相关论文: Naive Philosophical Foundations
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…
Research in foundations of physics is stagnant, as claimed by many scientists during the last years. I suggest that one reason might be the reification of language, particularly of mathematics, which favour the search for answers to wrong…
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
Remarks on mathematical proof and the practice of mathematics.
Since I first became enthralled with physics as a teenager, I've been intrigued by the philosophical aspects of the discipline. As I approached the end of my career as an experimental physicist and observational astronomer (I'm now…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
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…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
We review the philosophical framework of mathematical conceptualism as an alternative to set-theoretic foundations and show how mainstream mathematics can be developed on this basis. The paper includes an explicit axiomatization of the…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…
It is rare to succeed in getting mathematics into ordinary conversation without meeting all kinds of reservations. In order to raise public awareness of mathematics effectively, it is necessary to modify such attitudes. In this paper, we…
Arising out of an attempt at a new foundations of mathematics, in which relations are more primitive than sets, and out of the theoretical physicists' concept of underlying causes of empirical phenomena, the idea of a purely mathematical…
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
Recent contributions address the problem of language coexistence as that of two species competing to aggregate speakers, thus focusing on the dynamics of linguistic traits across populations. They draw inspiration from physics and biology…
All sciences need and many arts apply mathematics whereas mathematics seems to be independent of all of them, but only based upon logic. This conservative concept, however, needs to be revised because, contrary to Platonic idealism…