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  1. Jeffrey Ketland & Panu Raatikainen, Truth and Provability Again.
    Lucas and Redhead ([2007]) announce that they will defend the views of Redhead ([2004]) against the argument by Panu Raatikainen ([2005]). They certainly re-state the main claims of Redhead ([2004]), but they do not give any real arguments in their favour, and do not provide anything that would save Redhead’s argument from the serious problems pointed out in (Raatikainen [2005]). Instead, Lucas and Redhead make a number of seemingly irrelevant points, perhaps indicating a failure to understand the logico-mathematical points at (...)
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  2. Jeffrey Ketland, The Model Theoretic Conception of Scientific Theories.
    Ordinarily, in mathematical and scientific practice, the notion of a “theory” is understood as follows: (SCT) Standard Conception of Theories : A theory T is a collection of statements, propositions, conjectures, etc. A theory claims that things are thus and so. The theory may be true, and may be false. A theory T is true if things are as T says they are, and T is false if things are not as T says they are. One can make this Aristotelian (...)
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  3. Jeffrey Ketland, How Weak is the T-Scheme?
    Theorem 1 of Ketland 1999 is not quite correct as stated. The theorem would imply that the disquotational T-scheme – suitably restricted to avoid the liar paradox – is conservative over pure logic. But it has been pointed out (e.g. Halbach 2001, “How Innocent is Deflationism?”, Synthese 126, pp. 179-181) that this is not the case, for one can prove ∃x∃y(x ≠ y) from the T-scheme (lemma 2 below).
     
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  4. Jeffrey Ketland (2014). There's Glory for You! Philosophy 89 (1):3-29.
    This dialogue concerns metasemantics and language cognition. It defends a Lewisian conception of languages as abstract entities (Lewis 1975), arguing that semantic facts are necessities (Soames 1984), and therefore not naturalistically reducible. It identifies spoken languages as idiolects, in line roughly with Chomskyan I-languages. It relocates traditional metasemantic indeterminacy arguments as indeterminacies of what language an agent speaks or cognizes. Finally, it aims to provide a theoretical analysis of the cognizing relation in terms of the agent's assigning certain meanings to (...)
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  5. Jeffrey Ketland (2011). Identity and Indiscernibility. Review of Symbolic Logic 4 (2):171-185.
    The notion of strict identity is sometimes given an explicit second-order definition: objects with all the same properties are identical. Here, a somewhat different problem is raised: Under what conditions is the identity relation on the domain of a structure first-order definable? A structure may have objects that are distinct, but indiscernible by the strongest means of discerning them given the language (the indiscernibility formula). Here a number of results concerning the indiscernibility formula, and the definability of identity, are collected (...)
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  6. Jeffrey Ketland (2011). Nominalistic Adequacy. Proceedings of the Aristotelian Society 111 (2pt2):201-217.
    Instrumentalist nominalism responds to the indispensability arguments by rejecting the demand that successful mathematicized scientific theories be nominalized, and instead claiming merely that such theories are nominalistically adequate: the concreta behave ‘as if’ the theory is true. This article examines some definitions of the concept of nominalistic adequacy and concludes with some considerations against instrumentalist nominalism.
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  7. Jeffrey Ketland (2009). Beth's Theorem and Deflationism — Reply to Bays. Mind 118 (472):1075-1079.
    Is the restricted, consistent, version of the T-scheme sufficient for an ‘implicit definition’ of truth? In a sense, the answer is yes (Haack 1978 , Quine 1953 ). Section 4 of Ketland 1999 mentions this but gives a result saying that the T-scheme does not implicitly define truth in the stronger sense relevant for Beth’s Definability Theorem. This insinuates that the T-scheme fares worse than the compositional truth theory as an implicit definition. However, the insinuation is mistaken. For, as Bays (...)
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  8. Jeffrey Ketland (2009). Empirical Adequacy and Ramsification, II. In. In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. 29--45.
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  9. Jeffrey Ketland (2009). Truth. In John Shand (ed.), Central Issues of Philosophy. Wiley-Blackwell.
     
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  10. Jeffrey Ketland (2007). A Comment on Bermúdez Concerning the Definability of Identity. Analysis 67 (296):315–318.
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  11. Jeffrey Ketland, Craig's Theorem.
    In mathematical logic, Craig’s Theorem (not to be confused with Craig’s Interpolation Theorem) states that any recursively enumerable theory is recursively axiomatizable. Its epistemological interest concerns its possible use as a method of eliminating “theoretical content” from scientific theories.
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  12. Jeffrey Ketland (2006). Structuralism and the Identity of Indiscernibles. Analysis 66 (292):303–315.
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  13. Jeffrey Ketland, Second-Order Logic.
    Second-order logic is the extension of first-order logic obtaining by introducing quantification of predicate and function variables.
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  14. Jeffrey Ketland (2005). Deflationism and the Gödel Phenomena: Reply to Tennant. Mind 114 (453):75-88.
    Any (1-)consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a nontrivial fashion. The extended methods of formal proof must capture the essentials of the so-called 'semantical argument' for the truth of the Gödel sentence. We are concerned to show that (...)
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  15. Jeffrey Ketland (2005). Jacquette on Grelling's Paradox. Analysis 65 (287):258–260.
    This discusses a mistake (concerning what a definition is) in “Grelling’s revenge”, Analysis 64, 251-6 (2004), by Dale Jacquette, who claims that the simple theory of types is inconsistent.
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  16. Jeffrey Ketland (2005). Review of Paul Horwich, From a Deflationary Point of View. [REVIEW] Notre Dame Philosophical Reviews 2005 (12).
  17. Jeffrey Ketland (2005). Some More Curious Inferences. Analysis 65 (285):18–24.
    The following inference is valid: There are exactly 101 dalmatians, There are exactly 100 food bowls, Each dalmatian uses exactly one food bowl Hence, at least two dalmatians use the same food bowl. Here, “there are at least 101 dalmatians” is nominalized as, "x1"x2…."x100$y(Dy & y ¹ x1 & y ¹ x2 & … & y ¹ x100) and “there are exactly 101 dalmatians” is nominalized as, "x1"x2…."x100$y(Dy & y ¹ x1 & y ¹ x2 & … & y ¹ (...)
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  18. Jeffrey Ketland (2005). Yablo's Paradox and Ω-Inconsistency. Synthese 145 (3):295 - 302.
    It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is also (...)
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  19. Jeffrey Ketland (2004). Bueno and Colyvan on Yablo's Paradox. Analysis 64 (2):165–172.
    This is a response to a paper “Paradox without satisfaction”, Analysis 63, 152-6 (2003) by Otavio Bueno and Mark Colyvan on Yablo’s paradox. I argue that this paper makes several substantial mathematical errors which vitiate the paper. (For the technical details, see [12] below.).
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  20. Jeffrey Ketland (2004). Empirical Adequacy and Ramsification. British Journal for the Philosophy of Science 55 (2):287-300.
    Structural realism has been proposed as an epistemological position interpolating between realism and sceptical anti-realism about scientific theories. The structural realist who accepts a scientific theory thinks that is empirically correct, and furthermore is a realist about the ‘structural content’ of . But what exactly is ‘structural content’? One proposal is that the ‘structural content’ of a scientific theory may be associated with its Ramsey sentence (). However, Demopoulos and Friedman have argued, using ideas drawn from Newman's earlier criticism of (...)
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  21. Jeffrey Ketland (2003). Can a Many-Valued Language Functionally Represent its Own Semantics? Analysis 63 (4):292–297.
    Tarski’s Indefinability Theorem can be generalized so that it applies to many-valued languages. We introduce a notion of strong semantic self-representation applicable to any (sufficiently rich) interpreted many-valued language L. A sufficiently rich interpreted many-valued language L is SSSR just in case it has a function symbol n(x) such that, for any f Sent(L), the denotation of the term n(“f”) in L is precisely ||f||L, the semantic value of f in L. By a simple diagonal construction (finding a sentence l (...)
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  22. Jeffrey Ketland (2003). On Wright's Inductive Definition of Coherence Truth for Arithmetic. Analysis 63 (1):6–15.
    In “Truth – A Traditional Debate Reviewed” (1999), Crispin Wright proposed an inductive definition of “coherence truth” for arithmetic relative to an arithmetic base theory B. Wright’s definition is in fact a notational variant of the usual Tarskian inductive definition, except for the basis clause for atomic sentences. This paper provides a model-theoretic characterization of the resulting sets of sentences "cohering" with a given base theory B. These sets are denoted WB. Roughly, if B satisfies a certain minimal condition (for (...)
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  23. Jeffrey Ketland (2002). Hume = Small Hume. Analysis 62 (1):92–93.
    We can modify Hume’s Principle in the same manner that George Boolos suggested for modifying Frege’s Basic Law V. This leads to the principle Small Hume. Then, we can show that Small Hume is interderivable with Hume’s Principle.
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  24. Jeffrey Ketland (2001). Stephen G. Simpson Subsystems of Second-Order Arithmetic. British Journal for the Philosophy of Science 52 (1):191-195.
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  25. Stephen G. Simpson & Jeffrey Ketland (2001). Reviews-Subsystems of Second-Order Arithmetic. British Journal for the Philosophy of Science 52 (1):191-196.
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  26. Jeffrey Ketland (2000). A Proof of the (Strengthened) Liar Formula in a Semantical Extension of Peano Arithmetic. Analysis 60 (1):1–4.
    In the Tarskian theory of truth, the strengthened liar sentence is a theorem. More generally, any formalized truth theory which proves the full, self-applicative scheme True(“f”) f will prove the strengthened liar sentence. (This scheme is sometimes called (T-Out).).
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  27. Jeffrey Ketland (2000). Conservativeness and Translation-Dependent T-Schemes. Analysis 60 (4):319–328.
    Certain translational T-schemes of the form True(“f”) « f(f), where f(f) can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.
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  28. Geoffrey Stokes & Jeffrey Ketland (2000). Reviews-Popper: Philosophy, Politics and Scientific Method. British Journal for the Philosophy of Science 51 (2):363-370.
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  29. Jeffrey Ketland (1999). Deflationism and Tarski's Paradise. Mind 108 (429):69-94.
    Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called (...)
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