input: One way of refuting Johns statement I believe is to use Humes research along with Arif Ahmeds research which states that we cannot have justified belief in a statement which has low probability to occur in reality, the probability we are being misled by a lie is to high. Even if Tom tells us that the UFO told him something he did not know about Linda before, such as she owning a cat named Tom, and uses it as proof of the UFO:s existence, the probability of it being told my the UFO is much lower than the probability that Tom got this information through one of Lindas friends.

Relevant research: Ahmed, Arif. (2015). Hume and the Independent Witnesses. Mind. 124. fzv076. 10.1093/mind/fzv076.

Many thanks for your time!

Answer 1

First of all, Lisa can't do much to "expose John's statement as being false". It's not falsifiable. It might be true, for all she knows.

You are right to say that the probability of her having aquired through other means is higher, but that doesn't help in "exposing as false". Imagine that instead he claims Fred told him, and there are about 10 people including Fred that Lisa judges as equally likely to have told John. So does she disbelieve him that Fred told him?

Probably not, because it is without consequence. Or she does, because John is frequently unreliable. The same applies to whether or not an UFO appeared and told John about the pet. And because of that, whether she believes or disbelieves is simply her choice. She doesn't "have to believe" anyone anything.

Also: Unlikely things happen every day.

Answer 2

It's interesting that you used the name "Linda", as this was the name used in Amos Tversky and Daniel Kahneman discussion of the conjunction fallacy. John's evidence establishes that he has acquired knowledge that presumably would be difficult to acquire. If "John acquired difficult to acquire information" is referred to as A, and "John saw a UFO [it's not quite clear what "UFO" means, but let's put that aside for the moment]" as B, then clearly P(A) > P(A&B).

Now, John may say that he is not trying to claim P(A&B) > P(A), but rather he is making another claim, such as P(A&B) > P(A&~B) or P(A|B) > P(A) (I believe those latter claims are equivalent).

The problem with that argument that should be obvious to anyone familiar with Bayesian reasoning is that that if our prior probability for B is sufficiently low, then this evidence will not be sufficient to overcome that.

However, another issue is what reason do we have to think P(A|B) > P(A) in first place? Are UFOs known for keeping track of childhood pets and reporting their names to acquaintances? John is trying to get Linda to focus on how unlikely him knowing the name of her pet is in general, and ignore the issue of how likely him knowing the name of her pet, given that he saw a UFO, is. It's reasonable to believe that the probability, given that John see a UFO, that that UFO will bother telling him the name of Linda's cat (or even that it will know it to begin with), is not much greater than the probability in general of him knowing.

Simply noting some unlikely occurrence and then asserting some unlikely claim is a non sequitur. For one unlikely event to be unlikely event to be evidence for another claim, the claim being true must significantly increase the probability of the event. For instance, if Linda wins the lottery, and John says "Doesn't that make you believe in God?", that would be a valid argument only if Linda has some reason to think that God would want her in particular to win the lottery. If there's nothing special about her that would make God want her to win the lottery rather than anyone else, then her winning the lottery isn't evidence for God.

Going back to the UFO hypothetical, there are other hypotheses, such as that John has talked with her parents, that are both more likely, and more explanatory of the fact that John knows the name of her pet. So John knowing the name of her pet should push her towards believing those hypotheses, rather than the UFO one.