Abstract
The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying principles through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation.
Highlights
The process of axiomatization is ancient, with wide array of applications in mathematics and in philosophy to coherently establish a theory to reach out to truth
It is important to note that the monadism of Leibniz may have some Platonic elements, and the concept of continuous evolution is embodied within the mathematical philosophy of Leibniz
The existential life forms are in an equivalent class of the 0-0 state everywhere outside of the corresponding local path-homotopy interval. It indicates that there is an extended interval t ae < t a, tbe > tb, [t ae, tbe ] where almost every existential life form in universe U will preserve the 0-0 transition in the cosmological time-scale horizon, which is in line with the theory of evolution and disappearance of species in nature. It is generally an accepted theory in evolutionary biology and social choice theory that life forms in nature follow the dynamic trajectories highly influenced by the probabilities of various events in nature
Summary
The process of axiomatization is ancient, with wide array of applications in mathematics and in philosophy to coherently establish a theory to reach out to truth. Alonzo Church, as a philosopher and mathematical logician, applied the method of hypothetico-deductive-rationalism while theorizing epistemological aspects of mathematics, logic and philosophy [3]. Philosophies 2021, 6, 84 to note that the method of mathematical and philosophical investigations made by Church can be viewed as a Platonic realism, and sometimes his opinion about realism conflicts with Frege. The Platonic and Aristotelian philosophies include the elements of Pythagorean doctrines [4]
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