|Newton's first rule of reasoning|
|«We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.»
— Isaac Newton: Principia
Occam's razor (sometimes Ockham's razor) is a principle that, in short, can be described as the hypothesis that makes the least assumptions is the best answer for the phenomenon in question. Note that Occam's razor does not say that the more simple a hypothesis, the better. It is also called a methodological tool reflecting the imperative don't invent unnecessary entities to explain something.
Ockham's Razor is one of the most widely used logical razors in all fields of applied logic, most notably philosophy, theology, science, and systemology. It is attributed to William of Occam, an English Franciscan Friar who lived in the late thirteenth and early fourteenth centuries. Briefly, it can be stated as follows:
- "From any set of equally probable explanations, we should assume the one which makes the fewest fundamental assumptions is correct, until we have reason to believe otherwise"
This is different from the shortest explanation, the shortest logical argument, and the simplest explanation, and the razor is often incorrectly quoted and/or applied. Some people have argued that these criteria qualify as better principles than the razor.
Occam's razor is a guiding principle. That is, it says that the explanation with the fewest assumptions is to be preferred, not is correct. The explanation with the fewest assumptions can turn out to be the wrong explanation.
When addressing the cosmological argument in Article 3 ("asks the question whether God Exists") of Question 2 (called "The existence of God") of the first part of the Summa, Aquinas argues that "it is superfluous to suppose that what can be accounted for by a few principles has been produced by many." This constraint is now familiar as Occam's Razor, even though William of Occam lived and wrote after Aquinas's death.
Ockham's razor can be illustrated by the following common example. A tree is found uprooted in the middle of a field with no apparent cause. Two people offer competing hypotheses for how this occurred. Person A says that there must have been a storm last night, which combined with heavy rainfall the previous day, resulted in the uprooting of the tree. Person B says that last night aliens visited the planet Earth, and uprooted the tree as a message to mankind. There is no way of determining which of these hypotheses is correct after the fact, but as A's hypothesis makes far fewer fundamental assumptions (basically that the planet Earth has weather) than B's hypothesis (basically that aliens exist, have a way of finding humans in the cosmos, have a way of traversing space to reach our planet, could topple such a tree without being noticed, and so forth), we should assume A is correct and that a storm felled the tree unless B can provide some other evidence to support their claim.
Use by atheists
Among its practical applications, Occam's Razor has been used by atheists to argue against the existence of God. Let us take for an example the origin of intelligent life on Earth. One possibility for intelligent life is naturalistic evolution via natural selection. A second possibility is that God used intelligent design as His means of creation. Occam's Razor allows us to eliminate God from the hypothesis since the idea of intelligent design entails unnecessary additional assumptions. The simpler explanation (that which makes fewer fundamental assumptions) is that God had nothing to do with the development of intelligent life and that it came about as a result of natural processes. Therefore, the earlier explanation is the most reasonable to believe.
It is, however, important to note that Occam himself did not accept this reasoning; indeed, he considered the existence of God and the authority of Scripture to be truths which trumped the principle. While Occam's Razor is frequently (and wrongly) articulated as "The simplest explanation is to be preferred," what he actually said was "For nothing ought to be posited without a reason given, unless it is self-evident (literally, known through itself) or known by experience or proved by the authority of Sacred Scripture." 
Use by Christians
The problem with the atheist example above is that it assumes that naturalistic evolution can explain the origin of intelligent life. Most theists would argue that God is not an unnecessary additional assumption, but a necessary additional assumption. Logical arguments for the existence of God, such as ontological and cosmological arguments, intended to justify the conclusion that the existence of a God is necessary for the existence of the universe. For example, Thomas Aquinas, heavily influenced by the earlier works of Aristotle, attempted to use a posteriori reasoning to logically prove that a God must exist, in order for the universe to exist. 
Christian apologist William Lane Craig also has used Occam's razor to argue against polytheism. He argues that the Kalam Cosmological Argument argues against atheism, and that Occam's Razor would only require the existence of one god.
Additionally, some supporters of intelligent design argue that the nature of the Universe is so complex that it is almost certain to have a dedicated creator. There is approximately a 1 in 1040 chance of the Universe and all its life generating properties occurring purely by chance. For instance, water is the only substance that expands when frozen. Were it not for this property, frozen bodies of water would probably never unfreeze. Since intelligent design advocates believe in evolution (albeit not of the Darwinian variety), they argue that life could never have evolved were it not for this property of water. Additionally, ID advocates (who are by extension old earth creationists) point out that if the force of gravity were even slightly stronger than it is, the Universe would have collapsed shortly after the Big Bang. Additionally, if it were slightly weaker, stars and planets would never have formed. There are numerous other examples, and this does not even include the complexity of amino acids needed to form life. The odds of this happening by chance are, according to EvolutionDeceit.com 1 in 10950. Of course, this could only happen in the event that the Universe has its current potential. Therefore, the odds of the amino acids emerging by chance in a Universe that can support it (that also emerges by chance) are 1 in 10990. Occam's razor would therefore state that if there is more than a 1 in 10990 chance that God created the Universe and humans, and that it therefore did not occur by chance, then this is the most likely explanation.
However, an alternate explanation can be found in the anthropic principle.
- Occam's razor (The Skeptic's Dictionary).
- Grigg, Russell, Occam’s Razor and creation/evolution 22 May 2007 (Creation Ministries International).
- Strobel, Lee. The Case for a Creator. Zondervan 2004
- Rhoda Rappaport (1997). When Geologists Where Historians, 1665-1750. Cornell University Press, 62. ISBN 978-0801-433863. “In the famous language of Newton's first rule of reasoning in the Principia, ...”
- David Berlinski (2009). "Darwinism versus Intelligent Design: David Berlinski &critics", The Deniable Darwin. Seattle, USA: Discovery Institute Press (reprinted from Commentary February 1998 by permission), 319. ISBN 978-0-9790141-2-3. “[actual quote from] Morton Rosof: ...It is true that science has its own phiposophical or faith-like underpinnings. They consist of methodological tools like Occam's Razor (don't invent unnecessary entities to explain something), falsification (can a hypothesis, in principle, be falsified?), and balance (extraordinary claims need extraordinary evidence). These devices have served science with great success for 300 years.”
- David Berlinski. "The Cause", The Devil’s Delusion. Basic Books, New York, 2009, 66. ISBN 978-0-465-01937-3.
- The Skeptic's Dictionary
- Strobel, 2004