Wittgenstein's Elimination of Identity for Quantifier-Free Logic

One of the central logical ideas in Wittgenstein's Tractatus logico-philosophicus is the elimination of the identity sign in favor of the so-called "exclusive interpretation" of names and quantifiers requiring different names to refer to different objects and (roughly) different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier's account, the first concerning the treatment of individual constants, the second concerning so-called "pseudo-propositions" ("Scheinsätze") of classical logic such as a=a or a=b v b=c -> a=c. We argue that overcoming these problems requires two fairly drastic departures from Wehmeier's account: (1) Not every formula of classical first-order logic will be translatable into a single formula of Wittgenstein's exclusive notation. Instead, there will often be a multiplicity of possible translations, revealing the original "inclusive" formulas to be ambiguous. (2) Certain formulas of first-order logic such as a=a will not be translatable into Wittgenstein's notation at all, being thereby revealed as nonsensical pseudo-propositions which should be excluded from a "correct" conceptual notation. We provide translation procedures from inclusive quantifier-free logic into the exclusive notation that take these modifications into account and define a notion of logical equivalence suitable for assessing these translations

Wittgenstein's Elimination of Identity for Quantifier-Free Logic

One of the central logical ideas in Wittgenstein's Tractatus logico-philosophicus is the elimination of the identity sign in favor of the so-called "exclusive interpretation" of names and quantifiers requiring different names to refer to different objects and (roughly) different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier's account, the first concerning the treatment of individual constants, the second concerning so-called "pseudo-propositions" ("Scheinsätze") of classical logic such as a=a or a=b v b=c -> a=c. We argue that overcoming these problems requires two fairly drastic departures from Wehmeier's account: (1) Not every formula of classical first-order logic will be translatable into a single formula of Wittgenstein's exclusive notation. Instead, there will often be a multiplicity of possible translations, revealing the original "inclusive" formulas to be ambiguous. (2) Certain formulas of first-order logic such as a=a will not be translatable into Wittgenstein's notation at all, being thereby revealed as nonsensical pseudo-propositions which should be excluded from a "correct" conceptual notation. We provide translation procedures from inclusive quantifier-free logic into the exclusive notation that take these modifications into account and define a notion of logical equivalence suitable for assessing these translations

CtIP tetramer assembly is required for DNA-end resection and repair.

Mammalian CtIP protein has major roles in DNA double-strand break (DSB) repair. Although it is well established that CtIP promotes DNA-end resection in preparation for homology-dependent DSB repair, the molecular basis for this function has remained unknown. Here we show by biophysical and X-ray crystallographic analyses that the N-terminal domain of human CtIP exists as a stable homotetramer. Tetramerization results from interlocking interactions between the N-terminal extensions of CtIP's coiled-coil region, which lead to a 'dimer-of-dimers' architecture. Through interrogation of the CtIP structure, we identify a point mutation that abolishes tetramerization of the N-terminal domain while preserving dimerization in vitro. Notably, we establish that this mutation abrogates CtIP oligomer assembly in cells, thus leading to strong defects in DNA-end resection and gene conversion. These findings indicate that the CtIP tetramer architecture described here is essential for effective DSB repair by homologous recombination.We thank M. Kilkenny for help with the collection of X-ray diffraction data, A. Sharff and P. Keller for help with X-ray data processing and J.D. Maman for assistance with SEC-MALS. This work was supported by a Wellcome Trust Senior Research Fellowship award in basic biomedical sciences (L.P.), an Isaac Newton Trust research grant (L.P. and O.R.D.) and a Cambridge Overseas Trust PhD studentship (M.D.S.). Research in the laboratory of S.P.J. is funded by Cancer Research UK (CRUK; programme grant C6/A11224), the European Research Council and the European Community Seventh Framework Programme (grant agreement no. HEALTH-F2-2010-259893 (DDResponse)). Core funding is provided by Cancer Research UK (C6946/A14492) and the Wellcome Trust (WT092096). S.P.J. receives his salary from the University of Cambridge, supplemented by CRUK. J.V.F. is funded by Cancer Research UK programme grant C6/A11224 and the Ataxia Telangiectasia Society. R.B. and J.C. are funded by Cancer Research UK programme grant C6/A11224. Y.G. and M.D. are funded by the European Research Council grant DDREAM.This is the accepted manuscript of a paper published in Nature Structural & Molecular Biology, 22, 150–157 (2015) doi: 10.1038/nsmb.293

Wittgenstein's Elimination of Identity for Quantifier-free logic

One of the central logical ideas in Wittgenstein’s Tractatus logico-philosophicus is the elimination of the identity sign in favor of the so-called “exclusive interpretation” of names and quantifiers requiring different names to refer to different objects and (roughly) different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier’s account, the first concerning the treatment of individual constants, the second concerning so-called “pseudo-propositions” (Scheins¨atze) of classical logic such as a = a or a = b ^ b = c ! a = c. We argue that overcoming these problems requires two fairly drastic departures from Wehmeier’s account: (1) Not every formula of classical first-order logic will be translatable into a single formula of Wittgenstein’s exclusive notation. Instead, there will often be amultiplicity of possible translations, revealing the original “inclusive” formulas to be ambiguous. (2) Certain formulas of first-order logic such as a = a will not be translatable intoWittgenstein’s notation at all, being thereby revealed as nonsensical pseudo-propositions which should be excluded from a “correct” conceptual notation.We provide translation procedures from inclusive quantifier-free logic into the exclusive notation that take these modifications into account and define a notion of logical equivalence suitable for assessing these translations.Peer Reviewe

How Is the Explanation of Action Possible? Theory of Action in Davidson's "Unified Theory of Meaning and Action"

In seiner „Einheitlichen Bedeutungs- und Handlungstheorie“ versuchte Davidson, das Szenario der „radikalen Interpretation“ von der Sprachphilosophie auf die Handlungstheorie zu übertragen. Die Arbeit untersucht diese Theorie mit dem Ziel, eine Grundfrage der Methodologie der Sozialwissenschaften zu beantworten: Wie ist es möglich, absichtliche Handlungen wissenschaftlich zu erklären?In his „Unified Theory of Meaning and Action“, Davidson tried to extend the perspective of the “radical interpreter” from the philosophy of language to the theory of action. The present book examines this theory in an attempt to answer a basic methodological question of social science: How is the scientific explanation of intentional action possible

Wie ist Handlungserklärung möglich? Handlungstheorie in Davidsons Unified Theory of Meaning and Action

In his „Unified Theory of Meaning and Action“, Davidson tried to extend the perspective of the “radical interpreter” from the philosophy of language to the theory of action. The present book examines this theory in an attempt to answer a basic methodological question of social science: How is the scientific explanation of intentional action possible?In seiner „Einheitlichen Bedeutungs- und Handlungstheorie“ versuchte Davidson, das Szenario der „radikalen Interpretation“ von der Sprachphilosophie auf die Handlungstheorie zu übertragen. Die Arbeit untersucht diese Theorie mit dem Ziel, eine Grundfrage der Methodologie der Sozialwissenschaften zu beantworten: Wie ist es möglich, absichtliche Handlungen wissenschaftlich zu erklären

Dosimetric methods for and influence of exposure parameters on the establishment of reference doses in mammography

For the establishment of reference doses in mammography it is important to apply a dosimetric model relevant for risk assessment. Differences in dosimetric methods applied in mammography are related to the dosemeters used, e.g. thermoluminescent detectors and ionisation chambers, and the dosimetric quantities determined, i.e. entrance surface air kerma, entrance surface dose or average glandular dose. The exposure parameters influencing absorbed dose due to mammography include the X ray tube assembly, i.e. anode material, filtration and tube voltage; the exposure conditions, e.g. antiscatter grid, automatic exposure control and magnification; and characteristics of the film-screen combination including film processing and film density. The female breasts examined can be represented, on average, by a phantom or by a representative sample of patients. Reference values established in various protocols for entrance surface air kerma, entrance surface dose and average glandular dose are presented and discussed