In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.

This paper presents and defends a way to add a transparent truth predicate to classical logic, such that T A and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STT (for Strict-Tolerant Truth), is that it supports a nontransitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STT allows for arise in paradoxical cases.

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning-one which takes meaning to be constituted by assertibility and deniability conditions-and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system-ST-that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be nontransitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for nonclassical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favorably to more familiar related systems, and some objections are considered and responded to.

This paper shows how to conservatively extend a classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth-involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system features admissible Cut, but the other does not.)

A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson's objections.

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The Multi-Attribute Method (MAM) Consortium was initially formed as a venue to harmonize best practices, share experiences, and generate innovative methodologies to facilitate widespread integration of the MAM platform, which is an emerging ultra-high-performance liquid chromatography–mass spectrometry application. Successful implementation of MAM as a purity-indicating assay requires new peak detection (NPD) of potential process- and/or product-related impurities. The NPD interlaboratory study described herein was carried out by the MAM Consortium to report on the industry-wide performance of NPD using predigested samples of the NISTmAb Reference Material 8671. Results from 28 participating laboratories show that the NPD parameters being utilized across the industry are representative of high-resolution MS performance capabilities. Certain elements of NPD, including common sources of variability in the number of new peaks detected, that are critical to the performance of the purity function of MAM were identified in this study and are reported here as a means to further refine the methodology and accelerate adoption into manufacturer-specific protein therapeutic product life cycles.