This paper discusses an earlier emendation to fr. 54 GRF Funaioli from Varro's De bibliothecis and argues that, while the text et citro refers to cedar oil, it should not be emended to et cedro. A comparison with a passage from Pliny the Elder (HN 13.86) is used to support the view presented in the article.

Serendipities is a careful unraveling of the fabulous and the false, a brilliant exposition of how unanticipated truths often spring from false ideas. From Leibniz's belief that the I Ching illustrated the principles of calculus to Marco Polo's mistaking a rhinoceros for a unicorn, Umberto Eco offers a dazzling tour of intellectual history, illuminating the ways in which we project the familiar onto the strange to make sense of the world. Uncovering layers of mistakes that have shaped human history, (...) Eco offers with wit and clarity such instances as Columbus's voyage to the New World, the fictions that grew around the Rosicrucians and Knights Templar, and the linguistic endeavors to recreate the language of Babel, to show how serendipities can evolve out of mistakes. With erudition, anecdotes, and scholarly rigor, this new collection of essays is sure to entertain and enlighten any reader with a passion for the curious history of languages and ideas. (shrink)

In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete axiomatisation for (...) this class, without having the number of individuals or alternatives specified in the language. We are able to express classical axiomatic requirements in our first-order language, giving formal axioms for three classical theorems of preference aggregation by Arrow, by Sen, and by Kirman and Sondermann. We explore to what extent such theorems can be formally derived from our axiomatisations, obtaining positive results for Sen’s Theorem and the Kirman-Sondermann Theorem. For the case of Arrow’s Theorem, which does not apply in the case of infinite societies, we have to resort to fixing the number of individuals with an additional axiom. In the long run, we hope that our approach to formalisation can serve as the basis for a fully automated proof of classical and new theorems in social choice theory. (shrink)

Essays discuss poetry, communication, television, form, aesthetics, bad taste, and art.

This is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic |$FL_{ew}$| (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. |$FL_{ew}$|-algebras) that includes both Heyting and Nelson algebras (...) and can be characterized algebraically in several alternative ways. The present paper focuses on the algebraic counterpart (a class we dub quasi-Nelson implication algebras, QNI-algebras) of the implication–negation fragment of QNL, corresponding to the connectives that witness the algebraizability of QNL. We recall the main known results on QNI-algebras and establish a number of new ones. Among these, we show that QNI-algebras form a congruence-distributive variety (Cor. 3.15) that enjoys equationally definable principal congruences and the strong congruence extension property (Prop. 3.16); we also characterize the subdirectly irreducible QNI-algebras in terms of the underlying poset structure (Thm. 4.23). Most of these results are obtained thanks to twist representations for QNI-algebras, which generalize the known ones for Nelson and quasi-Nelson algebras; we further introduce a Hilbert-style calculus that is algebraizable and has the variety of QNI-algebras as its equivalent algebraic semantics. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite logical (...) matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

In this book, the Italian novelist and philosopher Umberto Eco presents a learned summary of medieval aesthetic ideas.

In a companion volume to his "History of Beauty," the renowned philosopher and cultural critic analyzes our attraction to the gruesome, horrific, and repellant in visual culture and the arts, drawing on abundant examples of painting and sculpture, ranging from antiquity to the works of Bosch, Goya, and others.

"Eco wittily and enchantingly develops themes often touched on in his previous works, but he delves deeper into their complex nature... this collection can be read with pleasure by those unversed in semiotic theory." —Times Literary Supplement.