Cohabiting with the Logical Paradoxes: A Negative Assessment and a Proposal

At the commonsensical level of the manifest image, we seem to take for granted logical laws of all sorts, including classical logic (CL) and naive principles of truth and predication (TP), which, however, generate logical paradoxes such as the liar, Russell’s paradox and Curry’s paradox. The formal logic of the scientific image comes to the rescue by proposing many competing formal systems that restore consistency, by sacrificing either principles of CL or principles of TP. We wish to explore a different path, which aims at saving both CL and TP, and deals with the paradoxes when they come to the fore, without swallowing contradictions or explosion. We consider the viability of Batens’ Inconsistency-Adaptive Logic (IAL) to pursue this goal and we end up with a negative assessment. We then sketch an alternative proposal that incorporates IAL’s distinction between provisional and final derivability

A new bridge principle for the normativity of logic

Logic appears to be normative for rational belief. The thesis of the normativity of logic holds that indeed logic has such a normative status. Gilbert Harman has questioned it, thereby giving rise to what has been called “Harman’s skeptical challenge”. MacFarlane has clarified that in order to answer this challenge and support the normativity of logic, one needs a “bridge principle” that appropriately connects logical entailments and norms for belief, as well as relevant desiderata for the evaluation of candidate bridge principles. Steinberger has identified a list of desiderata, on the basis of which he has proposed his own bridge principle and shown the inadequacy of previous proposals. This paper argues that Steinberger’s list is in need of revision and his principle is unsatisfactory, and then puts forward a revised list of desiderata and a new bridge principle in support of the normativity of logic

Properties

Panorama aggiornato delle principali teorie filosofiche su propriet\ue0 e relazioni intese come universal

Properties

survey of major approaches to properties understood as universal

The Lambda Calculus

The λ-calculus is, at heart, a simple notation for functions and application. The main ideas are applying a function to an argument and forming functions by abstraction. The syntax of basic λ-calculus is quite sparse, making it an elegant, focused notation for representing functions. Functions and arguments are on a par with one another. The result is a non-extensional theory of functions as rules of computation, contrasting with an extensional theory of functions as sets of ordered pairs. Despite its sparse syntax, the expressiveness and flexibility of the λ-calculus make it a cornucopia of logic and mathematics. This entry develops some of the central highlights of the field and prepares the reader for further study of the subject and its applications in philosophy, linguistics, computer science, and logic

Singular reference. A descriptivist perspective

Singular reference to ourselves and the ordinary objects surrounding us is a most crucial philosophical topic, for it looms large in any attempt to understand how language and mind connect to the world. This book explains in detail why in the past philosophers such as Frege, Russell and Reichenbach have favoured a descriptivist approach to this matter and why in more recent times Donnellan, Kripke, Kaplan and others have rather favoured a referentialist standpoint. The now dominant referentialist theories however still have a hard time in addressing propositional attitudes and empty singular terms. Here a way out of this difficulty emerges in an approach that incorporates aspects of the old-fashioned descriptivist views of Frege, Russell and Reichenbach without succumbing to the anti-descriptivist arguments that back up the current referentialist trend. The resulting theory features a novel approach to the semantics and pragmatics of determiner phrases, definite descriptions, proper names and indexicals, all treated in uniform fashion in both their anaphoric and non-anaphoric uses. This work will be of interest to researchers in philosophy of language, philosophy of mind and theoretical linguistics