In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted (...) a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, (...) in fact, reasonable and related to Gödel’s proof. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...) with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. (shrink)

This dissertation is a discussion of Wittgenstein's later philosophy. In it, Wittgenstein's answer to the "going on problem" will be presented: I will give his reply to the skeptic who denies that rule-following is possible. Chapter One will describe this problem. Chapter Two will give Wittgenstein's answer to it. Chapter Three will show how Wittgenstein used this answer to give the standards of mathematics. Chapter Four will compare Wittgenstein's answer to the going on problem to Plato's. Chapter Five will describe (...) Kant's influence on Wittgenstein's later philosophy. The leitmotif of these chapters will be that the way human beings apply a rule is the source of justification for its application. 1. (shrink)

This thesis explores the significance of Godel's Theorem for an understanding of law as rules, and of legal adjudication as rule-following. It argues that Godel's Theorem, read through Wittgenstein's understanding of rules and language as a contextual activity, and through Derrida's account of 'undecidability,' offers an alternative account of the relationship of judging to justice. Instead of providing support for the 'indeterminacy' claim, Godel's Theorem illuminates the predicament of undecidability that structures any interpretation and every legal decision, and which constitutes (...) the opening to justice. The first argument in this thesis examines Godel's proof, Wittgenstein's views on rules, and Derrida's undecidability, as manifestations of a common concern with the limits of what can be formalized. The meta-argument examines their misinterpretation and misappropriation within legal theory as a case study of just what they mean about meaning, context, and justice as necessarily co-implicated. (shrink)