[1. Without special title] -- [2]. Anastatica.

Since its rediscovery in 1903, the Logica Demonstrativa by Girolamo Saccheri is known in three editions ?1697, 1701, and 1735, the 1735, edition being posthumous. The 1697 edition is without the name of the author. This article calls attention to two unnoticed editions (1696? and 1699), the first one unsigned and the second by ?Carolus Iosephus Saccarellus?, a Saccheri pseudonym. The publishing history of the work has been partially clarified, though a number of problems remain unsolved. Après (...) sa redécouverte in 1903, on connait trois éditions de la Logica demonstrativa par Girolamo Saccheri (1697, 1701, 1735: cette dernière édition après sa mort). L'édition du 1697 est anonyme. L'article veut faire connaitre deux éditions inconnues (1696? et 1699), dont la première est ancore anonyme et la deuxième a comme auteur ?Carolus Saccarellus?, un pseudonyme de Saccheri. Ça éclaircit, en part, les questions liées à l'histoire des éditions de l'oeuvre. Hieronymi Saccherii Logica demonstrativa ex oblivione tracta est a Johannes Vailati, Italiae philosopho, Anno Domini 1903. Ter Logica edita fuit, in commune doctorum virorum opinione, annis Domini 1697, 1701, 1735. Quorum editionum, prima sine nomine auctoris est, postrema eius mortem secuta. Duas autem ignotas Logicae editiones inveni, alteram pariter sine auctoris nomine, alteram quodam Iosepho Saccarello ascriptam, certe ipsius Saccherii alienum nomen. Quae omnia nonnullas quaestiones de Logica demonstrativa illustrant. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's (...) "Introduction" are devoted. At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

I will apply a technique employed by Giovanni Girolamo Saccheri in Logica demonstrative to concisely prove the invalidity of moods of the First Figure of the Theory of the Assertoric Syllogism without appealing to facts outside logic.

One of the key concepts in XVIII century political thought was despotism. Also Diderot utilised this complex idea. According to him, who followed Hobbes and Montesquieu, despotism was the result of the love of power, which was able to bring forth the passion of fear in the society. In this sense, Machiavelli belonged to this line of reflection: like that of Hobbes, his system was intended to show the danger of despotism and to learn the true foundation of natural law. (...) But rethinking this paradox Diderot was led to elaborate a new theory of despotism, no longer based on the mechanism of power. His interpretation of Machiavelli – and Hobbes – had opened up a new perspective, which did not move from the enigma of power – Machiavelli's and Hobbes’ chief concern – but from the nature of subjection. Along this path Diderot came across de la Boëtie's Discours de la servitude volontaire, which explained the origin of despotism in a different way. Despotism was not the result of the passion of fear, but of that of interest. The discussion of these two different ideas of despotism led Diderot to a new perspective from which he answered the problem of liberty in an original way. (shrink)

SummaryThe Enlightened theory of civilisation was expressed through the formula of ‘doux commerce’, a form of commerce which acknowledged the need for the European conquest of non-European lands and nations, and the opportunity to bring European civilisation to other peoples without violence. Montesquieu was the first to express this idea, condemning the Spanish conquest and empire. In the Histoire des deux Indes, this idea was dramatically discussed: Raynal wanted to defend it; Diderot dismantled this project showing that civilisation was but (...) the mask of violent conquest. In this way the latter offered an extraordinary refutation of both Enlightened ideology and its strategy of civilisation. (shrink)

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Benedetto Croce was the author of the most important and original theory of history in the 20th century. His theory was that of ‘absolute historicism’, and this necessarily entailed an acute critique of inherited ideas about the Enlightenment. This article studies both Croce's theoretical analysis of Enlightenment and his historical analysis of the Neapolitan Enlightenment. Croce's interest in the Enlightenment had political as well as philosophical roots. All over Europe in the 1920s and 1930s historical and theoretical research was occurring (...) into in the Age of Enlightenment. The broad goal of such research was to bring forth a new concept of reason, which would have purchase in the contemporary debate about rationalism and irrationalism. This debate, which flourished in the era of totalitarian regimes, raised a series of further questions: What was culture? What was the task of culture in the fight against political irrationalism? What was the relationship between culture and the growth of public opinion? With respect to the latter relationship an important role was played by intellectuals, as evinced by the works of Benda, Max Weber and Croce himself. The genealogy of the modern intelligentsia led again to Enlightenment. In the third part of the article Croce's position on this issue is discussed in the light of his historical researches on Enlightenment by reference to his correspondence with two young historians, Delio Cantimori and Franco Venturi. (shrink)

ABSTRACT This article outlines the concept of the early modern idea of religion through the notion of sacrifice, from Socinus on through Grotius and Spinoza to Diderot’s Encyclopedia. It is generally held that the philosophical representation of religion of the seventeenth century ‘set the stage’ for later Enlightenment philosophers. My argument runs in a different direction. I intend to show that the Enlightenment philosophers’ concept of religious history stemmed not only from the philosophical tradition, but also from their knowledge of (...) antiquarianism. In order to understand the genealogy of the Enlightenment idea of religion it is essential to acknowledge its roots in the antiquarian history of religions of the seventeenth century when a new idea of religious belief emerged with practice of sacrifice at its core. Grotius and the antiquarians inquired into whether religion was a universal phenomenon, what were its categories – such as belief and sacrifice – and the truth and falsehood of these. Diderot considered this history of sacrifice and ceremonies as the fundamental ‘deed’ of the religious experience, which he analysed employing both the philosophical and the historical perspectives through the category of fetishism. (shrink)

v. 1. Compendium logicae. Apologeticus de ratione poeticae artis. Trattato contra li astrologi -- v. 2. Compendium philosophiae naturalis, Compendium philosophiae moralis.

SummaryThe problem of converting the Amerindian world to Catholicism was given a radically new solution, both at a theoretical and a missionary level, by the Jesuit Acosta: since American societies were of a completely different nature to Mediterranean ones, the preaching of the Gospel, too, had to be different from the classical approach. He gave a new definition to both preaching and American societies, especially the latter's religion and social organisation. Acosta's approach to American sauvagerie was pioneering; he conceptualised ideas (...) that had never been thought of before. There existed societies which were neither barbarous nor political (like the empires of Incan Peru and Aztec Mexico), which nonetheless had social organisation. With regard to their religious life, Acosta maintained that cult and belief without faith was not a sign of atheism, but of an early form of religion. These two reassessments gave rise to a new image of the savage society, which attained enormous success, even outside the missionary world. Fitting the theological structure into the secularised theories of radical enlightenment, both Locke and Hume had recourse to the ethnologic aspects which Acosta had set out. (shrink)

Tra gli intellettuali italiani della seconda metà del Novecento, Norberto Bobbio ha giocato un ruolo di grande importanza. Girolamo Cotroneo è intervenuto, spesso in maniera polemica per discutere le posizioni assunte da Bobbio di fronte ai problemi più pressanti del dibattito politico. Ad ognuno degli interventi Bobbio ha replicato con una lettera privata all’autore. Quegli articoli e le lettere di Bobbio sono contenute ora in questo volume che costituisce un prezioso documento per una maggiore conoscenza di taluni aspetti del (...) dibattito politico italiano di un passato recente. (shrink)

This article describes Cosa Nostra bosses’ psychological characteristics starting from research data collected over almost twenty years. Through the use of fragments of interviews to justice collaborators and their wives, children, and sisters-in-law, we analyze the boss’ role and relational context. This article also reports the results of a recent research on the relationship between boss and white-collar workers, carried out through the analysis of environmental tapping recorded at a famous Sicilian Mafia boss’ house: Giuseppe Guttadauro. This research highlights the (...) psychological diversity the relationship between boss and white-collar worker is based on. The analysis of environmental tapping transcriptions has also allowed discovery of the main relational modalities used by the boss and white-collar worker in their conversations. (shrink)