Some comments on Ian Rumfitt's bilateralism

Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of `exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use' (Rumfitt (2000): 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of bilateral logic which also meets those requirements. Thus Rumfitt cannot claim that only classical bilateral rules of inference succeed in imparting a coherent sense onto the connectives. My system can be extended to classical logic by adding the intuitionistically unacceptable half of a structural rule Rumfitt uses to codify the relation between assertion and denial. Thus there is a clear sense in which, in the bilateral framework, the difference between classicism and intuitionism is not one of the rules of inference governing negation, but rather one of the relation between assertion and denial

Ethnic-minority groups in England and Wales-factors associated with the size and timing of elevated COVID-19 mortality: a retrospective cohort study linking census and death records

BACKGROUND: We estimated population-level associations between ethnicity and coronavirus disease 2019 (COVID-19) mortality using a newly linked census-based data set and investigated how ethnicity-specific mortality risk evolved during the pandemic. METHODS: We conducted a retrospective cohort study of respondents to the 2011 Census of England and Wales in private households, linked to death registrations and adjusted for emigration (n = 47 872 412). The outcome of interest was death involving COVID-19 between 2 March 2020 and 15 May 2020. We estimated hazard ratios (HRs) for ethnic-minority groups compared with the White population, controlling for individual, household and area characteristics. HRs were estimated on the full outcome period and separately for pre- and post-lockdown periods. RESULTS: In age-adjusted models, people from all ethnic-minority groups were at elevated risk of COVID-19 mortality; the HRs for Black males and females were 3.13 (95% confidence interval: 2.93 to 3.34) and 2.40 (2.20 to 2.61), respectively. However, in fully adjusted models for females, the HRs were close to unity for all ethnic groups except Black [1.29 (1.18 to 1.42)]. For males, the mortality risk remained elevated for the Black [1.76 (1.63 to 1.90)], Bangladeshi/Pakistani [1.35 (1.21 to 1.49)] and Indian [1.30 (1.19 to 1.43)] groups. The HRs decreased after lockdown for all ethnic groups, particularly Black and Bangladeshi/Pakistani females. CONCLUSION: Differences in COVID-19 mortality between ethnic groups were largely attenuated by geographical and socio-demographic factors, though some residual differences remained. Lockdown was associated with reductions in excess mortality risk in ethnic-minority populations, which has implications for a second wave of infection

Correlation Between the Deuteron Characteristics and the Low-energy Triplet np Scattering Parameters

The correlation relationship between the deuteron asymptotic normalization constant, $A_{S}$, and the triplet np scattering length, $a_{t}$, is investigated. It is found that 99.7% of the asymptotic constant $A_{S}$ is determined by the scattering length $a_{t}$. It is shown that the linear correlation relationship between the quantities $A_{S}^{-2}$ and $1/a_{t}$ provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant $A_{S}$ and for the root-mean-square deuteron radius $r_{d}$, the results obtained with the experimental value recommended at present for the triplet scattering length $a_{t}$ are exaggerated with respect to their experimental counterparts. By using the latest experimental phase shifts of Arndt et al., we obtain, for the low-energy scattering parameters ($a_{t}$, $r_{t}$, $P_{t}$) and for the deuteron characteristics ($A_{S}$, $r_{d}$), results that comply well with experimental data.Comment: 19 pages, 1 figure, To be published in Physics of Atomic Nucle

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

General-elimination stability

General-elimination harmony articulates Gentzen's idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies' test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett's notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable.Publisher PDFPeer reviewe