30 found
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  1. Deflationism and Tarski’s Paradise.Jeffrey Ketland - 1999 - 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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  2. (2 other versions)Empirical adequacy and ramsification.Jeffrey Ketland - 2004 - 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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  3.  84
    Structuralism and the identity of indiscernibles.Jeffrey Ketland - 2006 - Analysis 66 (4):303-315.
  4. Yablo’s Paradox and ω-Inconsistency.Jeffrey Ketland - 2005 - 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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  5. Deflationism and the gödel phenomena: Reply to Tennant.Jeffrey Ketland - 2005 - 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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  6. Identity and indiscernibility.Jeffrey Ketland - 2011 - 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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  7.  42
    Foundations of applied mathematics I.Jeffrey Ketland - 2021 - Synthese 199 (1-2):4151-4193.
    This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.
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  8. Bueno and Colyvan on Yablo’s Paradox.Jeffrey Ketland - 2004 - 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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  9. Can a many-valued language functionally represent its own semantics?Jeffrey Ketland - 2003 - 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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  10. Some more curious inferences.Jeffrey Ketland - 2005 - Analysis 65 (1):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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  11.  19
    Bases for Structures and Theories I.Jeffrey Ketland - 2020 - Logica Universalis 14 (3):357-381.
    Sometimes structures or theories are formulated with different sets of primitives and yet are definitionally equivalent. In a sense, the transformations between such equivalent formulations are rather like basis transformations in linear algebra or co-ordinate transformations in geometry. Here an analogous idea is investigated. Let a relational signature \ be given. For a set \ of \-formulas, we introduce a corresponding set \ of new relation symbols and a set of explicit definitions of the \ in terms of the \. (...)
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  12.  40
    VI—Nominalistic Adequacy.Jeffrey Ketland - 2011 - 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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  13.  62
    There's Glory for You!Jeffrey Ketland - 2014 - 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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  14.  45
    A Proof of the (Strengthened) Liar Formula in a Semantical Extension of Peano Arithmetic.Jeffrey Ketland - 2000 - 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 will prove the strengthened liar sentence..).
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  15.  39
    Conservativeness and translation-dependent T-schemes.Jeffrey Ketland - 2000 - Analysis 60 (4):319-328.
    Certain translational T-schemes of the form True « f, where 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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  16.  62
    On Wright’s Inductive Definition of Coherence Truth for Arithmetic.Jeffrey Ketland - 2003 - Analysis 63 (1):6-15.
    In “Truth – A Traditional Debate Reviewed”, 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, then WB (...)
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  17.  35
    Standard Formalization.Jeffrey Ketland - 2022 - Axiomathes 32 (3):711-748.
    A standard formalization of a scientific theory is a system of axioms for that theory in a first-order language (possibly many-sorted; possibly with the membership primitive $$\in$$ ). Suppes (in: Carvallo M (ed) Nature, cognition and system II. Kluwer, Dordrecht, 1992) expressed skepticism about whether there is a “simple or elegant method” for presenting mathematicized scientific theories in such a standard formalization, because they “assume a great deal of mathematics as part of their substructure”. The major difficulties amount to these. (...)
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  18. Hume = small Hume.Jeffrey Ketland - 2002 - 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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  19. How weak is the t-scheme?Jeffrey Ketland - manuscript
    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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  20. The model theoretic conception of scientific theories.Jeffrey Ketland - unknown
    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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  21.  45
    Computation and Indispensability.Jeffrey Ketland - forthcoming - Logic and Logical Philosophy:1.
    This article provides a computational example of a mathematical explanation within science, concerning computational equivalence of programs. In addition, it outlines the logical structure of the reasoning involved in explanations in applied mathematics. It concludes with a challenge that the nominalist provide a nominalistic explanation for the computational equivalence of certain programs.
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  22.  9
    A comment on Bermudez concerning the definability of identity.Jeffrey Ketland - 2007 - Analysis 67 (4):315-318.
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  23.  13
    Bases for Structures and Theories II.Jeffrey Ketland - 2020 - Logica Universalis 14 (4):461-479.
    In Part I of this paper, I assumed we begin with a signature $$P = \{P_i\}$$ P = { P i } and the corresponding language $$L_P$$ L P, and introduced the following notions: a definition system$$d_{\Phi }$$ d Φ for a set of new predicate symbols $$Q_i$$ Q i, given by a set $$\Phi = \{\phi _i\}$$ Φ = { ϕ i } of defining $$L_P$$ L P -formulas \leftrightarrow \phi _i)$$ ∀ x ¯ ↔ ϕ i ) ); (...)
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  24.  85
    Beth's theorem and deflationism — reply to Bays.Jeffrey Ketland - 2009 - 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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  25.  89
    Craig’s Theorem.Jeffrey Ketland - unknown
    In mathematical logic, Craig’s 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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  26. Jacquette on Grelling’s Paradox.Jeffrey Ketland - 2005 - Analysis 65 (3):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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  27. Stephen G. Simpson subsystems of second-order arithmetic.Jeffrey Ketland - 2001 - British Journal for the Philosophy of Science 52 (1):191-195.
  28. Second-Order Logic.Jeffrey Ketland - unknown
    Second-order logic is the extension of first-order logic obtaining by introducing quantification of predicate and function variables.
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  29. Truth.Jeffrey Ketland - 2009 - In John Shand (ed.), Central Issues of Philosophy. Malden, MA: Wiley-Blackwell.
     
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  30.  59
    Review of Paul Horwich, From a Deflationary Point of View[REVIEW]Jeffrey Ketland - 2005 - Notre Dame Philosophical Reviews 2005 (12).