One of the central questions in the philosophy of science is under what conditions, if any, it can be said that a scientific law has been conclusively established and if there exist similar conditions that would allow us to conclude that a law has been conclusively refuted. A number of different answers have been proposed in response to these questions throughout the history of Philosophy of Science. In this essay I will examine the the views of Carnap, Popper, and Lakatos, and will then attempt to defend one of these views as the most adequate understanding of scientific law.
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)
“It is easy to refute a law; it is exceedingly difficult to find strong confirmation.” (18)
According to Karl Popper, the verification or confirmation of theories can easily be found if one simply makes one’s theory comprehensive enough. In his attempt to address the central question of whether or not theories and laws can be conclusively established or refuted, Popper examines three famous so called “scientific theories” using his falsifiability criterion: Marx’s theory of history, Freud’s psycho-analysis, and Alfred Adler’s “individual psychology.” Popper’s view on science stem from his observation that practically any observable fact could be accounted for by any theory one wants to defend if one makes it vague and broad enough. To Popper it seemed as though “the world was full of verifications of a theory. Whatever happened always confirmed it.” (5) It seemed odd (and suspicious) that two very different examples of human behavior could be explained with equal ease by adherents of a theory like Adler’s. Popper’s example is that of a man who pushes a child into the water with the intention of drowning it; and that of a man who sacrifices his life in an attempt to save the child. What struck Popper as odd was that under Freud’s theory
“the first man suffered from repression (say, of some component of his Oedipus complex), while the second man had achieved sublimation.” and that under Adler’s “the first man suffered from feelings of inferiority (producing perhaps the need to prove himself that he dared to commit some crime), and so did the second man (whose need was to prove to himself that he dared to rescue the child).” (6)
He continues that
“it was precisely this fact- that they always fitted, that they were always confirmed- which in the eyes of their admirers constituted the strongest argument in favour of these theories. It began to dawn on me that this apparent strength was in fact their weakness.” (6)
In contrast with Carnap’s reliance upon confirmation as the source of epistemic confidence in a scientific theory, Popper places the emphasis on the role of falsification instead. To Popper, the mark of a good, productive theory is one that makes bold predictions that are, at least in principle, falsifiable. What distinguished Einstein’s theory of relativity from the social theories Popper criticizes is the element of risk involved in the predictions the theory makes. Popper writes that
“If observation shows that the predicted effect is definitely absent, then the theory is simply refuted. The theory is incompatible with certain possible results of observation- in fact with results which everybody before Einstein would have expected.” (6-7)
Popper then is not much concerned with the verification of theories, he thinks such verifications come cheaply and easily. What he’s most interested in is in producing theories that make predictions, risky predictions. A good scientific theory must also forbid certain states of affairs from obtaining. If a theory is compatible with every possible combination of events then the theory explains too much. A good theory should be able to tell us not only what is the case but necessarily what can also not be the case. The proper method for science to proceed is then to test theories. However, what Popper means by testing a theory is to attempt to refute it. Since verifications are easy to find, if we allowed testability to simply mean finding such confirmations then practically every theory could be vindicated. We should therefore attempt to falsify theories.
Like Popper, Lakatos rejects the idea that scientific theories can be justified merely by accumulating instances of certain laws holding and generalizing from there. Unlike Popper however, Lakatos rejects the idea that a scientific theory or law can ever be completely falsified. Lakatos believes that such “dogmatic falsificationism” rests on two false assumptions:
That “there is a natural psychological borderline between theoretical or speculative propositions and factual (basic) propositions on the other.”
“If a proposition satisfies the psychological criterion of being factual or observational then it is true.” (173)
Lakatos believes both assumptions are wrong. Firstly, Lakatos points out that there is no such thing as “pure” and “direct” observation. Galileo’s observations were not unaided pure observations which then led to the refutation of his Aristotelian critics; it was rather his “observations” in light of his optical theory that confronted Aristotelian observations in light of their theory of the heavens. Lakatos thus writes that “there is no natural demarcation between observational and theoretical propositions...” (173)
Lakatos’s main argument against falsificationism however is this: no (or at least not many) well established scientific theories forbid any observable states of affairs. Lakatos argues that any clever scientist, through the use of additional auxiliary hypotheses, will be able to rescue a pet theory from falsification. Lakatos believes that it is
“a specific theory together with (some) clause which may be refuted. But such a refutation is inconsequential for the specific theory under test because by replacing the ceteris paribus clause by a different one the specific theory can always be retained whatever the tests say.” (175)
One further argument Lakatos brings forward against falsificationism is the fact that probabilistic theories are in principle undisprovable, for “no finite sample can ever disprove a universal probabilistic theory.” (175)
Lakatos’s solution is to adopt what he calls “Sophisticated Methodological Falsificationism.” Under this banner,
“a theory is ‘acceptable’ or ‘scientific’ only if it has corroborated excess empirical content over its predecessor (or rival), that is, only if it leads to the discovery of novel facts.” (182)
The main idea behind sophisticated methodological falsificationism is that
“no experiment, experimental report, observation statement or well-corroborated low-level falsifying hypothesis alone can lead to falsification...there is no falsification before the emergence of a better theory.” (184)
In this view, neither verifications nor falsifications take center stage but rather the corroborating instances of excess information. Theories are not “refuted” in the naive sense of a crucial experiment showing some fatal flaw in a theory, but rather theories are superseded by better theories that can incorporate the so called anomalies in a non-ad-hoc way. The crucial distinction between Lakatos’s views and those of Popper are that Popperian falsificationism calls
“for the replacement of falsified hypotheses by a better one, sophisticated falsificationism stresses the urgency of replacing any hypothesis by a better one.”
It seems that Lakatos’s method is the most rigorous of the three and can account for the complexity of scientific progress in a more realistic way than Carnap’s confirmation views or the naive falsificationism of Popperianism. Lakatos’s arguments against naive falsificationism seem to be decisive. If a scientific law simply describes what ought to be the case under “ideal conditions” then any observation that doesn’t meet the expected result can simply be interpreted as an instance in which those ideal conditions were not met through the invocation of numerous auxiliary hypotheses.
The “ideal condition” theory thus remains untouched while the observation in question is seen as somehow being “contaminated” by some outside force. This can be done ad-nauseum since it is difficult to imagine any part of our universe producing ideal conditions for any real type of interesting scientific law. Lakatos’s view on the other hand sees the scientific enterprise as a process of competing theories, hardly any of them being individually falsifiable through some “crucial experiment” but rather judged on the merits of their explanatory scope and how they can acomodate discordant data. Popperian falsificationism also falls victim to Duhem’s attacks against crucial experiments in science. If a scientific theory T1 can only be put forward by accepting parent theories A1, A2, and A3, and T1 makes prediction H1 which does not come to pass, then a Popperian will say we ought to reject T1. Duhem on the other hand correctly points out that it is not merely T1 which is threatened but rather the conjunction of T1, A1, A2, and A3. The theory in question plus the scaffolding upon which it rests is falsified. What falsification can’t do is point out where the problem lies. Popper would argue that a good scientist ought to reject the theory and move on.
If Duhem’s arguments are sound then the conjunction of theories ought to be rejected, but this would not be good for science. Perhaps the problem lies with A1, while A2 and A3 are okay. Perhaps the only thing necessary is to replace A1 with A1+. Under falsificationism, the entire edifice is thrown away. A better approach would be to re-examine the theories in question and look for where the problem lies by isolating the individual components of the structure and looking for weaknesses in those background assumptions and theoretical commitments that inform and give shape to the entire edifice.