Substituting our problem in, we get:
P(Absent|~Find) = P(~Find|Absent) P(Absent) /
P(~Find)
Since
P(~Find|Absent) = 1
this implies
P(Absent|~Find) = P(Absent) / P(~Find)
Now, here’s the tricky bit…
Let’s assume for a moment that, I already knew that I couldn’t ever find my earbuds cause they vanished out of existence. In this case,
P(~Find) = 1
which would mean
P(Absent|~Find) = P(Absent)
In English, that would mean the fact that I have looked and haven’t found my earbuds has no bearing on the probability of them being absent.
In reality,
P(~Find)< 1
because, why in the world would I be looking if I didn’t believe there was a chance of finding them?
So now, the only obvious conclusion is that the probability that my earbuds are absent after not finding them
must be greater than the probability that it is absent.
P(Absent|~Find) > P(Absent)
That’s it.
The absence of evidence is, in fact, evidence of absence (just not proof of absence.)
Conclusion
You might scoff at my silly example.
Losing your earbuds or keys is inconsequential.
Unfortunately, this misconception rears its ugly head EVERYWHERE, and the topics in question are far from inconsequential.
In a NATO conference in 2002, the then Secretary of Defence, Donald Rumsfeld proclaimed that the military action in Iraq in search of weapons of mass destruction was justified, despite the fact, that after multiple inspections and assessment of various intelligence, no evidence for such weapons was discovered.
The very foundation upon which we built scientific hypotheses — regular old hypothesis testing — depends on being able to assume that in certain contexts of inquiry an absence of evidence can serve as evidence of absence.
So… The next time you’re having that heated argument about the existence of [name your entity — think on it for a second], keep in mind that the longer we keep looking without finding, the more evidence we are accumulating that it does not exist.
Have some strong opinions on this topic? Comment and don’t hold back!
View Comments
This is so asinine. Read some Taleb - he's arrogant but at least he has logic.
Hi Katrina,
Thank you for your input.
I'm curious which part you felt the logic doesn't follow?