According to Rudolf Carnap, the laws of science are nothing more than statements that express as precisely as possible the repetitions or regularities that we observe in nature (Carnap, 15). He writes that

“If a certain regularity is observed at all times and all places, without exception, then the regularity is expressed in the form of a ‘universal law’.” (15)

Carnap is careful to make a distinction between universal laws and statistical laws. Statistical laws are in the form of “Ripe apples are usually red”. (15) Universal laws on the other hand take the following logical form:

(x) (Px > Qx)

This can be translated as: for all x, if x has the property P then x will have the property Q. In Carnap’s terms:

“If ‘x’ stands for any material body, then the law states that, for any material body x, if x has the property P, it also has the property Q.” (15)

This understanding of a universal law is what gives rise to the central question Carnap wishes to investigate:

“What justifies us in going from the direct observation of facts to a law that expresses certain regularities of nature?” (17)

Carnap writes that

“Science begins with direct observations of single facts. Nothing else is observable. A regularity is not directly observable. It is only when many observations are compared with one another that regularities are discovered. These regularities are expressed by statements called ‘laws.’”

Can we ever be fully certain that a law will hold at all times and at all places? In Carnap’s view, we can’t. At most laws can only be verified by cumulative observations. His reasoning is as follows: he writes that “A law about the world states that, in any particular case, at any place and any time, if one thing is true, another thing is entirely true.” (18) This implies an infinite number of possible instances in which this law should hold. Yet no law has ever been tested an infinite number of times. What we have are a finite number of observations in which the law has held. From these finite observations we generalize, predict, and expect that the law will hold constant in future observations. Yet, if there is an infinite range of instances that the law should cover, then “no number of finite observations, however large, can make the ‘universal’ law certain.” (18) Thus, on Carnap’s view, we can never arrive at full verification of a scientific law, they can only be confirmed via repeated observations of the law holding.

Even though a scientific law may never be fully verified, they can nevertheless be conclusively refuted. One need only find a single counter-example in order to refute a scientitic theory. He writes that

“if a law says that every object that is P is also Q and we find an object that is P and not Q, the law is refuted.” (18)

Thus