Related papers: Aristotle and Gautama on Logic and Physics
This history of the concept of fact reveals that the fact-oriented practices of German physicists and historians derived from common origins. The concept of fact became part of the German language remarkably late. It gained momentum only…
Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. It turned out that full propositional Linear Logic is undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more expressive than…
Perhaps one of the most intriguing questions in philosophy concerns the true nature of external reality. In this paper, we discuss some of the theories that have been put forth regarding the nature of reality and of our perceived universe.…
The analysis of problematic mathematical texts, particularly from India, has required the introduction of a new category of rigorous discourse, apodictic discourse. We briefly recall why this introduction was necessary. We then show that…
We discuss the work of a brilliant line of Mathematicians who lived in central Kerala and starting with its founder Madhava (1350 CE) developed what can best be described as Calculus and applied it to a class of trigonometric functions. We…
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…
In this paper I study the connection between logic and metaphysics in Plato's participation theory, from the structural properties of the latter. Although Plato was the first ever to formulate the contradiction principle explicitly (in the…
Mathematical approaches to modeling the mind since the 1950s are reviewed. Difficulties faced by these approaches are related to the fundamental incompleteness of logic discovered by K. G\"odel. A recent mathematical advancement, dynamic…
Since the early days of humankind, people have been asking questions about Nature of two kinds: why did that happen? And how can that be used? In a broad sense, science was born that day. We show indeed that science has two complementary…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
The evolution of theoretical physics in the XX century differs significantly from that in XVII-XIX centuries. While continuous progress is observed for theoretical physics in XVII-XIX centuries, modern physics contains many questions that…
The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…
Gravity plays an important part in the experiments and discoveries of the modern world. But how was it discovered? Surely Newton and Einstein were not the only people to observe it and account for it. It had been a long path before the full…
We report on a pedagogical experiment to make mathematics easy by changing its philosophy. The Western philosophy of math originated in religious beliefs about mathesis, cursed by the church. Later, mathematics was "reinterpreted", in a…
Do we have two kinds of reality: physical and mathematical? What is the role of mathematics in physics? These fundamental questions have intrigued original and brilliant minds since ancient times. A recent article (Aharonov, Cohen and…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
This paper provides an overview of the birth and early development of Indian astronomy. Taking account of significant new findings from archaeology and literary analysis, it is shown that early mathematical astronomy arose in India in the…
A classical reconstruction of Wright's first-order logic of strict finitism is presented. Strict finitism is a constructive standpoint of mathematics that is more restrictive than intuitionism. Wright sketched the semantics of said logic in…
Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…