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Karl Popper (1902–1994) was an important figure in the philosophy of science. He wrote his first book, the Logic of Scientific Discovery on what science is and how it works (in German) in 1934, and translated it to English in the 1950s. Popper argued that scientific theories can never be proven, merely tested and corroborated. Scientific inquiry is distinguished from all other types of investigation by its testability, or, as Popper put it, by the falsifiability of its theories. Unfalsifiable theories are unscientific precisely because they cannot be tested.
The criterion of demarcation
While the logical positivists sought a demarcation between meaningful propositions and gibberish, Popper sought to distinguish science from non-science. It is important to note non-science in the previous statement. Falsifiability, according to Popper, only applies to science or claims with the pretense of being scientific. In this schema, unfalsifiable claims presented as science are in fact pseudoscience. However, not all unfalsifiable claims are pseudoscience; they may simply be un-scientific. For example, Popper also believed in the necessity of what he called "metaphysical research programs," which he claimed could contribute to science.
He grounded this distinction in a logical asymmetry between falsification and verification of a universal law; this asymmetry was dependent, in turn, on the equivalence of a universal statement and a negative existential statement. An "existential statement" claims that a state of affairs exists somewhere and sometime, for example "there exists a black swan". A universal statement, such as "all swans are white", is also the denial of an existential statement: in this case a denial that "there exists a non-white swan".
It is clear that it is much easier to confirm an existential statement than a universal statement. In order to confirm that a black swan exists we would only need to see a black swan. In order to confirm that no black swans exist we would need to trawl through the whole of space and time.
Neither can viewing a great many white swans make "all swans are white" any more likely - some people in fact suggest the opposite, as these observations create an illusion of confidence in our hypothesis that can be highly detrimental. Each existential statement can be expressed as “at w,x,y,z point in space time there existed a non-white swan”, for all intents and purposes an infinite number of potentially falsifications and certainly a number we are unable to make a significant dent into by observations. (Bayesians may consider the prior probability of any universal statement to be extremely low as a result of the vast number of opportunities for falsification).
Verification, then, is simply off the menu. Falsification, on the other hand is both possible ("Hey guys! That swan is black!") and useful: we can discard theories we have discovered to be in error. As "verification" is an illusion science may only advance by means of falsification. It is therefore critical that science does not try to make its theories immune to falsification.
Politically, Popper was a firm believer in the virtues of liberal democracy and the open society on which he felt it depended. In his book The Open Society and Its Enemies, he criticized Plato, Aristotle, Hegel, and Marx as having been forerunners of totalitarianism, largely through a shared historicist approach to human events. He believed that historicism, a set of theories claiming to have uncovered laws of historical development, were unscientific and were especially harmful because they substituted alleged historical prophecy for rational decision-making and conscious political value judgments. He argued that the reason why scholars in his time were so reluctant to criticize Plato in particular was due to his status in the canon of the great philosophers of ancient Greece.
On the topic of Christians who feel they are somehow superior to those with different beliefs:
“”Their thoughts are endowed ... with 'mystical and religious faculties' not possessed by others, and who thus claim that they "think by God's grace". This claim with its gentle allusion to those who do not possess God's grace, this attack upon the potential spiritual unity of mankind, is, in my opinion, as pretentious, blasphemous and anti-Christian, as it believes itself to be humble, pious, and Christian.
|—Open Society and Its Enemies (II,242/3)|
On how science creates theories:
“”Science must begin with myths, and with the criticism of myths.
|—Ch. 1 "Science : Conjectures and Refutations", Section VII|
“”Unlimited tolerance must lead to the disappearance of tolerance. If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them… We should therefore claim, in the name of tolerance, the right not to tolerate the intolerant. We should claim that any movement preaching intolerance places itself outside the law, and we should consider incitement to intolerance and persecution as criminal, in the same way as we should consider incitement to murder, or to kidnapping, or to the revival of the slave trade, as criminal.
|—Vol. 1, Notes to the Chapters: Ch. 7, Note 4|
On "great men":
“”(I)f our civilisation is to survive, we must break with the habit of deference to great men.
|—Open Society and Its Enemies (I,vii)|