Wittgenstein's ab-Notation: An Iconic Proof Procedure

This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how to extend his method to a subset of first-order formulas, namely, formulas that do not contain dyadic sentential connectives within the scope of any quantifier.     

Underdetermination and provability: a reply to Olaf Müller

Newton claims to have proven the heterogeneity of light through his experimentum crucis. However, Olaf Müller has worked out in detail Goethe’s idea that one could likewise prove the heterogeneity of darkness by inverting Newton’s famous experiment. Müller concludes that this invalidates Newton’s claim of proof. Yet this conclusion only holds if the heterogeneity of light and the heterogeneity of darkness is logically incompatible. This paper shows that this is not the case. Instead, in Quine’s terms, we have two logically compatible theories based on mutually irreducible theoretical terms. From a Quinean point of view, this does no harm to the provability of the corresponding statements.     

The once and future Jew: The Croxton Play of the Sacrament, little Robert of Bury and historical memory

The Jews who purchase and attack the host in the fifteenth-century East Anglian drama, the Croxton Play of the Sacrament, have long been regarded by critics as referents to Lollards or to doubters more generally, not to Jews. However, the play does refer to the history of Jews in Bury St. Edmunds, where, most likely, it was performed, and more specifically, it refers to the 1181 ritual murder accusation surrounding Little Robert of Bury. This accusation was commemorated in a variety of forms in Bury well into the fifteenth century. Further, in its representation of host desecration as a literal reenactment of the Passion, the play creates a temporal mode in which the Jews re-enact the Passion in the present, just as the Mass is a re-enactment of the Crucifixion. The play simultaneously makes the audience witness to the murder of little Robert and to the Crucifixion, with both existing in a kind of “eternal present,” a temporality central to the Mass and also to related late-medieval English devotional practices. The story of little Robert comes to exist not only in historical memory, but also in the eternal present in which the Crucifixion and its re-enactments are joined. This powerful temporality creates a conception of the Jew as perpetual murderer, guilty not only of crucifying Christ in the historical past, but in the present, and until the Parousia in the future, thus enabling a particular aspect of the negative stereotype of “the Jew,” the perpetually present enemy, ever plotting against Christ and Christendom. This revised version was published online in June 2006 with corrections to the Cover Date.     

Health locus of control and health behaviour: results from a nationally representative survey

The present study aims to examine the association between sociodemographic variables and health locus of control (HLC) as well as HLC and health behaviour. Data from a representative sample of the German adult population, the Telephone Health Survey 2006 (GSTel06; N=5542), were used. A German version of the MHLC (multidimensional HLC) scales was used. Associations between sociodemographic variables and three dimensions of HLC (internal, powerful others and chance) and between HLC and health behaviour were calculated. In particular, higher age, low socioeconomic status and migration background were associated with higher HLC scores on the powerful others and chance dimension. Subjects scoring high on the chance dimension did less sports activity (OR: 0.8; CI: 0.7-0.9), had less medical teeth protection (0.7; 0.6-0.9), fewer health courses (0.8; 0.7-0.9) and conducted less systematic information-seeking (0.8; 0.6-0.9), while results regarding internal and powerful others HLC remained mainly insignificant. High chance HLC can be regarded as risk factor of adequate health behaviour. The associations between high chance HLC, low socioeconomic status and migration background emphasise the need for treatments and prevention programmes tailored to modify the high chance HLC of socially disadvantaged populations.     

Wittgenstein on the Infinity of Primes

It is controversial whether Wittgenstein's philosophy of mathematics is of critical importance for mathematical proofs, or is only concerned with the adequate philosophical interpretation of mathematics. Wittgenstein's remarks on the infinity of prime numbers provide a helpful example which will be used to clarify this question. His antiplatonistic view of mathematics contradicts the widespread understanding of proofs as logical derivations from a set of axioms or assumptions. Wittgenstein's critique of traditional proofs of the infinity of prime numbers, specifically those of Euler and Euclid, not only offers philosophical insight but also suggests substantive improvements. A careful examination of his comments leads to a deeper understanding of what proves the infinity of primes.