(May 21, 2018 05:05 PM)Zinjanthropos Wrote: . . . This causes me to wonder about not only the completeness of today's information but mathematics itself. How much incorrect math does science rely on? What are mathematicians doing that enables them to piece together equations that support theory? I think I read somewhere that it is not uncommon for mathematicians to inject their own variables to an equation to make it work. Maybe it's those added equation symbols that encourages science to look for the unknown factors necessary to complete the math, idk.
Arguably, quantitative symbolism is just the language of science disciplines that are pregnant with conceptual tools and schemes (like physics). Akin to how a knife is a murder weapon, a dining utensil, or a generic purpose implement -- depending. The significance, motivation, and directional influence is carried in the human user rather than the knife itself -- but what the former projects upon the latter can have a return influence.
So instead of blaming the manner of expression (mathematics), I'd maybe refine it down to potential affairs like
theory-ladenness,
underdetermination /
overdetermination, etc. The allegiance to a "background interpretation" or set of them that the technical description rests in may provoke the practitioner to keep seeking adjustments in a model / construct. Rather than, say, just abandoning it due to loose ends (incongruities and suspended conclusions slash ambiguities).
Hempel's Dilemma revolves around the idea that contemporary physics, cosmology, etc is incomplete in the current time. Thereby any "grand judgments" about "what's going on" or "what is" that is abstracted from such science enterprises are premature or bound to be altered or outright dismissed as erroneous in the future. However, that itself carries a presupposition that such can be completed -- that there is a "progress toward immutable truth" taking place rather than practical, variegated success at manipulating, controlling, and predicting (events in) the environment. It's not an operating condition "found" under a rock in nature but instead prescribed (an invented thought orientation).
For instance, early humans survived -- they had success at manipulation, control, and prediction despite the conjectural side of their activity being far from any capitalized Truth (wallowing in myths and superstition). That success was much more limited than today because there wasn't the diversification of
effective multiple ways of representing / conceiving the world. An ordinary bricklayer still gets by via treating bricks and mortar as just the tangible, empirical phenomena s/he sees and feels. Which is to say, s/he doesn't convert them to the alternative conceptions of chemists and physicists, though those may much factor into an architectural engineer's planning.
In somewhat the same context, scientific activity itself can be interpreted in variable ways. The non-mainstream, rationalist tendency to construe it as progress toward an eventual static and immutable truth (completion) with no more disruption by revisions, assimilation, and paradigm shifts is just one. Having a lineage going back to the "beyond appearances" metaphysics of the Eleatic school, as well as later
monotheistic influences.
20th Century Philosophy of Science (Book 6, p1)
http://www.philsci.com/book6.htm
EXCERPT: James B. Conant (1883-1978) is the principal influence on the professional thinking of [Thomas] Kuhn. Kuhn dedicated his Structure of Scientific Revolutions to Conant, “Who Started It”, and Conant acknowledged Kuhn’s contributions to the “Case Histories in Experimental Science” course that Conant started at Harvard University.
Conant advocates what he calls the “dynamic view” of science, and he contrasts it with the “static view”, which he identifies with the positivist philosophy and specifically with the philosophy set forth by Karl Pearson in the latter’s Grammar of Science. The static view represents science as a systematic body of knowledge, while the dynamic view represents science as an ongoing and continuing activity. On the dynamic view the present state of knowledge is of importance chiefly as a basis for further research activity. Conant defines science as an interconnected series of concepts and conceptual schemes that have developed as a result of experimentation, and that are fruitful of further experimentation and observations. He explicitly rejects positivism, which he portrays as a quest for certainty, and he emphasizes that science is a speculative enterprise that is successful only to the degree that it is continuing.
Conant also maintains what he calls his “skeptical” view. On this view microphysical theory does not actually describe reality, but rather is a “policy” that serves as a guide for fruitful future research activity. He maintains that the wave-particle duality thesis in the quantum theory has changed the attitude of physicists, such that science is now viewed in terms of “conceptual schemes”, which arise from experiment and are fruitful of more experiments. The wave-particle duality is one such conceptual scheme, and it justifies his “skeptical” approach, because this conceptual scheme does not describe what light “really” is. Instead modern physics describes the properties of light and formulates them on the simplest possible principles. The history of science is a history of the succession of such conceptual schemes. Conant references the view of the Harvard pragmatist philosopher, William James, who maintained that man’s intellectual life consists almost wholly in the substitution of a conceptual order for the perceptual order from which experience originally comes. Different universes of thought arise as concepts and percepts interpenetrate and “melt” together, “impregnate” and “fertilize” each other. As a result the series of conceptual schemes in the history of science is one in which the conceptual schemes are of increasing adequacy to the perceptions in experimentation.
Conant had initially believed that natural sciences have an accumulative character that reveals progress, but following Kuhn’s Structure of Scientific Revolutions (1962) Conant modified his view of the accumulative nature of science. He continues to find accumulative progress in the empirical-inductive generalizations in science and also in the practical arts, but he excludes accumulative progress from the theoretical-deductive method, which admits to scientific revolutions.
Conant identifies the static view with the logical perspective, while he admits the psychological and the sociological perspectives in his dynamic view. The sociological perspective reveals that science is a living organization, which exists due to close communication that enables new ideas to spread rapidly, and that enables discoveries to breed more discoveries. Scientists pool their information, and by so doing they start a process of cross-fertilization in the realm of ideas. As a social phenomenon, science is a recent invention starting with the scientific societies of the seventeenth and eighteenth centuries, and then evolving in the universities in the nineteenth century. Communication was initially through letters, then later through books, and now through journals.
He maintains that historically one of the more important psychological aspects of the development of science is prejudice, a matter toward which he admits he himself has an ambivalent attitude. On the one hand the traditions of modern science, the instruments, the high degree of specialization, the crowd of witnesses that surround the scientist – all these things exert pressures that make impartiality in matters of science almost automatic. If the scientist deviates from the rigorous rôle of impartial experiment or observation, he does so at his peril. On the other hand Conant says that to put the scientist on a pedestal because he is an impartial inquirer is to misunderstand the historical situation. This misunderstanding results both from the dogmatic character of textbooks and from the view of positivist philosophers such as Karl Pearson. Conant emphasizes the stumbling way in which even the ablest of the scientists of every generation have had to fight through thickets of erroneous observation, misleading generalization, inadequate formulations and unconscious prejudice. He notes that these problems are rarely appreciated by those who obtain their scientific knowledge from textbooks and by those who expound on “the” scientific method.
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May 21, 2018 03:16 PM
(This post was last modified: May 21, 2018 03:26 PM by C C.)
