(This unpublished article was written October 24th, 2006.)
If you saw the movie "Contact", starring Jodie Foster, you might know "Occam's Razor" as: "the scientific principle that, all things being equal, the simplest answer is usually the right one." And since Occam's Razor seems to be a recurring theme lately, let us explore it a bit. First, some background. William of Occam (or Ockham, or any number of alternate spellings) was a 14th-century English logician and Catholic friar on whose writings the phrase "entia non sunt multiplicanda praeter necessitatem" is based, or, for you and me: "entities should not be multiplied beyond necessity". Are we lost yet? What Occam was trying to say was that, when trying to explain or prove something, we should refrain from making more assumptions than are necessary. The fewer assumptions we make, the better.
An example: the last application of Occam's Razor I encountered was in a (macro) evolution vs. intelligent design argument, so I will make an attempt to show its correct application in this context.
We have our two streams of thought, one that assumes that all living organisms started from a single celled organism that divided and mutated millions and trillions of times over millions and billions of years, where some of these mutations were not only "good" and useful, but also persistent down the generations, which led to all the distinct and varying complex organisms we have today. The other, states that there was a single intelligent force or being capable of designing and creating all these said complex organisms. Right off the bat, we see that to apply Occam's Razor as stated, the explanation that makes the least assumptions is the one that makes the single assumption, and hence our preferred selection with the other stream of thought being rejected as undesired. Interestingly enough, however, the person who originally mentioned Occam's Razor in our example made the opposite claim, which leads us to believe he might have been applying one of the existing "anti-razors" developed by Leibniz, Kant and others, instead.
An anti-razor is, as the name implies, the opposite of Occam's Razor, and states that we should continuously add entities until we can support our argument. Or as stated by Walter of Chatton, a contemporary of Occam, "If three things are not enough to verify an affirmative proposition about things, a fourth must be added, and so on". So, instead of entities (assumptions) being "shaved off", which, incidentally, is where the "Razor" in Occam's Razor gets its name, we are adding entities. These two principles are usually applied in the search for the simpler of multiple explanatory theories for some phenomenon. The introduction of assumptions such as, for example, the statement that encountering fossils of non-extant organisms similar to other living organisms proves that they are "precursor" or ancestral organisms, as opposed to simply distinct organisms that just happen to be similar, violate Occam's Razor and should instead be treated as separate hypotheses on their own. These hypotheses, if provable (though in our specific example it is scientifically impossible, as you cannot observe this transition taking place) can then be used as one of the bases for our argument, but if refuted should not be able to affect our theorem, as they should be treated separately.
Outside of science, Occam's Razor is a good principle to hold. Assume as little as you can, because in a world where something like 70% of conversation is based on assumption, the well known phrase "assumption is the mother of all screw ups" takes on greater relevance.