Consistency with the formal Church’s thesis, for short CT, and the axiom of choice, for short AC, was one of the requirements asked to be satisfied by the intensional level of a two-level foundation for constructive mathematics as proposed by Maietti and Sambin From sets and types to topology and analysis: practicable foundations for constructive mathematics, Oxford University Press, Oxford, 2005). Here we show that this is the case for the intensional level of the two-level Minimalist Foundation, for short MF, (...) completed in 2009 by the second author. The intensional level of MF consists of an intensional type theory à la Martin-Löf, called mTT. The consistency of mTT with CT and AC is obtained by showing the consistency with the formal Church’s thesis of a fragment of intensional Martin-Löf’s type theory, called \, where mTT can be easily interpreted. Then to show the consistency of \ with CT we interpret it within Feferman’s predicative theory of non-iterative fixpoints \ by extending the well known Kleene’s realizability semantics of intuitionistic arithmetics so that CT is trivially validated. More in detail the fragment \ we interpret consists of first order intensional Martin-Löf’s type theory with one universe and with explicit substitution rules in place of usual equality rules preserving type constructors -rule which is not valid in our realizability semantics). A key difficulty encountered in our interpretation was to use the right interpretation of lambda abstraction in the applicative structure of natural numbers in order to model all the equality rules of \ correctly. In particular the universe of \ is modelled by means of \-fixpoints following a technique due first to Aczel and used by Feferman and Beeson. (shrink)

Roscoe Pound, in the introduction, gives a panorama of the various schools of legal philosophy, & places natural law in its proper perspective relative to ...

This note concerns the model theoretic properties of logics extending the first-order logic with monadic second-order variables equipped with the stationarity quantifier. The eight variations of the strong downward Löwenheim–Skolem Theorem down to <ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<\aleph _2$$\end{document} for this logic with the interpretation of second-order variables as countable subsets of the structures are classified into four principles. The strongest of these four is shown to be equivalent to the conjunction of CH and the (...) Diagonal Reflection Principle for internally clubness of S. Cox. We show that a further strengthening of this SDLS and its variations follow from the Game Reflection Principle of B. König and its generalizations. (shrink)

"Contents: " "Man Without Letters." Newton, the Enigma. Paolo Toscanelli and His Friends. Alessandro Volta. Galileo Today. Necessity, Contingency, and Natural Law. Prologue to Parmenides. Galileo and Oppenheimer. The Role of Art in the Scientific Renaissance. The Italian Novel Today--A Note on Realism. The Seventeenth-Century Legacy: Our Mirror of Being. Philolaos in Limbo, Or: What Happened to the Pythagoreans? Paralipomena of the Future. Vico and Descartes. Eudodux and Plato: A Study in Chronology. "Scientific Rationalism." Einstein (pour le decennal de sa (...) mort). Les Grandes Doctrines Cosmologiques. De Bruno a Leibnitz. Postface a Galilee; Les Suites de l'Affaire. La Storia da Riscrivere. Fato Antico--Fato Moderno. Salvemini. Il Rovescio della Medaglia. (shrink)

This title is a book of three richly detailed treatments of the myth of Kore. Kore, also called Persephone and referred to poetically by the Greeks as 'the unspeakable girl', was the daughter of Dermeter and Zeus who was abducted by Hades and made queen of the netherworld.

Continuing, we study the Strong Downward Löwenheim–Skolem Theorems of the stationary logic and their variations. In Fuchino et al. it has been shown that the SDLS for the ordinary stationary logic with weak second-order parameters \. This SDLS is shown to be equivalent to an internal version of the Diagonal Reflection Principle down to an internally stationary set of size \. We also consider a version of the stationary logic and show that the SDLS for this logic in internal interpretation (...) \\) for reflection down to \ is consistent under the assumption of the consistency of ZFC \ “the existence of a supercompact cardinal” and this SDLS implies that the continuum is weakly Mahlo. These three “axioms” in terms of SDLS are consequences of three instances of a strengthening of generic supercompactness which we call Laver-generic supercompactness. Existence of a Laver-generic supercompact cardinal in each of these three instances also fixes the cardinality of the continuum to be \ or \ or very large respectively. We also show that the existence of one of these generic large cardinals implies the “\” version of the corresponding forcing axiom. (shrink)

Apparently, aiming to comply with the norm ‘Believe that P if and only if the proposition that P is true’ can hardly differ from aiming to comply with the norm ‘Believe that P if and only if the proposition that P is epistemically justified’. So one may be tempted to agree with Richard Rorty that the distinction between truth and justification is pragmatically useless because it cannot make any difference ‘when the question is about what I should believe now’. I (...) resist this conclusion by arguing that the distinction between truth and justification is pragmatically useful even if the two properties are indeed normatively coincident. The argument I offer turns on the claim that truth plays an explanatory role that justification is inherently incapable of playing. However, my contention is not just that the distinction between truth and justification is pragmatically useful because truth is a bona fide explanatory notion. It is that the distinction between truth and justification is pragmatically useful because the realization that the former plays an explanatory role that the latter is inherently incapable of playing gives access to reasons which would otherwise escape our attention. If truth is a bona fide explanatory notion, the distinction between truth and justification is pragmatically useful because it is precisely when the question is about what I should believe now that attending to such a distinction will often make a difference – and it will make a difference even if the two properties are in fact normatively coincident. (shrink)

Low Power Society is a new approach to social complexes. It is not about slow scale but fast, it is not about absence of power but intense power. It is a possible answer to the negative aspects of our present globalization. The archetype (C.G. Jung) of this concept-paradigm is Eros or, from another point of view, HermAfrEros - a synthesis of Hermes, Aphrodite and Eros.

Semblanza de G. Tagliacozzo a través de las distintas voces que, desde su infancia hasta su muerte, lo llamaron en su vida: las primeras vocaciones de grandeza , las voces de la academia , la voz de América , la impelente voz de Vico , la voz de los caminos que la naturaleza recorre .Semblance of G. Tagliacozzo through the voices that he followed from his younger age to his death: the first calls for greatness , the voices of academy (...) , the voice of America , the impelling voice of Vico , and the voice of the ways that nature runs. (shrink)

Giorgio Levi Della Vida (1886-1967) was not only an eminent Islamologist, belonging to that tradition of Italian Oriental studies that stretches from Ignazio Guidi to Leone Caetani, Carlo Alfonso Nallino and Francesco Gabrieli - he was also a man with solid roots in his own time. He taught in Naples and Rome, then for the ten years 1939-1948 at the University of Pennsylvania. He was one of the few university teachers who, when the oath of loyalty to the Italian (...) fascist regime was introduced, in October 1931, opted not to accept that act of submission. (shrink)

How and why did experience and knowledge become separated? Is it possible to talk of an infancy of experience, a "dumb" experience? For Walter Benjamin, the "poverty of experience" was a characteristic of modernity, originating in the catastrophe of the First World War. For Giorgio Agamben, the Italian editor of Benjamin's complete works, the destruction of experience no longer needs catastrophes: daily life in any modern city will suffice. Agamben's profound and radical exploration of language, infancy, and everyday life (...) traces concepts of experience through Kant, Hegel, Husserl and Benveniste. In doing so he elaborates a theory of infancy that throws new light on a number of major themes in contemporary thought: the anthropological opposition between nature and culture; the linguistic opposition between speech and language; the birth of the subject and the appearance of the unconscious. Agamben goes on to consider time and history; the Marxist notion of base and superstructure (via a careful reading of the famous Adorno–Benjamin correspondence on Baudelaire's Paris); and the difference between rituals and games. Beautifully written, erudite and provocative, these essays will be of great interest to students of philosophy, linguistics, anthropology and politics. (shrink)