Paul Teller

Science is widely taken to aim, and often to succeed, in producing truths, a “mirror of nature”. Not so. Instead, science fashions models, understood broadly as representations that are never both completely precise and completely accurate. . This chapter discusses how the misconception arose and how it is now being corrected. The account begins with a tension between the founding metaphors of the Scientific Revolution, reading God’s book of nature and the clock metaphor. The former pre-frames laws and physics fundamentalism; the latter the discovery of mechanisms, how things work. Laws aimed at truth, but the world is too complicated for us to get generalizations exactly right. Likewise, the complexity of mechanisms always requires simplifying idealization. Further, different problems require different idealizations and so a pluralism of accounts. The pluralism is unproblematic as different problems about the same subject matter can be consistently dealt with using very different schemes of simplification.

If the semantic value of predicates are, as Williamson assumes, properties, then epistemicism is immediate. Epistemicism fails, so also this properties view of predicates. I use examination of Williamsons position as a foil, showing that his two positive arguments for bivalence fail, and that his efforts to rescue epistemicism from obvious problems fail to the point of incoherence. In Part II I argue that, despite the properties view’s problems, it has an important role to play in combinatorial semantics. We may separate the problem of how smallest parts of language get attached to the world from the problem of how those parts combine to form complex semantic values. For the latter problem we idealize and treat the smallest semantic values as properties (and referents). So doing functions to put to one side how the smallest parts get worldly attachment, a problem that would just get in the way of understanding the combinatorics. Attachment to the world has to be studied separately, and I review some of the options. As a bonus we see why, mostly, higher order vagueness is an artifact of taking properties as semantic values literally instead of as a simplifying idealization.

In the contemporary discussion of hidden variable interpretations of quantum mechanics, much attention has been paid to the “no hidden variable” proof contained in an important paper of Kochen and Specker. It is a little noticed fact that Bell published a proof of the same result the preceding year, in his well-known 1966 article, where it is modestly described as a corollary to Gleason's theorem. We want to bring out the great simplicity of Bell's formulation of this result and to show how it can be extended in certain respects

One can give a strong sense to the idea that a relation does not 'reduce' to non-relational properties by saying that a relation does not supervene upon the non-relational properties of its relata. That there are such inherent relations I call the doctrine of relational holism, a doctrine which seems to conflict with traditional ideas about physicalism. At least parts of classical physics seem to be free of relational holism, but quantum mechanics, on at least some interpretations, incorporates the doctrine in an all pervasive way

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