Abstract:I discuss and try to evaluate the argument about constructible sets made by Putnam in Ô'Models and Reality'Õ, and some of the counterarguments directed against it in the literature. I shall conclude that Putnam's argument, while correct in substance, nevertheless has no direct bearing on the philosophical question of unintended models of set theory.Erkenntnis (2005) 62: 395-409 Ó Springer 2005
“…5. 35 In general, a majority of researchers agree that this problem is solvable by moving to a class theory (of Kelley-Morse)-due to (Bellotti, 2005;Button, 2011). 36 Since some conclusions elaborated for difficulty D1 appear to be useful by difficulty 3, we consider it achronologically before difficulty 2.…”
Section: Moment Of Rejecting Realism: a Perspective Of The Putnam The...mentioning
confidence: 99%
“…The main goal of this article is to propose a meta-reconstruction of Putnam's semantic anti-realism and his model-theoretic argument-due to its exposition in Putnam (1980, Footnote 3 continued against Putnam's intentions. This critique met a reaction in Bellotti (2005). Many authors, such as Benacerraf and Wright (1985) and Bays (2001Bays ( , 2007, found Putnam's "Just-More-Theory" postulate-as a remedy for these difficulties-entirely question-begging.…”
Section: The Goals and Structure Of The Articlementioning
confidence: 99%
“…Shapiro, 1985, p. 724). In Bellotti's opinion, this property discredits this model as the intended one (Bellotti, 2005), but it is unproblematic for Putnam (cf. Putnam, 1980, p.…”
Section: B a Remedy -The Idea Of Objectivization Of Pragmaticsmentioning
confidence: 99%
“…Fortunately, the original Skolemization idea in the form of the Skolem Hull postulate provides a reasonable solution to difficulty D3 and to different objections to Putnam's using DSL for class-models 43 -Levin (1997), Bays (2001). Simultaneously, due to Levin (1997), Velleman (1998), Bellotti (2005), the idea of exploiting the formal apparatus of Kelley-Morse's class theory and the Skolem Hull might be replaced by an alternative method of assuming an inaccessible cardinal κ, which provides a corresponding model L κ the desired set model (See: Bellotti, 2005, pp. 396).…”
Section: N ∀X A(x) ≡ ∀P(n • P A( P)); N ∃X A(x) ≡ ∃P∃m(n = P M ∧ M A(...mentioning
confidence: 99%
“…Some commentators of Putnam's work-as Haukioja in Haukioja (2001)-seem to be delighted by its hard-hitting nature. Some of them-as Anderson in Anderson (1993), Bellotti in (2005, or Button in (2011), formulate some hints on how to improve and defend Putnam's argument. Finally, many others would insist that Putnam's argument is "completely wrongheaded" (Cleve, 1992, p. 349), "fatally flawed" (Lewis, 1984, p. 236), or "question-begging."…”
In “Models and Reality”, H. Putnam formulated his model-theoretic argument against “metaphysical realism”. The article proposes a meta-reconstruction of Putnam’s model-theoretic argument in the light of two mutually compatible interpretations of it–elaborated by Manuel Garcia-Carpintero and Igor van Douven. A critical reflection on these interpretations and their adequacy for Putnam’s argument allows us to expose new theses coherent with Putnam’s reasoning and indicate new paths to improve this argument for our reconstruction task. In particular, we show that Putnam’s position may be coherent with van Douven’s versions of Global Descriptivism under some conditions, but Putnam cannot reject realism as quickly as Carpintero suggests. We show that Suszko’s canonic axiomatic system and Sneed’s concept of theory may provide valuable support for Putnam’s argument. Finally, we critically evaluate Carpintero’s theses about the genesis of unintended interpretations of our languages, adopting the machinery of the Upward Skolem–Loewenheim Theorem and Knight’s Theorem.
“…5. 35 In general, a majority of researchers agree that this problem is solvable by moving to a class theory (of Kelley-Morse)-due to (Bellotti, 2005;Button, 2011). 36 Since some conclusions elaborated for difficulty D1 appear to be useful by difficulty 3, we consider it achronologically before difficulty 2.…”
Section: Moment Of Rejecting Realism: a Perspective Of The Putnam The...mentioning
confidence: 99%
“…The main goal of this article is to propose a meta-reconstruction of Putnam's semantic anti-realism and his model-theoretic argument-due to its exposition in Putnam (1980, Footnote 3 continued against Putnam's intentions. This critique met a reaction in Bellotti (2005). Many authors, such as Benacerraf and Wright (1985) and Bays (2001Bays ( , 2007, found Putnam's "Just-More-Theory" postulate-as a remedy for these difficulties-entirely question-begging.…”
Section: The Goals and Structure Of The Articlementioning
confidence: 99%
“…Shapiro, 1985, p. 724). In Bellotti's opinion, this property discredits this model as the intended one (Bellotti, 2005), but it is unproblematic for Putnam (cf. Putnam, 1980, p.…”
Section: B a Remedy -The Idea Of Objectivization Of Pragmaticsmentioning
confidence: 99%
“…Fortunately, the original Skolemization idea in the form of the Skolem Hull postulate provides a reasonable solution to difficulty D3 and to different objections to Putnam's using DSL for class-models 43 -Levin (1997), Bays (2001). Simultaneously, due to Levin (1997), Velleman (1998), Bellotti (2005), the idea of exploiting the formal apparatus of Kelley-Morse's class theory and the Skolem Hull might be replaced by an alternative method of assuming an inaccessible cardinal κ, which provides a corresponding model L κ the desired set model (See: Bellotti, 2005, pp. 396).…”
Section: N ∀X A(x) ≡ ∀P(n • P A( P)); N ∃X A(x) ≡ ∃P∃m(n = P M ∧ M A(...mentioning
confidence: 99%
“…Some commentators of Putnam's work-as Haukioja in Haukioja (2001)-seem to be delighted by its hard-hitting nature. Some of them-as Anderson in Anderson (1993), Bellotti in (2005, or Button in (2011), formulate some hints on how to improve and defend Putnam's argument. Finally, many others would insist that Putnam's argument is "completely wrongheaded" (Cleve, 1992, p. 349), "fatally flawed" (Lewis, 1984, p. 236), or "question-begging."…”
In “Models and Reality”, H. Putnam formulated his model-theoretic argument against “metaphysical realism”. The article proposes a meta-reconstruction of Putnam’s model-theoretic argument in the light of two mutually compatible interpretations of it–elaborated by Manuel Garcia-Carpintero and Igor van Douven. A critical reflection on these interpretations and their adequacy for Putnam’s argument allows us to expose new theses coherent with Putnam’s reasoning and indicate new paths to improve this argument for our reconstruction task. In particular, we show that Putnam’s position may be coherent with van Douven’s versions of Global Descriptivism under some conditions, but Putnam cannot reject realism as quickly as Carpintero suggests. We show that Suszko’s canonic axiomatic system and Sneed’s concept of theory may provide valuable support for Putnam’s argument. Finally, we critically evaluate Carpintero’s theses about the genesis of unintended interpretations of our languages, adopting the machinery of the Upward Skolem–Loewenheim Theorem and Knight’s Theorem.
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