Related papers: Naive Philosophical Foundations
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…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
Mathematicians invented Mathematics to escape from words, but at last they depend on them just as much as everybody else. At the end, all basic definitions will be reliant on words, yet the mathematician believes that he's elevated from…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
This is a very basic introduction to some notions related to logic and complexity.
In this paper I propose the idea to establish a clear distinction between the foundations of truth and the foundations of meaning in Mathematics. I explore on the most basic example, the mathematical line, the possibility that the…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
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…
We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
Philosophical thinking has a side effect: by aiming to find the essence of a diverse set of phenomena, it often makes it difficult to see the differences between them. This can be the case with Mathematics, Programming, Writing and…
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…
I advocate an extreme "shut-up-and-calculate" approach to physics, where our external physical reality is assumed to be purely mathematical. This brief essay motivates this "it's all just equations" assumption and discusses its…
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…
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers…
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…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…