Related papers: Unity and Disunity in Mathematics
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
The concept of measurement is discussed. It is argued that counting process in mathematics is also measurement which requires a basic unit. The idea of scale is put forward. The basic unit itself, which are composed of the infinitesimal of…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
There are many scientific problems generated by the multiple and conflicting alternative definitions of linguistic recursion and human recursive processing that exist in the literature. The purpose of this article is to make available to…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…