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Reflections on Skolem's Paradox
"... In 1922, Thoraf Skolem published a paper titled "Some remarks on Axiomatized Set Theory". The paper presents a new proof of... This dissertation focuses almost exclusively on the first half of this project  i.e., the half which tries to expose an initial tension between Cantor's the ..."
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In 1922, Thoraf Skolem published a paper titled "Some remarks on Axiomatized Set Theory". The paper presents a new proof of... This dissertation focuses almost exclusively on the first half of this project  i.e., the half which tries to expose an initial tension between Cantor's theorem and the LöwenheimSkolem theorem. I argue that, even on quite naive understandings of set theory and model theory, there is no such tension. Hence, Skolem's Paradox is not a genuine paradox, and there is very little reason to worry about (or even to investigate) the more extreme consequences that are supposed to follow from this paradox. The heart of my...
The Grounds for the Modeltheoretic Account of the Logical Properties
 Notre Dame Journal of Formal Logic
, 1993
"... Abstract Quantificational accounts of logical truth and logical consequence aim to reduce these modal concepts to the nonmodal one of generality. A logical truth, for example, is said to be an instance of a "maximally general" statement, a statement whose terms other than variables are &qu ..."
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Abstract Quantificational accounts of logical truth and logical consequence aim to reduce these modal concepts to the nonmodal one of generality. A logical truth, for example, is said to be an instance of a "maximally general" statement, a statement whose terms other than variables are "logical constants." These accounts used to be the objects of severe criticism by philosophers like Ramsey and Wittgenstein. In recent work, Etchemendy has claimed that the currently standard modeltheoretic account of the logical properties is a quantificational account and that it fails for reasons similar to the ones provided by Ramsey and Wittgenstein. He claims that it would fail even if it were propped up by a sensible account of what makes a term a logical constant. In this paper I examine to what extent the modeltheoretic account is a quantificational one, and I defend it against Etchemendy's criticisms. 1 In earlier days of analytic philosophy, Frege and Russell defended an account of the logical properties {logical truth and logical consequence) that was soon severely criticized (and discredited, I would dare to say) by Wittgenstein and
on Truth and Its Definition, in
 Logica ’96 – Proceedings of 10 th International Symposium (Filosofia
, 1997
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Reflections on Consequence
, 1999
"... This paper is not meant to be a "reply to my critics." Such a reply would be of very little interest to any one reader, inasmuch as the critics themselves disagree so sharply on fundamental points, and so the lines of criticism are often at odds with one another. Instead, the paper is mean ..."
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This paper is not meant to be a "reply to my critics." Such a reply would be of very little interest to any one reader, inasmuch as the critics themselves disagree so sharply on fundamental points, and so the lines of criticism are often at odds with one another. Instead, the paper is meant to be a rethinking of my overall argument in light of what I have learned from the various critiques, in particular what I have learned about ways in which CLC was confusing, incomplete, or otherwise misleading. Where appropriate, I indicate in footnotes how points made in this paper relate to specific criticism that has appeared in print
On Tarski on Models
, 2001
"... This paper concerns Tarski's use of the term "model" in his 1936 paper "On the Concept of Logical Consequence." Against several of Tarski's recent defenders, I argue that Tarski employed a nonstandard conception of models in that paper. Against Tarski's detracto ..."
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This paper concerns Tarski's use of the term "model" in his 1936 paper "On the Concept of Logical Consequence." Against several of Tarski's recent defenders, I argue that Tarski employed a nonstandard conception of models in that paper. Against Tarski's detractors, I argue that this nonstandard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski's #rule example.
CARNAP, TARSKI, AND QUINE’S YEAR TOGETHER: LOGIC, MATHEMATICS, AND SCIENCE
, 2006
"... This dissertation was presented by Gregory G. FrostArnold It was defended on ..."
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This dissertation was presented by Gregory G. FrostArnold It was defended on
Panu Raatikainen TRUTH, CORRESPONDENCE, MODELS, AND TARSKI
"... In the early 20 th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies a ..."
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In the early 20 th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition, more philosophical reasons were being given for this aversion. 1 The atmosphere changed dramatically with Alfred Tarski’s pathbreaking contribution. What Tarski did was to show that, assuming that the syntax of the object language is specified exactly enough, and that the metatheory has a certain amount of set theoretic power, 2 one can explicitly define truth in the object language. And what can be explicitly defined can be eliminated. It follows that the defined concept cannot give rise to any inconsistencies (that is, paradoxes). This gave new respectability to the concept of truth and related notions. Nevertheless, philosophers ’ judgements on the nature and philosophical relevance of Tarski’s work have varied. It is my aim here to review and evaluate some threads in this debate. 1 For more of the historical background, see e.g. Niiniluoto (1999b), Sluga (1999), Wole�ski
Tarski’s influence on computer science
"... The following is the text of an invited lecture for the LICS 2005 meeting held in ..."
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The following is the text of an invited lecture for the LICS 2005 meeting held in