Philosophy of Computer Science: An Introductory Course

There are many branches of philosophy called “the philosophy of X,” where X = disciplines ranging from history to physics. The philosophy of artificial intelligence has a long history, and there are many courses and texts with that title. Surprisingly, the philosophy of computer science is not nearly as well-developed. This article proposes topics that might constitute the philosophy of computer science and describes a course covering those topics, along with suggested readings and assignments

Relating Turing's Formula and Zipf's Law

An asymptote is derived from Turing's local reestimation formula for population frequencies, and a local reestimation formula is derived from Zipf's law for the asymptotic behavior of population frequencies. The two are shown to be qualitatively different asymptotically, but nevertheless to be instances of a common class of reestimation-formula-asymptote pairs, in which they constitute the upper and lower bounds of the convergence region of the cumulative of the frequency function, as rank tends to infinity. The results demonstrate that Turing's formula is qualitatively different from the various extensions to Zipf's law, and suggest that it smooths the frequency estimates towards a geometric distribution.Comment: 9 pages, uuencoded, gzipped PostScript; some typos remove

Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?

Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general, scientific, discourse cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic is verifiably complete. We show how some paradoxical concepts of Quantum mechanics can be expressed, and interpreted, naturally under a constructive definition of mathematical truth.Comment: 73 pages; this is an updated version of the NQ essay; an HTML version is available at http://alixcomsi.com/Do_Goedel_incompleteness_theorems.ht

Computational Natural Philosophy: A Thread from Presocratics through Turing to ChatGPT

Modern computational natural philosophy conceptualizes the universe in terms of information and computation, establishing a framework for the study of cognition and intelligence. Despite some critiques, this computational perspective has significantly influenced our understanding of the natural world, leading to the development of AI systems like ChatGPT based on deep neural networks. Advancements in this domain have been facilitated by interdisciplinary research, integrating knowledge from multiple fields to simulate complex systems. Large Language Models (LLMs), such as ChatGPT, represent this approach's capabilities, utilizing reinforcement learning with human feedback (RLHF). Current research initiatives aim to integrate neural networks with symbolic computing, introducing a new generation of hybrid computational models.Comment: 17 page

Numerical modelling of dynamical systems in isothermal chemical reactions and morphogenesis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Mathematical models of isothermal chemical systems in reactor problems and Turing's theory of morphogenesis with an application in sea-shell patterning are studied. The reaction-diffusion systems describing these models are solved numerically. First- and second-order difference schemes are developed, which are economical and reliable in comparison to classical numerical methods. The linearization process decouples the reaction-diffusion equations thereby allowing the use of different time steps for each differential equation, which may be large due to the excellent stability properties of the methods. The methods avoid having to solve a non-linear algebraic system at each time step. The schemes are suitable for implementation on a parallel machine.This study is funded by the University of Dokuz Eylul