Solutions to the Knower Paradox in the Light of Haack’s Criteria

The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three of which hinge on intricacies of provability logic and its arithmetical interpretations. To check whether Égré’s solutions are satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack and we propose some refinements of them. This article aims to describe to what extent the knower paradox can be solved using provability logic and to what extent the solutions proposed in the literature satisfy Haack’s criteria. Finally, the article offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox and its solutions.</p

Provability logic meets the knower paradox

The knower paradox states that the statement `We know that this statement is false' leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Egré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, including one by Solovay. To check whether this solution is satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack. This extended abstract aims to describe to what extent the knower paradox can be solved using provability logic and to what extent a solution proposed in the literature satisfies Haack's criteria. Finally, the extended offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox

Growth of transcendental entire solution of some q-difference equation

Technical Reports of Mathematical Sciences, Chiba University, Vol.18(2002

Assessing disability weights based on the responses of 30,660 people from four European countries

Background: In calculations of burden of disease using disability-adjusted life years, disability weights are needed to quantify health losses relating to non-fatal outcomes, expressed as years lived with disability. In 2012 a new set of global disability weights was published for the Global Burden of Disease 2010 (GBD 2010) study. That study suggested that comparative assessments of different health outcomes are broadly similar across settings, but the significance of this conclusion has been debated. The aim of the present study was to estimate disability weights for Europe for a set of 255 health states, including 43 new health states, by replicating the GBD 2010 Disability Weights Measurement study among representative population samples from four European countries. Methods: For the assessment of disability weights for Europe we applied the GBD 2010 disability weights measurement approach in web-based sample surveys in Hungary, Italy, Netherlands, and Sweden. The survey included paired comparisons (PC) and population health equivalence questions (PHE) formulated as discrete choices. Probit regression analysis was used to estimate cardinal values from PC responses. To locate results onto the 0-to-1 disability weight scale, we assessed the feasibility of using the GBD 2010 scaling approach based on PHE questions, as well as an alternative approach using non-parametric regression. Results: In total, 30,660 respondents participated in the survey. Comparison of the probit regression results from the PC responses for each country indicated high linear correlations between countries. The PHE data had high levels of measurement error in these general population samples, which compromises the ability to infer ratio-scaled values from discrete choice responses. Using the non-parametric regression approach as an alternative rescaling procedure, the set of disability weights were bounded by distance vision mild impairment and anemia with the lowest weight (0.004) and severe multiple sclerosis with the highest weight (0.677). Conclusions: PC assessments of health outcomes in this study resulted in estimates that were highly correlated across four European countries. Assessment of the feasibility of rescaling based on a discrete choice formulation of the PHE question indicated that this approach may not be suitable for use in a web-based survey of the general population. Electronic supplementary material The online version of this article (doi:10.1186/s12963-015-0042-4) contains supplementary material, which is available to authorized users

The USP7-TRIM27 axis mediates non-canonical PRC1.1 function and is a druggable target in leukemia

In an attempt to unravel functionality of the non-canonical PRC1.1 Polycomb complex in human leukemogenesis, we show that USP7 and TRIM27 are integral components of PRC1.1. USP7 interactome analyses show that PRC1.1 is the predominant Polycomb complex co-precipitating with USP7. USP7 inhibition results in PRC1.1 disassembly and loss of chromatin binding, coinciding with reduced H2AK119ub and H3K27ac levels and diminished gene transcription of active PRC1.1-controlled loci, whereas H2AK119ub marks are also lost at PRC1 loci. TRIM27 and USP7 are reciprocally required for incorporation into PRC1.1, and TRIM27 knockdown partially rescues USP7 inhibitor sensitivity. USP7 inhibitors effectively impair proliferation in AML cells in vitro, also independent of the USP7-MDM2-TP53 axis, and MLL-AF9-induced leukemia is delayed in vivo in human leukemia xenografts. We propose a model where USP7 counteracts TRIM27 E3 ligase activity, thereby maintaining PRC1.1 integrity and function. Moreover, USP7 inhibition may be a promising new strategy to treat AML patients