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“But as for certain truth, no man has known it, nor will he know it; neither of the gods, nor yet of all the things of which I speak. And even if by chance he were to utter the perfect truth, he would himself not know it: For all is but a woven web of guesses.” - Xenophanes
WHY IS THERE SUCH A METHOD?
In the 1920’s, scientists have this notion that theories are scientific only if they are provable through observation and experimentation. True enough; theories can be valid only if they have taken series of tests and rigorous studies. Religious statements like “there are angels in heaven” or “God exists” are unscientific because they are not testable through observation and experimentation. What makes a statement scientific therefore is its openness to verification. Scientific statements must be verified through experience, i.e. they are proven through our five senses. In philosophy of science, we call this as the theory of Verification. A statement must be “empirically verifiable” in order for it to be meaningful and scientific.
Verificationism was then the criterion for judging whether a statement is scientific or unscientific. It was the answer to the important problem of Demarcation. This problem of demarcation sought to find the dividing line between what was scientific and what was non-scientific. It was the famous group known as the Vienna Circle – mostly composed of Logical Positivist – that proposed verification as the criterion of demarcation.
In the beginning of the 1930’s, Sir Karl Popper introduced his ingenious theory of Falsification. In this theory, he proposed another answer to the problem of demarcation. However, he did not simply propose this theory just for the sake of having another option for scientists to choose from. His theory was a clever solution to the various problems faced by philosophers of science. Basically, the theory of falsification or rational criticism sought to review the important problems that the theory of verification overlooked, solved the logical discrepancies found in the method (inductive) used by verificationism, and more importantly reoriented the scientists in their authoritarian attitude to the problem of knowledge.
SPLITTING THE PROBLEMS OF DEMARCATION AND MEANING
By means of the criterion of verification, one can tell whether a statement is scientific or not scientific. For the philosophers of the Vienna Circle, only a scientific statement can be meaningful. In this case, the theory of verification is not only the proposed solution for the problem of demarcation but also for the problem of meaning. Now, this poses a grave threat to all “non-scientific” or “non-verifiable” statements such as religious and theological statements, metaphysical and philosophical statements, and other purely speculative assertions. This principle renders them all meaningless! That “an all-powerful invisible Being called God exists” is of no meaning and significance to those who embrace this principle.
Karl Popper pointed out that a theory may be meaningful without being scientific. St. Thomas’ doctrine of the Imago Dei for instance may not be scientific but it is meaningful, even more meaningful than most scientific theories. Plato’s Doctrine of Ideas may not obviously be scientific but it is of exuberating significance. Thus for Popper, the problem of demarcation must be differentiated from the problem of meaning; the criterion of demarcation does not necessarily coincide to the criterion of meaningfulness.
Popper proposed falsifiability in place of verifiability as the criterion of demarcation. He altogether distinguished this criterion of demarcation from a criterion of meaningfulness. For him, falsifiability only applies to distinguishing which statements are scientific, and not which statements are meaningful. Thus, for Popper scientific statements are always falsifiable but not necessarily meaningful.
POPPER’S ANTI-AUTHORITARIAN ATTITUDE TO THE PROBLEM OF KNOWLEDGE
Rudolf Carnap, one of the leaders of the Vienna Circle, wrote in one of his later works that “assertions must be justified through observation.” For Popper this criterion is unsatisfactory. To say that our assertions are reliable because of our appeal to the authority of observations as the sources of knowledge presuppose an authoritarian attitude to the problem of knowledge. Popper emphatically states that no amount of observation or source of knowledge can give certainty to our assertions. For one, there has never been any theory that presented itself as error-free. Pessimistically, he states “all sources leads to error” so that no theories can be certain. Scientific theories are just guess works and conjectures. He claims that there can be no such authorities and that a moment of certainty clings to all assertions. Neither observation nor reason is an authority.
Popper’s contemporaries believe that true knowledge is certain and that this knowledge can be achieved. They embrace the classical notion of true knowledge, i.e. that true knowledge is certain. Popper distinguishes true knowledge from a knowledge which is certain. For him, no knowledge is certain and perfectly reliable. No matter how well corroborated and applicable a theory may be, there will always be an error to it. Newton’s theory of gravitation is an attestation to this claim. It is the best-tested and best-corroborated scientific theory but it itself is contested by Einstein’s theory of gravitation. Inasmuch as there can be no amount of observation that can render an assertion certain, we can never be certain whether what we have asserted is true. As Popper states, “no theories are certain” so that, as a consequence, we cannot achieve certain knowledge.
However, science aims at truth. All theories proclaim themselves as a guess about the truth of reality, and we are not really certain about it. Quoting Popper himself, “we are only rarely successful in guessing the truth; and we can never be certain whether we have succeeded.” It may be the case that our theories are already true but we cannot be certain about it.
UNDER THE GEIST OF SOCRATIC PHILOSOPHY
Popper thinks in the light of Socratic philosophy. He believes that human knowledge is finite, which of course is almost self-evident. The human ability to reason, although it proves to be very beneficial, is by nature infinitely finite. This attitude towards human knowledge which the (Socratic) Greeks also embraced may have come from the experience of being overwhelmed by the vastness of the universe. Well man himself cannot fully know his own self. Thus what is certain is not certitude but man’s uncertainty. Socrates once told that wisest is he who knows that he does not know. Yes indeed, the one who knows that he does not know has the upper hand over the one who thinks to know what he truly does not know. Our recognition of our ignorance elevates us from the misleading sophistic all-knowing mentality. The more we know, the more we know of our ignorance.
So what does our ignorance benefit us? Like Socrates, Popper uses this knowledge of our ignorance to advance our knowledge of truth. This may sound ironic to the philosophers of the Vienna Circle but this harbors a very important place in Popper’s philosophy. Although there is no criterion of truth, there is a rational criterion for progress in the search for truth. And it is our knowledge of our ignorance, errors, and uncertainties that underlie this criterion. Here is what Popper says:
“Science is a critical activity. We examine our hypotheses critically. We criticize them so that we can find errors, in the hope of eliminating the errors and thus getting closer to the truth.”
We are not certain about what we know but we are certain that there are errors in what we know. It is precisely these errors that we ought to remove and criticize in order to advance our search for the truth. If science is the search for truth, then it must be progressive. We progress by scraping little by little the errors (ignorance) of what we know, and from which we clear our eyes from what blurs truth.
So what does this now make of our knowledge? Knowledge is a combination of guess work (theories) and rational criticism. We start with guess works or conjectures. Although these are just guesses they are very important because we cannot start from nothing – from tabula rasa. By modifying and correcting them we come closer to realizing the ideal of science, i.e. the attainment of truth. Popper uses the phrase “Rational Criticism” is naming this attitude towards knowledge. He boldly admits that it is a view he owes to the Greeks, in particular to Socrates. His rational criticism brought forth his method of falsification.
THE IDEA OF FALSIFIABILITY IN GENERAL
The scientific method proposed by Popper is a product of his epistemological view of knowledge. If we cannot by all means prove the certainty of our statements through observation, and if what is only certain is the presence of errors in them, then what we can only do is to prove the errors in our statements. In which case the statements must in themselves be structurally falsifiable. Obviously, we cannot criticize a statement which is not criticizable. It is in this area that Logic plays an important role.
As was stated earlier, falsification was Popper’s principle of demarcation. If a statement, hypothesis, or theory is not falsifiable then it is not scientific. Falsifiable statements must not however be mistaken with “false” statements. There is a big difference between the two; “false statements” need not be proven anymore because they are already proclaimed false, while “falsifiable statements” must be evaluated because they are by nature capable of being criticized using observational reports. If for Popper only falsifiable statements are scientific, then all scientific statements must be open to the possibility of being falsified.
For example, the statement “all men are mortal” is unfalsifiable because there can never be any positive data of an immortal man to falsify the statement. The statement “all men are immortal” is falsifiable because there can be a positive data of a mortal man to falsify the statement. Popper will identify, basing on their structure, the first statement as unscientific and the second scientific. Nevertheless, most unfalsifiable statements can be transposed to falsifiable statements. For all we know, many unfalsifiable statements are derived from falsifiable statements. The example above, All men are mortal, must have been inferred from the falsifiable statement “All men die before they reach the age of 150 years.” This proves to us that falsifiable statements does not exclude the unfalsifiable, it embraces and exceeds it. By restating unfalsifiable statements to its falsifiable form, we can proceed with rational criticism.
In a way, falsification still lives by the spirit of verification inasmuch as it shows that an assertion is scientific only if it is “open” to data of observation and experimentation. The possibility of being open to experience is after all the main property of all scientific statements. But what differentiates falsification from verification is a matter of logical procedure. Unlike verification which proves a theory by presenting data that support the said theory, falsification aims at disproving a theory by presenting data or experiments that invalidate the said theory. So if we say that an assertion is “falsifiable”, then it has the logical possibility of being falsified using data from observation or physical experiment.
LOGIC OF FALSIFICATION
There are two types of statements that are of value to scientists: the “observational statements” and the “universal statements.” Observational statements, which are also known in logic as “singular existential statements,” are assertions about the existence of some particular thing. “This is a white swan” is an example of this type of statement. In Logic, a singular existential statement such as the example is stated in the form: “There is an x that is a swan, and x is white.” Universal statements, on the other hand, are assertions that categorize all instances of something. In logic, they are stated in the following form: “For all x, if x is a swan, then x is white.”
By their nature, scientific theories and hypothesis are all universal statements about the way nature as a system works. If science seeks to find the pattern that weaves nature together, then it must see a cause that could have not only produced an isolated event in nature. Scientific theories, and especially what we call natural laws, must be stated in a way that encompasses the entirety of nature; or else they will not be called as such. From the inductivist point of view, universal statements can be inferred from observational statements. Deductive-wise, this manner of inference is invalid because it leaves an enormous gap of error. But inductivists, spearheaded by Francis Bacon, still claim that this is the method of science. Now how does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements? Philosophers of science consider these questions as great problems that beset the inductivist method of reasoning. These questions were nonetheless answered by Popper’s method of falsification. Popper’s method claims that observational statements (single existential statements) cannot affirm a universal statement. Observations can never be a source of certainly true knowledge. That this is a white swan can never affirm that all swans are white. Nonetheless, observational statements (single existential statements) can be used to show that a universal statement is “false.” The singular existential observation of a black swan shows that the universal statement “all swans are white” is false.
The method of falsification can be stated symbolically in logic as the Modus Tollens.
U – O If U, then O
-O not O
-U Therefore, not U
The capital letter U stands for Universal statements, while the capital letter O stands for Observational statements or singular existential statements. The reasoning used in here is hypothetico-deductivism. It is hypothetical because it starts with hypothetical universal statements. It is deductive because it arrives at a necessarily true conclusion. The basic flow of the argument is as follows: (1) start with a hypothesis or universal statement (U); (2) make a prediction of the hypothesis about a certain singular happening (U – O); (3) make an observational statement that contradicts the expected prediction (-O); (4) Falsify the hypothesis or universal statement (-U).
The Inductive method directly breaks this logical rule of Modus Tollens. It has the following form:
U – O If U, then O
U Therefore, U.
In its first premise (U – O), the argument starts with a universal statement and its prediction (1 & 2). In the second premise (O), it states a singular existential observation which corroborates the first premise. And in the conclusion (U), we accept the universal statement. The grave mistake of the argument lies in the second premise and the conclusion. We cannot simply accept the Universal statement using only observational or singular existential statements. Affirming the prediction is not a warrant to affirm the theory that explains it. A singular existential statement is not equivalent to a universal statement.
(To be continued next meeting)
- Michael Jhon M. Tamayao, Ph.L., M.A.
 Karl Popper, “On the So-called Sources of Knowledge”, In Search of a Better World: Lectures and Essays from Thirty Years, trans. by Laura J. Bennett (London: Routledge, 1992), p. 45. This section of the book was originally a lecture given on July 1979 at the University of Salzburg when the author was awarded an honorary doctorate.
This book where this article and all other articles of Popper that I will use in this paper will henceforth be referred to as In Search in all the succeeding referrals to it.
 Ibid., p. 50.
 Karl Popper, “On Knowledge and Ignorance”, In Search, p. 37.
 “On Knowledge and Ignorance”, p. 39.
 “On the So-called Sources of Knowledge”, p. 49.
 Examples are taken from Wikipedia free encyclopedia.
 All scientific theories are hypothetical inasmuch as they are all guesses.