this paper, I examine one version of Putnam's argument---a version closely related to the traditional Lowenheim-Skolem Paradox. I defend three claims about this argument. First, I argue that a key step in Putnam's argument rests on a mathematical mistake, and I discuss some of the philosophical ramifications of this mistake. Second, I argue that, even if Putnam could get his mathematics to work, his argument would still fail on purely philosophical grounds. Third, I argue that Putnam's mathematical mistakes and his philosophical mistakes are surprisingly closely related. At the end of the day, I conclude that realists have little to fear from Putnam and his models

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 Löwenheim-Skolem 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...

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.