On Occam’s Razor
Sven Gelbhaar
2/17/2025
So this whole series is named after Occam’s Razor, but what exactly is this
rule of Philosophy?
Given that all things are equal (/ as likely), the explanation that relies
on the fewest assumptions has the highest chance of none of its assumptions
being wrong, thereby ensuring that the explanation is correct as long as all
the facts are accounted for, and all assumptions/premises are true.
Let’s say for instance that you have a theory which relies on 5 assumptions,
and a theory which only needs two assumptions to be correct in order to win
out. If all assumptions have a 50% chance of being right, then let us apply
probability theory and see what the chances of theory 1 being right against
the chances of theory 2 being right are. Please let me refer you to
https://goodcalculators.com/probability-calculator/
for a refresher on Bayesian Probability. In particular the following:
P(A INCLUSIVE-AND B) = P(A) × P(B)
Using the above formula, we can simply multiply the chance of five 50%
probable events being true and the case by multiplying 0.5 * 0.5 * 0.5 *
0.5 * 0.5, which comes out to: 0.03125. In other words the theory has a
3.125% chance of being right.
Meanwhile, the second theory, with only two assumptions
has a 25% ( P(A INCLUSIVE-AND B) = P(A) × P(B) ) chance of being correct
if the conclusion follows from the premises/ assumptions, and all assumptions
have a 50% chance of being true.
Clearly the theory which only makes two assumptions is far more likely than
the theory which makes five to be correct, given that all probabilities of
the assumptions being correct are equal.
Occam’s Razor is — hopefully — therefore vindicated for you, dear reader.