Let I be a quasimaximal subset of a computable basis of the fully efective vector space V ∞ . We give a necessary and sufficient condition for the existence of an isomorphism between the principal filter respectivelly. We construct both quasimaximal sets that satisfy and quasimaximal sets that do not satisfy this condition. With the latter we obtain a negative answer to Question 5.4 posed by Downey and Remmel in [3].

Upon introspection, we judge that suffering feels bad. I argue there is no appearance-reality gap when it comes to introspective judgments about simple, intrinsic, nonrepresentational phenomenal states like itches, tingling, and suffering's feeling bad. On constitutivism about phenomenal introspection, there is no appearance-reality gap here because these judgments are literally constituted by the phenomenal states they are about. As a result, we are directly acquainted with the intrinsic properties of experience in having these judgments. Reflecting on our direct acquaintance with (...) intrinsic badness, we can know that our suffering instantiates this judgment-independent evaluative property. (shrink)

According to leading Kant scholars, in mid-1760s Kant realizes that his program for the reform of metaphysics cannot be developed by the method of conceptual analysis which he had previously considered to be more adequate than the synthetic method of the Wolffians that imitates the mathematical one. In this paper, I put into question the claim of a pre-Critical project of ‘analytical metaphysics’ by trying to show that even for the ‘pre-Critical’ Kant the proper method of metaphysics is genuinely synthetic, (...) but the synthetic construction in question should have been prepared by a Critical and subsequent exhaustive analysis of key material-instrumental concepts of the peculiar philosophical science under question. (shrink)

Let I0 be a a computable basis of the fully effective vector space V∞ over the computable field F. Let I be a quasimaximal subset of I0 that is the intersection of n maximal subsets of the same 1-degree up to *. We prove that the principal filter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}^{\ast}(V,\uparrow )}$$\end{document} of V = cl(I) is isomorphic to the lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}(n, \overline{F})}$$\end{document} of subspaces (...) of an n-dimensional space over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{F}}$$\end{document}, a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma _{3}^{0}}$$\end{document} extension of F. As a corollary of this and the main result of Dimitrov (Math Log 43:415–424, 2004) we prove that any finite product of the lattices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\mathcal{L}(n_{i}, \overline{F }_{i}))_{i=1}^{k}}$$\end{document} is isomorphic to a principal filter of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{ L}^{\ast}(V_{\infty})}$$\end{document}. We thus answer Question 5.3 “What are the principal filters of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}^{\ast}(V_{\infty})?}$$\end{document} ” posed by Downey and Remmel (Computable algebras and closure systems: coding properties, handbook of recursive mathematics, vol 2, pp 977–1039, Stud Log Found Math, vol 139, North-Holland, Amsterdam, 1998) for spaces that are closures of quasimaximal sets. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Role of Scepticism in Modern Philosophy Reconsidered RICHARD H. POPKIN THE THEORY that the revival of ancient scepticism, and the application of its arguments to the controversies of the sixteenth century, played a vital role in the development of modern philosophy was first suggested by me almost forty years ago. A three-part article in the Review of Metaphysics entided "The Sceptical Crisis and the Rise of Modern Philosophy" (...) contained much of the theory.' What was added by the time of my History of Scepticism from Erasmus to Descartes (published in x96o,' but finished by 1958 ) was the importance of the sceptical arguments in the controversies of the Reformation and the CounterReformation, and the development of a religious scepticismmfideism--as a way of fending off criticism of basic religious beliefs.s One of the first reviews of my book was by Charles B. Schmitt,4 which he soon followed with his volume on Gianfrancesco Pico and then one on Cicero Scepticus.5 Before Charles Schmitt and I entered this arena, scepticism as a living philosophical view was hardly mentioned in histories of philosophy, which, by and large, saw modern philosophy as a rejection of Scholasticism, with nothing in between. One leaped from William of Ockham and Duns Scotus to Francis Bacon and Descartes, with perhaps a momentary nod to Montaigne as an amus- ' R. H. Popkin, "The ScepticalCrisisand the Riseof Modern Philosophy," Parts I, II, and III, ReviewofMetaphysics8 0953-54): 131--51,3O7--33,and 499-51o. First published in the University of Utrecht series of Texts and Studies in the History of Philosophy (Assen:Van Gorcum). sThis part of the story appeared independently in my article, "Scepticismand the CounterReformation in France," Archivfiir Reformatio~geschichte51 (a96o): 58-88. 4This appeared in Philosophyand PhenomenologicalResearch~3 (1963):455. 5His GianfrancescoPico dellaMirandola(I469-x533) and His Critiqueof Aristotleappeared in 1967, and CiceroScepticus:A Studyof theInfluenceof theAcademicain the Renaissancein 197~,both published in the International Archivesof the History of Ideas put out by Nijhoffin The Hague. [5ol] 502 JOURNAL OF THE HISTORY OF PHILOSOPHY 3 1:4 OCTOBER 1993 ing figure who provided Bacon with his stylistic form and Descartes with the opening line for the Discourse on Method. There were practically no articles about or studies of scepticism as a philosophical attitude or activity in modern philosophy before we went to work. The American philosopher Roderick Chisholm had written an article on Sextus and modern empiricism, and that was about it.6 When I took my first course in the history of philosophy with John Herman Randall, I frankly could not make much out of Plato or Aristotle, but when we were assigned to read Sextus Empiricus, I found an author who made sense. Later in the course I was introduced to Hume, whom Randall hated, and I loved. In a course with Paul Oskar Kristeller a few years later, on Hellenistic philosophy, Sextus appeared as a serious figure. A couple of years after that, in a seminar with Charles Hendel on Hume, I wrote a paper on Sextus and Hume. I showed it to Kristeller, who said drily and carefully that it might be worth looking into whether Hume had read Sextus, and whether there was a prior tradition of scepticism in European philosophy. Thus was I set off on the quest. Schmitt and I not only offered a lot of evidence previously ignored or unknown about the recovery of sceptical texts and their use in the philosophical discussions of the sixteenth and early seventeenth centuries, but we also offered a new paradigm, a new way of conceiving what problems were being agitated, a new way of understanding the kinds of answers being given as ways of resolving the sceptical crisis. The reception of our theory indicated that it provided a more meaningful picture of the making of the modern mind than what had previously been proposed.7 What I should like to deal with now are three questions: Has our theory stood up over almost four decades? Has it had to be revised or amended? And does it need to be expanded (as I have been doing) to encompass another kind of scepticism, that directed against traditional religion from about... (shrink)

Translation:Hendrik Josephus POS, „Phénoménologie et linguistique.“ In: Keur uit de verspreide geschrift en van Dr. H. J. Pos. Vol. I. Assen: Van Loghum Slaterus 1957, p. 131–141.

In lieu of an abstract, here is a brief excerpt of the content:Giulio Castellani (1528-1586): A Sixteenth-Century Opponent of Scepticism CHARLES B. SCH1VHTT THE PROBLEMOF THE ORIGINS of scepticism in early modern philosophy has been a much debated issue. Sanches, Montaigne, Charron, and Bayle all contributed to the milieu which made it possible for the sceptical direction of thought to develop into such a potent force by the time of David Hume. The actual origins of modern scepticism, which seem to (...) go back to a slightly earlier date, lie in the confluence of several different intellectual movements during the early years of the sixteenth century: Christian anti-intellectualism, the reintroduction of the literary remains of the ancient sceptical tradition, the epistemological developments of scholastic nominalism, and certain inherent tendencies of Renaissance humanism. It is in the early decades of the sixteenth century that the seeds which later blossomed forth at the time of Hume originally took root. Hume himself merely reaped the harvest of several hundred years of sceptical preparation? Aside from certain manifestations of doubt which developed out of the epistemological theories of fourteenth-century nominalism, the origins of modern scepticism are generally held to date from the first publication of Sextus Empiricus' ancient summaries of Pyrrhonism during the decade of the 1560's. While it has previously been recognized that at least hints of scepticism were current in the fifteenth and early sixteenth centuries, the implications to be derived from this fact do not seem to have been adequately exploredT I shall not here go into these early manifestations of scepticism in a detailed way. Rather, I shall briefly touch upon a few little-known examples of the influence of ancient scepticism during the Reniassance and, then, I shall focus upon an early and practically neglected attack upon scepticism published before the first printings of Sextus Empiricus' writings. I shall discuss the circumstances of the composition of Giulio Castellani's anti-sceptical work, Adversus Marci TuIlii Ciceronis academicas questiones disi For a recent survey of early modem scepticism see Richard H. Popkin, The History o] Scepticism /tom Erasmus to Descartes (Assen: 1960). Of the large literature which connects scepticism with religious doubt during this period see especially Henri Busson, Les sources et le dgveloppement du rati~nalizme dar~ la litt~rature ]ran~aise de la Renaissance (Paris: 1957) and Don Cameron Allen, Doubt's Boundless Sea (Baltimore: 1964). The di.~cussionof this period seems to be the weakest part of Popkin's excellent book, particularly with regard to the treatment which he gives to Italian thought. See, also, his other articles, especially,"Skepticismand the Counter-Reformation in France," Archiv/fir Re/armationsgeschichte, LI (1960),58-86and "The High Road to Pyrrhonism," American Philosophical Quarterly, II (1965),18--32.In my forthcoming study, Gian]rancesco Pico (1469-1533) and His Critique o/Aristotle, I give a detailed analysis of the major representative of early sixteenthcentury scepticism. [151 16 HISTORY OF PHILOSOPHY putatio (1558), which antedates the first printing of Sextus Empiricus by four years, indicating that scepticism was already widespread enough to provoke an attack from the camp of the dogmatists. Furthermore, I shall analyze Castellani 's arguments in the context of the philosophical views of the mid-sixteenth century. Scepticism in the Early Renaissance Direct knowledge of the major ancient source of scepticism, the already mentioned writings of Sextus Empiricus, was rare throughout the Middle Ages. There are but two known extant Latin manuscripts which date before 1400. s From the fifteenth century we know of two more manuscripts, neither complete in itself, but together containing a significant portion of the extant writings of Sextus. 4 This evidence indicates that Sextus' works were not well known in translation before the first Latin editions of The Oulines o] Pyrrhonism (1562) and of Against the Mathematicians (1569). With the advent of an increased interest in and knowledge of Greek in Western Europe in the fifteenth century, we find a corresponding increase in the number of Greek manuscripts of Sextus Empiricus. Consequently, by the time of the first printings, an appreciable number of copies of his writings were available. Some were brought from the East, but a large number also are attributable to European scribes. 5 We also know that in... (shrink)

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

v. 1. Sŏngnihak pʻyŏn -- v. 2. Kyŏngse sasang pʻyŏn.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.2 (2003) 272-273 [Access article in PDF] Matthew of Orléans. Sophistaria sive summa communium distinctionum circa sophismata accidentium. Edited by Joke Spruyt. Leiden: Brill, 2001. Pp. ix + 581. Cloth, $151.00. Matthew of Orléans is not a famous author (indeed, even his name is given tentatively by the editor on the basis of the explicit of one manuscript). And the Sophistaria was apparently (...) not one the most influential works of its time, the early thirteenth century (its full text is preserved only in a couple of manuscripts, and it has never been printed before). Yet, the Sophistaria of Matthew of Orléans is a fine example of a characteristic genre in the rich tradition of medieval logical literature. The genre itself is an interesting combination of two other characteristic genres: treatises on syncategoremata and sophismata. The sophismata treatises are discussions of problem-sentences (sophismata) usually grouped together to illustrate some logical doctrinal points, especially concerning the resolution of ambiguities caused by the logical behavior of syncategorematic terms in various contexts. The treatises on syncategoremata provide systematic discussions of the logical behavior of syncategorematic words, i.e., logical connectives, themselves. But these treatises also illustrate their doctrinal points by resolving the ambiguities of sophismata, mostly using some commonly accepted distinctions concerning how the function of the syncategoremata is to be construed in the contexts provided by these problem-sentences. The proper subject matter of the sophistaria treatises is the discussion of these common distinctions, dealing especially with ambiguities caused by (what we would describe as) the different possible scopes of the syncategoremata occurring in the paradigmatic sophismata.For example, take the sentence "Someone seeing nothing is someone seeing something." This sentence can be regarded as ambiguous, if we analyze "nothing" into "not... a thing," yielding (1) "Someone not seeing a thing is someone seeing something," which can be taken to be ambiguous between (a) "Someone not seeing anything is someone seeing something" and (b) "Someone not seeing something is someone seeing something," depending on whether we take "not" in (1) to be operating (a) on "seeing a thing," or (b) only on "seeing." On this analysis, the ambiguous sentence is obviously false in the first sense, but may be true in the second, for it may be true of Socrates who does not see Plato but sees Coriscus.To be sure, this is not the only possible way to account for the (genuine or putative) ambiguity of the original sentence. In fact, this is not the account considered by Matthew of Orléans or in a parallel passage by Peter of Spain in their analyses of the corresponding Latin sentence (Nihil videns est aliquid videns), although one of the arguments for the truth of the sophisma they reject would be a good argument for the second reading provided here (cf. Peter of Spain, Tractatus [Van Gorcum: Assen, 1972], 220, ll. 10-6, and Sophistaria, 88, ll. 16-20). In any case, the point of the sophistaria treatises is precisely the discussion of the merits and demerits of such possible accounts.The Sophistaria of Matthew of Orléans is a well-organized, highly structured treatise, divided into eight chapters, corresponding to the eight groups of syncategorematic terms [End Page 272] it deals with. The first chapter is devoted to the discussion of common distinctions concerning negations (both propositional and term-negations, including privative negation), the second deals with exclusive words (such as "only"), the third with exceptive words ("besides," "except," "unless"), the fourth with the conditional sign "if," the fifth with the modalities "necessarily" and "contingently," the sixth with the verbs "begins" and "ceases," the seventh with the word "whether," and the eighth with the distributive sign "every," that is, the universal sign that causes the terms it is construed with to be distributed for everything that falls under it.The discussion of these topics in the individual chapters is organized around typical scholastic questions raised concerning the validity of some common distinction in connection with typical sophismata, involving ambiguities in the operation... (shrink)

jild-i 1. Chand maqālah darbārah-ʼi maqāmāt-i [i.e. maqālāt] ʻilmī, va mujāhadāt-i farhangī, va khadamāt-i Islāmī-i ū-- -- jild-i 2. Chand maqālah az Prūfisūr ʻAbd al-Javād Falāṭūrī Iṣfahānī.