Suppose there is a world where there are facts F1, F2, F3, … Fn that need to be explained. Suppose further that someone advances an infinite amount of theories that aims to explain the facts. Suppose even further that all the theories presented happen to explain the facts equally well.
The first theory implies the existence of one entity, E1. The second implies the existence of E1 and E2. The third implies the existence of E1, E2 and E3. … The N’th theory implies the existence of E1, E2, E3, … En entities. How should one choose which theory is more likely to be correct? The intuition I have is that the first is the most plausible and the one with the most implied entities (there is no one with the most though) is the most implausible. In other words: the more entities implied, the less probably the theory is. So, if we are to formulate this as a general reasoning principle we could do it like this:
Of two equivalent theories or explanations, all other things being equal, the simplest one is to be preferred.1
More reading:
http://en.wikipedia.org/wiki/Occam%27s_Razor
http://plato.stanford.edu/entries/simplicity/
http://www.iep.utm.edu/o/ockham.htm#H2
1Common phrasing of the principle. http://en.wikipedia.org/wiki/Occam%27s_Razor#Variations
You do not have to resort to intuition as means for defending the principle of simplicity. Let’s assume two theories, T1 and T2 that explain a set of facts F equally well. T1 and T2 are similar in their implications apart from that T2 postulates the existence of E1.
Not considering E1, we can then say that the probability P for T1 is equal to T2, that is:
P(T1)=P(T2)
Consider however E1. If E1 is a non-tautological, ad hoc-free proposition regarding the natural world, it can be said that E1 produces an hypothesis H1. With our current understanding of knowledge, it can be said that no theory or hypothesis concerning the natural world can be certain, and therefore it is true that:
P(H1)<1
Consider now elementary probability theory. If two statements S1 and S2 have a probability which is P(S1+S2) or
P(S2) > P(S1+S2)
If we apply the principle of probability above to T1 and T2 we can show why a simpler theory is always more probable. We see that there is T1 and T2 which are equal in all respects apart from that T2 implies H1 which probability is P(T2+H1)
The E1 can be skipped, and one can say that T2 directly implies H1.
Ah. That’s pretty clever.
Thanks.
Wow!! I find it funny that simplicity has become so complicated.. hehe!! Thanks for the info..