In the modus tollens argument the hypothetical-conditional statement expressing the proposed theory is falsified, when the antecedent clause is true and the consequent clause is false. On the other hand in the modus ponens argument for explanation both the antecedent clause describing initial conditions and the hypothetical-conditional statement having law status are accepted as true, such that affirmation of the antecedent clause validly concludes to affirmation of the consequent clause describing the explained phenomenon.
Thus the schematic form of an explanation is “For every A if A, then C” is true. “A” is true. Therefore “C” is true (and explained). The conditional statement “For every A if A, then C” represents a set of one or several related universally quantified law statements applying to all instances of “A” and to all consequent instances of “C”. “A” is the set of one or several particularly quantified statements describing the realized initial conditions that cause the occurrence of the explained phenomenon as in a test. “C” is the set of one or several particularly quantified statements describing the explained individual consequent effect, which whenever possible is a prediction.
In the explanation the statements in the hypothetical-conditional schema express scientific laws accepted as true due to their empirical adequacy as demonstrated by nonfalsifying test outcomes. These together with the antecedent statements describing the initial conditions in the explanation constitute the explaining language some call the explanans. And they call the logically consequent language, which describes the explained consequent phenomenon, the explanandum.
It has also been said that theories “explain” laws. Neither untested nor falsified theories occur in a scientific explanation. Explanations consist of laws, which are formerly theories that have been tested with nonfalsifying outcomes. Proposed explanations are merely untested theories. Since all the universally quantified statements in the nontruth-functional hypothetical-conditional schema of an explanation are laws, the “explaining” of laws means that a system of logically related laws forms a deductive system partitioned into dichotomous subsets of explaining antecedent axioms and explained consequent theorems.
But in a formal axiomatic system the choice of axioms is arbitrary, so long as the chosen axioms are independent, i.e., no one of them can be derived deductively as theorems in the system from any of the other chosen axioms. And this arbitrariness permits the choice of axioms to be changed, such that what were originally theorems can be deemed axioms, and the original axioms can then be derived as theorems from the new axioms.
In his Patterns of Discovery Norwood Russell Hanson examines this feature in the case of Newton’s dynamical law statements. Hanson says that a statement may be deemed an empirical generalization, which can be explained by derivation as a theorem. Or it may be deemed a definitional statement or what Hanson calls a “functionally a priori” statement having no need of explanation and thus having axiomatic status. Thus it is always ambiguous as to just what statements are explaining and what statements are explained in any axiomatic system. Hanson says that microphysics has been misrepresented by philosophers who study the logic of the deductive systems. He says that their error is to regard as paradigms of scientific inquiry not unsettled, dynamic, research sciences like microphysics, but instead finished systems like planetary mechanics. Elsewhere in his literary corpus he ridicules them as “axiomitizers”.
Integrating laws into axiomatic systems confers psychological satisfaction by contributing semantical coherence. Influenced by some renderings of Newton’s physics many positivists had believed that producing reductionist axiomatic systems is part of the aim of science. But the reductionist preconception is not validated by the history of science. Great developmental episodes in the history of science have had the opposite effect, namely of fragmenting science. And while the fragmentation has occasioned the communication constraint and consequently opposition to the new discoveries, it has only delayed but has not halted the advancement of science in its history. Eventually pragmatic empiricism prevails.
BOOK II – Mach and Duhem
This BOOK examines two variations on positivism formulated by two turn-of-the-twentieth-century physicists, Ernst Mach and Pierre Duhem. And it previews the story of positivism’s rejection by the physicists who made the two great scientific revolutions in twentieth-century physics, Einstein and Heisenberg.
Mach’s Phenomenalism
Ernst Mach (1838-1916) is a representative figure of the early positivist philosophy of science in physics at the turn of the twentieth century. He earned a doctorate in physics from the University of Vienna in 1860, taught experimental physics for most of his career at the University of Prague (1867-1895), and then held the chair of Inductive Philosophy at the University of Vienna (1895-1901). He was several times nominated for the Nobel Prize. He set himself the philosophical task of implementing the phenomenalist philosophy of David Hume in physics while Newtonian mechanics still prevailed in physics.
Prior to contemporary pragmatism philosophers based their philosophies of science on one or another metaphysical viewpoint. Though positivists philosophers including Mach were explicitly “antimetaphysical” (Mach even denied that he was a philosopher), they were actually advocating their own metaphysics while labeling the views they opposed as “metaphysical”, and used the term pejoratively. Positivism is a philosophy that evolved in reaction against the various romantic philosophies, and what the positivists meant by “metaphysics” was the metaphysics of the romantics. Just as the views of the romantics evolved from the philosophical tradition of the rationalists, similarly those of the positivists evolved from the tradition of the empiricists. Thus Mach’s epistemology is very similar to the views of the empiricists Berkeley and Hume, and he explicitly expressed indebtedness to them in his works.
Mach’s principal work setting forth his phenomenalist philosophy is his Analysis of Sensations (1885), which went through five editions in both German and English, although Mach also discussed his epistemological views in many of his other works. His epistemology postulates “elements” such as individual sounds, temperatures, pressures, spaces, times, and colors. When these elements are considered in relation to one another, they are studied by the physical sciences, and when they are considered in relation to the human mind or rather the nervous system of the human body, they are called “sensations” and are studied by psychology.
One of the central theses of Mach’s Analysis of Sensations is that the only difference between elements and sensations is the aspect under which they are viewed, and that physics and psychology therefore have the same subject matter. The distinction between the physical and the psychical is entirely a matter of convenience or practicality, because everything is merely a function of these elements. Everything other than these elements is a mental construct consisting of complexes of sensations. All material things including our own bodies and even the ego are nothing but complexes of elements that are constructs made by the human mind and that have some fixedness or constancy in sense experience.
A fundamental thesis of Mach’s philosophy is that material bodies do not produce sensations, but rather complexes of sensations are associated together by the human mind to produce material bodies. Ultimately all that is valuable in science is the discovery of functional relations of dependency of sensations upon one another. The constancies that enable our mental construction of physical bodies have no privileged reality status. This is even more so with such mental constructs as the physicists’ molecules and atoms, which are mental constructs that unlike those of physical bodies are not found in experience. The positivist phenomenalist philosophy is a nonrealist metaphysics, and if it is generously said to have an ontology, the ontology consists merely of the phenomenal elements/sensations.
Mach’s Philosophy of Science
Aim of Science
Mach’s
