“A scientific and philosophic rule that entities
should not be multiplied unnecessarily which is interpreted as requiring that
the simplest of competing theories be preferred to the more complex or that
explanations of unknown phenomena be sought first in terms of known quantities”

Here’s an example that should make this clearer:

Let’s say you just put a slice of pizza in the oven to reheat, but you
didn’t place it on a cookie sheet to keep it from dripping. You then proceed to
go to the living room to watch some television. All of the sudden, you smell
smoke. Where is this smoke coming from? Here are 3 scenarios:

- Aliens have inserted a device into your brain which makes you perceive the smell of smoke in order to further their experiments, which will eventually lead to the subjugation of the human race.
- Someone in a nearby apartment has burned a bag of popcorn.
- The cheese from the pizza is dripping onto the oven coil, causing it to burn and thus produce smoke.

Scenario 1 is quite farfetched, since it tends to rest on a number of
assumptions that are not only complicated, but which are not based on any
legitimately documented phenomena. In other words, while there may be stories
of alien probes and mind control devices, no one has actually been able to provide
sufficient evidence that aliens have ever visited earth let alone that they
have the technology to cause people to smell smoke. In addition, how could making
someone smell smoke help aliens take over the world? It is simply not logical.

Scenario 2 is quite plausible. The chemical process involved in burning
materials is well documented. You have also previously experienced the smell of
your neighbor’s burnt popcorn. However, this scenario requires you to make
assumptions (i.e. that your neighbor was making popcorn) which have not yet
been verified.

Scenario 3 is the most plausible. Why? Because you already know that
you put your pizza in the oven without anything to keep the cheese from melting
onto the coils. Per the definition, “explanations of unknown
phenomena [should] be sought first in terms of known quantities.” Since you

*know*about the pizza, this explanation should be sought first.
Occam’s Razor can also be expressed mathematically. For example, let’s
say there are a number of possible events which have their own probability of
occurring, and:

- The probability of Event 1 happening is 1/2.
- The probability of Event 2 happening is 1/3.
- The probability of Event 3 happening is 1/4.
- The probability of Event 4 happening is 1/5.

(Remember that the probability of getting heads after a coin toss is 1/2
and the probability of rolling a one on a six sided die is 1/6)

To determine the probability of multiple events happening, you multiply
the probabilities of each event together:

- The probability of Events 1 and 2 happening is 1/6
- The probability of Events 1, 2, and 3 happening is 1/25
- The probability of Events 1, 2, 3, and 4 happening is 1/125

Thus, the fewer the events required to explain a phenomena, the higher
the probability the events led to the phenomena. Now, consider the aspect of
Occam’s Razor which states “explanations of unknown phenomena
[should] be sought first in terms of known quantities.” In probabilistic terms, explanations are more
probable when they are based on established knowledge of the context of the
phenomena. Thus, when you see a moving light in the sky at night, the
probability of it being an airplane is greater than the probability of it being
a flying saucer. In mathematical terms, you could say the probability of it
being an airplane is 4/5, whereas the probability of it being a flying saucer
might be more like 1/1,000 (to be generous).

Resources

Good video overview of Occam’s Razor

In depth Wikipedia article on Occam’s Razor

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