The strongly innovative theory of whole-parts relations outlined by Husserl in his Third logical Investigation—to which he attributed a basic value for his entire phenomenology—has recently attracted a renewed interest. Although many important issues have been clarified (especially by Kit Fine) the subject seems still worth being revisited. To this aim Husserlian universes are introduced. These are lower bounded distributive lattices endowed with a unary operation of defect and a binary relation of isogeneity. Husserl's contents are identified with nonzero elements (...) of a Husserlian universe and the dependence relations among contents are defined and studied starting from the idea that the defect of xis what x needs in order to ‘exist’ i.e., in order to be ‘closed’ with respect to the closure operation defined as the sup of x and its defect. It turns out that there are (at least) eight dependence relations which are worth to be considered. Many other questions concerning the world of contents (among them the proofs of the famous Husserl's Sätze) may now be discussed and clarified. Then the theory of species and genera is developed. Ultimate species (for short: species) are identified with equivalence classes of contents modulo isogeneity, and species in general (for short: genera) are identified with arbitrary unions of species. On the basis of the relation obtaining among two contents when they are isogeneous to two contents the first of which is a part of the second it becomes possible to develop a rather satisfying interpretation of Husserl's theory of the dependencies among species and genera and of the material a priori laws. By strengthening the notion of Husserlian universe into the notion of rigid Husserlian universe, the theory of species and genera obtains a stronger version. Three models of the theory are exhibited. The first one, suggested by combinatorial-topological considerations, identifies contents with finite non-empty sets of natural numbers; the second one identifies contents with non-empty sets of formulas of a formal language; the third one (not totally ‘rigid’) identifies contents with positive integers. (shrink)

We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.

A residuated lattice is said to be integrally closed if it satisfies the quasiequations \ and \, or equivalently, the equations \ and \. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed residuated lattice is integral. It is proved that the mapping \\backslash {\mathrm {e}}\) on any integrally closed residuated lattice is a homomorphism onto a lattice-ordered group. A Glivenko-style property is then established for varieties of integrally closed residuated lattices with respect (...) to varieties of lattice-ordered groups, showing in particular that integrally closed residuated lattices form the largest variety of residuated lattices admitting this property with respect to lattice-ordered groups. The Glivenko property is used to obtain a sequent calculus admitting cut-elimination for the variety of integrally closed residuated lattices and to establish the decidability, indeed PSPACE-completenes, of its equational theory. Finally, these results are related to previous work on BCI-algebras, semi-integral residuated pomonoids, and Casari’s comparative logic. (shrink)

Hermann's Weyl Das Kontinuum has inspired several studies in logic and foundations of mathematics over the last century. The book provides a remarkable reconstruction of a large portion of classical mathematics on a predicative basis. However, diverging interpretations of the predicative system formulated by Weyl have been proposed in the literature. In the present work, I analyze an early formalization of Weyl's ideas proposed by [Casari, E. 1964. Questioni di Filosofia Della Matematica, Milano: Feltrinelli] and compare it with other, (...) more well-known, accounts, such as those proposed respectively by Feferman and Avron. In this way, I fill a gap in the literature on Weyl's predicative mathematics by shedding light on an interpretation that has never been studied. Moreover, Casari's work is plausibly the first systematic reconstruction of Weyl's system. In particular, I highlight the different insights about predicativity that can be found in Weyl's work. Casari's reconstruction focuses on the logical and mathematical processes described by Weyl in the first part of his book. Through the analysis of this unexplored perspective, I shed light on fundamental aspects of Weyl's work and elucidate the alleged ambiguities it presents. In particular, in line with Avron's most recent reconstruction of Weyl's ideas, this analysis supports a stronger conception of predicativity than what is commonly attributed to Weyl in the literature. As a result, this work not only provides an analysis of a neglected interpretation of Das Kontinuum, but also contributes to elucidating Weyl's classical conception of predicativity. (shrink)

Hermann's Weyl Das Kontinuum has inspired several studies in logic and foundations of mathematics over the last century. The book provides a remarkable reconstruction of a large portion of classical mathematics on a predicative basis. However, diverging interpretations of the predicative system formulated by Weyl have been proposed in the literature. In the present work, I analyze an early formalization of Weyl's ideas proposed by [Casari, E. 1964. Questioni di Filosofia Della Matematica, Milano: Feltrinelli] and compare it with other, (...) more well-known, accounts, such as those proposed respectively by Feferman and Avron. In this way, I fill a gap in the literature on Weyl's predicative mathematics by shedding light on an interpretation that has never been studied. Moreover, Casari's work is plausibly the first systematic reconstruction of Weyl's system. In particular, I highlight the different insights about predicativity that can be found in Weyl's work. Casari's reconstruction focuses on the logical and mathematical processes described by Weyl in the first part of his book. Through the analysis of this unexplored perspective, I shed light on fundamental aspects of Weyl's work and elucidate the alleged ambiguities it presents. In particular, in line with Avron's most recent reconstruction of Weyl's ideas, this analysis supports a stronger conception of predicativity than what is commonly attributed to Weyl in the literature. As a result, this work not only provides an analysis of a neglected interpretation of Das Kontinuum, but also contributes to elucidating Weyl's classical conception of predicativity. (shrink)

What is the nature of the intellectual enterprise - general equilibrium analysis - that so many economists regard as the centerpiece of their discipline? In this book, Roy Weintraub considers both the modern history of the analysis, and the methodological puzzles that it, and mathematical economic theory in general, pose. Professor Weintraub argues that previous writings on the history and method of general equilibrium theory have been curiously biased and misleading. He provides a clear and careful presentation of the development (...) of the theory from the 1930s through to the Arrow-Debreu work of the 1950s. This historical analysis is the centre of the book: a case study which permits the author to justify the status of general equilibrium theory in economics and the activity in which economic theorists engage. He argues that previous methodological investigations have been distorted by their use of inappropriate models taken from the philosophy of science that were developed to appraise work in the physical sciences. (shrink)

A szabadság dilemmái -- A megrendült öntudat mítoszai -- Irás az éthoszról.

Throughout the long history of Classic Maya hieroglyphs, a logosyllabic writing system used from the late first millennium BCE through the mid-second millennium CE in southern Mesoamerica, the most commonly recorded phonetic value was the syllable u (/ʔu/). With over a dozen different u hieroglyphs, Classic Maya scribes had more options for recording /ʔu/ than any other syllable or logograph. Cognitive approaches to writing systems typically attribute graphemic variation (i.e., alternation between signs with equivalent linguistic value) to semantic differences like (...) animacy or to non-linguistic factors like identity. Distribution of Classic Maya u hieroglyphs, however, suggests that morphosyntactic context influenced which grapheme scribes wrote and when. This case suggests that scribal knowledge of Classic Maya hieroglyphs included ideas about writing's relationship to language. It also highlights the cognitive relevance of morphosyntax for a writing system's users as they differentiate among graphic signs with identical linguistic denotation. (shrink)

J'examine plusieurs sources selon lesquelles Swyneshed (malgré les prétentions d'Angel D'Ors dans ses articles récents) donne une nova responsio en partie sous forme de la règle « On peut nier une proposition conjonctive après avoir concédé ses deux parties. » Je montre que cette nova responsio est liée à un rejet de la règle « Chaque proposition qui suit de l'ensemble de propositions déjà concédées doit être concédée », et j'attribue ce rejet à une théorie selon laquelle une inférence se (...) base sur le rapport logique entre seulement deux propositions. I examine a number of sources according to which Swyneshed (despite the claims made by Angel D'Ors in his recent articles) does give a nova responsio partly in the form of the rule « One can deny a conjunction whose conjuncts have already been granted. » I show that this nova responsio is linked to a rejection of the rule « Every proposition following from a set of propositions which have already been granted must be granted », and I attribute this rejection to a theory whereby an inference is based on the logical relations between just two propositions. (shrink)

How can we find any satisfying assignment for a Boolean formula that has many satisfying assignments? There exists an obvious randomized algorithm for solving this problem: one can just pick an assignment at random and check the truth value of the formula for this assignment, this is iterated until a satisfying assignment occurs. Does there exist a polynomial-time deterministic algorithm that solves the same problem? This paper presents such an algorithm and shows that its worst-case running time is linear when (...) input formulas are in k-CNF and a fraction of satisfying assignments is greater than a constant. This algorithm is almost the same as the algorithm proposed by Monien and Speckenmeyer in the early 1980s for less than 2n steps 3-SAT decision.Another result of this paper is that if a formula in k-CNF has many satisfying assignments, then there exists a short satisfying assignment, i.e. an assignment of truth values to a small number of variables. The proposed algorithm yields just such a short satisfying assignment. We also show that there exist formulas in general CNF having many satisfying assignments, that have no short satisfying assignments. (shrink)

Across a wide range of legal contexts, E. Thomas Sullivan and Richard S. Frase identify three basic ways that government measures and private remedies have been ...

A scholarly edition of The Clarendon Edition of the Works of John Locke: Correspondence: Letters 1242-1701 by E. S. de Beer. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus.

A scholarly edition of The Clarendon Edition of the Works of John Locke: Correspondence: Letters 2199-2664 by E. S. de Beer. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus.

An awareness of the wide scope of medieval logic and the role it played in university education at all levels, together with the way it was used in writings on both science and theology, is crucial for the historian of medieval thought. The growth of this awareness since the mid-twentieth century is shown by the ongoing expansion of editorial work, together with the discussion of the logic actually found in such prominent authors as Aquinas and Scotus. It has gone hand (...) in hand with the use of developments in modern logic. First came the realization that medieval logic extended beyond basic Aristotelian syllogistic, and could be related to modern developments in propositional and quantificational logic in... (shrink)

A scholarly edition of The Clarendon Edition of the Works of John Locke: Correspondence: Letters 3287-3648 by E. S. de Beer. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus.