相关论文: Naive Philosophical Foundations

As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…

Statistics is one of the most valuable of disciplines. Science is based on proof and it alone produces results, other approaches are not, and do not. Statistics is the only acceptable language of proof in science. Yet statistics is…

We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for…

It is a fascinating subject to explore how well we can understand the processes of life on the basis of fundamental laws of physics. It is emphasised that viewing biological processes as manipulation of information extracts their essential…

This invited paper is a passionate pitch for the significance of logic in scientific education. Logic helps focus on the essential core to identify the foundations of ideas and provides corresponding longevity with the resulting approach to…

These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…

A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…

"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…

A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…

A hundred years ago, logic was almost synonymous with foundational studies. The ongoing AI revolution raises many deep foundational problems involving neuroscience, philosophy, computer science, and logic. The goal of the following dialog…

The aim of this paper is to introduce a mathematical logic based approach investigating why-type questions in physics.

Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…

Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…

The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…

Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

An origin is often an intriguing issue. It becomes doubly intriguing when the logical form of thinking is considered. In this paper we will investigate exactly that: we will conjecture on the origin of basic instruments of logical thinking.…

Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…

The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are…