Wittgenstein on the Foundations of Mathematics

In Part I, an attempt is made to survey the original source material on which any detailed assessment of Wittgenstein's remarks on the foundations of mathematics from his middle and later periods ought to be based. This survey is presented within the context of a sketch of Wittgenstein's biography, which also mentions some of the major developments in his thinking. In addition, certain main themes are emphasized; these have to do primarily with the Kantian aspects of Wittgenstein's thought and with his mysticism or the 'religious point of view'. In Part II, Kreisel's critique of Wittgenstein's remarks on the foundations of mathematics, which has been developed since 1958 in a series of published articles, receives close examination, and, in connection with this, different approaches to the philosophical investigation of mathematics are considered which represent genuine alternatives to Wittgenstein's approach. There are separate sections on Lakatos's Proofs and Refutations and Bourbaki's 'L'Architecture des Mathématiques'. Finally, besides a bibliography which surveys the reception of Wittgenstein's views on the foundations of mathematics, there are two substantial appendices, which are supplemental to Part I. The first of these gives the manuscript sources for typescripts 221 and 222-4, and the correspondences in both directions between these typescripts. The second appendix is part of a chronological version of von Wright's catalogue of Wittgenstein's papers, beginning in 1929

Postgenomics Characterization of an Essential Genetic Determinant of Mammary Pathogenic <i>Escherichia coli</i>

Escherichia coli are major bacterial pathogens causing bovine mastitis, a disease of great economic impact on dairy production worldwide. This work aimed to study the virulence determinants of mammary pathogenic E. coli (MPEC). By whole-genome sequencing analysis of 40 MPEC and 22 environmental (“dairy-farm” E. coli [DFEC]) strains, we found that only the fec locus (fecIRABCDE) for ferric dicitrate uptake was present in the core genome of MPEC and that it was absent in DFEC genomes (P &lt; 0.05). Expression of the FecA receptor in the outer membrane was shown to be citrate dependent by mass spectrometry. FecA was overexpressed when bacteria were grown in milk. Transcription of the fecA gene and of the inner membrane transport component fecB gene was upregulated in bacteria recovered from experimental intramammary infection. The presence of the fec system was shown to affect the ability of E. coli to grow in milk. While the rate of growth in milk of fec-positive (fec+) DFEC was similar to that of MPEC, it was significantly lower in DFEC lacking fec. Furthermore, deletion of fec reduced the rate of growth in milk of MPEC strain P4, whereas fec-transformed non-mammary gland-pathogenic DFEC strain K71 gained the phenotype of the level of growth in milk observed in MPEC. The role of fec in E. coli intramammary pathogenicity was investigated in vivo in cows, with results showing that an MPEC P4 mutant lacking fec lost its ability to induce mastitis, whereas the fec+ DFEC K71 mutant was able to trigger intramammary inflammation. For the first time, a single molecular locus was shown to be crucial in MPEC pathogenicity.is system