Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of the discipline, (...) combining both historical and systematic analyses. -/- The debates this text surveys are among the latest and most urgent ones: the crisis of foundations in mathematics and the birth of the decision problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational experiments. By covering these topics, On the Foundations of Computing provides a much-needed resource to contextualize these foundational issues. -/- For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to figure out the challenges of its future. (shrink)

This book is a systematic analysis of John R. Searle’s philosophy of mind. Searle’s view of mind, as a set of subjective _and_ biologically embodied processes, can account for our being part of nature _qua_ mindful beings. This model finds support in neuroscience and offers reliable solutions to the problems of consciousness, mental causation, and the self.

No paradox exists in the fact that, in the Special Relativity, for the mass of a material body, considered in motion at constant speed, whose measure is u, the formula: m = m0/√ can be written, while for a photon the same formula holds, when between its source and the observer a state of relative motion at constant speed, whose measure is u, exists and it is observed along the direction perpendicular to the direction of his speed.

This paper proposes a critical analysis of that interpretation of the Nāgārjunian doctrine of the two truths as summarized—by both Mark Siderits and Jay L. Garfield—in the formula: “the ultimate truth is that there is no ultimate truth”. This ‘semantic reading’ of Nāgārjuna’s theory, despite its importance as a criticism of the ‘metaphysical interpretations’, would in itself be defective and improbable. Indeed, firstly, semantic interpretation presents a formal defect: it fails to clearly and explicitly express that which it contains logically; (...) the previously mentioned formula must necessarily be completed by: “the conventional truth is that nothing is conventional truth”. Secondly, after having recognized what Siderits’ and Garfield’s analyses contain implicitly, other logical and philological defects in their position emerge: the existence of the ‘conventional’ would appear—despite the efforts of semantic interpreters to demonstrate quite the contrary—definitively inconceivable without the presupposition of something ‘real’; moreover, the number of verses in Nāgārjuna that are in opposition to the semantic interpretation (even if we grant semantic interpreters that these verses do not justify a metaphysical reconstruction of Nagarjuna’s doctrine) would seem too great and significant to be ignored. (shrink)

This article considers the function and value of the mythos in Plato's Statesman. As first, I recall the context of the story and its function within the framework of diairetic inquiry about the definition of the real politician. Secondly, I point out that the formulation of the myth is based on a series of traditional stories to which a historical-reconstructive method is applied. I then highlight the ways of reasoning used by the characters in order to reconstruct a rational and (...) plausible account from the mythical tradition. Finally, I try to show that the story, even though it cannot reach the truth of the most stable objects of knowledge, displays a certain degree of plausibility, based on the internal coherence, on the respect of a series of principles admitted as true and, eventually, on its correspondence with the mythical tradition. (shrink)

Focused sequent calculi are a refinement of sequent calculi, where additional side-conditions on the applicability of inference rules force the implementation of a proof search strategy. Focused cut-free proofs exhibit a special normal form that is used for defining identity of sequent calculi proofs. We introduce a novel focused display calculus fD.LG and a fully polarized algebraic semantics FP.LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FP.LG}$$\end{document} for Lambek–Grishin logic by generalizing the theory of multi-type calculi and their (...) algebraic semantics with heterogenous consequence relations. The calculus fD.LG has strong focalization and it is sound and complete w.r.t. FP.LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FP.LG}$$\end{document}. This completeness result is in a sense stronger than completeness with respect to standard polarized algebraic semantics, insofar as we do not need to quotient over proofs with consecutive applications of shifts over the same formula. We also show a number of additional results. fD.LG is sound and complete w.r.t. LG-algebras: this amounts to a semantic proof of the so-called completeness of focusing, given that the standard (display) sequent calculus for Lambek–Grishin logic is complete w.r.t. LG-algebras. fD.LG and the focused calculus fLG of Moortgat and Moot are equivalent with respect to proofs, indeed there is an effective translation from fLG-derivations to fD.LG-derivations and vice versa: this provides the link with operational semantics, given that every fLG-derivation is in a Curry–Howard correspondence with a directional λ¯μμ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{\lambda }\mu \widetilde{\mu }$$\end{document}-term. (shrink)

In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.

This paper proposes an interpretation of Nāgārjuna’s doctrine of the two truths that considers saṃvṛti and paramārtha-satya two visions of reality on which the Buddhas, for soteriological and pedagogical reasons, build teachings of two types: respectively in agreement with (for example, the teaching of the Four Noble Truths) or in contrast to (for example, the teaching of emptiness) the category of svabhāva. The early sections of the article show to what extent the various current interpretations of the Nāgārjunian doctrine of (...) the dve satye—despite their sometimes even macroscopic differences—have a common tendency to consider the notion of śūnyatā as a teaching not based on, but equivalent to supreme truth. This equivalence—philologically questionable—leads to interpretative paths that prove inevitably aporetic: indeed, according to whether the interpretation of śūnyatā is ‘metaphysical’ or ‘anti-metaphysical’, it gives rise to readings of Nāgārjuna’s thought incompatible, respectively, with anti-metaphysical and realistic types of verses traceable in the works of the author of the Mūla-madhyamaka-kārikā (MMK). On the contrary, by giving more emphasis to the expression samupāśritya (“based on”), which recurs in MMK.24.8, and therefore, by epistemologically separating the notion of śūnyatā from the notion of paramārtha-satya (and of some of its conceptual equivalents such as nirvāṇa, tattva and dharmatā), we may obtain an interpretation—at once realistic and anti-metaphysical—of the theory of the two truths compatible with the vast majority (or even totality) of Nāgārjuna’s verses. (shrink)