Presents a guide to the basics of quantum mechanics and measurement.

This is the third volume of Hilary Putnam's philosophical papers, published in paperback for the first time. The volume contains his major essays from 1975 to 1982, which reveal a large shift in emphasis in the 'realist'_position developed in his earlier work. While not renouncing those views, Professor Putnam has continued to explore their epistemological consequences and conceptual history. He now, crucially, sees theories of truth and of meaning that derive from a firm notion of reference as inadequate.

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)

It’s sometimes suggested that we can (in a sense) settle the truth-value of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in Clarke-Doane (2020b) and a series of recent APA presentations, Clarke-Doane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the model-theoretic representability of languages like ours) we can’t (...) know ourselves to have any such freedom. (shrink)

This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...) to resolving indeterminacy, before offering some brief closing reflections. We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic. (shrink)

I know, for the most part, what I think, want, and intend, and what my sensations are. In addition, I know a great deal about the world around me. I also sometimes know what goes on in other people's minds. Each of these three kinds of empirical knowledge has its distinctive characteristics. What I know about the contents of my own mind I generally know without investigation or appeal to evidence. There are exceptions, but the primacy of unmediated self-knowledge is (...) attested by the fact that we distrust the exceptions until they can be reconciled with the unmediated. My knowledge of the world outside of myself, on the other hand, depends on the functioning of my sense organs, and this causal dependence on the senses makes my beliefs about the world of nature open to a sort of uncertainty that arises only rarely in the case of beliefs about my own states of mind. Many of my simple perceptions of what is going on in the world are not based on further evidence; my perceptual beliefs are simply caused directly by the events and objects around me. But my knowledge of the propositional contents of other minds is never immediate in this sense; I would have no access to what others think and value if I could not note their behaviour. (shrink)

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.