Teleology is the philosophical study of purpose (from the Greek teleos, perfect, complete, which in turn comes from telos, end, result). One of the classic arguments for the existence of God is the teleological argument, which says that the world (and particularly living things) has clearly been constructed in a purposeful telic rather than a chaotic manner, and must therefore have been made by a rational being.
"Philosophical naturalism", see W.V.O. Quine as a proponent for instance, considers teleological explanations to be invalid. Naturalism posits that nothing beyond measurable phenomena actually exists, and therefore the argument that some unknown and/or unknownable rational being is responsible is invalid. Other philosophers, such as Allan Sandage and Alvin Plantinga, argue that teleology and other "arguments from design" are perfectly valid.
Charles Darwin's theories of evolution, which hold that species develop by natural selection, reduced the influence of traditional teleological arguments (though Darwin himself was criticized by some, accused of being a teleologist). Such arguments were still advanced by many during the resurgence of creationist sentiment in the early 1980s.
However, through Darwin's theory of evolution, purpose received a new justification in the context of survival of the fittest. For example: The tiger has claws so it can hunt and kill its prey. Even though this sounds like a teleogical argument it can be explained in terms of evolution: Having claws provided the tiger with an advantage in the selection process, hence the reason it survived. This justifies the slightly incorrect use of the notion of purpose in the theory of evolution. Because now, the seemingly teleological argument has a scientific justification, this argumentation is called teleonomy as opposed to teleology - like astronomy stands in contrast to astrology.
In recent years, some scientists have advocated an "Anthropic Principle" which explains the values of certain physical constants etc. as being the ones necessary for the existence of the human beings who make the relevant observations. Critics have suggested that some forms of this argument have a fatal tinge of teleology.
An illegitimate teleology may occur when one speculates, without sufficient proof, that X causes Y. See logical fallacy.