Papers by Ásgeir Berg Matthíasson
Inquiry, 2022
In this paper, I present a game-theoretic solution to the rule-following paradox in terms of what... more In this paper, I present a game-theoretic solution to the rule-following paradox in terms of what I will call basic constitutive practices. The structure of such a practice P constitutes what it is to take part in P by defining the correctness conditions of our most basic concepts as those actions that lie on the correlated equilibrium of P itself. Accordingly, an agent S meant addition by his use of the term ‘+’ because S is taking part in a basic constitutive practice of adding where quus-like answers are ruled out by not lying on the equilibrium. The resulting picture of language will preserve the objectivity and correctness conditions of meaning, all the while providing room for the community as a whole to make a mistake. I also argue that by accepting the account presented, we have a strong reason to reject the idea that language is rule-governed.
British Journal for the History of Philosophy, 2020
In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they... more 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, for example in building a bridge, 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 to inconsistency, and thus contradictions do not have any special status as a thing to be avoided.
MSc. Thesis by Ásgeir Berg Matthíasson
This thesis offers a critical overview of the debate on Wittgenstein’s
remarks on Gödel. These r... more This thesis offers a critical overview of the debate on Wittgenstein’s
remarks on Gödel. These remarks—which have since their publication been the source of much controversy—were said by early commentators to show that (a) Wittgenstein did not understand the role consistency plays in the proof of Gödel’s theorem and logic in general, and that (b) he mistakenly thought that a natural language interpretation of the Gödel sentence was necessary to establish the incompleteness of Principia Mathematica.
Later commentators have been more sympathetic to Wittgenstein’s
remarks and have with few exceptions denied both claims. We examine their interpretations and evaluate their cogency and exegetical value.
M.Litt Thesis by Ásgeir Berg Matthíasson
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Papers by Ásgeir Berg Matthíasson
MSc. Thesis by Ásgeir Berg Matthíasson
remarks on Gödel. These remarks—which have since their publication been the source of much controversy—were said by early commentators to show that (a) Wittgenstein did not understand the role consistency plays in the proof of Gödel’s theorem and logic in general, and that (b) he mistakenly thought that a natural language interpretation of the Gödel sentence was necessary to establish the incompleteness of Principia Mathematica.
Later commentators have been more sympathetic to Wittgenstein’s
remarks and have with few exceptions denied both claims. We examine their interpretations and evaluate their cogency and exegetical value.
M.Litt Thesis by Ásgeir Berg Matthíasson
remarks on Gödel. These remarks—which have since their publication been the source of much controversy—were said by early commentators to show that (a) Wittgenstein did not understand the role consistency plays in the proof of Gödel’s theorem and logic in general, and that (b) he mistakenly thought that a natural language interpretation of the Gödel sentence was necessary to establish the incompleteness of Principia Mathematica.
Later commentators have been more sympathetic to Wittgenstein’s
remarks and have with few exceptions denied both claims. We examine their interpretations and evaluate their cogency and exegetical value.