The ontology of number

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates

Philosophical foundations of the Death and Anti-Death discussion

Perhaps there has been no greater opportunity than in this “VOLUME FIFTEEN of our Death And Anti-Death set of anthologies” to write about how might think about life and how to avoid death. There are two reasons to discuss “life”, the first being enhancing our understanding of who we are and why we may be here in the Universe. The second is more practical: how humans meet the physical challenges brought about by the way they have interacted with their environment. Many persons discussing “life” beg the question about what “life” is. Surely, when one discusses how to overcome its opposite, death, they are not referring to another “living” thing such as a plant. There seems to be a commonality, though, and it is this commonality is one needing elaboration. It ostensibly seems to be the boundary condition separating what is completely passive (inert) from what attempts to maintain its integrity, as well as fulfilling other conditions we think “life” has. In our present discussion, there will be a reminder that it by no means has been unequivocally established what life really is by placing quotes around the word, namely, “life”. Consider it a tag representing a bundle of philosophical ideas that will be unpacked in this paper

Hegel's Eurocentric Triads of Dialectics and its Transformation to Kelly's Planetary Paradigm

This article introduces Hegel's Eurocentric philosophy of dialectics in the 19th century and its transformation to Kelly’s planetary paradigm at the turn of the 20th-21st century. The new theory develops Hegel’s thesis—antitheses—synthesis to identity—difference—new-identity which is applicable for the entire human history, including the planetary era. The new triad generalizes Hegel’s mechanic view of nature by suggesting a dominant worldview which is featured by a series of tightening and converging dynamic fractal cycles

THE NOTHING THAT REALLY IS!

The denial of the existence of contradiction is at the root of all idealism in epistemology and the cause for alienations.This alienation has become a hindrance for the understanding of the nature and the historical evolution mathematics itself and its role as an instrument in the enquiry of the physical universe (1). A dialectical materialist approach incorporating  the role of the contradiction of the unity of the opposites, chance and necessity etc., can provide a proper understanding of the historical evolution of mathematics and may ameliorate  the negative effect of the alienation in modern theoretical physics and cosmology. The dialectical view also offers a more plausible materialist interpretation of the bewildering wave-particle duality in quantum dynamics (2)

On the Correct Formulation of the Starting Point of Classical Mechanics

The correct scientific and critical analysis of the generally accepted foundations of classical mechanics is proposed. The methodological basis for the analysis is the unity of formal logic and of rational dialectics. The main results of the analysis are as follows: (1) the correct starting point of kinematics is formulated: the informational  definition of the concept of time; definitions of the concepts of motion, speed, and acceleration of material point in the metric system of coordinates; the principle of motion of quantum particle (photon); proof of the mathematical, physical, and formal-logical erroneousness (fallaciousness) of Lorentz transformations; (2) the correct starting point of dynamics is formulated: the definition of force as a physical property of the structure of the system of the interacting objects; (3) the correct starting point of the theory of gravitation is formulated: the condition of existence of the gravitational interaction which represents the condition of existence of the region of overlap (superposition, intersection) of the gravitational fields of the material objects; (4) the correct formulation of the law of gravitation within the framework of the system approach is given (the formulation represents the system of the proportions); (5) it is proved that the formulation of Newton’s empirical law of gravitation represents the formal-logical and dialectical errors. Keywords: general physics, special relativity, quantum mechanics, classical mechanics, formalisms in classical mechanics, Newtonian mechanics, post-Newtonian approximation, gravity, philosophy of science, history of science. PACS:  01.55.+b, 01.65.+g, 01.70.+w, 02.90.+p, 03.30.+p, 03.65.-w, 04.25.Nx, 45.05.+x,  45.20.-d,  45.20.D

Dialectical-Ontological Modeling of Primordial Generating Process ↔ Understand λόγος ↔Δ↔Logos & Count Quickly↔Ontological (Cosmic, Structural) Memory

Fundamental Science is undergoing an acute conceptual-paradigmatic crisis of philosophical foundations, manifested as a crisis of understanding, crisis of interpretation and representation, “loss of certainty”, “trouble with physics”, and a methodological crisis. Fundamental Science rested in the "first-beginning", "first-structure", in "cogito ergo sum". The modern crisis is not only a crisis of the philosophical foundations of Fundamental Science, but there is a comprehensive crisis of knowledge, transforming by the beginning of the 21st century into a planetary existential crisis, which has exacerbated the question of the existence of Humanity and life on Earth. Due to the unsolved problem of justification of Mathematics, paradigm problems in Computational mathematics have arisen. It's time to return ↔ Into Dialectics. The solution to the problem of the foundations of Mathematics, and therefore knowledge in general, is the solution to the problem of modeling (constructing) the ontological basis of knowledge - the ontological model of the primordial generating process. The idea and model of the primordial generating process, its ontological structure directs thinking to the need for the introduction of superconcept → ontological (cosmic, structural) memory, concept-attractor, supercategory, substantial semantic core of the scientific picture of the world of the nuclear-ecological-information age. Model of basic Ideality→ “Space-MatterMemory-Time” [S-MM-T]

Process in Reality: A logical offering

The conjunction of process and reality is familiar from the original theory of A. N. Whitehead and the subsequent development of process philosophy and metaphysics by Nicholas Rescher. Classical logic, however, is either ignored or stated to be inappropriate to a discussion of process. In this paper, I will show that the value of a process view of reality can be enhanced by reference to a new, transconsistent logic of reality that is grounded in the physical properties of energy in its various forms. These properties justify a principle of dynamic antagonism or opposition that explicates the phenomena of change at all levels of reality. It can be, accordingly, a preferred logic for understanding the dynamics of real processes

Some Antecedents of Leibniz’s Principles

An objective of thisthesis is to investigate whether philosophical tradition can justify or support some of the arguments that are at the basis of Leibniz’s system (for example, monads have no window to the exterior world, a phrase that summarises the structure of Monadology). I shall demonstrate how Leibniz reflects the concerns and the positions of his key predecessors. Thus, the aim of the thesis is to explore key antecedents to Leibniz’s central doctrines. The thesis argues that Leibniz carried out a logical development of some principles in the eclectic system of Plotinus, which resulted in the structure of Monadology. Whether Leibniz’s project was successful or not will depend on how we view those principles

Why the Glove of Mathematics Fits the Hand of the Natural Sciences So Well :How Far Down the (Fibonacci) Rabbit Hole Goes

Why does the glove of mathematics fit the hand of the natural sciences so well? Is there a good reason for the good fit? Does it have anything to do with the mystery number of physics or the Fibonacci sequence and the golden proportion? Is there a connection between this mystery (golden) number and Leibniz’s general question, why is there something (one) rather than nothing (zero)? The acclaimed mathematician G.H. Hardy (1877-1947) once observed: “In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.” Is this also true of great physics? If so, is there a simple “preestablished harmony” or linchpin between their respective ultimate foundations? The philosopher-mathematician, Gottfried Leibniz, who coined this phrase, believed that he had found that common foundation in calculus, a methodology he independently discovered along with Isaac Newton. But what is the source of the harmonic series of the natural log that is the basis of calculus and also Bernhard Riemann’s harmonic zeta function for prime numbers? On the occasion of the three-hundredth anniversary of Leibniz’s death and the one hundredth-fiftieth anniversary of the death of Bernhard Riemann, this essay is a tribute to Leibniz’s quest and questions in view of subsequent discoveries in mathematics and physics. (In the Journal of Interdisciplinary Mathematics, Dec. 2008 and Oct. 2010, I have already sympathetically discussed in detail Riemann’s hypothesis and the zeta function in relation to primes and the zeta zeros. Both papers were republished online in 2013 by Taylor and Francis Scientific Publishers Group.