This is the topic of the paper: Describe the impact, implications, and/or significance the revolutions of twentieth century science and mathematics (as typified by Godel's Incompleteness Theorem, Heisenberg's Uncertainty Principle, and Einstein's Theory of Relativity) have on the ontological questions, epistemological questions, their relationships and/or their potential answers. The readings we did that can be used are "Improbable" by Adam Fawer, "A Certain Ambiguity" by Gaurav Suri and "A Mathematician's Lament" by Paul Lockhart.
Impact/implications and significance of the twenty century revolutions of science:
The revolutions of twenty century science are a clear shift from the old Paradigm of scientific enquiry and it brought a whole new dimension in the world. Looking beyond and tracing the origins of older paradigm which was epistemologically rooted in Rene Descartes Philosophy of” Dualism” has been challenged by Godel’s Incompleteness theorem, Heisenberg uncertainty principle, and Einstein’s theory of Relativity.
We start our debate by first defining Paradigm, According to Ralph H Kilman, Paradigm is something strict, fundamental and basic through which all the entities of universe and life on earth is studied and sense is developed(Kilmann, 2001). According to Kuhn, the “Unstated, Untested and Unquestioned assumptions” about the basics of universal makeup is what we name paradigm(Kuhn, 1970).
The world today is moving away from old Cartesian-Newtonian Paradigm to new Quantum Relativistic Paradigm. Comparing the characteristics of two paradigms we can clearly indicate the changes in epistemology and ontology of today’s science(Kilmann, 2001).
The primitive western thinking is rooted in Greek Civilization which is inspired by thinking of Aristotle and Euclid. Euclid gave the idea of “two parallel lines “and rested the groundings of straight line geometry(Heath, 1956; Lehmer, 1938). On the other hand Aristotle laid the foundation of “logic “and “determinism” in science. The time period of renaissance witnessed the contribution Newton and Descartes who separated mind and matter. Descartes treated this world as a mechanical object, where mind has no connection with matter. This philosophy is termed as Dualism (Descartes & Veitch, 1969). Newton laid the foundation of objectivity and treated every object that can be measured, hence laying the foundation of empiricism (Newton, 1960). There are following seven underlying assumptions of old paradigm based on Descartes and Newton(Kilmann, 2001),
1 The dualistic Separation of consciousness/ matter
There is a complete separation of humans and physical world surrounding them
2 The universe as the motion of inert molar objects
The universe is created by matter. It is a hierarchical relation between atoms, molecules and they come closer to form inert molars which follow rules of Newton.
3 The Space between molar objects:
It is empty and flat.
4 The uniqueness of one universe:
The universe is made up of three things: length, width and depth. Space and time are absolute and hence the laws of physics are absolute and eternal.
5 The Deterministic certainty of Inert Molar objects:
The force of gravitation is the source of moving the objects
6 The fundamental separation of inert molar objects:
The inert objects are totally different from each other. They are united only by force of gravity which is not visible
7 The eventual death of universe:
The “big bang” or God will bring temperature of universe to absolute zero and eventually there will be death of universe.
Now we look at the new paradigm and its basic assumptions.
The mid of 1800s witnessed two prominent questions all around the world,
1Why don’t all wavelengths of light radiate at all levels of heat which became known as the ultraviolet catastrophe
2 Is light a wave or particle, or it behaves in both ways?
These two questions lead to introduction of new paradigm which is Relativistic quantum paradigm. Here one thing is important light is the concern which attracted the attention of all scientist and its explanation lead to new paradigm shift. There are seven underlying assumptions of new paradigm(Kilmann, 2001),
1 The monistic Unification of Consciousness with matter:
The physical world exists via the proactive participation of self aware individuals.
2 Universe as materialized by conscious participation:
The entire universe is built on consciousness. The theory of relativity and quantum mechanics bring together creation and evolution of universe.
3 Space time as curved and filled with matter/energy:
The geometry of space time is never empty; it is filled with mass and energy. It is holographic in nature.
4 The natural selection of many relativistic universes:
There is nothing absolute all the theories are relative. Only light is absolute for all observers.
5 The probabilistic uncertainty of self motion monads:
Both the human beings and nuclear entities are self motion monads. Both move with their own will and are prone to external pressures. So it is not possible to separate mind and matter all together.
6 The eternal connections among self motion monads
Both humans and nuclear particles are bounded in universal consciousness. They affect all other related to them.
7 The eternal self-organizations of relativistic universes:
There is no eventual death of universe; it will generate itself step by step
To this point we have come to two major conclusions.
1 Newton’s paradigm is totally objective with positivistic epistemology and objective ontology
2 On the other hand Relativistic challenged this paradigm of economic growth where mind and matter are separate.
The new paradigm shift which encompasses the Godel's Incompleteness Theorem, Heisenberg's Uncertainty Principle, and Einstein's Theory of Relativity is totally different from older paradigm of Cartesian Newton paradigm.
Changes brought by new revolution evidence from A Certain Ambiguity:
“How can space be unbounded but finite?” The three dimensions of universe and to explore it further and assuming that there is a fourth dimension(Suri & Bal, 2007). Then the introduction if infinity and man thinking again towards God that there is someone who is ruling all this. These though provoking dimensions of new science which are bringing together both mind and matter together and including Meta physical objects in inquiry again is the revolution of new science.
A Mathematician’s Lament:
Mathematics is not a mere knowledge of numbers it is a body of knowledge that encompasses whole science in it (Lockhart, 2009). As it is believed mathematics is the mother of all sciences so treating math just as number is not is proper use.
In our discussion of two dueling paradigms we set the stage for this debate. Mathematics is the key to universe. In older science we used Euclid Geometry of two lines never intersecting each other. In today scientific revolution two lines can intersect each other. That is why we have three dimensions and looking forward towards fourth also. These changes brought the whole new revolution in scientific inquiry, below are discussed Epistemological and Ontological Assumptions,
Epistemological assumptions of older paradigm:
The new relativistic paradigm brought a revolution in epistemology and ontology of whole science.
The new paradigm opened the domains of qualitative research and questioned the objective reality of older science. And today besides use of two variables, constructionism, feminism, structuralisms is common. When new paradigm shifted the old philosophy of dualism new domains of research opened.
The world of science today is passing through a paradigm shift. The older paradigm of objectivity and dualism is shifting towards a real and conscious paradigm. This new paradigm challenged the epistemology and ontology of older paradigm of objectivity. The relativistic quantum paradigm is taking qualitative frame of research into consideration.