The Model-Theoretic Argument: From Skepticism to a New Understanding (original) (raw)
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Putnam's Model-theoretic Argument(s). A Detailed Reconstruction
Journal for General Philosophy of Science, 1999
Two of Hilary Putnam's model-theoretic arguments against metaphysical realism are examined in detail. One of them is developed as an extension of a model-theoretic argument against mathematical realism based on considerations concerning the so-called Skolem-Paradox in set theory. This argument against mathematical realism is also treated explicitly. The article concentrates on the fine structure of the arguments because most commentators have concentrated on the major premisses of Putnam's argument and especially on his treatment of metaphysical realism. It is shown that the validity of Putnam's arguments is doubtful and that realists are by no means forced to accept the theses Putnam ascribes to them. It is concluded that Putnam fails to give convincing arguments for rejecting mathematical or metaphysical realism. Furthermore, Putnam's internal realism is discussed critically.
The model-theoretic argument: Another turn of the screw
Erkenntnis, 1996
My aim in this paper is -dreadful though the prospect may appear-to add to the already enormous amount of literature on Putnam's "modeltheoretic" argument against realism.1 I shall do so even though I believe that the argument has already been conclusively refuted, and that everything of substance which could be said to refute the argument has already been said. 2 However, recent attempts to defend the model-theoretic argument in the face of the aforementioned criticisms -showing how what I take to be the main point of previous rebuttals of the argument can be easily missed -justify my purpose. 3 It may be illuminating and helpful, I believe, to expound the same point again in a different guise, by having recourse to ideas on models and the model-theoretic account of the logical properties I have developed in another place. 4
Putnam’s model-theoretic argument (meta)reconstructed
Synthese
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 metamathematics of Putnam's model-theoretic arguments
Erkenntnis, 2011
Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely immune to metamathematical challenges. Philip Scowcroft has written a very useful review of this paper, on MathSciNet, MR2785345 (2012e:03005).
Putnam's Model-Theoretic Argument Reconstructed
The Journal of Philosophy, 1999
Among those addressed by Putnam's model-theoretic argument it is common opinion that the argument is invalid because question-begging. If the standard analysis of the argument is along the right lines, then what has been called the 'just more theory move' is to be held responsible for this. In the present paper, an alternative reading of Putnam's argument is offered that makes the 'just more theory move' come out perfectly legitimate, and the argument as a whole valid.
The Metaphysics of the Model-Theoretic Arguments
Outstanding Contributions to Logic, 2018
This paper presents a exposition of Putnam's model theoretic arguments in the context of his broader philosophical position. I argue that Putnam used the arguments not just to undermine metaphysical realism, but to reveal that the philosophical debate between metaphysical realism and internal realism is dialectically problematic in that the metaphysical realist defence cannot "count against" (Putnam in Philosophical Topics: The philosophy of Hilary Putnam 20(1):355, 1992c) the converse position. Putnam's response is that this is a debate that we should simply undercut. Putnam's model theoretic arguments have posed challenges of interpretation since their publication. In this article I shall make two claims about the arguments that add to this debate. One is to clarify the arguments' target: while it is clear that the arguments are designed to refute the position of metaphysical realism, it is less clear just which hypothesis is at stake. I present a thesis that Putnam takes to be constitutive of metaphysical realism and targets with the model-theoretic arguments. This is the posit of epistemic humility, which states that it is possible that there is an aspect of the world that is epistemically inaccessible as a matter of principle. The second aim of this paper is to suggest a new direction in which to seek justification for the notorious 'just more theory' response that Putnam gives to critics of the model-theoretic arguments. Metaphysical or "external" realism and Putnam's own internal realism are broad positions, comprising two "philosophical temperaments" (1981, p. 49) or "tendencies" (1980, p. 474). They are also foundational: Putnam hints that their consequences affect almost every area of philosophy (1981, p. 49), particularly scepticism ("the question of'Brains in a Vat' would not be of interest if it were not for the sharp way in which it brings out the difference between these philosophical perspectives"; Ibid.) The distinction between the two positions is inspired by Kant, with internal realism representing Kant's own position (1992d, p. 114, 1987, pp. 36-37), although the relationship between Kant and Putnam's views is complicated. Metaphysical real
Journal of Philosophy, 2001
It is not my claim that the 'Löwenheim-Skolem paradox' is an antinomy in formal logic; but I shall argue that it is an antinomy, or something close to it, in philosophy of language. Moreover, I shall argue that the resolution of the antinomy-the only resolution that I myself can see as making sense-has profound implications for the great metaphysical dispute about realism which has always been the central dispute in the philosophy of language.
Philosophical Quarterly, 2008
Over the last 20 years or so, Hilary Putnam has developed a series of arguments which use basic theorems of model theory to undermine semantic realism. Here, I discuss two generalizations of these arguments. The first employs some new forms of model theory to generate substantially stronger conclusions than Putnam's original arguments generated. The second illustrates a method for replacing the model theory in Putnam's arguments with results from other branches of science-in particular, with results from astronomy. Now, I should say at the outset that neither of these new arguments is supposed to be persuasive: each of them fails, and fails rather badly, when regarded as a serious objection to realism. Nevertheless, the arguments serve three purposes. First, the parallels between my new arguments and Putnam's original arguments help to highlight what's really going on in the latter, and the obvious flaws in my arguments help to isolate the corresponding flaws in Putnam's arguments. Second, these new arguments expose the inadequacy of several recent defenses of Putnam. (Very roughly, I argue that if these defenses saved Putnam's arguments, then they would save my arguments as well. But, my arguments are unsalvageable. So, the defenses don't save Putnam.) Finally, the arguments present a new challenge to Putnam and his defenders: to provide a formulation of the model-theoretic argument which makes that argument seem compelling without doing the same for mine.