About this book Hilary Whitehall Putnam was one of the leading philosophers of the second half of the 20th century. As student of Rudolph Carnap's and Hans Reichenbach's, he went on to become not only a major figure in North American analytic philosophy, who made significant contributions to the philosophy of mind, language, mathematics, and physics but also to the disciplines of logic, number theory, and computer science. He passed away on March 13, 2016. The present volume is a memorial (...) to his extraordinary intellectual contributions, honoring his contributions as a philosopher, a thinker, and a public intellectual. It features essays by an international team of leading philosophers, covering all aspects of Hilary Putnam's philosophy from his work in ethics and the history of philosophy to his contributions to the philosophy of science, logic, and mathematics. Each essay is an original contribution. -/- Author information James Conant, Univ. of Chicago/Univ. of Leipzig, USA/Germany; Sanjit Chakraborty, IISER Kolkata/VIT-AP University, India. (shrink)

Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...) instead flows naturally from three independently motivated elements; and to show that severe limitations afflict the proposal. In conclusion, I pick out the element of the eligibility response that is responsible for the limitations: future work in this area should therefore concentrate on amending this aspect of the overall theory. (shrink)

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.

The doctrines of scientific realism have enjoyed a close and enduring, if not always harmonious, association with Tarski's semantic conception of truth and theories of formal semantics generally. From its inception Tarski's theory received unqualified support from some realists, like Karl Popper, who saw it as legitimizing the use of semantic notions in epistemology and the philosophy of science.

Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the sentences of the language of set theory are understood in their standard meaning, each sentence has a determinate truth value, so that there is a fact of the matter whether the cardinality of the continuum is א2 or whether there are (...) measurable cardinals, whether or not those facts are knowable by us. (shrink)

I think recent discussions of content and reference have not paid enough attention to the role of language as a convention-governed system of communication. With this as a background theme, I explain the role of A-intensions in elucidating one important notion of content and correlative notions of reference.

David Lewis's account of intentionality is a version of what he calls 'global descriptivism'. The rough idea is that the correct interpretation of one's total theory is the one (among the admissible interpretations) that come closest to making it true. I give an exposition of this account, as I understand it, and try to bring out some of its consequences. I argue that there is a tension between Lewis's global descriptivism and his rejection of a linguistic account of the intentionality (...) of thought. I distinguish some different senses in which Lewis's theory might permit, or be committed to, a kind of holism about intentional content, and I consider the sense in which Lewis's account might be said to be an internalist account, and the motivation for this kind of internalism. (shrink)

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.

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

I discuss and try to evaluate the argument about constructible sets made by Putnam in ‘ ”Models and Reality”, 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.

I present two generalizations of Putnam's model-theoretic argument against realism. The first replaces Putnam's model theory with some new, and substantially simpler, model theory, while the second replaces Putnam's model theory with some more accessible results from astronomy. By design, both of these new arguments fail. But the similarities between these new arguments and Putnam's original arguments illuminate the latter's overall structure, and the flaws in these new arguments highlight the corresponding flaws in Putnam's arguments.

The HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V or HOD is “far” from V. The question is whether the future will lead to the first or the second side of the dichotomy. Is HOD “close” to V, or “far” from V? There is a program aimed at establishing the first alternative—the “close” side of the HOD Dichotomy. This is the program of inner model theory. In recent years the (...) third author has provided evidence that there is an ultimate inner model—Ultimate-L—and he has isolated a natural conjecture associated with the model—the Ultimate-L Conjecture. This conjecture implies that that the first alternative holds—HOD is “close” to V. This is the future in which pattern prevails. In this paper we introduce a very different program, one aimed at establishing the second alternative—the “far” side of the HOD Dichotomy. This is the program of large cardinals beyond choice. Kunen famously showed that if AC holds then there cannot be a Reinhardt cardinal. It has remained open whether Reinhardt cardinals are consistent in ZF alone. It turns out that there is an entire hierarchy of choiceless large cardinals of which Reinhardt cardinals are only the beginning, and, surprisingly, this hierarchy appears to be highly ordered and amenable to systematic investigation, as we shall show in this paper. The point is that if these choiceless large cardinals are consistent then the Ultimate-L Conjecture must fail. This is the future where chaos prevails. (shrink)

First, I discuss the older “theory-centered” and the more recent semantic conception of scientific theories. I argue that these two perspectives are nothing more than terminological variants of one another. I then offer a new theory-centered view of scientific theories. I argue that this new view captures the insights had by each of these earlier views, that it’s closer to how scientists think about their own theories, and that it better accommodates the phenomenon of inconsistent scientific theories.

Mathematical realists have long invoked the categoricity of axiomatizations of arithmetic and analysis to explain how we manage to fix the intended meaning of their respective vocabulary. Can this strategy be extended to set theory? Although traditional wisdom recommends a negative answer to this question, Vann McGee (1997) has offered a proof that purports to show otherwise. I argue that one of the two key assumptions on which the proof rests deprives McGee's result of the significance he and the realist (...) want to attribute to it. I consider two strategies to deal with the problem --- one of which is outlined by McGee himself (2000) --- and argue that both of them fail. I end with some remarks on the prospects for mathematical realism in the light of my discussion. (shrink)