From Traditional Set Theory – that of Cantor, Hilbert , Gödel, Cohen – to Its Necessary Quantum Extension

The original purpose of the present study, 2011, started with a preprint «On the Probable Failure of the Uncountable Power Set Axiom», 1988, is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum — this genuine, even if mostly forgotten today raison d’être of all traditional set-theoretical enterprises to Infinity and beyond, from Georg Cantor to David Hilbert to Kurt Gödel to W. Hugh Woodin to Buzz Lightyear

Is Maddy's naturalism a defensible view of mathematics?

The thesis is an examination of Penelope Maddy's book Naturalism in Mathematics and of the defensibility of the arguments she presents in support of her version of naturalism, with emphasis on the philosophical significance of her work. In Part A I first give an overview of the aim of the book and the methods used to achieve this aim. I then set out and appraise the arguments Maddy advances showing how she supports these arguments with her appeals to historical and current scientific and mathematical practice, I discuss and appraise her comments on the work of the authors she cites and give examples of the way in which she presents her case. I examine the extent to which the work of these authors can be seen to give support to Maddy's arguments. I also examine the validity of her appeals to the analogy between naturalism in science and naturalism in mathematics with reference to her descriptions of scientific practice. In Part B I discuss the objections advanced against Maddy's version of naturalism by contemporary critics of her book, with reference to seven authors in particular, considering the similarities and differences of the approach taken by each to Maddy. I show how their objections fall under two specific heads and appraise the persuasiveness of their criticisms. Finaly, I assess the effect of the objections which can be raised against Maddy's naturalism and examine the question of how compelling they are and whether Maddy's naturalism is still a convincing approach to mathematics in the light of these criticisms

Formal methods and digital systems validation for airborne systems

This report has been prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook. Its purpose is as follows: to outline the technical basis for formal methods in computer science; to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used on board aircraft; and to suggest factors for consideration when formal methods are offered in support of certification. These latter factors assume the context for software development and assurance described in RTCA document DO-178B, 'Software Considerations in Airborne Systems and Equipment Certification,' Dec. 1992

Finitism--an essay on Hilbert's programme

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1991.Includes bibliographical references (p. 213-219).by David Watson Galloway.Ph.D

Virtual Reality: Consciousness Really Explained! (Third Edition)

Employing the ideas of modern mathematics and biology, seen in the context of Ernst Cassirer's "Symbolic Forms, the author presents an entirely new and novel solution to the classical mind-brain problem. This is a "hard" book, I'm sorry, but it is the problem itself, and not me which has made it so. I say that Dennett, and, indeed, the whole of academia is wrong