Philosophy and Science, Essay Example

Introduction

Science and history have a relationship which dates back to the 16^th and 17^th centuries when scientific philosophers like Galilei and Newton were starting to convert natural philosophy into science. The existing relationship between the two fields is still evidenced by the distrust that sustains the divine between dissimilar cultures. A rising number of philosophers are making significant contributions to sciences in the fields such as quantum mechanics and evolutionary biology while some scientists are conducting some investigation useful in the study of classical philosophical theories. The research has been done in specific areas such as consciousness and moral decision making. According to Michael Friedman, Kant provided the best identification of the a priori circumstances of the likelihood of experience and its features that were possible relative to the real scientific presumption of the eighteenth century (Friedman 8).

Friedman’s View

In Dynamics of Reason, Michael Friedman who is a philosopher of science and Kant aficionado offered a rich and synthetic vision of the manner in which science should progress which in turn attributes some respect to mathematics. Friedman also borrowed some ideas from the modification of Einstein’s General Theory of Relativity. This was basically referred to as the Exemplar or Friedman’s scheme. New forms of geometry and also calculus were developed from ideas borrowed from Newtonian gravitational theory which was drafted in a mathematical language modified in the calculus of Euclidean setting. This was coupled by meta-scientific foundation in the Kant’s philosophical system. With the possessions of this language which were availed, Einstein was able to provide new constitutive laws in the field of physics of the cosmos in a manner that Newtonian cosmology could be redefined almost as one of a wider set of empirical probabilities. The task of redefining earlier theories is a significant part of scientific work (Friedman 6).

Retrospective Communicative Rationality

The redefinition or reinterpretation described above is termed by Friedman as retrospective communicative rationality. Though this did not fully satisfy Friedman, the most significant aspect of this account is the manner in which the retrospective communicative rationality is realized and the prospective version. In the case of universal relativity, the associated meta-scientific task was executed by Helmholtz, Mach and Poincare, extending the Kantian schematism in view of the conversions of geometry by Riemann, Lie and Klein and also in Helmholtz work in psychophysical research. Poincara’s meta-scientific work was carried out in the perspective of his conventionalist philosophy. After the Einsteinian work, further meta-scientific research proceeded by modifying the theory further and hence igniting a novel philosophy.

According to Friedman, when all the above mentioned components are incorporated, then science is working at its optimum. It is thus a truly optimistic picture which depicts a glow of pride for preparing the noble channel of philosophy which is a field that could make a significant contribution to one of man’s biggest intellectual achievement (Friedman 6).

Philosophy and Physics

It is a regularly held presumption that the explanation of quantum mechanics has not been done properly. The fault of this misconception lies in the speed in which this interpretation was done. Had the revolution or the interpretation been done on the basis of Friedman’s scheme, then there would have been significant contributions in mathematics in fields such as integral equations, spectral theory and Fourier analysis. Other theorems such as Neumann algebras and harmonic analysis offered a constitutive language in which the physics laws especially in the area of quantum mechanics could be showed. Together with the new powerful mathematical framework, the capability of viewing the manner in which earlier classical theories achieved was established. Quantum mechanics cannot therefore be blamed for its retrospective expansive rationality. The failure of Quantum mechanics can only be attributed to lack of a meta-scientific structure. Friedman claims that philosophical contributions have been untimely in the field of quantum mechanics though the field has been successful. The mathematical path outlined by Friedman is more detailed than that described by Einsteinian revolution. The latter appears to lead inevitably to the rational empiricist view of mathematics as a part of logic in addition to the odd principle (Friedman 98).

Friedman has also borrowed ideas from Euclidean geometry, Riemannian geometry and Hilbert’s Foundations of geometry and also from quantum logic. He suggests that the quantum logic of von Neumann and Birkhoff could be the basis for success in mathematics by widening its constitutive principles. No matter how advanced quantum logic is, it is usually viewed as a means of describing the structure of orthomodular lattices (Van Fraassen 55).

There are predictions for meta-scientific philosophical activity to assist in opportune fashion to facilitate the success of quantum field theory, quantum gravity as well as quantum mechanics. Philosophy has played a significant part in the formulation of the human success the General Theory of Relativity. It is also expected to make vital contributions to the scientific field in future. Other theories that have emerged include the Habermas’s notion of communicative rationality which heavily borrows from Friedman’s ideas (Van Fraassen 55).

In reference to the quantum theory, Freedman Dyson argued that mathematics and physics separated in the 1930s due to difficulties in handling the infinities that are found in the theory. Where mathematics had initially the resources necessary to handle the problems brought about by physics, quantum field theory became a stumbling block. Hating the inconsiderate attitude of the physicists, they withdrew leaving the physicists to proceed with in the best possible manner. There was reconciliation between the two when they realized that they needed each other in order to succeed.

Philosophy in Algebraic Topology

Eilenberg and Maclane introduced a language of categories in mathematics called functors. Without functors algebraic topology would be meaningless in mathematics. It was likely that such a language would appear to make topology meaningful. It was indeed not predictable that such an early systematization would have been significant and appropriate and also difficult to visualize that this language would ever be displaced. Friedman suggests that May is displaying category hypothesis as a constitutive language for other areas of mathematics apart from science. There appears to be a barrier that blocks philosophers from accepting post-1930s mathematics. This barrier was not even clearly surmounted by Lakatos.  He could not comprehend where the dialectical excitement could arise from once an individual is locked into a prevailing formal system. Friedman is also held in the same problem. This can be observed when Friedman attempts to identify the prime distinction between mathematics and science. One of the most striking aspects of his scheme is the incident in the course of insurgency of observed laws becoming constitutive doctrines and likewise former constitutive doctrines becoming empirical facts. For instance, what is described as a contingent theory of the Newtonian universe, that is, the inertial mass and the gravitational mass are similar, converts to constitutive doctrine of the Einsteinian picture. Similarly, the constitutive lack of curving of the Newtonian universe becomes an almost true though in some places false description of the world. According to Friedman, this is the main disparity between mathematics and natural sciences (Friedman 120).

Disparities Between Mathematics and Natural Sciences

Occurrences of parallel shifts in the nature of laws between being pragmatic and being constitutive even in mathematics of the 1930s can also be found. Many methods of shifting from space to group had been devised by mid-1940s. These methods include: Cech cohomology, singular cohomology and simplicial cohomology. The theories gave similar solutions in some places while they differed significantly in others. After the axiomatisation  of homology and cohomology hypothesis by Eilenberg and Steenrod, which was made possible by the language of category hypothesis, the contingent characteristics of a group of methods of deriving algebraic information from a topological space were converted to constitutive of the homology or cohology theory. Cech homology was found to lack one of these characteristics, codified as the accuracy axiom and was enhanced to Steenrod homology. This was later on revitalized as an example of an incomplete exact homology hypothesis (Van Fraassen 60).

Conclusion

There is a significant relationship between science and philosophy. Philosophy has also been applied in analyzing the differences and disparities between different fields of science and also the differences between mathematics and natural sciences. Philosophy has enabled a smooth passage of mathematics and physics revolution. Philosophical theories have assisted researchers in revitalizing the philosophy of mathematics. Philosophers of mathematics are at the moment progressing from alluding temporarily in a postscript to category hypothesis as another structuralism principle.

Works Cited

Friedman Michael. Dynamics of Reason, Chicago: The University of Chicago Press, 2001

Van Fraassen . The Empirical Stance, Yale: Yale University Press, 2002