Christian Faith and Scientific Revolution Epistemology
Notes on Karl Popper's Theory of Scientific Method:
Demarcation between Science and Metaphysics
For we learn from our hypotheses what kind of observations we ought to make: whereto we ought to direct our attention; wherein to take an interest. Thus it is the hypothesis which becomes our guide, and which leads us to new observational results. ... In this way science appears clearly as a straightforward continuation of the pre-scientific repair work on our horizons of expectations. Science never starts from scratch; it can never be described as free from assumptions; for at every instant it presupposes a horizon of expectations, as it were. Today's science is built upon yesterday's science (and so it is the result of yesterday's searchlight); and yesterday's science, in turn, is based on the science of the day before. And these oldest scientific theories are built on pre-scientific myths, and these in their turn, on still older expectations. Ontogenetically (that is, with respect to the development of the individual organism) phylogenetically (with respect to the evolution of the race, the phylum) we get to state of expectations of unicellular organism. (There is no danger here of a vicious infinite regress if for no other reason than that every organism is born with some horizon of expectations.) There is as it were, only one step from the amoeba to Einstein. . . . Thus it seems to men that it is the tradition of criticism which constitutes what is new in science, and what is characteristic of science. On the other hand it seems to me that the task which science set s itself (that is, the explanation of the world) and the main ideas which it uses, are taken over without any break from pre-scientific myth-making. ..." (Objective, 346-317).
This adventure relies upon the demarcation between science and metaphysics. This line of demarcation is a rough one. Popper does not despise metaphysics. On the contrary, "Metaphysics has led the way:
I do not propose to draw the line of demarcation in such a way that it coincides with the limits of a language, leaving science inside, and banning metaphysics by excluding it from the class of meaningful statements. On the contrary: beginning with my first publication on this subject, I stressed the fact that it would be inadequate. . .so as to exclude metaphysics as nonsensical from a meaningful language. (Conjectures, 256-257)
This adventure Popper directs toward verisimilitude. It is critical and eliminative:
The method described may be called the critical method. It is a method of trial and the elimination of errors, of proposing theories and submitting them to the severest tests we can design. If, because of some limiting assumptions, only a finite number lead us to single out the true theory by eliminating all its competitors normally—that is to say, in all cases in which the number of possible theories is infinite—this method cannot ascertain which of the theories is true; nor can any other method. It remains applicable, though inconclusive. . . . There is no assurance that we shall be able to make progress towards better theories. (Objective, 16-17)
The intention of this paper is to argue: (1) that Popper's view of science meets with contradiction, and (2) Popper must incorporate into his system a meta-system in order to maintain his conjectures. The writer will hope to accomplish this task through the premise: A system will contradict itself without reference to an ultimate ground; this ultimate ground need be transcendent, not bound by the time/space continuum, and personal.
"Physics is the most objective of all the sciences." Yet, "metaphysical research programmers have influenced the development of physics since the days of Pythagoras." (Schlipp, 120). Epistemology has also played an important part:
Epistemology becomes, from an objectivist point of view, the theory of the growth of knowledge. It becomes the theory of problem-solving, or, in other words, of the construction, critical discussion, evaluation, and critical testing, of competing theories. . . . The evaluation of competing theories is partly prior to testing (a priori valid) and partly posterior to testing (a posteriori, again in a sense which does not imply validity). Also prior to testing is the (empirical) content of a theory, which is closely related to its (virtual) explanatory power; that is to say, its power to solve pre-existing problems—those problems which give rise to the theory, and with respect to which the theories are competing theories. (Objective, 142-143)
Popper has spent a great deal of time refuting subjectivism which has gained a stronghold in physics since 1926. (See Objective, 141-152) Popper has also suggested a third influence: Mach's influence on the new generation of atomic physicists became so persuasive is indeed one of the ironies of history. For he was a vehemenent opponent of atomism and the 'corpuscular theory of matter' ..." (Schlipp, 121). To make matters more difficult Physics holds within its bounds contradictory notions concerning the actual state of affairs (i.e., the theory of light, etc.). One now understands why Popper deals with the "myth of the framework:" one does not have to possess the same world view as another who wishes to discuss (See Ackermann, p. 46).
At this point it may be helpful to consider Hegel's critique of the Kantian system: It is possible to show that Popper's system shares to a degree the same essential weaknesses. This writer recognizes that the basic problem Hegel deals with is Kant's vicious rejection of metaphysics. Popper is not found wanting in this aspect. Yet, is the concern of Hegel only Kant's rejection of the non-critical philosophy? This writer suggests that Hegel was establishing his critique on the premise: Critical Philosophy is contradictory without the Absolute. Why is this so? Kant had no ultimate ground. To what extent would Popper be found, as Kant, without ultimate ground? Hegel sets forth the basic tenants science must incorporate in order to be existent without contradiction:
(1) Science must be possessors of 'opposition' and 'negativity', yet not absolute negativity (i.e. infinity) which alone is the element of science; on the contrary they no more possess the purely positive than they do the purely negative, but are mixtures of both. (Natural Law, 58)
(2) Science must be relational. . . the only true distinction that can be acknowledged as marking the true principle of the science is whether the science lies within the absolute, or outside absolute unity (i.e. in opposition). If the latter, it would simply not be science if its principle were not some incomplete and relative unity or the concept of a relation, even if the principle were only the empty abstraction of a relation itself under the name of attractive forces or the force of identity. In the sciences whose principle is not a concept of relation, or only the empty force of identify, there remains nothing ideal except the first ideal relation, the way the child is different from the world, as with the form of picture-thinking in which the sciences place empirical qualities and can rehearse their variety—these sciences would primarily be called pre-eminently empirical science (Natural Law, 57).
(3) Science sees itself as formal unity. "This formal unity, into which the determinacy is placed by thinking, also provides the appearance of that necessity which science strives for. For the unity of opposites in relation to science, regarded as a real unity, is sciences' necessity. But because the matter of this formal unity is not the whole of the opposites, but only one of them (i.e., only one determinacy), the necessity too is only formal and analytic and is concerned only with the form of an identical or analytic proposition in which the determinacy can be presented." (Natural Law, p. 61)
As for absolute unity, as that essence of necessity which for appearance is an external bond the first point is that empiricism can have nothing to say about it; for in the unity which is the essential one, the multiplex is immediately annihilated and is null. Since multiplex being is the principle of empiricism, empiricism is precluded from pressing on to the absolute nullity of its qualities which for it are absolute and which besides, owing to the concept in accordance with which they are many, are infinitely many. This original unity can therefore mean, so far as possible, only a single, simple, and small mass of qualities, whereby it believes it can suffice for a knowledge of the rest. In that ideal, empiricism, in which what thus passes vaguely for capricious and accidental is blurred, and the smallest indispensable mass of the multiplex is posited; it is chaos in the physical as in the ethical world. In this way, what on the one hand is asserted to be simply necessary in itself, absolute, is at the same time acknowledge on the other hand to be something not real, purely imaginary, an ens rationis—in the first case to be fiction, in the second possibility; and this is the harshest contradiction (Natural Law, p. 63).
How has Popper replied to these notions? In a consideration of (1): Popper holds to the method of falsification. He suggests that a grasp of the truth may never be attained. Yet, Popper must hold to those concepts which appear to be the most acceptable. This is clearly seen in his concern of Darwinism. The element of time plays an important part, especially in the development of that which is:
For although we have acquired the art of rational criticism, and the regulative idea that a true explanation is one which corresponds to the facts, nothing else has changed; the fundamental procedure of the growth of knowledge remains that of conjecture and refutation, of the elimination of unfit explanations; and since the elimination of a finite number of such explanations cannot reduce the infinity of the surviving possible explanations Einstein may err, precisely as the amoeba may err (Objective, 264-265)
In other places Popper states, "I do not think that Darwinism can explain the origin of life. I think it quite possible that life is so extremely improbable that nothing can ‘explain’ why it originated." Popper notes, using Boltzmann's ‘explanation’ (an unlimited amount of time), "that it is possible to 'explain' almost everything." (Schlipp, 133-135). Popper's refutation of Tarski’s thesis (an improbability criterion for the choice of scientific hypotheses) is corrected: content = improbability (Objective, 17). What of (2)? This writer suggests that Popper's ultimate ground is Darwinism. Since there is no variation of method and goal from the emergence of the amoeba to Einstein one may posit: (1) there can be communication: an episode of understanding through critical discussion or relationship and (2) a notion of direction to verisimilitude. This is the embodiment of Popper's scientific method. The method itself is naturally ground. That which is unnatural is the uncritical attitude. This attitude will be self-destructive (i.e., myth). Popper sees the Christian epistemology as uncritical: "Theism was worse than an open admission of failure, for it created the impression that an incontrovertible explanation had been reached”. Christianity may only offer subjective explanations. Popper's notion of the emergence of language and the autonomous third world are less laden with such implications. Popper makes the distinction between Hegel and himself at this point: "My third world has no similarity whatever to human conscious ideas or from thoughts in the subjective sense." (Objective, 126). Is there a possible notion of an objective truth? Popper says that with Tarski and Go'del's finding one may answer, "Yes:"
The correspondence theory of truth which Tarski rescued is a theory which regards truth as objective: as a property of theories, rather than as an experience or belief or something subjective like that. It is also absolute, rather than relative to some set of assumptions (or beliefs); for we may ask of any set of assumptions whether these assumptions are true (Schlipp, 114).
Popper considers the consequences of Tarski’s discovery:
(1) That this concept was definable in logical terms which nobody had questioned before, and therefore legitimate; (2) that it was applicable to every unambiguously formulated (closed) statement (of any non-universalistic language), provided it was not applicable to its negation, and therefore obviously not vacuous, in spite of the fact; (3) that it was not linked to any general criterion, although every sentence derivable from a true sentence or from a true theory was, demonstrably, true; (4) that the class of true sentences was a deductive system, and; (5) that it was an undecidable deductive system provided the language under consideration was rich enough. (In connection with this result, Tarski referred to Godel.) (Objective, 322).
Tarski's theory is both the "rehabilitation" and "criticism" of the correspondence theory of truth. The three minimum requirements for Tarski's semantic meta-language apart form the "usual logical words" were these expressions:
(1) Names of statements
(2) Statements describing facts under discussion in that language.
(3) Terms denoting predicates of, and relations between these two fundamental kinds of expressions (Objective, 325)
With Tarski's theorem one is able to "introduce an entirely new (and suspect) category of terms on the basis of (unsuspect) established categories; it is a rehabilitation, an act of saving the honour of the suspect term." "Without Tarksi's theory of truth which provides a semantical meta-language free from any specifically semantical terms, the philosophers' suspect of semantical terms may not have been overcome." What Popper does with the theorum is interesting. "Tarski's theory allows us to define truth as correspondence to the facts; but we can use it also to define reality as that to which real facts, that is (alleged) facts that are real, from (alleged) facts that are not real (that is, from non-facts)." "And just as Tarski allows us to replace the term 'truth' by 'the set of true statements (or sentences)', so we can replace the term ‘reality’ by 'the set of real facts.' Thus, "the approach to the ‘whole truth’ through a greater and greater truth content." There are problems worth noting: Tarski takes L of the set L n to L n+1 to be "the smallest or the zero deductive system" while Popper reinterprets the suggested L as "a set of measure zero" in 'measure of content' instead of Tarskian "content." How does one work within axiomatic construct objectively? Does this theorem prove too much? Popper has considered the consequences of the Tarskian demonstration and corrected the improper elements of the construct but, there seems to be a necessary regress of meta-systems.
What of the postulate (3)? Hegel sees the Absolute as providing the unity necessary for a non-contradictory system. As has been suggested, Popper, who sees the Darwin model as ultimate ground, would show that this model has brought unity to science: "Everyone accepts it," "I have been very ready to accept evolution as a fact." (Schlipp, 133) It has already been mentioned that Popper cannot reasonably ascertain the evolution of life and language. Yet this metaphysical research program is leading physics to the ultimate grasp of the truth. Hegel considers this possibility:
As for the way of treating natural law which we have called empirical, the first point is that we cannot concern ourselves with the matter of the determinacies and relational concepts which it seizes upon and asserts under the name of principles. On the contrary, this separation and fixation of determinacies is just what must be negated. The nature of this separation implies that the scientific procedure applies only to the form of unity; and in an organic relation to the manifold qualities into which the unity is divided (if they are not simply to be enumerated), one certain determinate aspect must be emphasized in order to reach a unity over this multiplicity; and that determinate aspect must be regarded as the essence of the relation. But the totality of the organic is precisely what cannot be thereby attained, and the remainder of the relation, excluded from the determinate aspect that was selected, falls under the dominion of this aspect which is elevated to be the essence and purpose of the relation (Natural Law, 59-60).