10.4. Devaluation of the Program of Unifying All Theories
Already Ernst Mach (1896) invited to study the mathematical homeomorphisms between
theories insisting on different fields of phenomena: e.g. a RC electric circuit and a damped
mechanical oscillator are represented in mathematics by a same differential equation. This link
between theories leads to many useful considerations. But many scholars think that it is
imaginative to generalize this link to the entire two theories, i.e. electromagnetism and
mechanics. However, in the name of a same, universal scientific method neo-positivists claimed
that all theories have to be unified. Subsequently, also reductionists and physicalists reiterated
this program.
In the above an accurate analysis showed that a singular limit does not allow a reduction of the
mathematical frameworks M of one theory to another theory in its entirety; it connects only
parts of the two physical theories (e.g. in the case of QM to CM one obtains many but not all
formulas of the latter one: the formulas for extended bodies, or those for motions with
friction, etc.). In general, it is not known whether these common parts (e.g. semiclassical
quantum mechanics) constitute autonomous theories, or open theories, or merely
mathematical models.
Therefore, reductionists are emphasizing the few successful cases of partial connections of the
mathematical frameworks M of two theories as the starting point of the application of a general
program of reductions of all theories; actually, they are suggesting a program that, after almost
a century of so many unsuccessful attempts, has to be considered clearly unattainable; hence,
their final result the unity of the entire science has to be considered as mythical.
After half a century of a specific research on the subject of the neo-positivist notion of reduction,
Feyerabend’s appraisal on the philosophy of reduction seems well-adequate:
… a formal account of reduction is impossible for general theories… Nagel’s theory of reduction…
[is] not in accordance with actual scientific practice and with a reasonable empiricism
(Feyerabend, 1962: p. 28).
This conclusion is even more valid if the empirism in theoretical physics is associated to
constructive mathematics.
Also Batterman has devalued the program of reductionists. He countered Sober’s reductionist
theses (quoted in Sect. 3):
I have argued that [his] theses are essentially meaningless.[…] I think that the ideal of in principle
derivations of behavior of systems (or laws, or theories) from more “fundamental” lower-scale
details (or more fundamental laws or theories) is largely mistaken. Any examination of the actual
practice of scientists interested in modeling systems at different scales will reveal nothing as
simple as the kind of derivations that the proponents of this ideal believe is possible. [Sober’s]
appeal to a completed ideal physics the main feature that underwrites these in principle claim is
purely aspirational and speculative. We have no idea what such a physics would like look, nor we
have any evidence that it exists (Batterman, 2018: p. 871).
