This translation of four of Plato's dialogues brings these classic texts alive for modern readers. Allen introduces and comments on the dialogues in an accessible way, inviting the reader to re-examine the issues Plato continually raises.

Perhaps even more radically than under the criticism of the ‘Maîtres du soupçon’, a whole world goes down in Greek comedy. Not only traditional religion, but also ethical life and finally even reason itself seem to be affected by the all-destroying power of laughter.The title of Aristophanes’ famous play ‘The Clouds’ has a symbolic meaning: in the comedy, Greek ethical life dissolves into a vanishing mist. Behind the player’s mask hides the principle of this total decomposition: the autonomous, selfconfident individual. (...) This event does not only have a theatrical meaning. It does not only exist in the artist’s imagination. It concerns a whole nation, a whole culture. The comedy is an expression of the way society understands itself. It represents in an aesthetic way the fact that the individual human being sees himself as ‘principium essendi et cognoscendi’ of everything. The comedy voices a new truth, namely that all truth begins and ends with man. The gods — symbols of truth and actuality- have dissolved in the shamelessness of a laughter, which does not halt for anything anymore. Formulated in modern terms: the comedy voices the philosophical principle that from now on the subject will be the reference point of all reality. Long before Descartes’s Cogito, a metaphysics of subjectivity here finds one of its remarkable expressions.At least, that is how Hegel interprets the comedy in his Phenomenology of Spirit. According to him, the destruction of the Greek world announces itself in the comedy. It signals the experience that a certain culture has grown old, that something new is coming. This new actuality will get its first, symbolic expression in the Christian religion. However, this transition is only possible if consciousness undergoes new experiences, by which the self-sufficient and frivolous cheerfulness of the comedy gets lost. In these new experiences the implications of the principle of the autonomous subjectivity, which is decisive for the comedy, come to light. Hegel defines this principle as following: “das Selbst ist das absolute Wesen; das Wesen, das Substanz und an dem das Selbst die Akzidentalität war, ist zum Prädikate herunter gesunken ...”.These new experiences are indicated by a term which is already familiar to the readers of the Phenomenology, namely ‘the unhappy consciousness’. Hegel writes: “We see that this Unhappy Consciousness constitutes the counterpart and the completion of the comic consciousness that is perfectly happy within itself”. The text is clear: the unhappy consciousness is not only that into which the comic consciousness turns. It is at the same time a change in which this consciousness accomplishes itself.The “Self which is for itself the absolute being” could not durably maintain itself in its position. Its “Leichtsinn” makes it “light”, too light to be the substance of everything. Very quickly, it loses its uncomplicated enjoyment of itself and becomes unhappy, even more: it has to become unhappy. I will return to the reason for this “having to” later on. But first, how does Hegel typify this historical experience, which is connected with the origin of Christianity? What does the bitter fruit of Greek comedy consist of? (shrink)

We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. (...) We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using = ${(\vec{x}, \vec{y})}$ have. (shrink)

This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

Analytic philosophy--arguably one of the most important philosophical movements in the twentieth century--has gained a new historical self-consciousness, particularly about its own origins. Between 1880 and 1930, the most important work of its founding figures (Frege, Russell, Moore, Wittgenstein) not only gained attention but flourished. In this collection, fifteen previously unpublished essays explore different facets of this period, with an emphasis on the vital intellectual relationship between Frege and the early Wittgenstein.

Publisher's Foreword As the present book is reissued, The American Mental Health Foundation celebrates its 86th anniversary. Organized in 1924, AMHF is ...

Gottlob Frege and Ludwig Wittgenstein (the later Wittgenstein) are often seen as polar opposites with respect to their fundamental philosophical outlooks: Frege as a paradigmatic "realist", Wittgenstein as a paradigmatic "anti-realist". This opposition is supposed to find its clearest expression with respect to mathematics: Frege is seen as the "arch-platonist", Wittgenstein as some sort of "radical anti-platonist". Furthermore, seeing them as such fits nicely with a widely shared view about their relation: the later Wittgenstein is supposed to have developed his (...) ideas in direct opposition to Frege. The purpose of this paper is to challenge these standard assumptions. I will argue that Frege's and Wittgenstein's basic outlooks have something crucial in common; and I will argue that this is the result of the positive influence Frege had on Wittgenstein. (shrink)

In Frege's writings, the notions of truth, judgment, and objectivity are all prominent and important. This paper explores the close connections between them, together with their ties to further cognate notions, such as those of thought, assertion, inference, logical law, and reason. It is argued that, according to Frege, these notions can only be understood properly together, in their inter-relations. Along the way, interpretations of some especially cryptic Fregean remarks, about objectivity, laws of truth, and reason, are offered, and seemingly (...) opposed "realist" and "idealist" strands in his position reconciled. (shrink)

Gottlob Frege is often called a "platonist". In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in The Foundations of Arithmetic (1884), supplemented by a few asides on Basic Laws of (...) Arithmetic (1893/1903) and "Thoughts" (1918). My goal is to clarify in which sense the Frege of Foundations and Basic Laws is a platonist concerning the natural numbers.1.. (shrink)