[Vision2020] Karl Popper's Theory of Science

Tbertruss at aol.com Tbertruss at aol.com
Tue May 10 13:17:51 PDT 2005


I will start this post on Karl Popper with a brief excerpt from an essay (the 
whole essay is at the bottom here) written by Martin Gardner, who writes on 
theory of science:

"He refused to revise his falsificationism, and so condemned himself to a 
lifetime in the service of a bad idea.

Popper's great and tireless efforts to expunge the word induction from 
scientific and philosophical discourse has utterly failed. Except for a small but 
noisy group of British Popperians, induction is just too firmly embedded in the 
way philosophers of science and even ordinary people talk and think. 
Confirming instances underlie our beliefs that the Sun will rise tomorrow that dropped 
objects will fall, that water will freeze and boil, and a million other 
events. It is hard to think of another philosophical battle so decisively lost."


Steve Cooke posted to V2020 a summery of some of Karl Popper's ideas on 
theory of science yesterday.  The notion that empirically based inductive 
statements can never reach certainty, and that one valid observation that contradicts 
the predictions of a scientific theory is all that is required to show it is 
false, are ideas in theory of science that predate Popper.  He did develop some 
interesting theories about truth and falsehood in scientific theory, some of 
which have been shown to be false.  After reading an analysis of Popper's 
concept of falsification and verisimilitude from the Stanford Encyclopedia of 
Philosophy, I am inclined to think that Steve Cooke misstated aspects of Popper's 
Theory of Science.

Steve wrote:

"Karl Popper has shown that theories in science cannot be proven but
only disproved.( Popper, K. R. The logic of scientific discovery. London ;
New York: Routledge, 1992.) Deductive ideas or theories are subjected to
inductive or empirical tests. Since there are conceivably an infinite number
of empirical tests and since any one of them could disprove a theory, a
theory can never be verified once and for all time. The best you can ever
say about a scientific theory is that it has not yet been disproved. This is
the falsification methodology of science as opposed to a verification
approach. The latter is often implied when mention is made of scientific
facts. Science doesn't work that way."


Regarding Steve's statement that "Science doesn't work that way" Popper in 
fact recognized that the methodology of science, according to the Stanford 
Encyclopedia of Philosophy, does not follow his falsification theory:


"Popper has always drawn a clear distinction between the logic of 
falsifiability and its applied methodology. The logic of his theory is utterly simple: if 
a single ferrous metal is unaffected by a magnetic field it cannot be the 
case that all ferrous metals are affected by magnetic fields. Logically speaking, 
a scientific law is conclusively falsifiable although it is not conclusively 
verifiable. Methodologically, however, the situation is much more complex: no 
observation is free from the possibility of error - consequently we may 
question whether our experimental result was what it appeared to be.

Thus, while advocating falsifiability as the criterion of demarcation for 
science, Popper explicitly allows for the fact that in practice a single 
conflicting or counter-instance is never sufficient methodologically to falsify a 
theory, and that scientific theories are often retained even though much of the 
available evidence conflicts with them, or is anomalous with respect to them. 
Scientific theories may, and do, arise genetically in many different ways, and 
the manner in which a particular scientist comes to formulate a particular 
theory may be of biographical interest, but it is of no consequence as far as the 
philosophy of science is concerned. Popper stresses in particular that there 
is no unique way, no single method such as induction, which functions as the 
route to scientific theory, a view which Einstein personally endorsed with his 
affirmation that ‘There is no logical path leading to [the highly universal 
laws of science]. They can only be reached by intuition, based upon something 
like an intellectual love of the objects of experience’. Science, in Popper's 
view, starts with problems rather than with observations - it is, indeed, 
precisely in the context of grappling with a problem that the scientist makes 
observations in the first instance: his observations are selectively designed to test 
the extent to which a given theory functions as a satisfactory solution to a 
given problem."


And Popper developed a sophisticated method of analyzing what he termed the 
"truth content" and "falsity content" of a scientific theory, methods which 
have been at least in part refuted:

Again, from the Stanford Encyclopedia of Philosophy:

"Popper was initially uneasy with the concept of truth, and in his earliest 
writings he avoided asserting that a theory which is corroborated is true - for 
clearly if every theory is an open-ended hypothesis, as he maintains, then 
ipso facto it has to be at least potentially false. For this reason Popper 
restricted himself to the contention that a theory which is falsified is false and 
is known to be such, and that a theory which replaces a falsified theory 
(because it has a higher empirical content than the latter, and explains what has 
falsified it) is a ‘better theory’ than its predecessor. However, he came to 
accept Tarski's reformulation of the correspondence theory of truth, and in 
Conjectures and Refutations (1963) he integrated the concepts of truth and 
content to frame the metalogical concept of ‘truthlikeness’ or ‘verisimilitude’. A 
‘good’ scientific theory, Popper thus argued, has a higher level of 
verisimilitude than its rivals, and he explicated this concept by reference to the 
logical consequences of theories. A theory's content is the totality of its 
logical consequences, which can be divided into two classes: there is the ‘
truth-content’ of a theory, which is the class of true propositions which may be 
derived from it, on the one hand, and the ‘falsity-content’ of a theory, on the 
other hand, which is the class of the theory's false consequences (this latter 
class may of course be empty, and in the case of a theory which is true is 
necessarily empty).

Popper offered two methods of comparing theories in terms of verisimilitude, 
the qualitative and quantitative definitions. On the qualitative account, 
Popper asserted:

> Assuming that the truth-content and the falsity-content of two theories t1 
> and t2 are comparable, we can say that t2 is more closely similar to the 
> truth, or corresponds better to the facts, than t1, if and only if either: (a) 
> the truth-content but not the falsity-content of t2 exceeds that of t1, or(b) 
> the falsity-content of t1, but not its truth-content, exceeds that of t2. 
> (Conjectures and Refutations, 233).
Here, verisimilitude is defined in terms of subclass relationships: t2 has a 
higher level of verisimilitude than t1 if and only if their truth- and 
falsity-contents are comparable through subclass relationships, and either (a) t2's 
truth-content includes t1's and t2's falsity-content, if it exists, is included 
in, or is the same as, t1's, or (b) t2's truth-content includes or is the 
same as t1's and t2's falsity-content, if it exists, is included in t1's. 

On the quantitative account, verisimilitude is defined by assigning 
quantities to contents, where the index of the content of a given theory is its logical 
improbability (given again that content and probability vary inversely). 
Formally, then, Popper defines the quantitative verisimilitude which a statement ‘a
’ possesses by means of a formula:

> Vs(a)=CtT(a) - CtF(a),
where Vs(a) represents the verisimilitude of ‘a’, CtT(a) is a measure of the 
truth-content of ‘a’, and CtF(a) is a measure of its falsity-content. 

The utilisation of either method of computing verisimilitude shows, Popper 
held, that even if a theory t2 with a higher content than a rival theory t1 is 
subsequently falsified, it can still legitimately be regarded as a better 
theory than t1, and ‘better’ is here now understood to mean t2 is closer to the 
truth than t1. Thus scientific progress involves, on this view, the abandonment 
of partially true, but falsified, theories, for theories with a higher level 
of verisimilitude, i.e., which approach more closely to the truth. In this way, 
verisimilitude allowed Popper to mitigate what many saw as the pessimism of 
an anti-inductivist philosophy of science which held that most, if not all 
scientific theories are false, and that a true theory, even if discovered, could 
not be known to be such. With the introduction of the new concept, Popper was 
able to represent this as an essentially optimistic position in terms of which 
we can legitimately be said to have reason to believe that science makes 
progress towards the truth through the falsification and corroboration of theories. 
Scientific progress, in other words, could now be represented as progress 
towards the truth, and experimental corroboration could be seen an indicator of 

However, in the 1970's a series of papers published by researchers such as 
Miller, Tichý, and Grünbaum in particular revealed fundamental defects in 
Popper's formal definitions of verisimilitude. The significance of this work was 
that verisimilitude is largely important in Popper's system because of its 
application to theories which are known to be false. In this connection, Popper had 

> Ultimately, the idea of verisimilitude is most important in cases where we 
> know that we have to work with theories which are at best approximations—that 
> is to say, theories of which we know that they cannot be true. (This is 
> often the case in the social sciences). In these cases we can still speak of 
> better or worse approximations to the truth (and we therefore do not need to 
> interpret these cases in an instrumentalist sense). (Conjectures and Refutations, 
> 235).

For these reasons, the deficiencies discovered by the critics in Popper's 
formal definitions were seen by many as devastating, precisely because the most 
significant of these related to the levels of verisimilitude of false theories. 
In 1974, Miller and Tichý, working independently of each other, demonstrated 
that the conditions specified by Popper in his accounts of both qualitative 
and quantitative verisimilitude for comparing the truth- and falsity-contents of 
theories can be satisfied only when the theories are true. In the crucially 
important case of false theories, however, Popper's definitions are formally 


Finally, some contemporary thinkers have some rather strongly worded 
objections to some of Popper's central ideas:

The Skeptical Inquirer, July 2001, Martin Gardner

Sir Karl Popper, who died in 1994, was widely regarded as England's greatest 
philosopher of science since Bertrand Russell, indeed a philosopher of 
worldwide eminence. Today his followers among philosophers of science are a 
diminishing minority, convinced that Popper's vast reputation is enormously inflated.

I agree. I believe that Popper's reputation was based mainly on his 
persistent but misguided efforts to restate commonsense views in a novel language that 
is rapidly becoming out of fashion.

Consider Popper's best known claim: that science does not proceed by 
"induction"--that is, by finding confirming instances of a conjecture--but rather by 
falsifying bold, risky conjectures. Confirmation, he argued, is slow and never 
certain. By contrast, a falsification can be sudden and definitive. Moreover, 
it lies at the heart of the scientific method.

A familiar example of falsification concerns the assertion that all crows are 
black. Every find of another black crow obviously confirms the theory, but 
there is always the possibility that a non-black crow will turn up. If this 
happens, the conjecture is instantly discredited. The more often a conjecture 
passes efforts to falsify it, Popper maintained, the greater becomes its 
"corroboration," although corroboration is also uncertain and can never be quantified 
by a degree of probability. Popper's critics insist that "corroboration" is a 
form of induction, and Popper has simply sneaked induction in through a back 
door by giving it a new name. David Hume's famous question was "How can 
induction be justified?" It can't be, said Popper, because there is no such thing as 

There are many objections to this startling claim. One is that falsifications 
are much rater in science than searches for confirming instances. Astronomers 
look for signs of water on Mars. They do not think they are making efforts to 
falsify the conjecture that Mars never had water.

Falsifications can be as fuzzy and elusive as confirmations. Einstein's first 
cosmological model was a universe as static and unchanging as Aristotle's. 
Unfortunately, the gravity of suns would make such a universe unstable. It would 
collapse. To prevent this, Einstein, out of thin air, proposed the bold 
conjecture that the universe, on its pre-atomic level, harbored a mysterious, 
undetected repulsive force he called the "cosmological constant." When it was 
discovered that the universe is expanding, Einstein considered his conjecture 
falsified. Indeed, he called it "the greatest blunder of my life." Today, his 
conjecture is back in favor as a way of explaining why the universe seems to be 
expanding faster than it should. Astronomers are not trying to falsify it; they 
are looking for confirmations.

Falsification may be based on faulty observation. A man who claims he saw a 
white crow could be mistaken or even lying. As long as observations of black 
crows continue, it can be taken in two ways: as confirmations of "all crows are 
black," or disconfirmations of "some crows are not black." Popper recognized, 
but dismissed as unimportant, that every falsification of a conjecture is 
simultaneously a confirmation of an opposite conjecture, and every confirming 
instance of a conjecture is a falsification of an opposite conjecture.

Consider the current hypothesis that there is a quantum field called the 
Higgs field, with its quantized particle. If a giant atom smasher some day, 
perhaps soon, detects a Higgs, it will confirm the conjecture that the field exists. 
At the same time it will falsify the opinion of some top physicists, Oxford's 
Roger Penrose for one, that there is no Higgs field.

To scientists and philosophers outside the Popperian fold, science operates 
mainly by induction (confirmation), but also and less often by disconfirmation 
(falsification). Its language is almost always one of induction. If Popper bet 
on a certain horse to win a race, and the horse won, you would not expect him 
to shout, "Great! My horse failed to lose!"

Astronomers are now finding compelling evidence that smaller and smaller 
planets orbit distant suns. Surely this is inductive evidence that there may be 
Earth-sized planets out there. Why bother to say, as each new and smaller planet 
is discovered, that it tends to falsify the conjecture that there are no 
small planets beyond our solar system? Why scratch your left ear with your right 
hand? Astronomers are looking for small planets. They are not trying to refute 
a theory any more than physicists are trying to refute the conjecture that 
there is no Higgs field. Scientists seldom attempt to falsify. They are 
inductivists who seek positive confirmations.

At the moment the wildest of all speculations in physics is superstring 
theory. It conjectures that all basic particles are different vibrations of 
extremely tiny loops of great tensile strength. No superstring has yet been observed, 
but the theory has great explanatory power. Gravity, for example, is implied 
as the simplest vibration of a superstring. Like prediction, explanation is an 
important aspect of induction. Relativity, for instance, not only made rafts 
of successful predictions but explained data previously unexplained. The same 
is true of quantum mechanics. In both fields researchers used classical 
induction procedures. Few physicists say they are looking for ways to falsify 
superstring theory. They are instead looking for confirmations.

Ernest Nagel, Columbia University's famous philosopher of science, in his 
Teleology Revisited and Other Essays in the Philosophy and History of Science 
(1979), summed it up this way: "[Popper's] conception of the role of 
falsification . . . is an oversimplification that is close to being a caricature of 
scientific procedures."

For Popper, what his chief rival Rudolf Carnap called a "degree of 
confirmation:--a logical relation between a conjecture and all relevant evidence--is a 
useless concept. Instead, as I said earlier, the more tests for falsification a 
theory passes, the more it gains in "corroboration." It's as if someone 
claimed that deduction doesn't exist, but of course statements can logically imply 
other statements. Let's invent a new term for deduction, such as "justified 
inference." It's not so much that Popper disagreed with Carnap and other 
inductivists as that he restated their views in a bizarre and cumbersome terminology.

To Popper's credit he was, like Russell, and almost all philosophers, 
scientists, and ordinary people, a thoroughgoing realist in the sense that he 
believed the universe, with all its intricate and beautiful mathematical structures, 
was "out there," independent of our feeble minds. In no way can the laws of 
science be likened to traffic regulations or fashions in dress that vary with 
time and place. Popper would have been as appalled as Russell by the crazy views 
of today's social constructivists and postmodernists, most of them French or 
American professors of literature who know almost nothing about science.

Scholars unacquainted with the history of philosophy often credit Popper for 
being the first to point out that science, unlike math and logic, is never 
absolutely certain. It is always corrigible, subject to perpetual modification. 
This notion of what the American philosopher Charles Peirce called the 
"fallibilism" of science goes back to ancient Greek skeptics, and is taken for granted 
by almost all later thinkers.

In Quantum Theory and the Schism in Physics (1982) Popper defends at length 
his "propensity theory" of probability. A perfect die, when tossed, has the 
propensity to show each face with equal probability. Basic particles, when 
measured, have a propensity to acquire, with specified probabilities, such 
properties as position, momentum, spin and so on. Here again Popper is introducing a 
new term which says nothing different from what can be better said in 
conventional terminology.

In my opinion Popper's most impressive work, certainly his best known, was 
his two-volume The Open Society and Its Enemies (1945). Its central theme, that 
open democratic societies are far superior to closed totalitarian regimes, 
especially Marxist ones, was hardly new, but Popper defends it with powerful 
arguments and awesome erudition. In later books he attacks what he calls 
"historicism," the belief that there are laws of historical change that enable one to 
predict humanity's future. The future is unpredictable, Popper argued, because 
we have free wills. Like William James, Popper was an indeterminist who saw 
history as a series of unforeseeable events. In later years he liked to 
distinguish between what he called three "worlds"--the external physical universe, the 
inner world of the mind, and the world of culture. Like Carnap and other 
members of the Vienna Circle, he had no use for God or an afterlife.

Karl Raimund Popper was born in Vienna in 1902 where he was also educated. 
His parents were Jewish, his father a wealthy attorney, his mother a pianist. 
For twenty years he was a professor of logic and scientific method at the London 
School of Economics. In 1965 he was knighted by the Crown.

I am convinced that Popper, a man of enormous egotism, was motivated by an 
intense jealousy of Carnap. It seems that every time Carnap expressed an 
opinion, Popper felt compelled to come forth with an opposing view, although it 
usually turned out to be the same as Carnap's but in different language. Carnap 
once said that the distance between him and Popper was not symmetrical. From 
Carnap to Popper it was small, but the other way around it appeared huge. Popper 
actually believed that the movement known as logical positivism, of which 
Carnap was leader, had expired because he, Popper, had single-handedly killed it!

I have not read Popper's first and only biography, Karl Popper: The Formative 
Years (1902-1945), by Malachi Haim Hacohen (2000). Judging by the reviews it 
is an admirable work. David Papineau, a British philosopher, reviewed it for 
The New York Times Book Review (November 12, 2000). Here are his harsh words 
about Popper's character and work:

By Hacohen's own account, Popper was a monster, a moral prig. He continually 
accused others of plagiarism, but rarely acknowledged his own intellectual 
debts. He expected others to make every sacrifice for him, but did little in 
return. In Hacohen's words, "He remained to the end a spoiled child who threw 
temper tantrums when he did not get his way." Hacohen is ready to excuse all this 
as the prerogative of genius. Those who think Popper a relatively minor figure 
are likely to take a different view.

When Popper wrote "Logik der Forschung," he was barely thirty. Despite its 
flawed center, it was full of good ideas, from perhaps the most brilliant of the 
bright young philosophers associated with the Vienna Circle. But where the 
others continued to learn, develop and in time exert a lasting influence on the 
philosophical tradition, Popper knew better. He refused to revise his 
falsificationism, and so condemned himself to a lifetime in the service of a bad idea.

Popper's great and tireless efforts to expunge the word induction from 
scientific and philosophical discourse has utterly failed. Except for a small but 
noisy group of British Popperians, induction is just too firmly embedded in the 
way philosophers of science and even ordinary people talk and think. 
Confirming instances underlie our beliefs that the Sun will rise tomorrow that dropped 
objects will fall, that water will freeze and boil, and a million other 
events. It is hard to think of another philosophical battle so decisively lost.

Readers interested in exploring Popper's eccentric views will find, in 
addition to his books and papers, most helpful the two-volume Philosophy of Karl 
Popper (1970), in the Library of Living Philosophers, edited by Paul Arthur 
Schilpp. The book contains essays by others, along with Popper's replies and an 
autobiography. For vigorous criticism of Popper, see David Stove's Popper and 
After: Four Modern Irrationalists (the other three are Imre Lakatos, Thomas Kuhn, 
and Paul Feyerabend), and Stove's chapter on Popper in his posthumous Against 
the Idols of the Age (1999), edited by Roger Kimball. See also Catnap's reply 
to Popper in The Philosophy of Rudolf Carnap (1963), another volume in The 
Library of Living Philosophers. Of many books by Popperians, one of the best is 
Critical Rationalism (1994), a skillful defense of Popper by his top acolyte.

Martin Gardner collaborated with Carnap on a book currently available as a 
Dover paperback titled Introduction to the Philosophy of Science.



V2020 Post by Ted Moffett
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