Editing Karl Popper (section)

== Philosophy ==
{{Main|Critical rationalism}}

=== Background to Popper's ideas ===
Popper's rejection of [[Marxism]] during his teenage years left a profound mark on his thought. He had at one point joined a socialist association, and for a few months in 1919 considered himself a [[communist]].<ref name="JarvieMilford2006">{{Cite book |last1=Ian Charles Jarvie |url=https://books.google.com/books?id=w-BEoTj0axoC&pg=PA129 |title=Karl Popper: A Centenary Assessment Volume I |last2=Karl Milford |last3=David W. Miller |publisher=Ashgate Publishing, Ltd. |year=2006 |isbn=978-0-7546-5375-2 |pages=129–}}</ref> Although it is known that Popper worked as an office boy at the communist headquarters, whether or not he ever became a member of the Communist Party is unclear.<ref name="Hacohen2002">{{Cite book |last=Malachi Haim Hacohen |url=https://books.google.com/books?id=3VtHcYGp2pIC&pg=PA81 |title=Karl Popper. The Formative Years. 1902–1945: Politics and Philosophy in Interwar Vienna |date=4 March 2002 |publisher=Cambridge University Press |isbn=978-0-521-89055-7 |page=81}}</ref> During this time he became familiar with the Marxist view of economics, [[class conflict]], and history.{{sfn|Thornton|2015}} Although he quickly became disillusioned with the views expounded by Marxists, his flirtation with the ideology led him to distance himself from those who believed that spilling blood for the sake of a revolution was necessary. He then took the view that when it came to sacrificing human lives, one was to think and act with extreme prudence.

The failure of democratic parties to prevent fascism from taking over Austrian politics in the 1920s and 1930s traumatised Popper. He suffered from the direct consequences of this failure since events after the ''[[Anschluss]]'' (the annexation of [[Austria]] by the [[German Reich]] in 1938) forced him into permanent exile. His most important works in the field of [[social science]]—''[[The Poverty of Historicism]]'' (1944) and ''[[The Open Society and Its Enemies]]'' (1945)—were inspired by his reflection on the events of his time and represented, in a sense, a reaction to the prevalent [[Totalitarianism|totalitarian]] ideologies that then dominated Central European politics. His books defended democratic liberalism as a social and [[political philosophy]]. They also represented extensive critiques of the philosophical presuppositions underpinning all forms of [[totalitarianism]].{{sfn|Thornton|2015}}

Popper believed that there was a contrast between the theories of [[Sigmund Freud]] and [[Alfred Adler]], which he considered non-scientific, and [[Albert Einstein]]'s [[theory of relativity]] which set off the revolution in [[physics]] in the early 20th century. Popper thought that Einstein's theory, as a theory properly grounded in scientific thought and method, was highly "risky", in the sense that it was possible to deduce consequences from it which differed considerably from those of the then-dominant [[Newtonian physics]]; one such prediction, that gravity could deflect light, was verified by [[Arthur Eddington|Eddington's]] [[Eddington experiment|experiments in 1919]].<ref>{{Cite web |title=Gravitational deflection of light – Einstein Online |url=http://www.einstein-online.info/spotlights/light_deflection.html |url-status=dead |archive-url=https://web.archive.org/web/20191121113731/http://www.einstein-online.info/spotlights/light_deflection.html |archive-date=21 November 2019 |access-date=31 May 2019 |website=www.einstein-online.info}}</ref> In contrast he thought that nothing could, even in principle, falsify psychoanalytic theories. He thus came to the conclusion that they had more in common with primitive myths than with genuine science.{{sfn|Thornton|2015}}

This led Popper to conclude that what was regarded as the remarkable strengths of psychoanalytical theories were actually their weaknesses. Psychoanalytical theories were crafted in a way that made them able to refute any criticism and to give an explanation for every possible form of human behaviour. The nature of such theories made it impossible for any criticism or experiment—even in principle—to show them to be false.{{sfn|Thornton|2015}} When Popper later tackled the [[Demarcation problem|problem of demarcation]] in the philosophy of science, this conclusion led him to posit that the strength of a scientific theory lies in its both being susceptible to falsification, and not actually being falsified by criticism made of it. He considered that if a theory cannot, in principle, be falsified by criticism, it is not a scientific theory.<ref>One of the severest critics of Popper's so-called demarcation thesis was [[Adolf Grünbaum]], cf. ''Is Falsifiability the Touchstone of Scientific Rationality?'' (1976), and ''The Degeneration of Popper's Theory of Demarcation'' (1989), both in his ''Collected Works'' (edited by Thomas Kupka), vol. I, New York: Oxford University Press 2013, ch. 1 (pp. 9–42) & ch. 2 (pp. 43–61).</ref>

=== Philosophy of science ===
{{See also|Falsifiability}}

==== Falsifiability and the problem of demarcation ====
Popper coined the term "critical rationalism" to describe his philosophy.{{refn|name=popperproposecriticalrationalism}} Popper rejected the empiricist view (following from Kant) that [[basic statement]]s are infallible; rather, according to Popper, they are descriptions in relation to a theoretical framework.{{sfn|Thornton|2018}}  Concerning the method of science, the term "critical rationalism" indicates his rejection of classical [[empiricism]], and the classical [[inductivism|observationalist-inductivist]] account of science that had grown out of it.{{refn|name=poppercriticsofVienna}} Popper argued strongly against the latter, holding that [[scientific theories]] are abstract in nature and can be tested only indirectly, by reference to their implications.{{sfn|Thornton|2018|loc=Sec. 4}} He also held that scientific theory, and human knowledge generally, is irreducibly conjectural or hypothetical, and is generated by the creative imagination to solve problems that have arisen in specific historico-cultural settings.

Logically, no number of positive outcomes at the level of experimental testing can confirm a scientific theory, but a single counterexample is logically decisive; it shows the theory, from which the implication is derived, to be false. Popper's account of the logical asymmetry between [[Verification theory|verification]] and [[falsifiability]] lies at the heart of his philosophy of science. It also inspired him to take falsifiability as his criterion of [[Demarcation problem|demarcation]] between [[metaphysics]] and science: a theory should be considered scientific if, and only if, it makes predictions that can be falsified. This led him to attack the claims of both [[psychoanalysis]] and contemporary [[Marxism]] to scientific status, on the basis that it is not possible to falsify the predictions that they make.

To say that a given statement (e.g., the statement of a law of some scientific theory)—call it "T"—is "[[falsifiable]]" does not mean that "T" is false. It means only that the background knowledge about existing technologies, which exists before and independently of the theory, allows the imagination or conceptualization of observations that are in contradiction with the theory. It is only required that these contradictory observations can potentially be observed with existing technologies—the observations must be inter-subjective. This is the material requirement of falsifiability.  Alan Chalmers gives "The brick fell upward when released" as an example of an imaginary observation that shows that Newton's law of gravitation is falsifiable.{{sfn|Chalmers|2013|p=62}}

In ''All Life is Problem Solving'', Popper sought to explain the apparent progress of scientific knowledge—that is, how it is that our understanding of the universe seems to improve over time. This problem arises from his position that the truth content of our theories, even the best of them, cannot be verified by scientific testing, but can only be falsified.  With only falsifications being possible logically, how can we explain the [[growth of knowledge]]? In Popper's view, the advance of scientific knowledge is an ''evolutionary'' process characterised by his formula:{{sfn|Popper|1994|pp=2–3}}{{sfn|De Bruin|2006}}

<math>\mathrm{PS}_1 \rightarrow \mathrm{TT}_1 \rightarrow \mathrm{EE}_1 \rightarrow \mathrm{PS}_2. \, </math>

In response to a given problem situation (<math>\mathrm{PS}_1</math>), a number of competing conjectures, or tentative theories (<math>\mathrm{TT}</math>), are systematically subjected to the most rigorous attempts at falsification possible. This process, error elimination (<math>\mathrm{EE}</math>), performs a similar function for science that [[natural selection]] performs for [[biological evolution]]. Theories that better survive the process of refutation are not more true, but rather, more "fit"—in other words, more applicable to the problem situation at hand (<math>\mathrm{PS}_1</math>). Consequently, just as a species' biological fitness does not ensure continued survival, neither does rigorous testing protect a scientific theory from refutation in the future. Yet, as it appears that the engine of biological evolution has, over many generations, produced adaptive traits equipped to deal with more and more complex problems of survival, likewise, the evolution of theories through the scientific method may, in Popper's view, reflect a certain type of progress: toward more and more interesting problems (<math>\mathrm{PS}_2</math>). For Popper, it is in the interplay between the tentative theories (conjectures) and error elimination (refutation) that scientific knowledge advances toward greater and greater problems; in a process very much akin to the interplay between genetic variation and natural selection.

Popper also wrote extensively against the famous [[Copenhagen interpretation]] of [[quantum mechanics]]. He strongly disagreed with [[Niels Bohr]]'s [[instrumentalism]] and supported [[Albert Einstein]]'s [[scientific realist]] approach to scientific theories about the universe. He found that Bohr's interpretation introduced subjectivity into physics, claiming later in his life that: {{blockquote|Bohr was "a marvelous physicist, one of the greatest of all time, but he was a miserable philosopher, and one couldn't talk to him. He was talking all the time, allowing practically only one or two words to you and then at once cutting in."<ref>{{Cite news |last=Horgan |first=John |date=2018-08-22 |title=The Paradox of Karl Popper |work=[[Scientific American]] |url=https://blogs.scientificamerican.com/cross-check/the-paradox-of-karl-popper/ |url-access=subscription |access-date=2023-03-12}}</ref>}}This Popper's falsifiability resembles [[Charles Sanders Peirce|Charles Peirce]]'s nineteenth-century [[fallibilism]]. In ''Of Clocks and Clouds'' (1966), Popper remarked that he wished he had known of Peirce's work earlier.

==== Falsification and the problem of induction ====
Among his contributions to philosophy is his claim to have solved the philosophical [[problem of induction]]. He states that while there is no way to prove that the sun will rise, it is possible to formulate the theory that every day the sun will rise; if it does not rise on some particular day, the theory will be falsified and will have to be replaced by a different one. Until that day, there is no need to reject the assumption that the theory is true. Nor is it rational according to Popper to make instead the more complex assumption that the sun will rise until a given day, but will stop doing so the day after, or similar statements with additional conditions. Such a theory would be true with higher probability because it cannot be attacked so easily:
* to falsify the first one, it is sufficient to find that the sun has stopped rising;
* to falsify the second one, one additionally needs the assumption that the given day has not yet been reached.
Popper held that it is the least likely, or most easily falsifiable, or simplest theory (attributes which he identified as all the same thing) that explains known facts that one should rationally prefer. His opposition to positivism, which held that it is the theory most likely to be true that one should prefer, here becomes very apparent. It is impossible, Popper argues, to ensure a theory to be true; it is more important that its falsity can be detected as easily as possible.

Popper agreed with [[David Hume]] that there is often a psychological belief that the sun will rise tomorrow and that there is no logical justification for the supposition that it will, simply because it always has in the past. Popper writes,
{{blockquote|I approached the problem of induction through Hume. Hume, I felt, was perfectly right in pointing out that induction cannot be logically justified.{{sfn|Popper|1962|p=[https://archive.org/details/conjecturesrefut0000popp/page/42 42]}}}}

=== Rationality ===
Popper held that rationality is not restricted to the realm of empirical or scientific theories, but that it is merely a special case of the general method of criticism, the method of finding and eliminating contradictions in knowledge without ad-hoc measures. According to this view, rational discussion about metaphysical ideas, about moral values and even about purposes is possible. Popper's student [[William W. Bartley|W.W. Bartley III]] tried to radicalise this idea and made the controversial claim that not only can criticism go beyond empirical knowledge but that everything can be rationally criticised.

To Popper, who was an anti-[[justificationism|justificationist]], traditional philosophy is misled by the false [[principle of sufficient reason]]. He thinks that no assumption can ever be or needs ever to be justified, so a lack of justification is not a justification for doubt. Instead, theories should be tested and scrutinised. It is not the goal to bless theories with claims of certainty or justification, but to eliminate errors in them. He writes,
{{blockquote|[T]here ''are'' no such things as good positive reasons; nor do we need such things [...] But [philosophers] obviously cannot quite bring [themselves] to believe that this is my opinion, let alone that it is right. (''The Philosophy of Karl Popper'', p.&nbsp;1043)}}

=== Philosophy of arithmetic ===
Popper's principle of falsifiability runs into ''prima facie'' difficulties when the epistemological status of mathematics is considered. It is difficult to conceive how simple statements of arithmetic, such as "2 + 2 = 4", could ever be shown to be false. If they are not open to falsification they can not be scientific. If they are not scientific, it needs to be explained how they can be informative about real world objects and events.

Popper's solution<ref>Popper, Karl Raimund (1946) Aristotelian Society Supplementary Volume XX.</ref> was an original contribution in the [[philosophy of mathematics]]. His idea was that a number statement such as "2 apples + 2 apples = 4 apples" can be taken in two senses. In its [[pure mathematics]] sense, "2 + 2 = 4" is [[logical truth|logically true]] and cannot be refuted. Contrastingly, in its [[applied mathematics]] sense of it describing the physical behaviour of apples, it can be falsified. This can be done by placing two apples in a container, then proceeding to place another two apples in the same container. If there are five, three, or a number of apples that is not four in said container, the theory that "2 apples + 2 apples = 4 apples" is shown to be false. On the contrary, if there are four apples in the container, the theory of numbers is shown to be applicable to reality.<ref>Gregory, Frank Hutson (1996) [[s:Arithmetic and Reality: A Development of Popper's Ideas|Arithmetic and Reality: A Development of Popper's Ideas]]. City University of Hong Kong. Republished in Philosophy of Mathematics Education Journal No. 26 (December 2011).</ref>

=== Political philosophy ===
In ''[[The Open Society and Its Enemies]]'' and ''[[The Poverty of Historicism]]'', Popper developed a critique of [[historicism]] and a defence of the "Open Society". Popper considered historicism to be the theory that history develops inexorably and necessarily according to knowable general laws towards a determinate end. He argued that this view is the principal theoretical presupposition underpinning most forms of [[authoritarianism]] and [[totalitarianism]]. He argued that historicism is founded upon mistaken assumptions regarding the nature of scientific law and prediction. Since the growth of human knowledge is a causal factor in the evolution of human history, and since "no society can predict, scientifically, its own future states of knowledge",<ref>The Poverty of Historicism, p. 21</ref> it follows, he argued, that there can be no predictive science of human history. For Popper, metaphysical and historical indeterminism go hand in hand.

In his early years Popper was impressed by Marxism, whether of Communists or socialists. An event that happened in 1919 had a profound effect on him: During a riot, caused by the Communists, the police shot several unarmed people, including some of Popper's friends, when they tried to free party comrades from prison. The riot had, in fact, been part of a plan by which leaders of the Communist party with connections to [[Béla Kun]] tried to take power by a coup; Popper did not know about this at that time. However, he knew that the riot instigators were swayed by the Marxist doctrine that class struggle would produce vastly more dead men than the inevitable revolution brought about as quickly as possible, and so had no scruples to put the life of the rioters at risk to achieve their selfish goal of becoming the future leaders of the working class. This was the start of his later criticism of historicism.<ref>{{Cite book |last=Hacohen |first=Malachi Haim |url=https://books.google.com/books?id=3VtHcYGp2pIC&pg=PA82 |title=Karl Popper – the Formative Years, 1902–1945: Politics and Philosophy in Interwar Vienna |date=4 March 2002 |publisher=Cambridge University Press |isbn=978-0-521-89055-7 |page=82 |access-date=12 August 2014}}</ref><ref>{{Cite book |last=Popper |first=Karl |url=https://books.google.com/books?id=W0jP04qn0uoC&q=popper+communism+1992&pg=PA126 |title=All Life is Problem Solving |date=15 April 2013 |publisher=Routledge |isbn=978-1-135-97305-6 |access-date=12 August 2014}}</ref> Popper began to reject Marxist historicism, which he associated with questionable means, and later [[socialism]], which he associated with placing equality before freedom (to the possible disadvantage of equality).<ref>Popper, Karl R. ([1976] 2002). ''[[Unended Quest: An Intellectual Autobiography]]'', pp. 32–[https://books.google.com/books?id=F_2WSLsDyvwC&pg=PA332 37]</ref>

Popper said that he was a socialist for "several years", and maintained an interest in egalitarianism,<ref name=":0" /> but abandoned it as a whole because socialism was a "beautiful dream", but, just like egalitarianism, it was incompatible with individual liberty.{{sfn|Popper|1976|p=36}} Popper initially saw totalitarianism as exclusively right-wing in nature,<ref name=":0">{{Cite web |title=Karl Popper: Political Philosophy {{!}} Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/popp-pol/ |access-date=2022-02-07 |language=en-US}}</ref> although as early as 1945 in ''The Open Society'' he was describing Communist parties as giving a weak opposition to fascism due to shared historicism with fascism.<ref name=":1">{{Cite journal |last=Hacohen |first=Malachi H. |date=1998 |title=Karl Popper, the Vienna Circle, and Red Vienna |url=https://www.jstor.org/stable/3653940 |journal=Journal of the History of Ideas |volume=59 |issue=4 |pages=711–734 |doi=10.2307/3653940 |issn=0022-5037 |jstor=3653940}}</ref>{{Rp|page=730}}<ref>{{Cite book |last=Popper |first=Karl |url=https://books.google.com/books?id=BzzJAwAAQBAJ |title=The Open Society and Its Enemies: Hegel and Marx |date=2005-07-26 |publisher=Routledge |isbn=978-1-135-55256-5 |pages=178–181 |language=en |chapter=19. The Revolution. VI}}</ref> Over time, primarily in defence of liberal democracy, Popper began to see [[Soviet-type economic planning|Soviet-type communism]] as a form of totalitarianism,<ref name=":0" /> and viewed the main issue of the [[Cold War]] as not capitalism versus socialism, but democracy versus totalitarianism.<ref name=":1" />{{Rp|page=732}} In 1957, Popper would dedicate ''The Poverty of Historicism'' to "memory of the countless men, women and children of all creeds or nations or races who fell victims to the fascist and communist belief in Inexorable Laws of Historical Destiny."<ref name=":0" />

In 1947, Popper co-founded the [[Mont Pelerin Society]], with [[Friedrich Hayek]], [[Milton Friedman]], [[Ludwig von Mises]] and others, although he did not fully agree with the think tank's charter and ideology. Specifically, he unsuccessfully recommended that socialists should be invited to participate, and that emphasis should be put on a hierarchy of humanitarian values rather than advocacy of a free market as envisioned by [[classical liberalism]].<ref>Daniel Stedman Jones (2014), ''Masters of the Universe: Hayek, Friedman, and the Birth of Neoliberal Politics'', p. 40: "Popper argued that some socialists ought to be invited to participate."</ref>

==== The paradox of tolerance<!-- This section should have further enumeration. It is close to outright copying. It's not explained. --> ====
{{Main|Paradox of tolerance}}
Although Popper was an advocate of toleration, he also warned against unlimited tolerance. In ''[[The Open Society and Its Enemies]]'', he argued:

{{blockquote|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. In this formulation, I do not imply, for instance, that we should always suppress the utterance of intolerant philosophies; as long as we can counter them by rational argument and keep them in check by public opinion, suppression would certainly be most unwise. But we should claim the ''right'' to suppress them if necessary even by force; for it may easily turn out that they are not prepared to meet us on the level of rational argument, but begin by denouncing all argument; they may forbid their followers to listen to rational argument, because it is deceptive, and teach them to answer arguments by the use of their fists or pistols. 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.<ref>{{Cite web|url=https://archive.org/details/opensocietyandit033120mbp|title=''The Open Society and Its Enemies: The Spell of Plato'' by Karl Raimund Popper, Volume 1, 1947, George Routledge & sons, ltd., p. 226, Notes to chapter 7}}</ref><ref>''The Open Society and Its Enemies: The Spell of Plato'', by Karl Raimund Popper, Princeton University Press, 1971, {{ISBN|0691019681}}, p. 265</ref><ref>{{Cite web|url=https://archive.org/details/OpenSocietyAndItsEnemies|title=''The Open Society And Its Enemies, Complete: Volumes I and II'', Karl R. Popper, 1962, Fifth edition (revised), 1966, (PDF)}}</ref><ref>{{Cite book |last=Popper |first=Karl |url=https://books.google.com/books?id=_M_E5QczOBAC&pg=PA581 |title=The Open Society and Its Enemies |date=12 November 2012 |publisher=Routledge |isbn=978-1-136-70032-3 |via=Google Books}}</ref>}}

==== The "conspiracy theory of society" ====
Popper criticized what he termed the "conspiracy theory of society", the view that powerful people or groups, godlike in their efficacy, are responsible for purposely bringing about all the ills of society. This view cannot be right, Popper argued, because "nothing ever comes off exactly as intended."<ref>{{Cite book |last=Popper |first=Karl |title=Conjectures and Refutations, 4th ed |publisher=Routledge Kegan Paul |year=1972 |location=London |pages=123–125}}</ref> According to philosopher David Coady, "Popper has often been cited by critics of conspiracy theories, and his views on the topic continue to constitute an orthodoxy in some circles."<ref>{{Cite book |last=Coady |first=David |title=Conspiracy theories : the philosophical debate |publisher=Ashgate |year=2006 |isbn=978-1-315-25957-4 |location=London |pages=4 |oclc=1089930823}}</ref> However, philosopher Charles Pigden has pointed out that Popper's argument only applies to a very extreme kind of conspiracy theory, not to conspiracy theories generally.<ref>{{Cite journal |last=Pigden |first=Charles |date=1995 |title=Popper Revisited, or What Is Wrong With Conspiracy Theories? |journal=Philosophy of the Social Sciences |language=en-US |volume=25 |issue=1 |pages=3–34 |doi=10.1177/004839319502500101 |issn=0048-3931 |s2cid=143602969|url=https://philpapers.org/rec/PIGPRO }}</ref>

=== Metaphysics ===
==== Truth ====
As early as 1934, Popper wrote of the search for truth as "one of the strongest motives for scientific discovery."<ref>{{Cite news |last=Williams |first=Liz |date=10 September 2012 |title=Karl Popper, the enemy of certainty, part 1: a rejection of empiricism |work=The Guardian |url=https://www.theguardian.com/commentisfree/2012/sep/10/karl-popper-enemy-uncertainty |access-date=22 February 2014}}</ref> Still, he describes in ''Objective Knowledge'' (1972) early concerns about the much-criticised notion of [[Correspondence theory of truth|truth as correspondence]]. Then came the [[semantic theory of truth]] formulated by the logician [[Alfred Tarski]] and published in 1933. Popper wrote of learning in 1935 of the consequences of Tarski's theory, to his intense joy. The theory met critical objections to [[truth]] as correspondence and thereby rehabilitated it. The theory also seemed, in Popper's eyes, to support [[metaphysical realism]] and the regulative idea of a search for truth.

According to this theory, the conditions for the truth of a sentence as well as the sentences themselves are part of a [[metalanguage]]. So, for example, the sentence "Snow is white" is true if and only if snow is white. Although many philosophers have interpreted, and continue to interpret, Tarski's theory as a [[Deflationary theory of truth|deflationary theory]], Popper refers to it as a theory in which "is true" is replaced with "[[correspondence theory|corresponds to the facts]]". He bases this interpretation on the fact that examples such as the one described above refer to two things: assertions and the facts to which they refer. He identifies Tarski's formulation of the truth conditions of sentences as the introduction of a "metalinguistic predicate" and distinguishes the following cases:

# "John called" is true.
# "It is true that John called."

The first case belongs to the metalanguage whereas the second is more likely to belong to the object language. Hence, "it is true that" possesses the logical status of a redundancy. "Is true", on the other hand, is a predicate necessary for making general observations such as "John was telling the truth about Phillip."

Upon this basis, along with that of the logical content of assertions (where logical content is inversely proportional to probability), Popper went on to develop his important notion of [[verisimilitude]] or "truthlikeness". The intuitive idea behind verisimilitude is that the assertions or hypotheses of scientific theories can be objectively measured with respect to the amount of truth and falsity that they imply. And, in this way, one theory can be evaluated as more or less true than another on a quantitative basis which, Popper emphasises forcefully, has nothing to do with "subjective probabilities" or other merely "epistemic" considerations.

The simplest mathematical formulation that Popper gives of this concept can be found in the tenth chapter of ''Conjectures and Refutations''. Here he defines it as:

: <math>\mathit{Vs}(a)=\mathit{CT}_v(a)-\mathit{CT}_f(a) \,</math>

where <math>\mathit{Vs}(a)</math> is the verisimilitude of ''a'', <math>\mathit{CT}_v(a)</math> is a measure of the content of the truth of ''a'', and <math>\mathit{CT}_f(a)</math> is a measure of the content of the falsity of ''a''.

Popper's original attempt to define not just verisimilitude, but an actual measure of it, turned out to be inadequate. However, it inspired a wealth of new attempts.{{sfn|Thornton|2015}}

==== Popper's three worlds ====
{{Main|Popper's three worlds}}
Knowledge, for Popper, was objective, both in the sense that it is objectively true (or truthlike), and also in the sense that knowledge has an ontological status (i.e., knowledge as object) independent of the knowing subject (''Objective Knowledge: An Evolutionary Approach'', 1972). He proposed [[Popper's three worlds|three worlds]]:<ref>Popper, Karl, "Three Worlds, The Tanner Lecture on Human Values", The University of Michigan, 1978.</ref> '''World One''', being the physical world, or physical states; '''World Two''', being the world of mind, or individuals' private mental states, ideas and perceptions; and '''World Three''', being the ''public'' body of human knowledge expressed in its manifold forms (e.g., "scientific theories, ethical principles, characters in novels, philosophy, art, poetry, in short our entire cultural heritage"<ref>[[Mario Vargas Llosa|Vargas Llosa, Mario]], ''The Call of the Tribe'' (''La llamada de la tribu'', 2018), trans. John King (New York: Farrar, Straus and Giroux, 2023), "Sir Karl Popper (1902–1994)", p. 148.</ref>), or the products of World Two made manifest in the materials of World One (e.g., books, papers, paintings, symphonies, cathedrals, [[particle accelerator]]s). World Three, Popper argued, was the product of individual human beings in exactly the same sense that an animal path in the jungle is the creation of many individual animals but not planned or intended by any of them. World Three thus has an existence and an evolution independent of any individually known subjects. The influence of World Three on the individual human mind (World Two) is in Popper's view at least as strong as the influence of World One. In other words, the knowledge held by a given individual mind owes at least as much to the total, accumulated wealth of human knowledge made manifest as to the world of direct experience. As such, the growth of human knowledge could be said to be a function of the independent evolution of World Three.

Many contemporary philosophers, such as [[Daniel Dennett]],<ref>Dennett, Daniel C., [https://dl.tufts.edu/pdfviewer/3x817009m/5712mk336 review of Karl R. Popper and John C. Eccles, ''The Self and Its Brain''], in ''[[The Journal of Philosophy]]''. '''76''' (2): 91–97. Retrieved 12 May 2025.</ref> have not embraced Popper's Three World conjecture, mostly due to what they see as its resemblance to [[mind–body dualism]].<ref>{{cite web |title=Karl Popper (Stanford encyclopedia) |url=https://plato.stanford.edu/entries/popper/ |website=Stanford encyclopedia |access-date=14 February 2025}}</ref>

==== Origin and evolution of life ====
The [[creation–evolution controversy]] raised the issue of whether creationistic ideas may be legitimately called science. In the debate, both sides and even courts in their decisions have invoked Popper's criterion of falsifiability (see [[Daubert standard]]). In this context, passages written by Popper are frequently quoted in which he speaks about such issues himself. For example, he famously stated "[[Darwinism]] is not a testable scientific theory, but a [[Metaphysics|metaphysical]] research program—a possible framework for testable scientific theories." He continued:
{{blockquote|And yet, the theory is invaluable. I do not see how, without it, our knowledge could have grown as it has done since Darwin. In trying to explain experiments with [[bacteria]] which become adapted to, say, [[penicillin]], it is quite clear that we are greatly helped by the theory of [[natural selection]]. Although it is metaphysical, it sheds much light upon very concrete and very practical researches. It allows us to study adaptation to a new environment (such as a penicillin-infested environment) in a rational way: it suggests the existence of a mechanism of adaptation, and it allows us even to study in detail the mechanism at work.<ref>''Unended Quest'' ch. 37 – see Bibliography</ref>}}

He noted that [[theism]], presented as explaining adaptation, "was worse than an open admission of failure, for it created the impression that an ultimate explanation had been reached".<ref name="popper_on_natural_selection">{{Cite web |date=2 November 2005 |title=CA211.1: Popper on natural selection's testability |url=http://www.talkorigins.org/indexcc/CA/CA211_1.html |access-date=26 May 2009 |publisher=[[talk.origins]]}}</ref> Popper later said:
{{blockquote|When speaking here of Darwinism...This is an immensely impressive and powerful theory. The claim that it completely explains evolution is of course a bold claim, and very far from being established. All scientific theories are conjectures, even those that have successfully passed many severe and varied tests. The [[Mendelian inheritance|Mendelian underpinning]] of modern Darwinism has been well tested, and so has the theory of evolution....<ref name="popper_on_natural_selection" />}}

He explained that the difficulty of testing had led some people to describe natural selection as a [[tautology (logic)|tautology]], and that he too had in the past described the theory as "almost tautological", and had tried to explain how the theory could be untestable (as is a tautology) and yet of great scientific interest:
{{blockquote|My solution was that the doctrine of natural selection is a most successful metaphysical research programme. It raises detailed problems in many fields, and it tells us what we would expect of an acceptable solution of these problems. I still believe that natural selection works in this way as a research programme. Nevertheless, I have changed my mind about the testability and logical status of the theory of natural selection; and I am glad to have an opportunity to make a recantation.<ref name="popper_on_natural_selection" />}}

Popper summarised his new view as follows:
{{blockquote|The theory of natural selection may be so formulated that it is far from tautological. In this case it is not only testable, but it turns out to be not strictly universally true. There seem to be exceptions, as with so many biological theories; and considering the random character of the variations on which natural selection operates, the occurrence of exceptions is not surprising. Thus not all phenomena of evolution are explained by natural selection alone. Yet in every particular case it is a challenging research program to show how far natural selection can possibly be held responsible for the evolution of a particular organ or behavioural program.<ref>{{Cite book |last1=Radnitzky |first1=Gerard |url=https://books.google.com/books?id=QnFiTrCzg5oC&pg=PA145 |title=Evolutionary Epistemology, Rationality, and the Sociology of Knowledge |last2=Popper |first2=Karl Raimund |publisher=Open Court |year=1987 |isbn=978-0-8126-9039-2 |access-date=12 August 2014}}</ref>}}

These frequently quoted passages are only a small part of what Popper wrote on evolution, however, and may give the wrong impression that he mainly discussed questions of its falsifiability. Popper never invented this criterion to give justifiable use of words like science. In fact, Popper stressed that "the last thing I wish to do, however, is to advocate another dogma"<ref>LScD, preface to the first english edition</ref> and that "what is to be called a 'science' and who is to be called a 'scientist' must always remain a matter of convention or decision."<ref>LScD, section 10</ref> He quotes Menger's dictum that "Definitions are dogmas; only the conclusions drawn from them can afford us any new insight"<ref>LScD, section 11</ref> and notes that different definitions of science can be rationally debated and compared:
{{blockquote|I do not try to justify [the aims of science which I have in mind], however, by representing them as the true or the essential aims of science. This would only distort the issue, and it would mean a relapse into positivist dogmatism. There is only ''one'' way, as far as I can see, of arguing rationally in support of my proposals. This is to analyse their logical consequences: to point out their fertility—their power to elucidate the problems of the theory of knowledge.<ref>LScD, section 4</ref>}}

Popper had his own sophisticated views on evolution<ref>Niemann, Hans-Joachim: Karl Popper and the Two New Secrets of Life: Including Karl Popper's Medawar Lecture 1986 and Three Related Texts.  Tubingen: Mohr Siebeck, 2014. {{ISBN|978-3161532078}}.</ref> that go much beyond what the frequently-quoted passages say.<ref>For a secondary source see H. Keuth: ''The philosophy of Karl Popper'', section 15.3 "World 3 and emergent evolution". See also John Watkins: Popper and Darwinism. ''The Power of Argumentation'' (Ed Enrique Suárez Iñiguez). Primary sources are, in particular,
* ''Objective Knowledge: An evolutionary approach'', section "Evolution and the Tree of Knowledge";
* ''Evolutionary epistemology'' (Eds. G. Radnitzsky, W.W. Bartley), section "Natural selection and the emergence of mind";
* ''In search of a better world'', section "Knowledge and the shaping of rationality: the search for a better world", p. 16;
* ''Knowledge and the Body-Mind Problem: In Defence of Interaction'', section "World 3 and emergent evolution";
* ''A world of propensities'', section "Towards an evolutionary theory of knowledge"; and
* ''The Self and Its Brain: An Argument for Interactionism'' (with John C. Eccles), sections "The biological approach to human knowledge and intelligence" and "The biological function of conscious and intelligent activity".</ref> In effect, Popper agreed with some points of both creationists and naturalists, but disagreed with both on crucial aspects. Popper understood the universe as a creative entity that invents new things, including life, but without the necessity of something like a god, especially not one who is pulling strings from behind the curtain. He said that evolution of the genotype must, as the creationists say, work in a goal-directed way<ref>D. W. Miller: Karl Popper, a scientific memoir. ''Out of Error'', p. 33</ref> but disagreed with their view that it must necessarily be the hand of god that imposes these goals onto the stage of life.

Instead, he formulated the spearhead model of evolution, a version of genetic pluralism. According to this, living organisms have goals, and act according to these goals, each guided by a central control. In its most sophisticated form, this is the brain of humans, but controls also exist in much less sophisticated ways for species of lower complexity, such as the [[amoeba]]. This control organ plays a special role in evolution—it is the "spearhead of evolution". The goals bring the purpose into the world. Mutations in the genes that determine the structure of the control may then cause drastic changes in behaviour, preferences and goals, without having an impact on the organism's [[phenotype]]. Popper postulates that such purely behavioural changes are less likely to be lethal for the organism compared to drastic changes of the phenotype.<ref>K. Popper: ''Objective Knowledge'', section "Evolution and the Tree of Knowledge", subsection "Addendum. The Hopeful Behavioural Monster" (p. 281)</ref>

Popper contrasts his views with the notion of the "hopeful monster" that has large phenotype mutations and calls it the "hopeful behavioural monster". After behaviour has changed radically, small but quick changes of the phenotype follow to make the organism fitter to its changed goals. This way it looks as if the phenotype were changing guided by some invisible hand, while it is merely natural selection working in combination with the new behaviour. For example, according to this hypothesis, the eating habits of the giraffe must have changed before its elongated neck evolved. Popper contrasted this view as "evolution from within" or "active Darwinism" (the organism actively trying to discover new ways of life and being on a quest for conquering new ecological niches),<ref>{{Cite web |date=2 October 1986 |title=Philosophical confusion? |url=http://www.science-frontiers.com/philosophical-confusion.htm |url-status=dead |archive-url=https://web.archive.org/web/20140812204024/http://www.science-frontiers.com/philosophical-confusion.htm |archive-date=12 August 2014 |access-date=12 August 2014 |publisher=Science-Frontiers.com}}</ref><ref>Michel Ter Hark: ''Popper, Otto Selz and the Rise Of Evolutionary Epistemology'', pp. 184 ff</ref> with the naturalistic "evolution from without" (which has the picture of a hostile environment only trying to kill the mostly passive organism, or perhaps segregate some of its groups).

Popper was a key figure encouraging patent lawyer [[Günter Wächtershäuser]] to publish his [[iron–sulfur world hypothesis]] on [[abiogenesis]] and his criticism of [[Primordial soup|"soup" theory]].

On the creation-evolution controversy, Popper initially wrote that he considered it
{{blockquote|a somewhat sensational clash between a brilliant scientific hypothesis concerning the history of the various species of animals and plants on earth, and an older metaphysical theory which, incidentally, happened to be part of an established religious belief}}
with a footnote to the effect that he
{{blockquote|agree[s] with Professor C.E. Raven when...he calls this conflict 'a storm in a Victorian tea-cup'...<ref>Karl R. Popper, ''The Poverty of Historicism'', p. 97</ref>}} In his later work, however, when he had developed his own "spearhead model" and "active Darwinism" theories, Popper revised this view and found some validity in the controversy:
{{blockquote|I have to confess that this cup of tea has become, after all, ''my'' cup of tea; and with it I have to eat humble pie.<ref>Section XVIII, chapter "Of Clouds and Clocks" of ''Objective Knowledge''.</ref>}}

==== Free will ====
Popper and [[John Eccles (neurophysiologist)|John Eccles]] speculated on the problem of [[free will]] for many years, generally agreeing on an [[Interactionist dualism|interactionist dualist]] theory of mind. However, although Popper was a body-mind dualist, he did not think that the mind is [[substance dualism|a substance separate from the body]]: he thought that mental or psychological properties or aspects of people [[property dualism|are distinct from physical ones]].<ref>Popper, K. R. "Of Clouds and Clocks," in his Objective Knowledge, corrected edition, pp. 206–255, Oxford, Oxford University Press (1973), p. 231 footnote 43, & p. 252; also Popper, K. R. ''[http://www.informationphilosopher.com/solutions/philosophers/popper/natural_selection_and_the_emergence_of_mind.html "Natural Selection and the Emergence of Mind"]'', 1977.</ref>

When he gave the second [[Arthur Holly Compton]] Memorial Lecture in 1965, Popper revisited the idea of [[quantum indeterminacy]] as a source of human freedom. Eccles had suggested that "critically poised neurons" might be influenced by the mind to assist in a decision. Popper criticised Compton's idea of amplified quantum events affecting the decision. He wrote:

{{blockquote|The idea that the only alternative to determinism is just sheer chance was taken over by [[Moritz Schlick|Schlick]], together with many of his views on the subject, from [[David Hume|Hume]], who asserted that "the removal" of what he called "physical necessity" must always result in "the same thing with ''chance''. As objects must either be conjoin'd or not,... 'tis impossible to admit of any medium betwixt chance and an absolute necessity".}}

{{blockquote|I shall later argue against this important doctrine according to which the alternative to determinism is sheer chance. Yet I must admit that the doctrine seems to hold good for the quantum-theoretical models which have been designed to explain, or at least to illustrate, the possibility of human freedom. This seems to be the reason why these models are so very unsatisfactory.<ref>Popper, K. R. "Of Clouds and Clocks," in: ''Objective Knowledge'', corrected edition, p. 227, Oxford, Oxford University Press (1973). Popper's Hume quote is from ''Treatise on Human Understanding'', (see note 8) Book I, Part I, Section XIV, p. 171</ref>}}

{{blockquote|Hume's and Schlick's ontological thesis that there cannot exist anything intermediate between chance and determinism seems to me not only highly dogmatic (not to say doctrinaire) but clearly absurd; and it is understandable only on the assumption that they believed in a complete determinism in which chance has no status except as a symptom of our ignorance.<ref>''Of Clouds and Clocks'', in ''Objective Knowledge: An Evolutionary Approach'', Oxford (1972) pp. 227 ff.</ref>}}

Popper called not for something between chance and necessity but for a combination of randomness and control to explain freedom, though not yet explicitly in two stages with random chance before the controlled decision, saying, "freedom is not just chance but, rather, the result of a subtle interplay between something almost random or haphazard, and something like a restrictive or selective control."<ref>''ibid'', p. 232</ref>

Then in his 1977 book with John Eccles, ''The Self and its Brain'', Popper finally formulates the two-stage model in a temporal sequence. And he compares free will to Darwinian evolution and natural selection:

{{blockquote|New ideas have a striking similarity to genetic mutations. Now, let us look for a moment at genetic mutations. Mutations are, it seems, brought about by quantum theoretical indeterminacy (including radiation effects). Accordingly, they are also probabilistic and not in themselves originally selected or adequate, but on them there subsequently operates natural selection which eliminates inappropriate mutations. Now we could conceive of a similar process with respect to new ideas and to free-will decisions, and similar things.}}

{{blockquote|That is to say, a range of possibilities is brought about by a probabilistic and quantum mechanically characterised set of proposals, as it were—of possibilities brought forward by the brain. On these there then operates a kind of selective procedure which eliminates those proposals and those possibilities which are not acceptable to the mind.<ref>Eccles, John C. and Karl Popper. ''The Self and Its Brain: An Argument for Interactionism,'' Routledge (1984)</ref>}}

=== Religion and God ===
Popper was not a religious man in the formal sense of the word. He neither maintained any link with his Jewish ancestry nor was he an observant Lutheran.  However, he did consider that every person including himself, was religious in the sense of believing in something more important and beyond us through which we can transcend ourselves. Popper called this something a [[Popper's three worlds|Third World]].{{sfn|Zerin|1998 |pp=46-47}} In an interview that Popper gave in 1969 with the condition that it should be kept secret until after his death, he summarised his position on God as follows: "I don't know whether God exists or not (...) Some forms of atheism are arrogant and ignorant and should be rejected, but [[agnosticism]]—to admit that we don't know and to search—is all right. (...) When I look at what I call the gift of life, I feel a gratitude which is in tune with some religious ideas of God. However, the moment I even speak of it, I am embarrassed that I may do something wrong to God in talking about God."{{sfn|Zerin|1998 |p=47}}<ref>Karl Popper (2008), ''After The Open Society: Selected Social and Political Writings'', ch. 5, "Science and Religion," Appendix.</ref> Aged fifteen, after reading [[Spinoza]] (at the suggestion of his father), Popper recounts that "it gave me a lifetime's dislike of theorizing about God".{{sfn|Popper|1976 |pp=17-18}}

In 1936, applying to the [[Council for At-Risk Academics|Academic Assistance Council]] to leave Austria, he described himself as "Protestant, namely evangelical but of Jewish origin." Responding to the question of whether he wanted religious communities
approached on his behalf, opposite the Jewish Orthodox
section he wrote "NO", underlining it twice.<ref name="Poker">David Edmonds and John Eidinow: ''[[Wittgenstein's Poker]]'' (2001), Chapter 10.</ref>

Popper objected to organised religion, saying "it tends to use the name of God in vain", noting the danger of fanaticism because of religious conflicts: "The whole thing goes back to myths which, though they may have a kernel of truth, are untrue. Why then should the Jewish myth be true and the Indian and Egyptian myths not be true?"{{sfn|Zerin|1998 |p=47}}

Ethical issues always constituted an important part of the background to Popper's philosophy.{{sfn|Kiesewetter|1995}} In later life he discussed ethics rarely, and religious questions hardly at all, but he sympathized with the religious stance of others, and was not prepared to endorse various "humanist and secular offensives".{{sfn|Miller|1997 |p=398}} For Popper religion was definitely not science, but "because something isn’t science, however, does not mean it is meaningless".{{sfn|Zerin|1998 |p=47}}

In a letter unrelated to the interview, he stressed his tolerant attitude: "Although I am not for religion, I do think that we should show respect for anybody who believes honestly."{{sfn|Miller|1997}}<ref>Correspondence I. American Academy of Arts and Sciences. Free Inquiry (Paul Kurtz) 1973–1983. Reel 319. Box/Folder 297:11. [https://oac.cdlib.org/view?docId=tf8c60064j&view=dsc&style=oac4&dsc.position=7501 Online Archive of California].</ref><ref>See also Karl Popper: On freedom. ''All life is problem solving'' (1999), chapter 7, pp. 81 ff</ref>