Inconsistency, paraconsistency and ω-inconsistency

In this paper I'll explore the relation between ω-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I'll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are ω-inconsistent. Although usually a theory of truth is generally expected to be ω-consistent, all conceptual concerns don't apply to inconsistent theories. Finally, I'll explore if it's possible to have an inconsistent, but ω-consistent theory of truth, restricting my analysis to substructural theories.Fil: Da Re, Bruno. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Investigaciones Filosóficas - Sadaf; Argentin

Frege's logicism

In this paper, I provide an interpretation of Frege's logicist project, drawing a connection between it and his idiosyncratic view of truth

Arithmetic, Set Theory, Reduction and Explanation

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences

Is the dream solution to the continuum hypothesis attainable?

The dream solution of the continuum hypothesis (CH) would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set theory, a missing axiom, widely regarded as true. Such a dream solution would indeed be a solution, since we would all accept the new axiom along with its consequences. In this article, however, I argue that such a dream solution to CH is unattainable. The article is adapted from and expands upon material in my article, "The set-theoretic multiverse", to appear in the Review of Symbolic Logic (see arXiv:1108.4223).Comment: This article is based upon an argument I gave during the course of a three-lecture tutorial on set-theoretic geology at the summer school "Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments", at the University of London, Birkbeck in August 201

Small Steps and Great Leaps in Thought: The Epistemology of Basic Deductive Rules

We are justified in employing the rule of inference Modus Ponens (or one much like it) as basic in our reasoning. By contrast, we are not justified in employing a rule of inference that permits inferring to some difficult mathematical theorem from the relevant axioms in a single step. Such an inferential step is intuitively “too large” to count as justified. What accounts for this difference? In this paper, I canvass several possible explanations. I argue that the most promising approach is to appeal to features like usefulness or indispensability to important or required cognitive projects. On the resulting view, whether an inferential step counts as large or small depends on the importance of the relevant rule of inference in our thought

Gödel’s Disjunction: The Scope and Limits of Mathematical Knowledge

acceptedVersionNon peer reviewe

Using the Proteus virtual environment to train future IT professionals

Abstract. Based on literature review it was established that the use of augmented reality as an innovative technology of student training occurs in following directions: 3D image rendering; recognition and marking of real objects; interaction of a virtual object with a person in real time. The main advantages of using AR and VR in the educational process are highlighted: clarity, ability to simulate processes and phenomena, integration of educational disciplines, building an open education system, increasing motivation for learning, etc. It has been found that in the field of physical process modelling the Proteus Physics Laboratory is a popular example of augmented reality. Using the Proteus environment allows to visualize the functioning of the functional nodes of the computing system at the micro level. This is especially important for programming systems with limited resources, such as microcontrollers in the process of training future IT professionals. Experiment took place at Borys Grinchenko Kyiv University and Sumy State Pedagogical University named after A. S. Makarenko with students majoring in Computer Science (field of knowledge is Secondary Education (Informatics)). It was found that computer modelling has a positive effect on mastering the basics of microelectronics. The ways of further scientific researches for grounding, development and experimental verification of forms, methods and augmented reality, and can be used in the professional training of future IT specialists are outlined in the article