Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

Individualism: The Cultural Logic of Modernity is an edited collection of sixteen essays on the idea of the modern sovereign individual in the western cultural tradition. Reconsidering the eighteenth-century realist novel, twentieth-century modernism, and underappreciated topics on individualism and literature, this volume provocatively revises and enriches our understanding of individualism as the generative premise of modernity itself.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

We prove the following results: (i) PV proves NP ⊆ P/poly iff PV proves coNP ⊆ NP/O(1). (ii) If PV proves NP ⊆ P/poly then PV proves that the Polynomial Hierarchy collapses to the Boolean Hierarchy. (iii) $S_{2}^{1}$ proves NP ⊆ P/poly iff $S_{2}^{1}$ proves coNP ⊆ NP/O(log n). (iv) If $S_{2}^{1}$ proves NP ⊆ P/poly then $S_{2}^{1}$ proves that the Polynomial Hierarchy collapses to PNP[log n]. (v) If $S_{2}^{2}$ proves NP ⊆ P/poly then $S_{2}^{2}$ proves that the Polynomial Hierarchy (...) collapses to PNP. Motivated by these results we introduce a new concept in proof complexity: proof systems with advice, and we make some initial observations about them. (shrink)