In work beginning in the 1930s, {Karl} Popper gave falsifiability a renewed emphasis as a criterion of empirical statements in science.
Popper noticed that two types of statements are of particular value to scientists.
The first are statements of observations, such as "there is a white swan." Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They are equivalent to a predicate calculus statement of the form: There exists an x such that x is a swan, and x is white.
The second are statements that categorize all instances of something, such as "all swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white. Scientific laws are commonly supposed to be of this type. One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?
Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement.
That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a non-white swan that has eluded observation (and, in fact, the discovery of the Australian black swan demonstrated the deductive invalidity of this particular statement).
http://en.wikipedia.org/wiki/Falsifiability#Two_types_of_statements:_observational_and_categorical
