相关论文: Truth as value and duty: lessons of mathematics

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…

Truth values of Modus Ponens and Modus Tollens rules for propositions having linguistic truth value that may be represented by lattice(Fig1, Fig2) are computed in this paper. The results show that the truth values are not always absolutely…

In this paper we suggest how the mathematical concept of hyperstructures may be a useful tool in the study of the higher, hierachical structure of languages.

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…

Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…

We define constructive truth for arithmetic and for intuitionistic analysis, and investigate its properties. We also prove that the set of constructively true (first order) arithmetical statements is Pi-1-2 and Sigma-1-2 hard, and we…

Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…

This is a brief overview of the role of mathematicians in the so-called "Luzin Case" as well as some analysis of the mathematical and humanitarian roots of the affair.

Mathematics has become inescapable in modern, digitized societies: there is hardly any area of life left that isn't affected by it, and we as mathematicians play a central role in this. Our actions affect what others, in particular our…

Mathematics is changing. Computers are verifying proofs, checking calculations, and exploring complex structures that would overwhelm human effort. Yet curiosity-driven research is where tomorrow's breakthroughs are quietly prepared. In…

We revisit Smullyan's paper ``Truth and Provability'' (2013) for three purposes. First, we introduce the notion of Smullyan models to give a precise definition for Smullyan's framework discussed in that paper. Second, we clarify the…

Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…

By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…

Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.

People sometimes change their opinions when they discuss things with other people. Researchers can use mathematics to study opinion changes in simplifications of real-life situations. These simplified settings, which are examples of…

Fairness for Machine Learning has received considerable attention, recently. Various mathematical formulations of fairness have been proposed, and it has been shown that it is impossible to satisfy all of them simultaneously. The literature…

This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…

The objective of this article is to stimulate discussions in mathematical society about the role of mathematical departments in the life of the community. University community is the center of knowledge and promotes the intellectual…