26.1.10

POPPERIAN THESIS OF FALSIFIABILITY.

The progress of science in many areas is indubitable and the profound changes wrought by modern science since its inception cannot be doubted. Sitting back to enumerate the long list of scientific achievements both constructive and destructive would be belabouring the obvious. The aim of science is that of widening the horizon of the knowledge of man. This launches man into the centre of conquering the world and thus the satisfaction of his quest for curiosity is ensured.

At the root of this scientific quest is a problem which has engineered many notions. This is the problem of the method of science. Through which method does science attain this progress attached to it? The solution to this problem has given rise to inductivism, instrumentalism and essentialism and so on. Those who propagate induction as a method of science emphasize the need to jump from one instance to generalisations of a whole if something must be scientific. The underlying idea in induction is that nature is uniform; so that what is true in some cases would automatically become true in all cases.

Central to this question of the method of science is the problem of demarcation. This traditional problem seeks for that particular distinguishing mark between science and pseudo-science. What then is that which makes science scientific and differentiates it from myth and metaphysics?

Perhaps no philosopher has made more contribution to the solution of this problem than Karl Raimund Popper, the Austrian philosopher of social and natural sciences. He sees science in a methodologically different light. The traditionally predominant inductive view of science that served both as the logic of scientific progress and the criterion for demarcating science from pseudo-science had the following stages in the following order, each giving rise to the next: (1) Observation and experiment (2) Inductive generalisation (3) hypothesis (4) attempted verification of hypothesis (5) Proof or disproof (6) knowledge. But Popper replaced this with (1) problem (2) proposed solution, in other words, a new theory (3) deduction of testable propositions from new theories (4) attempted refutation, observations and experiment (5) preference established between competing theories. Popper therefore believes that falsifiability should be the thesis of any scientific hypothesis. We should aim at the falsification rather than the verification of theories as the sign of their scientificity. Induction does not provide a terra firma for scientific theories.

Popper thus rejects induction and situates Falsifiability as the criterion of science. His repudiation of induction was purely on logical grounds because in his philosophy logic and science share a domicile. In other words, for any method to be scientific it must be logically justifiable. Induction did not pass this test and is therefore labelled unscientific by Popper.

Popper was influenced by many great scientists and philosophers: Einstein was Popper’s hero. There are over 120 references to him in just three books: The Logic Scientific Discovery, Conjectures and Refutations and Objective Knowledge. Alfred Tarski also influenced Popper especially in his Theory of Verisimilitude. Popper himself has in turn influenced many philosophers and scientists. Sir John Eccles openly admits the influence of Popper on his view. Other eminent scientists who acknowledged Popper’s influence include: Jacob Bronowski, Peter Medawar, and John Maynard Smith.
This work then is geared towards the exploration of this Popperian thesis of falsifiability. The four chapters will be discussed in a “methodological crescendo”. Chapter one will focus on the problems of demarcation and scientific method. Chapter two will shift its attention to the intellectual treatment of induction as the hallmark of science. The problem of induction and Popper’s solution to this problem will reflect in this chapter. It also furnishes the reasons for the rejection of inductive method as a scientific method by Karl Popper. Chapter three, which serves as the punctum puncti in this work will centre on the method of falsifiability which is Popper’s contribution to the solution of the problem of the scientific method. The gradual but methodical steps in falsifiability will be presented as having a common aim, that is, to falsify and thus render scientific a theory. Chapter four will be a critique geared towards the collective analysis of the work, the implications of Popper’s schemer will be drawn and a personal evaluation and conclusion which will reflect a personal contribution to the work.

CHAPTER ONE
The Problem Of Demarcation And The Logic Of Scientific Discovery

1.1 SCIENCE
“Man’s respect for knowledge is one of his most peculiar characteristics. Knowledge in Latin is scientia; and science comes to be the name of the most respectable kind of knowledge.”

Science in its popular usage designates some discipline as physics, chemistry, astronomy and biology. Understood thus, it can be seen as a body of systematic knowledge, hypothesis, theories and laws built up by the work of numerous scientists. It could then be defined in this light as:
An interconnected series of concepts and conceptual schemes that have been developed as a result of experimentation and observation….
It could as well be seen as an “...ordered knowledge of natural phenomena.” Again, science could also denote a method of obtaining knowledge. It could as well be explicative. Hence, Karl Popper says that science “…finds satisfactory explanation.”
Having considered these definitions of science, I would say summarily with Giacon C. that science:
Are elaborations of the human mind that generally have as their object, realities which we reach through [our] senses, either directly or by means of suitable instruments and which we can subject to measurement.

1.2 SCIENTIFIC METHODOLOGY
The enterprise of science has been progressive. Ever since it began to evolve into its modern form especially from the 16th century onward, most discoveries have tended to follow a pattern or procedure that can roughly be called scientific methodology.
Scientific methodology therefore refers to a “sequences or collection of procedures that are considered characteristic of scientific investigation and the acquisition of new scientific knowledge.” This method is believed to distinguish science from other intellectual traditions such as Arts, philosophy theology and so on.
This procedure, normally called “the idealized scientific method” is traditionally described in the following order each giving rise to the other:
(1) Observe (2) Hypothesize
(3) Predict (4) Experiment
(5) Conclude (6) Evaluate.
If the experiment clashes with the hypothesis, the hypothesis is either modified or a new hypothesis is formulated which may better explain the experimental data and the original observation. This is repeated until the experiment corroborates the hypothesis. When it does, the findings so made can be presented as a seminar paper or published as textbook in a learned journal. The finding serves as a paradigm for future research work.


1.3 THE PROBLEM OF DEMARCATION
Demarcation as a philosophical problem can be broadly defined as the problem of placing realities into different categories or the problem of separating one thing from another. However; we are concern with narrow sense (scientific) of demarcation.
Scientific demarcation as Popper saw it is “the central problem in the philosophy of science.” For him it is “the problem of how to draw a line of demarcation between those statements and systems which could be properly described as belonging to the empirical science and others which might perhaps be described as pseudo-scientific….”
L. Wolpert was interrogative in his approach to the question:
If scientific knowledge is special and privileged in the sense that it provides our best understanding of the world. How can we distinguish between science and non- science? How does one deal with claims to be included within this frame work of privilege knowledge from those whom scientists would wish to exclude?
Lakatos considers it as the problem of knowing “what distinguishes knowledge from superstitious ideology of pseudo- science.”
Traditionally, boundaries are commonly drawn between science and non- science or pseudo-science and between science and religion. However, a form of this problem known as the “generalized problem of demarcation” subsumes all three cases. The general problems look for criterion for deciding which of two theories is more scientific? What makes Einstein’s theory more scientific than Newton’s? Dr. R. Percival in his PhD thesis described the general problem as follows: “The question is not about which practice deserves the noble title ‘science’ but about the best method for promoting the growth of knowledge and the control of error.”

1.4 THE PROBLEM OF THE LOGIC OF SCIENTIFIC DISCOVER
Enshrined within the question of demarcation is the idea of scientific change. This problem as Newton Smith sees it “requires an explanation to the shifting of allegiance from one scientific theory to another [such as the shift from the Ptolemaic to Copernican system and from this to the Newtonian – Keplerian system and finally to Einsteinian system] that characterizes the growth of science.”
P. Smith was more explicit, he says: “how can we explain the growth of science? By this he is asking how can we explain what makes progress possible in science and how such progress comes about – t he problem of scientific progress.”
Summarily, this problem has its root in the assumption that there must invariably be something special about the method of science to effectively account or justify its superior achievements.

1.5 DEMARCATION OR LOGIC OF SCIENTIFIC DISCOVERY
It is clear from our analysis so far that the problem of demarcation and that of the logic of scientific discovery are one and the same problem. Our justification for taking this position is that both questions, seek for the justification of the progress, special place of value and rational image that is normally attributed to science. For what makes science unique and better than other ways of explaining reality or the world. On this ground, we shall be using the problem of demarcation and the problem of the logic of scientific discovery as referring to the same problem throughout this work.

1.6 METHOD AS CRITERION OF DEMARCATION
The whole problem in philosophy is the problem of justifying man’s understanding and interpretation of the world. Reductively, the whole problem in the philosophy of science is the problem of justifying the scientific enterprise, in other words the problem of demarcation. Generally, philosophers are agreed that knowledge in general and scientific knowledge in particular need justification.
Thus, Russell asserts: “without justification there is no intellectual difference between sanity and insanity. The Lunatic who believes that he is a poached egg is to be condemned solely on ground that he is in a minority.” Recalling Russell, J. Ladriere emphasized that:
Indeed without this justification science would be only the dream of the mathematicians and would have no consistency … it would not be science at all for we would not know if it can be justified or how it may eventually be justified.

Proponents of the scientific method consider scientific method as the principle that justifies scientific enterprise. That is method seen as the criterion of demarcation as well as the logic of scientific investigation. But the question is: which method, since there are many scientific camps with different views on the issue of scientific method?
1.8 CONTROVERSY OVER METHOD

As indicated above, strong difference of opinion exists among philosophers, historians, sociologists even among scientists about what processes truly characterize science. Some believe that no characteristic method exists and doubt even the possibility of such method.
For instance, Paul Feyerabend in his book “Against Method” urges us to:
Free society from the strangling hold of an ideologically petrified science, just as our ancestors freed us from the strangle hold of the one true religion.
I B. Cohen believed that scientific method was a “false view… imposed on us by empiricism.” C. D. Broad saw it as a “skeleton in the cupboard of philosophy.” While Popper says: “there is no such thing.” On the other hand, demarcationists and discovery theorists believe that there is a “method which describes the actual behavior of scientists as they study problems, invent and test hypothesis, produce concepts and theories and actually make discoveries.” However, Popper disagrees on what this procedure is. The idealized scientific method, or induction, described above is one of the many theories describing the way in which science works or should be conducted. Others include, “hypothetico-deductive” method, “falsification,” the “research programme” of Lakatos, “scientific Revolutions” of Thomas Samuel Kuhn, and so on.
We will now proceed to chapter two for a fuller treatment of induction, which according to Eboh, and as we noted in the introduction to this work:
…was traditionally held as the method and basic principle of science. So, that for over two hundred years [from Francis Bacon to Isaac Newton] induction was seen as the method guiding science.
And whose rejection by David Hume, according to J.P. Mbat, “generated the problem of demarcation, the resolution of which forms the major preoccupation of contemporary philosophers of science like Carnap Popper, Kuhn and others.” And I would add, which actually gave rise to Popper’s principle of falsifiability.




As indicated above, strong difference of opinion exists among philosophers, historians, sociologists even among scientists about what processes truly characterize science. Some believe that no characteristic method exists and doubt even the possibility of such method.
For instance, Paul Feyerabend in his book “Against Method” urges us to:
Free society from the strangling hold of an ideologically petrified science, just as our ancestors freed us from the strangle hold of the one true religion.
I B. Cohen believed that scientific method was a “false view… imposed on us by empiricism.” C. D. Broad saw it as a “skeleton in the cupboard of philosophy.” While Popper says: “there is no such thing.” On the other hand, demarcationists and discovery theorists believe that there is a “method which describes the actual behavior of scientists as they study problems, invent and test hypothesis, produce concepts and theories and actually make discoveries.” However, Popper disagrees on what this procedure is. The idealized scientific method, or induction, described above is one of the many theories describing the way in which science works or should be conducted. Others include, “hypothetico-deductive” method, “falsification,” the “research programme” of Lakatos, “scientific Revolutions” of Thomas Samuel Kuhn, and so on.
We will now proceed to chapter two for a fuller treatment of induction, which according to Eboh, and as we noted in the introduction to this work:
…was traditionally held as the method and basic principle of science. So, that for over two hundred years [from Francis Bacon to Isaac Newton] induction was seen as the method guiding science.
And whose rejection by David Hume, according to J.P. Mbat, “generated the problem of demarcation, the resolution of which forms the major preoccupation of contemporary philosophers of science like Carnap Popper, Kuhn and others.” And I would add, which actually gave rise to Popper’s principle of falsifiability.

CHAPTER TWO


2.0 INDUCTIVE METHOD: AN EVOLUTIONARY APPROACH

Induction as a method of science according to J. P. Mbat has evolved through two major stages: the traditional or static view associated with Aristotle and Francis Bacon and the dynamic or probabilistic view associated with Einstein, our discussion will swim through these stages. Before this let us explore the notion of induction.

2.1 INDUCTION EXPOSED
Induction is better explained when contrasted with deduction. In induction we move from inference of particular affirmative proposition (A is a swan, it is white, B is a swan, it is white, etc) to inference of universal proposition (all swans are white). While in deduction we move from the universal (all swans are white) to the particular (A is a swan, A is white). However, the basic difference between deduction and induction as noted by D. N. Ucheaga is that while conclusions in the former follow necessarily from the premises, in the later they follow probabilistically.
What this means is that deduction is analytic and does not give new knowledge, while induction is synthetic and therefore advances knowledge. It is on this ground that Jonathan Powers opined that:
…the 18th century science saw in induction a superior quality to the hitherto acclaimed deductive method.

2.2 ARISTOTLE: INDUCTION BY SIMPLE ENUMERATION
Even though induction was presupposed in the work of the Ionian philosophers, it was Aristotle who coined and developed it as a method of science. According to Popper, Aristotle followed Plato in seeing true knowledge or science as knowledge of the universals. But while Plato holds that the universals are in the world of forms and thus can only be known through intellectual intuition, Aristotle believes that they (universals) inhere in individual things and can be known by the combined processes of observation and intuition.
For Aristotle, therefore, induction is:
…a method, by which the particular sensation [observation] is turned into universal truth, that is method of generation from particular observation.
What Aristotle is implying here is that it is through observation that we arrive at the universal truth such as ‘all men are mortal’ which forms the major premise of deductive logic. Dr. Mbat confirms this when he says: “induction is complementary to deduction.” This is because deduction only makes explicit what is already known, while induction leads to the discovery of new knowledge. Since induction is reasoning from the, known to the unknown, in other words the only process by which new knowledge enters this world. Dr Mbat also gives this famous example of inductive argument attributed to Aristotle:
(1) Man, the horse and mule are long-lived
(2) But man, the horse and the mule are biless animals.
(3) Therefore all biless animals are long-lived.
Let us conclude our discussion on Aristotle by noting that for Aristotle the validity of inductive procedure is dependent upon the number of observed instances. If we can enumerate all the instances, we may claim to have perfect induction that provides or guarantees us of absolutely certain knowledge in the end. In Popper words “Aristotle’s notion of perfect inductions contains in itself an element of finality.”

2.2 FRANCIS BACON: INDUCTION BY ELIMINATION
The foundation of modern inductivism according to P. Eboh, was laid in the early Seventeen Century by the English philosopher, Francis Bacon (1561-1626). Bacon, in I. I.Copi’s account, rejected Aristotelian induction by simple enumeration on ground that it depends on too small number of facts and is therefore exposed to error.
In the place of simple enumeration he devised the method of elimination by which in P. Eboh words: “…Science can arrive to absolute certain conclusion.” The notion of induction by elimination is summarized by J. P. Mbat, when he says:
Bacon’s simple elimination recognizes that there are so many causes of events and things in nature. But the true cause is discovered only indirectly when the scientific investigator has recognized and eliminated all false causes of the event under study.
Conclusively, what characterizes the Aristotelian and Baconian static notion of

induction is, that facts already exist in nature, all the scientists needs to do is to find them.
Thus for them nature is strictly mechanistic.

2.4 THE PROBLEM OF INDUCTION: HUME’S PROBLEM
Consider the following argument:
1. A is a copper, It conducts electricity,
2. B is a copper, it conducts electricity,
3. Therefore all copper conducts electricity.
The structure is inductive. In it, we see, that there is an “inductive leap” or “logical jump” from the observed (copper A and B) to the unobserved (all copper). The justification of this “inductive leap”, which involves a plain logical fallacy (the fallacy of illicit process) is precisely the notorious and famous problem described by philosophers as the problem of induction. A. N. Whitehead calls it “the despair of philosophy.”
Although the problem of induction has been there since the times of Aristotle, traditionally, the history of the problem began with David Hume. Hume’s account of the matter is so authoritative that the problem of induction has become known as Hume’s problem. On this Popper says: “We call the problem of induction Hume’s problem.”
“Hume” as Mbat observed “did not use the word induction, but the principle of causality or universal causation which was the concern of his Treatise is implied by induction.” The point, he explained rests on the fact that, “the whole of science assumes that every event has a cause.”
The question that troubles Hume here is: What relation exists between a cause and an effect? Hume argues that when we say that an event A causes another event B, what we mean is that there is a power or necessary connection between A and B, so that whenever A is seen we assume that B will logically follow.
But this idea of necessary connection raises more serious question for Hume; namely since in Hume’s epistemology; “ideas” are “copies” of “impressions” from what impression can the idea of necessary connection be derived. Hume says that the idea of necessary connection cannot be derived from experience no matter how many times we observed two things happening together. Hume’s conclusion then according to R. S. Percival is that “we cannot sanction a logical or probable general inference from observed cases.” What this means in practical terms is that no true singular observation statements will entitle us to draw an unrestricted general statement. This was later called Hume’s logical problem (L1).
But a more acute problem comes up here for Hume. This question as formulated by Ekpo is:
If induction is unjustifiable, Why is it that sane and intelligent people still trust and discuss induction at great length; Why this resistance to elementary logic.
The trust and confidence in induction as Ekpo reasons derives principally from the general assumption that nature is uniform and that the future will continue to be like the past. But this idea of uniformity and necessary connection is what Hume is particularly against. He argued that Events are entirely “loose and separate… conjoined but never connected.”
Hume’s stance on this, is that all human judgments are based on ‘irrational faith’ or ungrounded faith in a future that represents the past. Hume therefore concludes that the problem why we put our confidence in induction derived from our psychological constitution or habit which, arose through repetition and conditioning. This was also called Hume’s psychological problem (Hp). The implication of this conclusion is that scientific knowledge in particular and human knowledge in general is unjustifiable. This is outrageous and terrifying for it reduces man to the level of irrational brutes or what B. Russell means when he says:
If Hume’s model is uphold then there is no intellectual difference between sanity and insanity and we might as well all regard ourselves as poached eggs.
It was to avoid the conclusion implicit in Hume’s analysis that according to N. Dykes “Libraries have been filled with attempts to solve the problem of induction.”


2.5 IMMANUEL KANT
The best spirited effort, and in my opinion, the best resolution outside Popper’s to Hume’s problem was the one made by Kant in his philosophical classics: The Critique of Pure Reason (1781). Kant’s resolution consists in what is generally known as “Kantian Copernican Resolution” by philosophers. The important issue in this is that Kant agrees with Hume that necessary connection or strict universality that characterizes scientific proposition does not derive from experience, but is imposed by the mind in the form of a priori category on the occasion of experience.
Thus Kant maintains as observed by I. Ekpo, that Hume was right in stating that necessary connection cannot be derived from experience because experience is limited. However Kant insisted that Hume’s failure drives from the fact that he was looking for necessary connection in experience while necessary connection is a priori. Kant’s account of the matter is very decisive but it is not all philosophers that accept his resolution. The logical positivists were especially antagonistic with Kant on this matter. Their issue with Kant is that he took the question out of context.
The crux of the matter for them as Hume originally formulated it is the justification of induction on empirical grounds. Kant’s synthetic a priori complicates the issue more for there is no way we can get out of our experiences to see things -in- themselves.



2.6 THE LOGICAL POSITIVISTS: INDUCTION BY VERIFICATION
As the name implies, Logical positivism espoused by members of the Vienna Circle according to E. M. Mackinnon represented: “a fusion of the empiricist tradition stemming from Hume, Mill and Mach with the new logic interpreted by Bertrand Russell and Wittgenstein.
The logical positivists accepted induction as both the logic and method of scientific discovery. They were convinced that the failure of previous philosophers especially Hume, Kant and Russell to justify induction was their inability to do away with non-empirical substances (Metaphysics). Consequently, their basic purpose in philosophy as contained in a document written by Carnap, Hahns and Neurath and dedicated to the group leader, Moritz Schlick, was (1) To establish a firm foundation for science and (2) To demonstrate the meaninglessness of Metaphysics.
To accomplish this aim they adopted a criterion of meaning, according to which, the meaning of statements is the measure of their logical and empirical verification. Analytic propositions are logically verifiable; for the verification of synthetic propositions, they postulated their famous verification principle.
For Lawhead, this principle states that “the meaning of synthetic or protocol statement is the method of its empirical verification.” The consequence of this principle as Mackinnon saw it is that: “Metaphysical and theological statements fit neither category and were dismissed as meaningless pseudo- propositions.”
Thus the logical positivists combined the problem of science and meaning and accordingly gave them the same solution—verification. In other words, for a non-logical statement to be meaningful i.e., cognitively significant, or scientific it must be factually and conclusively verified or verifiable by experience otherwise, it is a meaningless pseudo-statement
Empirical verification then became for the positivists the solution to Hume’s problem of induction. Mackinnon drawing further implication from the verification theory observed that: The positivists have an absolute view (infallible view) of science because their position implies that …with conclusive verification scientific hypothesis can be absolutely established as universal truth without exceptions.
But this absolute view of verification did not last long. In Gilles articulation:
The 20th century revolution in physics; that is the failure of important and well-confirmed theories which gave new significance to Hume’s problem and showed that all scientific theories are equally improvable, forced the logical positivists to change their absolute logical view of verification to probabilistic view.
Lakatos was very much alive to this change Following Gilles he observed:
…the inductive logician of the 20th century … set out to define the probabilities of theories according to available evidence. If the mathematical probability of a theory is high it qualifies as scientific; if it is low or even zero it is not scientific.
Thus the hallmark of scientific honesty would be never to say anything that is not at least highly probable. Probabilism has an attractive feature: instead of simply providing a clear distinction between science and pseudo-science, provides a continuous scale (probability calculus) from poor theories with low probability to good theories with high probability. This means that the position of each theory in the calculus is determined by the number of evidence in its support.
Following this development, Carnap distinguished himself as the most prominent and productive member of the Vienna circle. Firstly according to J. P. Mbat:
… he agreed to the criticism of Popper by accepting that scientific hypothesis cannot be conclusively verified by observational evidence…He shifted his position from verification to confirmation.
In Carnap’s own word: “…instead of verification, we may speak of gradually increased confirmation of laws.” This also led Carnap into adopting the frequentist view of probability to proffer solution to the logical view which according to him is the degree of “confirmation” or “weights of evidence.” This becomes necessary because for the frequentist probability is an estimation of the measurement of relative frequency value that can be expressed in quantitative terms. However, Carnap continues to insist on ‘total evidence for his degree of confirmation. According to him:
We cannot say with certainty what the value of probability is but if the series is long enough, we can say what the probability is by calculation.62
Carnap insistence on “total evidence” can be better explained according to R. S. Percival if we remember that Carnap initially held that the problem of confirmation was a logical problem; that assertions of confirmation by evidence of a hypothesis should be analytic and depend only on the logical relation between the hypothesis and evidence.
What this means according to Carnap is that, if the degree of confirmation ‘C’, of a hypothesis “h”, with respect to evidence ‘e’, we can define the function of “C”. And using the theorem: C {h/e} = q, the value of q of “C” for any given ‘h’ and ‘e’ can be calculated. The explanation is that increase in the number of evidence increases the value of q, so that with total evidence we can say with certainty that an event would occur or not.
Consequently, for Carnap, probability in the strict sense is a logical relation although it involves an estimate of relative frequency value in quantitative terms when used elliptically. But if the question is asked: how possible is total evidence since scientific theories are usually of infinite scope and what compatibility has the randomness of the frequency series of daily experience with the lawfulness or mathematical limit of inductive Calculus? Dr. Mbat suggested that “Carnap intended his principle of total evidence to be pragmatic.” Mbat’s view on this is that Carnap believes that with total evidence we will reduce the risk of over-estimating or under-estimating the likelihood of the actual occurrence of the event to which the hypotheses refers.
As is evident from our analysis mathematical calculus of probability does not solve the problem of induction for underneath the probabilistic interpretation we still have to jump from particular experience to universal law.
To this end, it is important to note that the logical positivist principle of verification in general and their theory of probability in particular have been visited with many criticisms. But more importantly, have stimulated philosophers to further and deeper investigation into the problem of induction as the logic of scientific discovery. Poppers theory of falsifiability which we shall discuss next is a direct reaction to it.
2.7 POPPER’S SOLUTION TO THE PROBLEM OF INDUCTION AND
DEMARCATION

David Hume saw the problem of induction as two related problems: the logical problem which then leads to the psychological problem. The logical problem is the problem of whether universal law or the belief that the future will be like the past, can ever be justified following evidence from past observation? Hume’s answer to this question was no; because we cannot rationally assert what we have not experienced. The psychological problem on the other hand is; if we cannot not derive universal law from particular observation or predict future event from past experience why is it that scientists still talk about universal laws proved from particular experience; why do we still trust that the future will be like the past? Hume’s reply is that this derives from subjective “custom” or “habit” which arises from repetition.
Popper accepted the division of Hume’s problem into logical and psychological problems. He schematically represented the logical and the psychological problems as (L1) and (Hp) respectively. The solution Popper gave to the logical problem (L1) is just a follow up to Hume’s solution. The only difference is that Popper realizing the insoluble nature of the problem in its original form; undertook a radical restatement of it.
The original logical problem (L1) as Popper saw it is: “can the claim that an explanatory universal theory is true be rationally justified assuming the truth of certain test statements such as experimental observation?”
Popper following Hume answers in the negative. He maintains that there is no logical or probabilistic justification of universal theories. Pushing further, he insisted that the mathematical probability of all theories (scientific or pseudo-scientific) given any amount of evidence is zero. He used the classical swan example for illustration:
…no matter how many instances of white swans we may have observed this does not justify the conclusion that all swans are white.
Popper then restated the logical problem (L1). He represented the reformulation as (L2). He asked "…whether the claim that an explanatory universal theory is true or false be justified by empirical reason?” Popper answered in the affirmative. He says:
Although no number of observations …allows us to derive universal statement ‘all swans are white’ one single observation statement allows logically to derive the statement ‘not all swans are white’.
What Popper is saying here is that we cannot verify a theory no matter the number of positive experimental evidence, but we can falsify a theory by single experimental evidence. There therefore is an essential asymmetry between verification and falsification here-the truth of a scientific theory can never be proved while its falsehood is made definite by a single well-chosen test condition.
Popper’s key idea here is that induction has no place in the logic of science. What really took place according, to Popper is, that science advances by means of conjectures and refutations: “...in my view there is no such thing as induction.” “What characterizes the empirical method is it manner of exposing to falsification, in every conceivable way the system to be tested.” “Hume” one of the most rational minds of all ages” said Popper “has shown that there is no argument of reason which permits an inference from one case to another … and I completely agree.”
Applying the “principle of transference” Popper maintained that the solution to the logical problem (L2)-i.e., that there is nothing like inductive logic, also applies to the psychological problem (Hp), because what is true in logic is also true in psychology. And since Hume is right that there is no such thing as induction by repetition in logic by the principle of transference there cannot be any such thing in psychology.
Thus, Popper disagrees with Hume for maintaining that induction originates from habit and habit from repetition. Popper argued that habit arises from expectation before the experience of repetition and when the human mind does not see this regularity in nature, it imposes it on nature. Induction therefore is not based on habit as Hume believed but on expectation imposed by our penchant for regularity in nature and this is then followed by observation.
The standard for the preferrability among competing theories is the next problem that arises from Popper’s answer to the logical problem (L2). This led popper to formulate a third logical problem (L3). He asked: “… are there rational grounds for preferring hypothesis say, A, over hypothesis B, given that they both have survived the same text.” The important point Popper stressed here is the distinction between the notions of preference for a theory as opposed to reliance on a theory, since for Popper while it is possible to show that a theory is false, a theory can never be shown to be true.
Still using the principle of falsifiability Popper provides two fold solutions to the question. First Popper says:
Yes, sometimes, it can, if we are lucky, for it may happen that our test statement may refute some of the competing theories.
Secondly Popper argues that we should prefer hypotheses which have the greatest ‘information content’ and ‘explanatory power’ in that these make them more suitable for future testing, that is, there is more scope for devising suitable test conditions by which to refute the hypotheses. Popper’s position here is that it is more rational to place our reliance in the best tested hypothesis; the one which has survived the most rigorous testing and explains all of the observation covered by the competing theories. Strictly speaking, it is the theory which has best survived critical discussion up to the present time. While we know that such a hypothesis can never be finally verified as true, it will however be a member of a set of hypotheses to which any true theory belongs. For all practical and pragmatic purposes Popper suggests it is rational to employ such best tested hypotheses as if they were true until they are either refuted or superseded by a better theory.
Popper’s resolution to the problem of induction also inspired him to take falsifiability as his criterion of demarcation. According to him: scientific theories can be distinguished from metaphysical theories because scientific theories can be falsified (as opposed to verified) by prediction and observation, whereas metaphysical theories (pseudo- sciences) cannot.
To summarize, Popper believes that his solution to the problem of induction consists in showing that there is no such thing as inductive logic: “I believe I have solved the problem of induction by the simple discovery that induction by repetition does not exist.” Elsewhere he referred to induction as a “myth which has been exploded by Hume.” He further asserted that “there is no rule of inductive inference leading to theories or universal laws ever proposed which can be taken seriously even for a minute.”

CHAPTER THREE

3.0 POPPER’S CRITERION OF SCIENCE
3.1 THE PRINCIPLE OF FALSIFIABILITY
The principle of falsifiability has also been referred to, as “critical rationalism” by Popper himself and others and as the theory of Falsification, Falsificationism or Fallibalism. As we saw in previous chapter, it begins by rejecting induction as a method of science. Thus for Popper, “There is no need even to mention induction.”
“The actual method of science and the way in which knowledge progresses especially our scientific knowledge”, Popper maintained, is:
…by unjustified and unjustifiable anticipation by trial and error or conjecture and refutation, of boldly proposing theories, of trying our best to show that they are erroneous and accepting them tentatively if our critical effort are unsuccessful … they can never be positively justified, they can be established neither as certainly true or even, as probable.
What this means is, that in Popper’s schema certainty or absolute truth is impossible. Thus the aim of science is not truth or certainty but the advancement of knowledge. Elsewhere Popper puts the matter more succinctly: “all knowledge is hypothetical.” Or “All knowledge remains … conjectural.” According to J.C. Lesteri: “it is in the form ‘all knowledge’ is conjectural”’, that his philosophy has been captured and has influenced others.”
R. S. Percival generalizes the methodological conclusions of Poppers investigation as follows:
1. Propound empirically testable theories;
2. Aim to refute them;
3. Given any theory T1, aim to replace it by another theory T2, which is more general and precise (i.e. has higher information content), one that explains the successes and failures of T1 and is moreover independently testable.
3.2 OBSERVATION AND FALSIFIABILITY
Popper rejects the empiricist’s Hume’s position that it is the object of experience that imposes itself on the mind. In a Kantian fashion Popper maintains that it is the mind which imposed its expectations (theories, hypothesis conjectures, problem, etc) on nature. This imaginatively invented conjectures is what “a scientist whether theorist or experimenter tests step by step.”
Popper therefore rejects the traditional inductivists position that observation leads to theory. For him scientific enterprise is basically problem solving, and scientists as “problem solvers”, when confronted with problem, imaginatively invent theories and carry out observations to test their correspondences to reality.
It may be good to emphasize here that the reason why the inductivists see scientific knowledge as infallible is because they think that theories are descriptions of the truth of nature discovered by pure observation. In other word, realities are the way we perceive them. Popper rather insists on the fallibility of scientific knowledge because theories are not descriptions of reality, but inventions of human imagination. Observation, for him is not haphazardly done but is guided by accepted theories or expectations already in the mind. Thus he observes: “Observations are impregnated with conjectural expectation … there can be no pure perception, no pure dictum.”
Popper’s contention here is that science is a creative and imaginative enterprise where the scientist does not just observe to discover ready made facts, but is actively involved in the creation and invention of facts which he then tries to overthrow in observation in other to make them prove their worth.
He claimed that the distinction between the origin and testing of theory is the major difference between himself and those who in the past favoured inductive methodology- the difference is that the inductivists do not make the distinction between the psychology of knowledge (i.e. the invention of theories) and the logic of knowledge (i.e. logical validity of the method).
Popper’s explanation here is that falsifiability concerns only the logical process of hypothesis testing, not where the hypothesis originates. He says: “the creativity involved in theoretical scientific discovery is a psychological matter, one that escapes logic for most part.” Pressing his case further, Popper insists that:
Any method that places observation before theory, and makes observation lead to generalization, must be rejected because of much pessimism it habours for science; for it disallows adventures hypothesis and relegates the creative and imaginative powers of scientific hypothesis into oblivion and this makes the rationalistic base of science to be corroded.
3.3 BOLDNESS SIMPLICITY AND PROBABILITY
A very important aspect of Popper’s falsifiability is that what makes a theory reliable is not just that it has not been proved wrong (falsified), but that it is boldly ready to be put forward for the most sever test. Boldness as a technical term used by Popper means “possessing a great empirical or informative content and predictive power.” Hopers understand this when he says: “The advantage of scientific theories is that they possess enormous explanatory powers.” Popper has similar idea when he observed that:
…a theory is bold if it is a new, daring hypothesis, and it is daring if it takes a large risk in being false … this risk can be analyzed ultimately in terms of the amount of possibilities that the idea excludes the degree to which it forbids state of affairs … severe attempts at refutation are severe critical discussion and sever empirical test.
To boldness Popper added simplicity. A simple theory is one that says more about the world. It has great informative content and predictive power and, hence, more open to falsification.
Additionally, unlike in inductive methodology where the choice of a theory is directly proportional to its probability, Popper argued rather paradoxically that the more improbable a theory is, the better it is scientifically. This is because probability and the boldness of a theory vary inversely – the higher the boldness of a theory the lower the probability; for the more information a statement contains; the greater will be the number of ways in which it may turn out to be false. Thus, Popper maintains that: “the statements which are of special interest to the scientist are those with high informative content and (consequently) a low probability which nevertheless comes closer to the truth. Thus, the severity of a test to which a theory can be subjected and by means of which it is falsified or corroborated is all important.
Thus, it is not truth which decides whether a theory is scientific; it is the theory's openness to refutation. More generally, it is whether the theory is an attempt to expand our knowledge -whether it represents an increase of information on the theory it replaces.
The explanation of all this is that Popper knows too well that such adventures hypothesis which are bold and simple are far more likely to be wrong than right. But even at that “in science we desire the growth of knowledge” , and the bolder theories, according, to him, will get us further: “… the wrong view of science betrays itself in caring to be right.”98
This goes again to show how adamant Poppers is that criticism and testability is the hallmark of science: “…the man who welcomes and acts on criticism will prize it above friendship. The man who fights it out of concern to maintain his position is clinging to ungrowth. Further he vehemently maintained that: “…irrefutability is not a virtue for a theory but a vice.”
But in reality how is the principle of falsifiability applied? This takes us to basic statement and its allied concepts.

3.4 BASIC STATEMENTS, IMMUNIZING STRATAGEM
BACKGROUND KNOWLEDGE AND CORROBORATION

Basic statements also called singular statements or test statements are technical terms used by Popper to denote an observable reality or fact of experience which when true, falsifies or rules out a theory. Consequently, Popper calls them “potential falsifiers.” For example the proposition “ALL swans are white”, can be tested by the basic statement: “Here is a black swan.” If there is really a black swan the proposition is falsified.
Basic statements thus form the greatest instruments in Popper’s scientific enterprise. Firstly they determine the scientific status of theories. For a theory to be scientific it must be prohibitive, in that it must forbid by implication those statements which, if true, falsify the whole theory. This is consistent with Popper’s subsequent assertion: “In so far as scientific statements refer to the world of experience, they must be refutable…in so far as they are irrefutable they do not refer to the world of experience and therefore unscientific”
The explanation here is that the scientificity of a theory is a measure of its basic statements. A theory with many basic statements is highly scientific; a theory without basic statement that can be used to test its validity is immunized from falsification and therefore unscientific.
Now if all scientific statements are necessarily prohibitive i.e., necessarily contain error, or potential falsifiers, it follows that in science we can never attain certainty: “No particular theory may ever be regarded as absolutely certain…. No scientific theory is sacrosanct.” In the Unended Quest Popper says: “Precision and certainty are false Ideals. They are impossible to attain and therefore dangerously misleading …”103
Secondly, basic statements are what make scientific progress possible. This is because, for Popper, science is the search for true theories and basic statements play the role of rejecting, eliminating and criticizing false theories thereby challenging the scientists to produce new theories which may stand up to these tests. In this way science advances .Popper also holds the idea that basic statement is related to boldness, simplicity and improbability:
The hypothesis which rules out more basic statements is more open to refutation …is simpler since it says more about the world, it also has the greatest empirical content [boldness] and are logically the least probable and also has strongest scientific status.
Moreover Popper gave some conditions which a statement must fulfill to be basic:
1) Basic statement states (truly or falsely) the existence of observable facts (occurrence) within some sufficiently spatio-temporal region. Explaining this, Popper says: “A statement of the form ‘there is so-and-so in a region K …may be called a singular existential statement or singular observational statement.”
2) The conjunction of two basic statements ‘p’ and ‘r’, which do not contradict each other, is in turn a basic statement. Popper even extends it by saying that the conjunction of a basic statement to another statement which is not basic gives rise to basic statement if they do not logically contradict each other. To put it symbolically we can say, given a theory ‘t’ conjoined with a statement of initial condition ‘r’ from which a prediction ‘p’ can be derived. It follows that r.p will be potential falsifier of ‘t’ and basic statement. Since (t.r)>p, then t>(r>p), that is, t >(r. p).
For this Encyclopedia of philosophy stated: “… a conjunction of a basic and a non basic statement may be a basic statement.”
3) It then (by the law of non contradiction) means that the negation of basic statement can never result in a basic statement.
Popper also excluded disjunctions and conditional statements of the type: “If there is raven in this room, then it is black,” from the class of basic statements because though empirical, they are not of the character of test statements of theory but rather instantiation statements and therefore less interesting and less basic.
IMMUNIZING STRATAGEM OR CONVENTIONALISM
This term is used by Popper to distinguish the critical and ever progressive nature of scientific theories, from the dogmatic tendencies of pseudo-science. While the former such as Keplers, Newton's and Einstein’s theories are highly risky. The later such as Freud’s Psychoanalysis, Adler’s individual psychology and Marxism do not accept criticisms of their theories but do everything possible to see to its confirmation and its freedom from falsification. In Popper’s words: “They appear to be able to explain particularly everything that [happens] within the fields to which they [refer].”
While Freudianism or Adlerianism incorporated immunizing stratagems from the beginning and does not need any immunization, to make it irrefutable; Marxism was originally an empirically testable theory but since Marx’s prophesy (Marx predicted that the first socialist revolution would take place in the industrially most developed society; this occurred in industrially backward Russia. He also predicted that there will be no conflict of interest among socialist countries; the Russian-Chinese conflict refuted this), failed to come true, the theory had been recast in the form of empirically irrefutable metaphysics. “This maneuver Popper argued “saved Marxism from refutation and immunized it against further attacks.” For the same reason also Popper had referred to Darwinian evolutionary theory as an unscientific “metaphysical research program.”
This was his case against inductivism, for it includes so many unscientific theories as scientific, also it seems to be confirmed by everything and is rendered unfalsifiable. In corroboration of this view Anthony O’Hare noted: “If we find that an inductively based experiment fails us, the inductivists will not conclude that his principle of induction is false, but simply that the inductive principles has been misapplied.”
Another important distinctive feature between Popper’s demarcation and that of the inductivists is that while the inductivists consider metaphysics or pseudo-science as meaningless or nonsensical, Popper thinks that metaphysics being pseudo-scientific does not mean that it is meaningless. He argued that the boundary between science and metaphysics is a vague one, and that metaphysical idea with criticism and suitable technology can inspire the creation of an empirically testable theory. In the Logic of Scientific Discovery, he gave a number of examples such as “atomism which inspired John Dalton’s atomic Theory”, “the corpuscular theory of light; which inspired Planck’s Photon theory and the theory of territorial motion.”
To Buttress the kind of demarcation he espouses, Popper creates an image of two squares, which I now put in diagrammatic form.

Science Testable
Metaphysics Non-testable
Fig. A. Fig. B.
Metaphysics (non-sensical)
Outside the class of
Meaningful statements

Language for formulation Class of meaningful statements
Popper subscribes to the specification of Fig. A but he rejects the demarcation principle of Fig. B that excludes metaphysics completely from meaningful language. Popper’s point here is that scientific theories can be developed from myth by subjecting them to criticism. In Conjecture and Refutations he remarks: “Science must begin with myths, with the criticism of myths, neither with the collection of observation nor with the invention of observation, but with critical discussion of myths and of magical techniques and practices.”
Here again Popper points out that the chief goal of science is the advancement of knowledge.

BACKGROUND KNOWLEDGE
Background knowledge as used by Popper constitutes those things which a scientist necessarily, accepts as unproblematic while conducting an experiment. E.g., in conducting an experiment the scientist necessarily assumes that the apparatus used is working in order. The importance of this term in Popper’s falsifiability is that it helps to draw a clear distinction between the logic of falsification and its applied methodology. Logically a theory that is in conflict with observational or experimental evidence is conclusively falsified. This is because “…contradictions are impermissible and avoidable…once a contradiction is admitted, all science must collapse.” However, methodologically the situation is more complex.
A theory is not thrown away because it contains anomalies. What happens in the face of an anomaly is that the error is blamed on the basic statements, the background knowledge or the auxiliary hypothesis, not on the ‘hard core’ of the theory. And an ad hoc or rescue hypothesis is usually invented to prevent the theory from being rejected.
Poppers position on this according to R. S. Percival is that: [Popper] while advocating falsifiability allows for the fact that in practice single conflict 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.”
Nicholas Dykes puts it more succinctly: “Popper also realized that there is a rational function to resistance, to criticism …clearly, if refutation is avoided at all cost in science, then one gives up science. But on the other hand, if a theory is abandoned too easily in the face of apparent refutation, then the theory has no opportunity to show its strengths which may only become apparent later in the course of the debate. Popper concludes that there is a room in science for dogmatism, by which means we stick to a theory even against very strong arguments.”
The conclusion we can derive from all this is that “irrational” stubbornness of some ideologist may in some cases be scientifically rational. The refutation of a complex theory is not an obvious and mechanical procedure. Certainly, stubbornness per say is not irrational. But two important questions arise here for Popper (1) how then do we determine when a theory is falsified? And (2) how do we distinguish between when we are using “ad hoc” hypotheses to help our theories prove their worth and when we are using them as immunizing stratagem to shield our theories from refutation. To the first question Popper’s answer is that the test should continue. If we are lucky enough we shall discover where the error is from. To the second questions he says, that while the addition of ad hoc hypothesis expands the theory making it more risky, immunizing stratagem is a development in theory that reduces testability.
In sum, Popper stresses that basic statements is not basic in the sense of being infallible, their function is that they help in the corroboration or falsification of theories.
CORROBORATION

Popper introduced this technical term to distinguish his position from that of the
the logical positivists. Unlike them, who see a theory consistently supported by experimental evidence as verified or confirmed and therefore a law of nature, Popper approached the issue in two ways. For him verification is too simple. He criticizes science done in this manner for its unwillingness to challenge itself. He describes what he means here by noting that “it is easy to obtain confirmations or verifications.” and that confirmation should count if they are the result of risky predictions; that is to say, if unenlightened by the theory in question, we should have expected an event which was incompatible with the theory- an event which would have refuted the theory.” In other words, if confirmation is to happen, it will only happen as a result of surviving a severe attempt at refutation.
Secondly, that a scientific theory is never verified or confirmed but can only be corroborated and used tentatively while awaiting falsification—since the purpose of experimentation is to falsify theories, or be overtaking by another theory with more explanatory power. Popper’s stance here, as summarized by Andrew Lawthwright is: No theory can ever be proven true. The must always be the possibility of refutation, otherwise science will become dogmatic regarding a well corroborated theory. As a result a theory that purports to explain everything (and appear to stand up in practice) limits the progress of scientific research (i.e. nothing new is discovered or investigated, we simply add to the mass of confirmation to the theory). But by adhering to the quality of refutability, the problem is avoided altogether.” On this point Popper insists that: “our scientific theories must always be hypothetical.” —“the belief in scientific certainty…is just a wishful thinking.”
Popper also speaks about degree of corroboration, however, knowing the misinterpretation that could be given to it in relation to the inductivists’ notion of probability, and confirmation where increase in confirmation increases the probability of a theory being true. He developed his own probability Calculus, where he showed that corroboration is allied to improbability than probability. Because corroborated theory is more risky and daring and has more “chances of being overthrown or coming to grief.”
Corroboration, according to Popper, is essentially employed in the choice of competing theories because we can say of two competing theories, A and B, that in the light of the best state of the critical discussion at the time t and the empirical evidence (test statements) available at the discussion, that A is more preferable to or better corroborated than theory B.
However, because Popper, like Hume, denies necessary connection between events, he maintained that this report says nothing about future performance of A or its acceptability; that is to say it cannot be used for prediction. It is the case also that a scientific theory which is more risky has a better chance of being corroborated in a higher degree and therefore more scientific. But this is not always the case because a theory may have a high falsifying power without being corroborated or accepted. Accordingly, this is because: “The degree of corroboration actually attained does not depend only on the degree of falsification; a theory can be falsifiable to a high degree yet it may be only slightly corroborated or it may in fact be refuted.”
On this account, the best statement is the one which undergoes vigorous test without succumbing. Popper, however, insisted that in the test of competing theories the accepted theory must not only surpass the theory it replaces in information content but it must also be able to explain the less competent one. Einstein theory did not only surpass Newton’s but also explains it.
3.5 TRUTH AND VERISIMLITUDE: THE AIM OF SCIENCE
If we assert the Aristotelian famous dictum "that all men by nature desire to know." The question a curious student would ask is; ‘Desire to know what’? The perennial desire or search for knowledge according to Popper is a perennial search for truth, for the thirst for knowledge is satisfied by the acquisition of truth. It is from this background that Popper sees the aim of science as well as philosophy as a search for truth: “… our main concern in science as well as philosophy is or ought to be the search for the truth, for the thirst for knowledge is satisfied by the acquisition of truth.” We then ask Popper what is truth? Popper was initially uneasy with the concept of truth and since all the theories are potentially false, he avoided asserting that a theory corroborated is true, but restrained himself to the contention that “a theory which is falsified is false and is known to be so, and that a theory which replaces a falsified theory (because it has a higher empirical content than the later and explains what has falsified it) is a better theory than its predecessor.
However, in the Conjectures and Refutation (1963), he came to accept Alfred Tarski’s reformulation of the correspondence theory of truth as “correspondence to facts” and integrated it into his epistemic programme. So we can say that Popper as a realist has an ontological notion of truth. Popper-Tarski’s position on this is better explained by Morris Wards when he says:
Many scientists particularly mathematicians are Platonists and view science as a gradual groping towards the truth which exists in some perfect intellectual realm; our current theories being mere approximation to the truth.
The explanation is that, truth though absolute there are degrees of truth in every statement (theory). So that a theory instead of being completely true or false, has its truth or falsity content or verisimilitude- degree of nearness to the absolute truth. Thus for Popper, though “all past and present theories are false and indeed the evidence is that any theory which is the product of finite minds like ours will turn out to be false.” But nevertheless we are drawing closer and closer to the objective truth without exhausting it. For Popper then absolute truth becomes a regulative principle for competing theories and the aim of science becomes increasing verisimilitude or truth nearness; for though we cannot get at the absolute truth, the more theories with less verisimilitude we propose the closer we get to the absolute truth. Thus for Popper, verisimilitude shows that science after all makes progress.
With the use of a square diagram, Popper explained the point. Take a square
diagram as representing the classes of all statements and divide it into two equal subclasses, the truth statement (T) and the false ones (F)



Change this arrangement by collecting the class of true statements round the center of the square.



Popper inferred that the task of science is metaphorically speaking to cover by hit as much as possible of the target (T) of the true statement, by methods of proposing theories or conjectures which seem to us promising and as little as possible of the false area (F).” But what of if the absolute truth is found, would that mean the end of science? Popper was optimistic: “…is there any danger that the advance of science will come to end because science has completed its task? I hardly think so, thanks to the infinite of our ignorance.”
Popper gave some conditions that would make this advance towards objective truth possible.


1) SIMPLICITY:
He maintained that the acquisition of truth is possible only when scientists learn to propose simple theories and conjectures which are ride of all technicalities and unnecessary complication. In the Objective Knowledge he writes: “…in my view is that aiming at simplicity and lucidity is a moral duty of all intellectuals’ lack of clarity is a sin, pretentiousness is a crime.” His reason as we noted before is that simple theories have more informative content and predictive power and are always very ready for the severest test that might be meted to them.
2) THE TRUTH MUST NOT BE TAUTOLOGICAL
Popper sees tautologies as true but maintained that they are very unexciting and so should not be the aim of science. Truth must be intellectually exciting which also makes science exciting. It must be capable of giving answers to problems. In his words: “we are not simply looking for truth, we are looking after interesting and enlightening truth, after theories which offer solutions to interesting problems.” Popper referred to history to illustrate his view with the nursery rhyme of a German Humorist Willtan Bush
Twice two equal four is true but too empty and trite, what I look for is a clue to some matters not so light.

In Popper’s methodology, verisimilitude is indispensable in comparing competing theories. Popper offered two methods of comparing theories in terms of verisimilitude, the qualitative and quantitative definitions.
Before applying this method, Popper maintained that except tautological statements which have zero content, every other statement has it truth values. He defines truth-content as: “the class of all true statements which follow from a given statement … which are not logical.” And falsity-content as “the class of false statements entailed by a statements – the sub-class of its content which consists exactly all those which are false …”
On the qualitative account, showing how they are related to verisimilitude Popper asserts, 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 truth, or corresponds better to the facts than t1, if and only if either.
(a) The truth content (CtT) but not the falsity content (CtF) of t2 exceeds that of t1, or
(b) The falsity –content (CtF) of t1, but not its truth–content, exceeds that of t2.
By this it is inferable that verisimilitude increases if truth –content (CtT) increases while falsity content (CtF) decreases and decreases if the falsity-content (CtF) increases while the truth-content (CtT) decreases.
As he did in corroboration Popper, understands the confusion that could arise between his notion of increasing verisimilitude and the logical positivist use of probability. He maintained that unlike the logical positivists’ probability Calculus. where increase in verification or confirmation leads to increase in probability and to decrease in informative content in his own probability Calculus increase in verisimilitude, leads to decrease in probability (improbability) and increase in information content and hence the growth of knowledge.
He demonstrated this by comparing the content ‘A’ of a statement ‘a’ the content ‘B’ of the statement ‘b’ and the content ‘AB’ of the statement ‘ab’, a conjunction of the statements ‘a’ and ‘b’.
(1) Ct(a)  Ct(ab)  Ct(b) – Meaning that the content of the statement ‘a’ is less than or equal to the content of the statement ‘ab’ which is greater than or equal to the content of the statement ‘b’.
(2) P(a)  P(ab)  P(b). The probability of the statement ‘a’ is greater than or equal to the probability of the ‘ab’ which is less than or equal to the probability of the statement ‘b’.
When taken together it states that with increasing content probability decreases and vice versa. Formally, 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 truth content of ‘a’, and CtF(a) is a measure of its falsity content.
We can summarize by saying that in the Popperian conception of scientific destination, informative content are what science aims at. These are the tools which Popper used to denote and arrive at a better approximation of truth. Thus for Popper the search for verisimilitude is a clearer and a more realistic aim than the search for truth. Verisimilitude shows that science truly makes progress, for while truth is the aim of science, ignorance is the route, because truth could not even be known if discovered. He summed up with an oft-repeated aphorism; “We never know what we are talking about.”
Finally Popper refused to grant any philosophical value to definitions: “Definitions do not play any very important part in science…. Our ‘scientific knowledge’…remains entirely unaffected if we eliminate all definitions.” Definition never gives any factual knowledge about ‘nature’ or about the ‘nature of things.’ “Definitions … are never really needed, and are rarely of any use.”
Although Popper held all these positions all his life, he did acknowledge that they were open to criticism: “nothing is exempt from criticism … not even this principle of the critical method itself.”

CHAPTER FOUR
4.0 IMPLICATIONS OF CRITICAL RATIONALISM
Many philosophers are said to have waged a methodological war against Popper’s Critical Rationalism on grounds of the implications that could be drawn from it. In this chapter, I will present these arguments together with my position and responses before giving the final evaluation and conclusion.
4.1 SCIENTIFIC IMPLICATION
One of the earliest critics to draw a scientific implication from Popper’s methodology was the American historian, of science, Thomas Kuhn. Kuhn in his most influential book; The Structure of Scientific Revolution argued that scientists work in a series of paradigms and found little evidence of scientists actually following a falsification methodology. According to him:
if the acceptance or failure of scientific theories relies on falsification then that would be the end of science for no theory would ever survive long enough to be fruitful as all theories contain anomalies.
For him, falsification is not possible, first, because observations always rely on specific paradigms and are always adjusted to correspond to it. Second, it is not possible to evaluate competing paradigms independently since paradigms are incommensurable. On this ground, Kuhn maintains that ‘paradigms shift’ is not determined by rational processes but by the community of scientists. So that the fundamental difference between science and other disciplines is sociological rather than strict adherence to logically obligatory method as Popper claimed. Furthermore, he held that no paradigm is abandoned until there is a replacement for it.
Imre Lakatos a former student of Popper attempted to reconcile Kuhn’s work with Falsificationism. In his, also influential book; The Methodology of Scientific Research Programme, Lakatos argued that science progresses by the falsification of scientific research programmes rather than the more specific universal statement of naïve falsification.
He says that the role of auxiliary hypothesis makes scientific theories difficult if not impossible to falsify conclusively on the bases of one failed anomaly. What this means according to him is that all scientific research programmes at any stage of development has unsolved problem and undigested anomalies: “All theories in a sense are born refuted and die refuted.” In other words, if Poppers naïve falsification principle is taking seriously science will ground to a halt. His idea of scientific progress or Revolution is that a decaying or a degenerating Research Programme is abandoned for a progressive one which explains the successes of the former and also its failures.
Paul Feyerabend in his book Against Method argued that Poppers falsificationism and indeed all other proposed methodology did not give accurate account of science. For him many revolutionary theories in science are either falsified or unfalsifiable. Thus
falsifiability cannot determine whether a theory is scientific or not.
He also maintains that almost all theories contain formal flaws and ad hoc adjustments hence if Popperian standards were applied strictly “they would wipe-out science as we know it and would never have permitted it to start in the first place.”
The conclusion, Feyerabend came to, was that since no method can give accurate account of scientific enterprise then there is no difference between the method of acquiring knowledge in science and other disciplines. “Therefore the only one principle that can be defended under all circumstance and in all stages of human development is the principle of anything goes.” By this he proposed a methodological anarchy. Here he means that all the method of acquiring knowledge-whether scientific or non scientific, should be treated equally and that individuals should be allowed to choose between science and pseudo-science without any policy of compulsion.
The Quine – Duhem Thesis argued against Popper’s idea of crucial experiment-an experiment that establishes the truth of one among a set of competing theories. According to this thesis;
…the physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses. When the experiment is in disagreement with the predictions, what he learns is that at least one of the hypotheses consisting this group is unacceptable and ought to be modified, but the experiment does not designate which part of the experiment should be changed.
The explanation of this from W. V. Quine’s point of view is that, any theory can be
made to correspond to certain fact simply by making few adjustments as auxiliary hypothesis. Thus when to reject one theory, and accept another (‘better’ one), is dependent on the judgments of individual scientist rather than on some [rational] law or authority.
The result of all the critics’ arguments suggests that Popper’s methodology is counter productive to the progress of science. However, I believe that these critics especially Kuhn, Lakatos and Feyerabend must have depended so much on secondary sources in their evaluation of Popper as R. S. Parcival had suggested. For instance they completely ignored the distinction between the logical and methodological application of Popper’s criterion. Logically Popper endorsed that any theory which conflicts with experimental evidence is conclusively falsified and should be dropped. However, methodologically, the issue is more complex.
They also suppressed the evidence that there was no mention of falsification of hypothesis in isolation any where in Popper’s discussion of his falsifiability. Because, hypotheses do not warrant consideration apart from their systemic membership, Popper’s emphasis was on scientific system (similar to Kuhn’s paradigm and Lakatos Research Programme).According to Popper: The answer is that we can indeed falsify only system of theories and that any attribution of falsity to any particular statement within such a system is always highly uncertain.”
The strong case against Popper here is the issue raised by Duhem-Quine thesis. That is, that the choice of falsification or corroboration of theories is arbitrary or conventional because the complex nature of scientific theories does not allow us to say exactly where an error is coming from during the course experimentation.
The difficulty associated with knowing when a theory can actually be said to be falsified is also related to Popper’s use of basic statements. For instance, Popper held that no statement is ever certain or proved to be certain in science, basic statements inclusive. Now if according to Popper basics statements are “fallible and theory-laden… and their acceptance as valid or not is an act of free will of individual scientists;” how then can basic statements whose acceptance or rejections are conventional be used as independent arbiters in deciding the fate of other statements. Also, if the acceptance of basic statement is conventional, then falsifiability falls into the kind of illogicality for which induction was rejected. This made Smith to describe Popper as an irrational rationalist, because his method rests on basic statements the acceptance of which can never be rationally justified. It is in relation to this also that C. S. Percival remarked: … It implies that it is almost entirely a matter of choice whether it is accepted that a ‘potential falsifier’ is actually one, and consequently that the falsification of a theory is itself the function of a free and arbitrary act. It also seems very difficult to reconcile this with Popper view that science progressively moves closer to the truth, conceived of in terms of the correspondence theory, for this kind of conventionalism is inimical to this (classical) conception of truth. This development has led to other barrage of criticism which I shall indicate shortly, against falsifiability.
Nicholas Dykes argued that falsifiability presupposes induction because “the process of reasoning is the same. Collecting disconfirmations and arguing negatively scarcely differ from collecting confirmations and arguing positively ….However, much Popper may have rejected induction his own method was in fact dependent upon it.”
It is also in this connection that Morris Wards maintained that Poppers model has some tacit element of induction. He asked:
… how are candidate hypothesis generated in the first place if not from some unconscious induction and how can we prefer and even rely on un-proven hypothesis that we know are likely to be refuted if not gaining confidence from past performance and assuming that this will continue into the future.
F. Uduigwomen accused Popper of introducing induction through the back door in his concept of corroboration because his idea was in accordance with the inductive claim that theory is not absolutely certain, but absolutely bound with degree of probability. Newton Smith, has also pointed out that “… if Popper genuinely abandons induction, there is no way in which he can justify the claim that there is growth of scientific knowledge and that science is a rational activity.”
Laundan, Omorogbe, G. O. Ozumba and Nicholas Dykes also criticized Popper on his reason for rejecting induction. On the one hand, the first three maintained that the failure of Hume and Popper derives from the fact that they were searching for the foundation of science (necessary connection) in observation whereas it is supra-empirical or metaphysical.
On the other hand Nicholas Dykes argued that induction does not depend on observation but on the law of identity. According to him:
Existence implies identity. It is not possible to exist without being something, and a thing can only be what it is: A is A Any action of that thing forms part of its identity: the way in which it acts must be regarded as partial expression of what it is. Thus to deny any connection between a thing, its actions, and their consequences is to assert that the thing is not what it is; it is to defy the law of identity.”
My position in this controversy is that, Popper was right that scientific theories are hypothetical or conjectural and will ever remain so because of their infinite scope in relation to the finitude of human knowledge (this need not apply to all knowledge, for all knowledge is not universal). He was also correct in holding the primacy of falsifiability against induction.
However, Popper went astray when he assumed that falsifiability is the actual method of science. His failure derives from his inability to make a clear distinction between the logic of discovery and the logic of the discovered. The logic of discovery is the key to the understanding of the actual behavior of scientists, as they study problems, invent and test hypothesis, formulate concepts or theories and actually make discovery. The logic of the discovered comes later. It is a logical presentation that makes the discovery fit into the scheme of rationalization of thought. Popper was wrong. Falsifiability is not the logic of discovery but the logic of the discovered. In short discovery has no logic as such.
Perhaps J. P. Mbat’s observation will be ad rem here: “I believe … that a better understanding … could be reached by an adequate understanding of the actual practice of science itself which is a dynamic knowledge yielding enterprise that may not ignore both inductive and deductive, direct and indirect method but consider all profitable for the discovery of truth about the world.”
4.2 EPISTEMOLOGICAL IMPLICATIONS
As a metaphysical realist, Popper upheld the correspondence theory of truth, that “a statement is true if and only if it corresponds to facts.” However, in contradiction to realism, which holds the possibility of objective truth, Popper maintained that truth is the goal of science, but the scientific condition to that truth is that of ignorance. This means that we are never entitled to claim the truth of any scientific theory. This idea of unattainability of truth and certainty places Popper in the category of skeptics like Kant. For Kant claimed that we can never know the noumena (things-in-themselves).
M., Artigas recognizes Popper’s skeptical attitude when he says: “… owing to Popper’s view on truth and his replacement with verisimilitude, he could be termed a skeptic.” Popper, thus by implication, regards science as an irrational activity the goal of which is truth; for it is absurd to consider as rational the pursuance of a goal whose realization is impossibly.
Initially Popper thought he has escaped the skeptical implication that falsifiability leads to, with his concept of verisimilitude which could be expressed in quantitative or qualitative terms. For as R. S. Percival expressed it: “…though we cannot know the truth, scientific progress can be represented as progress towards truth and experimental corroboration could be seen as inductors of verisimilitude.”
However, in 1974 Miller and Tichy working independently have shown that for any two distinct false theories A and B, it is false that A has less verisimilitude than B, and it is false that B has less verisimilitude than A. Therefore, no two false theories are comparable in regards to verisimilitude.
The effect of this demonstration was devastating; precisely because the whole idea of scientific progress in Popper philosophy is built around the notion of verisimilitude. The demonstration made Popper’s determined effort to avoid skepticism fruitless. Popper admits this: “my main mistake was my failure to see at once that …if the content of false statement ‘a’ exceeds that of a statement ‘b’ then the truth content of ‘a’ exceeds the truth content of ‘b’, and the same holds for the falsity content.” Critics as Percival noted, believe that this one admission blows apart the whole of Critical Rationalism. Another epistemological problem that Popper’s criterion is exposed to is: language difficulties. Popper called Conjecture and Refutations a “New way of knowing.” However, from an epistemological point of view, we do not normally claim to ‘know’ something which is unjustifiable, tentative or hypothetical. Epistemologically, too, and for most scientists, knowledge is something which it is possible to be sure of, to justify, to validate, to prove, or to know.
Conjecture on the other hand is by definition not knowledge. According to Chambers English Dictionary, a conjecture is “an opinion formed on slight or defective evidence or none: an opinion without proof, a guess.” Since one cannot define an idea by means of other ideas which are contrary to it, it is clearly illegitimate to place knowledge in the same category as conjecture. Moreover to say that, “all knowledge remains conjectural” is a contradiction in terms.
The objection gathers strength when one notices that Popper’s proposition: ‘all knowledge remains conjectural’ is itself not conjectural. It is a universal affirmative, it states that “All knowledge remains conjectural” – which is a claim to knowledge. The proposition thus asserts what it denies and is self contradictory on a second count.
Another immediate problem is that the notion of ‘conjecture’ depends for its intelligibility upon the prior concept of ‘knowledge’. The ideas of conjecture designates a form of mental activity which was unlike knowledge and to distinguish clearly from knowledge an idea put forward without proof. In Objectivist philosophy of Ayn Rand this error is known as the fallacy of stolen concept. A classic e.g., is the claim that property is ‘theft’. But the concept ‘theft’ depends on the prior concept of property, and would be unintelligible without it. In exactly the same way, the concept of conjecture cannot be understood in isolation of the concept of knowledge from which it is to be distinguished.
A further problem arises when one considers the concept ‘growth’ in Poppers claim that knowledge grows through conjecture and refutations. A legitimate response to this assertion is: “what exactly is it that grows? The concept of growth implies the existence of a thing, a body, an entity of some sort, that which grows; it may well be true that conjectures and refutations play a role in the growth of knowledge, but they could hardly do this without some knowledge to work on. The growth of knowledge via conjectures presupposes pre-existing knowledge not pre-existing conjecture. This again illustrates Poppers dependence on something he attempted to deny, effectively ‘stealing a concept’.
Again, all knowledge is conjectural is simply not true. The writer’s observation that the sun is shinning is not conjectural, it is a fact well known to him and countless other observers. That at 11am on 30th April, 2009 in St. Joseph Seminary the sun is shining. This observation is no more conjectural than: ‘Yar’Adua is president of Nigeria (at time of writing) or ‘2 plus 2 = 4’. These statements are true. They are demonstrable to any sane person; either ostensibly or through presentation of evidence beyond reasonable doubt via simple common sense, or by means of logic. They constitute knowledge not conjectures.
Another area of difficulties with Popper’s criterion which I want to discuss in this epistemological implication concerns theories which have successfully withstood criticism. Popper allowed that after scientific theories have passed a great number of severe tests, “their tentativeness may cease to be obvious.” But if asked about established theories he was likely to point to Isaac Newton’s “unquestionable truth” which seemingly
unassailable for over 200years, was questioned by “Einsteinian revolution”.
Yet theories does exist which, in fact are positively confirmed. As Grover Maxwell has pointed out, Copernicus’s heliocentric theory, for example was indeed hypothetical in 1543 because the instruments did not then exist with which to prove it. But now that huge telescopes and space probes have eliminated any rational doubt that the earth revolves around the sun, it would seem bizarre to maintain that heliocentricity remains conjectural.
Another famous theory is that of Harvey and the circulation of blood. Once, that was indeed a bold conjecture. But if one declared nowadays that Harvey’s theory is refutable, or that we don’t know what we are talking about when we say that blood circulates in the human body, one should expect laughter from one’s audience.
Popper was evidently aware of this problem. He once wrote the “realization” of the “conjecture” of an atomic bomb. But if a conjecture is realized it is very difficult to see how it remains a conjecture. One might fairly retort that this one admission blows apart the notion of demarcation by refutability and the whole of critical rationalism.
4.3 SOCIO-POLITICAL IMPLICATION OF CRITICAL
RATIONALISM

Critical Rationalism as stated by S., Meyer, is an attitude that says: “You may be right and I may wrong, and with little effort we may get nearer to the truth.” “This is more than it looks at first glance”, Meyer continued, “it is bold in that it presumes that there is absolute truth and humble in that it assumes the universal possibility of error and ignorance.
But it is bold also in assuming that there is a possibility of approximating the truth.”
The first socio-political implication Meyer drew from this is that it calls for both co-perration and competition. We must work together in the process of creating ideas and criticism them without restraint. The second implication Meyer drew was that it “completely explodes the notion of ‘authoritive’ or ‘expert’ sources of knowledge in the sense that they can be relied upon to decree what is true or false.” In other words it is against all forms of dogmatism. Popper was the first person who saw these implications and using it in the Open Society and The Poverty of Historicism; he developed a powerful critique of Historicism and a defense of the open society and liberal democracy.
“Historicism is the theory that history develops inexorably and necessarily according to knowable general laws towards a determinate end.” Popper considers this view to be the principal theoretical presupposition underpinning most forms of authoritarianism and totalitarianism since totalitarian leaders use knowledge more often than not to justify their atrocities. A good point in case is Hitler who claimed the supremacy of the German race and went on to prove this by killing six million Jews and attempting to colonize the whole of Europe.
R. S. Percival shared the same idea with Meyer on this, according to him “Popper promoted a critical ethos, a world in which the give and take of debate is highly esteemed in the precept that we are all infinitely ignorant, that we differ only in the little bit of knowledge that we have, and that with little co-operative effort we may get nearer to the truth.”
The implication of this is that in inter-personal relationship in the society no man should consider himself the custodian of knowledge or his solution to societal problems as the final solution. If one feels that one’s own solution is good others could be better. Because, we are infinitely ignorant, no knowledge is sacrosanct or dogmatic and final. The best is not achieved but we strive continually to reach or discover that best.
Even the state has not the final solution to problems no solution at all should be accepted dogmatically but critically. So every solution should be open to revision and not closed against criticism. All talents should also be used for betterment and growth of the society.
4.4 THE ULTIMATE TEST OF CRITICAL RATIONALISM
For a philosophy the most critical test of all may be whether its proponents actually followed it. In other word, what is the existential implication of living or following that particular philosophy? The first example of living-out Critical Rationalism was set by Hume, who admitted that he found his skepticism hard to live by.
Popper evidently experiences the same difficulty while trying to live-out Critical Rationalism. For instance, Popper in Critical Rationalism recommends that we should not treat any scientific theory as knowledge but as hypothesis or guess. However Popper did not abide consistently by this rule. Thus Popper’s use of the words such as ‘knowledge’, ‘known’, ‘truth and fact’ with reference to scientific theories is in direct contravention to Critical Rationalism. Another area where Popper showed this inconsistency with the rule of Critical Rationalism is in his treatment of natural law. For instance, in The Open Society he called natural law: “a strict unvarying regularity.… A law of nature is unalterable; there is no exceptions to it … laws of nature …. Can be neither broken no reinforced they are beyond human control...” But such absolutist claims are difficult to reconcile with the actual discovery of natural laws when according to Poppers: “There can be no value reasoning from singular observation statements to universal laws of nature.”
As a footnote here, it may be recorded that Popper was not renowned for living up to his philosophy in his professional life. His Obituary in The Time recorded his reputation as a difficult man.” The Daily Telegraph commented: “Popper belief in his own infallibility was remarkable.” Later The Times Magazine reported that Popper’s student at London School of Economics found him so intolerant of criticism that they used to talk about “The Open Society by one of its enemies.”
4.5 CONCLUSION
Not withstanding all this loopholes in Critical Rationalism one cannot but appreciate the ingenuity inherent in Popper as a philosopher. His Critical Rationalism is applicable not only in science but also in socio-economic and political life where it is even most effective. For instance, one of Popper’s student and advocates is the investor George Soros who says that: “his investment strategies are based on Popperian skepticism about the reliability of
the human belief.” Soros is one of the greatest investors in history.
The relevance of his principle of falsifiability to the society cannot be over emphasized, if this principle is applied, I think the co-existence of individual will be more enhanced because nobody will think that his own view is final. Likewise, leaders will give room to constructive criticism, which will enrich the society greatly, with development ensured.
He gave a very high and authentic recognition to myth or metaphysics and delivered it from the positivistic status of nonsensical verbiage. For Popper unlike Hume, metaphysics should not be committed to the flame but is something that can inspire scientific theories.
A critical attitude, particularly a self-critical one, is also important in science as Popper thought it was. This is because Popper appreciates the dynamism of science which consists in its growth, and that any one who does not allow his theory to be tested and improved upon, is indirectly proposing the stagnancy of scientific venture.
It is also well worth keeping in mind that even if Popper was mistaken in his overall rejection of induction falsifiability does share with induction one of its most important element—disconfirmation—an element which has not lost one iota of its importance since Francis Bacon first draw attention to it in the 17th century. Popper in this regard understands the finitude of our human knowledge. In other words he is telling us that our progress in any scientific venture must begin with the recognition of our inability to reach the best point of view-we are fallible likewise our theories. Therefore, disconfirming
instances must be sought and, where not found anticipated at any and all times.
One famous instance cited by Popper was the discovery of Deuterium (i.e., heavy water), prior to this discovery, nothing more certain and more settled could be imagined in the filed of chemistry, than our knowledge of water… This historical incident is typical…we cannot foresee which parts of our scientific knowledge may come to grief one day.”
There is much truth in that but “come to grief” overstates the case. And that is where Popper went wrong: he focused so much on disconfirmation to the exclusion of everything else. He tried to elevate an important but isolated premise to the status of a philosophical system. Critical Rationalism is not a replacement of induction it is an exaggerated focus on the negative element of induction.
In The Objectivist Philosophy of Ayn Rand referred to earlier in this work, Rand treated scientific theories as open-ended i.e., open to development and revision. Rand’s philosophy, though, less systematic as Popper’s philosophy, shares a lot of philosophical premises or idea in common with Popper’s thesis of falsifiability. This Memoir will therefore conclude by conjecturing that when Popper said: “In science there is no…‘knowledge’… in the sense which implies finality.” What he may have been after was Rand’s insight that concepts are open-ended.
For if Rand had been confronted with Einstein’s rewrite of Newton; or a black swan where there had only been white one’s; or the discovery of a new kind of water, she would not have said as Popper that our previous knowledge had been overthrown” or had “come to grief” or that “the belief in scientific certainty…is just wishful thinking.” Rather she would have said simply that our knowledge had been expanded.
The description of concepts as “open-ended”-i.e., self-correcting or open to revision, does appear to be the philosopher’s stone which Popper sought but never found (Popper touched on this: “the growth of knowledge consists in the modification [revision] of previous knowledge.” However, his refusal to define his terms makes it difficult to understand what he actually means when he says that old theories are modified or improved by new ones and when he says that old theories replaced by new ones have come to grief). He correctly saw that there is a problem with most people’s ideas of certainty, yet never quite fought his way through to an acceptable solution. But be that as it may, whatever one may think of Popper, or of Rand, the idea that scientific knowledge is open-ended is more comprehensive than Popper’s assertion that “we never know what we are talking about”.





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