Online research in philosophy

The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, and a more speculative argument for the claim that it does not include S4.2 is also presented.

We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first- and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to Γ0.

This paper examines the connection between model-theoretic truth and necessary truth. It is argued that though the model-theoretic truths of some standard languages are demonstrably ''''necessary'''' (in a precise sense), the widespread view of model-theoretic truth as providing a general guarantee of necessity is mistaken. Several arguments to the contrary are criticized.

Bas van Fraassen has recently argued for a "dissolution" of Hilary Putnam's well-known model-theoretic argument. In this paper I argue that, as it stands, van Fraassen's reply to Putnam is unsuccessful. Nonetheless, it suggests the form a successful response might take.

Tennenbaum's Theorem yields an elegant characterisation of the standard model of arithmetic. Several authors have recently claimed that this result has important philosophical consequences: in particular, it offers us a way of responding to model-theoretic worries about how we manage to grasp the standard model. We disagree. If there ever was such a problem about how we come to grasp the standard model, then Tennenbaum's Theorem does not help. We show this by examining a parallel argument, from a simpler model-theoretic result.

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.

The model-theoretic argument, which Putnam employs to argue againstmetaphysical realism, has faced serious objections of many realist opponents.Igor Douven in his recent paper offers a new interpretation of the model-theoreticargument, which avoids the previous objections. The purpose of this paper is toshow that Douven's reconstruction of Putnam's argument is not successful, andhence that the realist objections still stand.

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.

Model theoretic considerations purportedly show that a certain version of structural realism, one which articulates the nvtion of structure via Ramsey sentences, is in fact trivially true. In this paper we argue that the structural realist is by no means forced to Ramseyfy in the manner assumed in the formal proof. However, the structural realist's reprise is short-lived. For, as we show, there are related versions of the model theoretic argument which cannot be so easily blocked by the structural realist. We examine various ways in which the structural realist may respond, and conclude that the best way of blocking the model theoretic argument involves formulating his Ramseyfied theories using intensional operators. Introduction The model theoretic arguments On Ramseyfying away predicates The model theoretic argument bites back Restricting the second order quantifiers 5.1 Naturalness 5.2 Intrinsic 5.3 Qualitative 5.4 Contingent and causal Intensional operators and relations between properties Conclusion.

A variant of Hilary Putnam's model-theoretic argument against metaphysical realism appears to show that our quantifiers do not determinately range over absolutely everything. This paper argues that some recent attempts to respond to the quantificational skeptic are unsuccessful and offers an alternative response: the key to answering the skeptic is not to refute her argument but to realize that the argument's setup prevents it from being convincing to those it is directed at.