Causality (also referred to as causation) is the relationship between an event (the cause) and a second event (the effect), where the second event is understood as a consequence of the first.
This tag is here because many questions refer to cause and effect misconceptions.
In common usage Causality is also the relationship between a set of factors (causes) and a phenomenon (the effect). Anything that affects an effect is a factor of that effect. A direct factor is a factor that affects an effect directly, that is, without any intervening factors. (Intervening factors are sometimes called "intermediate factors.") The connection between a cause(s) and effect in this way can also be referred to as a causal nexus.
Though the causes and effects are typically related to changes or events, candidates include objects, processes, properties, variables, facts, and states of affairs; characterizing the causal relationship can be the subject of much debate.
The philosophical treatment of causality extends over millennia. In the Western philosophical tradition, discussion stretches back at least to Aristotle, and the topic remains a staple in contemporary philosophy.
Causality contrasted with conditionals
Conditional statements are not statements of causality. An important distinction is that statements of causality require the antecedent to precede or coincide with the consequent in time, whereas conditional statements do not require this temporal order. Confusion commonly arises since many different statements in English may be presented using "If ..., then ..." form (and, arguably, because this form is far more commonly used to make a statement of causality). The two types of statements are distinct, however.
For example, all of the following statements are true when interpreting "If ..., then ..." as the material conditional:
If Barack Obama is president of the United States in 2011, then Germany is in Europe. If George Washington is president of the United States in 2011, then <arbitrary statement>.
The first is true since both the antecedent and the consequent are true. The second is true in sentential logic and indeterminate in natural language, regardless of the consequent statement that follows, because the antecedent is false.
The ordinary indicative conditional has somewhat more structure than the material conditional. For instance, although the first is the closest, neither of the preceding two statements seems true as an ordinary indicative reading. But the sentence
If Shakespeare of Stratford-on-Avon did not write Macbeth, then someone else did.
intuitively seems to be true, even though there is no straightforward causal relation in this hypothetical situation between Shakespeare's not writing Macbeth and someone else's actually writing it.
Another sort of conditional, the counterfactual conditional, has a stronger connection with causality, yet even counterfactual statements are not all examples of causality. Consider the following two statements:
If A were a triangle, then A would have three sides. If switch S were thrown, then bulb B would light.
In the first case, it would not be correct to say that A's being a triangle caused it to have three sides, since the relationship between triangularity and three-sidedness is that of definition. The property of having three sides actually determines A's state as a triangle. Nonetheless, even when interpreted counterfactually, the first statement is true.
A full grasp of the concept of conditionals is important to understanding the literature on causality. A crucial stumbling block is that conditionals in everyday English are usually loosely used to describe a general situation. For example, "If I drop my coffee, then my shoe gets wet" relates an infinite number of possible events. It is shorthand for "For any fact that would count as 'dropping my coffee', some fact that counts as 'my shoe gets wet' will be true". This general statement will be strictly false if there is any circumstance where I drop my coffee and my shoe doesn't get wet. However, an "If..., then..." statement in logic typically relates two specific events or facts—a specific coffee-dropping did or did not occur, and a specific shoe-wetting did or did not follow. Thus, with explicit events in mind, if I drop my coffee and wet my shoe, then it is true that "If I dropped my coffee, then I wet my shoe", regardless of the fact that yesterday I dropped a coffee in the trash for the opposite effect—the conditional relates to specific facts. More counterintuitively, if I didn't drop my coffee at all, then it is also true that "If I drop my coffee then I wet my shoe", or "Dropping my coffee implies I wet my shoe", regardless of whether I wet my shoe or not by any means. This usage would not be counterintuitive if it were not for the everyday usage. Briefly, "If X then Y" is equivalent to the first-order logic statement "A implies B" or "not A-and-not-B", where A and B are predicates, but the more familiar usage of an "if A then B" statement would need to be written symbolically using a higher order logic using quantifiers ("for all" and "there exists").
Fallacies of questionable cause, also known as causal fallacies, non causa pro causa ("non-cause for cause" in Latin) or false cause, are informal fallacies where a cause is incorrectly identified.