Commentary on the Nyāyamañjarī of Jayanta Bhaṭṭa, fl. 850-910, exegesis of Gautama's Nyayasutra, basic statement of the classic Hindu Nyaya philosophy; critical edition.

We consider the well-known provability logic GLP. We prove that the GLP-provability problem for polymodal formulas without variables is PSPACE-complete. For a number n, let L0n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^{n}_0}$$\end{document} denote the class of all polymodal variable-free formulas without modalities ⟨n⟩,⟨n+1⟩,...\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle n \rangle,\langle n+1\rangle,...}$$\end{document}. We show that, for every number n, the GLP-provability problem for formulas from L0n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^{n}_0}$$\end{document} (...) is in PTIME. (shrink)

A central question in the history of metaphysics concerns the ontological status of such notions as 'redness,' 'humanity,' or 'animality,' which one calls 'universals.' Since one uses these notions to describe objects in the real world, it may seem intuitive that they exist in extramental reality: one says that universals are 'real'. Famously, though, several problems arise from this view. A central problem known both to medieval and contemporary scholars goes as follows: I look at a red rose and recognize (...) that there is 'redness' in it. Then, I look at a red apple and recognize that there is 'redness' in it, too. Does this mean that one and the same 'redness' appears in both the rose and the... (shrink)