Paul Teller

Previous work has shown that the problem of measurement in quantum mechanics is not correctly seen as one of understanding some allegedly univocal process of measurement in nature which corresponds to the projection postulate. The present paper introduces a new perspective by showing that how we are to understand the nature of the change of quantum mechanical state on measurement depends very sensitively on the interpretation of the state function, and by showing how attention to this dependence can greatly sharpen the problems and relations between them. In particular, the problems take a form resembling their traditional formulation only on an inexact value interpretation, according to which the state function attributes inexact values of quantities to systems. On other interpretations we can apply (with various drawbacks) the subensemble idea, according to which a discontinuous change of quantum mechanical description results on measurement simply because we need a new state function to describe a new object

Table of Contents Volume I Preface to Volumes I and II: A Guide to the Primer Chapter 1, Basic Ideas and Tools Chapter 2, Transcription between English and Sentence Logic Chapter 3, Logical Equivalence, Logical Truths, and Contradictions Chapter 4, Validity and Conditionals Chapter 5, Natural Deduction for Sentence Logic: Fundamentals Chapter 6, Natural Deduction for Sentence Logic: Strategies Chapter 7, Natural Deduction for Sentence Logic: Derived Rules and Derivations without Premises Chapter 8, Truth Tree for Sentence Logic: Fundamentals Chapter 9, Truth Trees for Sentence Logic: Applications Index for Volume 1 Solutions Manual for Volume 1 Table of Contents to Volume II Introduction to Predicate Logic Notes Chapter 1, Predicate Logic: Syntax Chapter 2, Predicate Logic: Semantics and Validity Chapter 3, More about Quantifiers Chapter 4, Transcription Chapter 5, Natural Deduction for Predicate Logic: Fundamentals Chapter 6, More on Natural Deduction for Predicate Logic Chapter 7, Truth Tress for Predicate Logic: Fundamentals Chapter 8, More on Truth Tress for Predicate Logic Chapter 9, Identity, Functions, and Definite Descriptions Chapter 10, Metatheory: The Basic Concepts Chapter 11, Mathematical Induction Chapter 12, Soundness and Completeness for Sentence Logic Trees Chapter 13, Soundness and Completeness for Sentence Logic Derivations Chapter 14, Koenig’s Lemma, Compactness, and Generalization to Infinite Sets of Premises Chapter 15, Interpretations, Soundness, and Completeness for Predicate Logic Index for Volume II Solutions Manual for Volume II Diagrammatic Summary of Rules Corrections to the Text.

Knowledge requires truth, and truth, we suppose, involves unflawed representation. Science does not provide knowledge in this sense but rather provides models, representations that are limited in their accuracy, precision, or, most often, both. Truth as we usually think of it is an idealization, one that serves wonderfully in most ordinary applications, but one that can terribly mislead for certain issues in philosophy. This article sketches how this happens for five important issues, thereby showing how philosophical method must take into account the idealized nature of our familiar conception of truth

This essay endorses the conclusion of Sklar’s “Dappled Theories in a Uniform World” that he announces in his abstract, that notwithstanding recent attacks foundational theories are universal in their scope. But Sklar’s rejection of a “pluralist ontology” is questioned. It is concluded that so called “foundational” and “phenomenological” theories are on a much more equal footing as sources of knowledge than Sklar would allow, that “giving an ontology” generally involves dealing in idealizations, and that a transfigured “ficitonalism” provides an (in many respects) better model of scientific knowledge than the model of “foundational truths.”.

The practice of describing multiparticle quantum systems in terms of labeled particles indicates that we think of quantum entities as individuatable. The labels, together with particle indistinguishability, create the need for symmetrization or antisymmetrization (or, in principle, higher-order symmetries), which in turn results in “surplus formal structure” in the formalism, formal structure which corresponds to nothing in the real world. We argue that these facts show quanta to be unindividuatable entities, things in principle incapable of supporting labels, and so things which support no factual difference_if two of them are thought of as being switched. When thinking of the metaphysics of quanta, we should eschew the misleading labels of the tensor product Hilbert space formalism and prefer the ontologically more faithful description of the Fock space formalism. This conception eliminates puzzles about the quantum statistics of bosons

Conventional scientific realism is just the doctrine that our theoretical terms refer. Conventional antirealism denies, for various reasons, theoretical reference and takes theory to give us only information about the word of the perceptual where reference, it would appear, is secure. But reference fails for the perceptual every bit as much for the perceptual as for the theoretical, and for the same reason: the world is too complicated for us to succeed in attaching specific referents to our terms. That would appear to leave us with a kind of latter day, representational idealism: All we have are representations. I argue that our representations tell us about an independent world without securing reference by showing that the world is very like the way it is represented in a range of different, often complementary modeling schemes. Though never exact, these representations are of something extra-representational because they present the world modally as going beyond what is represented explicitly.

This paper challenges “traditional measurement-accuracy realism”, according to which there are in nature quantities of which concrete systems have definite values. An accurate measurement outcome is one that is close to the value for the quantity measured. For a measurement of the temperature of some water to be accurate in this sense requires that there be this temperature. But there isn’t. Not because there are no quantities “out there in nature” but because the term ‘the temperature of this water’ fails to refer owing to idealization and failure of specificity in picking out concrete cases. The problems can be seen as an artifact of vagueness, and so doing facilitates applying Eran Tal’s robustness account of measurement accuracy to suggest an attractive way of understanding vagueness in terms of the function of idealization, a way that sidesteps the problems of higher order vagueness and that shows how idealization provides a natural generalization of what it is to be vague.