Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

I first characterize a moral mistake in coercion. The principle of independence with which I criticize coercion seems also to condemn exchange. I propose an account of exchange from which it follows that exchange upholds independence after all. In support of that account I argue that, of the accounts of exchange that occur to me, only this one has the consequence that, on general assumptions, a person can take part in exchange while acting, intending, and believing with sufficient reason. I (...) argue that the hiring of very poor people by very rich people for labor from which the rich draw a substantial surplus does not give rise to an exchange of this kind. These instances of the wage labor relation resemble coercion insofar as they violate independence. (shrink)

Explication is the conceptual cornerstone of Carnap’s approach to the methodology of scientific analysis. From a philosophical point of view, it gives rise to a number of questions that need to be addressed, but which do not seem to have been fully addressed by Carnap himself. This paper reconsiders Carnapian explication by comparing it to a different approach: the ‘formalisms as cognitive tools’ conception. The comparison allows us to discuss a number of aspects of the Carnapian methodology, as well as (...) issues pertaining to formalization in general. We start by introducing Carnap’s conception of explication, arguing that there is a tension between his proposed criteria of fruitfulness and similarity; we also argue that his further desideratum of exactness is less crucial than might appear at first. We then bring in the general idea of formalisms as cognitive tools, mainly by discussing the reliability of so-called statistical prediction rules, i.e. simple algorithms used to make predictions across a range of areas. SPRs allow for a concrete instantiation of Carnap’s fruitfulness desideratum, which is arguably the most important desideratum for him. Finally, we elaborate on what we call the ‘paradox of adequate formalization’, which for the Carnapian corresponds to the tension between similarity and fruitfulness. We conclude by noting that formalization is an inherently paradoxical enterprise in general, but one worth engaging in given the ‘cognitive boost’ it affords as a tool for discovery. (shrink)

Analytic philosophy - arguably the most important philosophical movement in the 20th century - has gained a new historical self-consciousness, particularly about it's own origins. The period between 1880 and 1930 saw the most important work of its founding figures (Frege, Russell, Moore, Wittgenstein) take root and flourish. The fifteen previously-unpublished essays in this collection explore different facets of this period, with an emphasis on the vital intellectual relationship between Frege and the early Wittgenstein.

For both Gottlob Frege and Bertrand Russell, providing a philosophical account of the concept of number was a central goal, pursued along similar logicist lines. In the present paper, I want to focus on a particular aspect of their accounts: their definitions, or re-constructions, of the natural numbers as equivalence classes of equinumerous classes. In other words, I want to examine what is often called the ‘Frege-Russell conception of the natural numbers’ or, more briefly, the Frege-Russell numbers. My main concern (...) will be to determine the precise sense in which this conception was, or could be, meant to constitute an analysis. I will be mostly concerned with Frege’s views on the matter; but Russell will come up along the way, for illustration and comparison, as will some recent neo-Fregean suggestions. (shrink)

According to the acousmatic thesis defended by Roger Scruton and others, to hear sounds as music is to divorce them from the source or cause of their production. Non-acousmatic experience involves attending to the worldly cause of the sound; in acousmatic experience, sound is detached from that cause. The acousmatic concept originates with Pythagoras, and was developed in the work of 20th century musique concrète composers such as Pierre Schaeffer. The concept yields important insights into the nature of musical experience, (...) but Scruton's version of the acousmatic thesis cannot overcome objections arising from timbral and spatial aspects of music, which seem to relate sounds to the circumstances of their production. These objections arise in part from music's status as a performing art rooted in human gesture and behaviour. Hence I defend a two-fold thesis of "hearing-in", which parallels Richard Wollheim's concept of "seeing-in": both acousmatic and.. (shrink)

It is well known that Frege and his writings were an important influence on Wittgenstein. There is no agreement, however, on the nature and scope of this influence. In this paper, I clarify the situation in three related ways: by tracing Frege's and Wittgenstein's actual interactions, i.e., their face‐to‐face meetings and their correspondence between 1911 and 1920; by documenting Wittgenstein's continued study of Frege's writings, until the very end of his life in 1951; and by constructing, on that basis, a (...) new framework for understanding the themes that connect Wittgenstein to Frege, both in his early and his later works. (shrink)

La nature de la conscience est au centre de la discussion actuelle sur la personne humaine. Bien que certains philosophes fassent de la conscience la clef fondamentale et de toute l'épistémologie, la plupart des scientifiques la réduisent aux intéractions complexes du cerveau. Le présent article tire sa matière de l'analyse que saint Thomas d'Aquin fait de cette notion dans son De Veritate . Il caractérise la conscience en termes de connaissance et d'application de la connaissance à l'agir. L'A. cherche à (...) donner une définition pour montrer que la conscience dépend directement d'un syllogisme pratique. (shrink)

In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style ofPrincipia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics of (...) axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition and two proponents of the first-order tradition, we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory. (shrink)

In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics (...) of axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition and two proponents of the first-order tradition, we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory. (shrink)

Steve Awodey and Erich H. Reck. Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.

This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)