We prove that the zero-set of a C ∞ function belonging to a noetherian differential ring M can be written as a finite union of C ∞ manifolds which are definable by functions from the same ring. These manifolds can be taken to be connected under the additional assumption that every zero-dimensional regular zero-set of functions in M consists of finitely many points. These results hold not only for C ∞ functions over the reals, but more generally for definable C (...) ∞ functions in a definably complete expansion of an ordered field. The class of definably complete expansions of ordered fields, whose basic properties are discussed in this paper, expands the class of real closed fields and includes o-minimal expansions of ordered fields. Finally, we provide examples of noetherian differential rings of C ∞ functions over the reals, containing non-analytic functions. (shrink)

We show that the theory of the real field with a generic real power function is decidable, relative to an oracle for the rational cut of the exponent of the power function. We also show the existence of generic computable real numbers, hence providing an example of a decidable o-minimal proper expansion of the real field by an analytic function.

Wilkie 5 397) proved a “theorem of the complement” which implies that in order to establish the o-minimality of an expansion of with C∞ functions it suffices to obtain uniform bounds on the number of connected components of quantifier free definable sets. He deduced that any expansion of with a family of Pfaffian functions is o-minimal. We prove an effective version of Wilkie's theorem of the complement, so in particular given an expansion of the ordered field with finitely many C∞ (...) functions, if there are uniform and computable upper bounds on the number of connected components of quantifier free definable sets, then there are uniform and computable bounds for all definable sets. In such a case the theory of the structure is effectively o-minimal: there is a recursively axiomatized subtheory such that each of its models is o-minimal. This implies the effective o-minimality of any expansion of with Pfaffian functions. We apply our results to the open problem of the decidability of the theory of the real field with the exponential function. We show that the decidability is implied by a positive answer to the following problem ): given a language L expanding the language of ordered rings, if an L-sentence is true in every L-structure expanding the ordered field of real numbers, then it is true in every o-minimal L-structure expanding any real closed field. (shrink)

In a departure from the tradition of the Neoplatonic commentators of the Organon, the sequence of summaries in the insert two treatises between the Prior Analytics and the Posterior Analytics, namely the Resolution and the Sophistical Refutations. And even though the Tal30), while it. The contents of kitl and the different titles that the fahiktist), lead one to realize that it is an addition to the Prior Analytics offering a theory concerning the generation of the premisses of the syllogism, something (...) that may have appeared to Alfarabi as missing from Kits. (shrink)

The Sufi saints, in their texts, successfully ingrained Love as the destination of spiritual path, to accomplish the Divine. The objective of this study was to focus on the cult of Sufism, in general, and on the Sufi poetry of Fakhr al-Din ʿIrāqī, in particular as reflected in his anthology, Kitāb al-lamaʿāt. Adopting a historical approach, the study analyzed the evolution of Sufi poetry since the beginning, and examined the poetry of ʿIrāqī in the context of Islamic mysticism. This qualitative (...) study adopted an exploratory content analysis method and documentation research to examine the Sufi philosophy as reflected in the sampled poetry of ʿIrāqī. For the realization of this goal, a research was conducted on the available published resources. The documentation survey helped discover the truth of ʿIrāqī ’s poetry in the context of Spiritual love. It was discovered that ʿIrāqī ’s philosophy of Love was based on metaphysical transcendentalism, where spiritual attainment was achieved through formlessness mirrored in the form of Beauty as the manifestation of Love. (shrink)

Abstrak: Pembacaan atas aspek apokaliptik Kitab Daniel sering dipusatkan pada bagian kedua kitab itu (Dan. 7-12). Bagian pertamanya (Dan. 1-6) hanya dibaca sebagai cerita-cerita heroisme iman. Dengan begitu, sifat apokaliptik tidak kelihatan sebagai karakteristik kitab itu secara keseluruhan. Apokaliptik sendiri cenderung dikaitkan dengan eskatologi, dan bagian kedua kitab tersebut secara mencolok memakai kata “akhir.” Pengaitan aspek apokaliptik dengan fatalisme akhir zaman berkembang di kalangan sekte kiamat. Kendati aspek eskatologisnya, apokaliptik seharusnya juga dipahami dalam matriks hikmat. Jika (...) dibaca dalam kesatuan dan keutuhannya, kitab itu memperlihatkan gagasan mengenai hidup berhikmat dalam mengantisipasi kiamat, bukan dengan menarik diri dari dunia, melainkan setia kepada Allah dan kritis terhadap arogansi kekuasaan. Kata-kata Kunci: apokaliptik, kiamat, radikal, Makabe, sektarian, nubuat, hikmat, eskatologi. Abstract: The reading of the apocalyptic aspect of the Book of Daniel is often focused on the book’s second part (Dan. 7-12). Its first part (Dan. 1-6) is read only as stories of faithful heroism. In this manner, the apocalyptic dimension is not seen as characteristic of the book as a whole. Apocalypse itself tends to be associated with eschatology, and indeed the second part of the book strikingly makes use of the word “end.” The association of apocalypse with the fatalism of the end time develops within the doomsday sect. Despite its eschatological dimension, the apocalyptic aspect should be read within the matrix of wisdom. When being read in its unity and integrity, the book demonstrates the idea of living wisely in the anticipation of the end, not by withdrawing oneself away from the world, but by being faithful to God and being critical of the arrogance of power. Keywords: apocalyptic, doomsday, radical, Maccabees, sectarian, prophecy, wisdom, eschatology. (shrink)

Thoughts of Ki Ageng Suryamentaram on Javanese philosophy and ethics.

Translator's introduction -- Mir Damad's introduction -- 1st qabas. On the kinds of creation (huduth) and the divisions of existence according to them, establishing the bases of judgment, and defining the area of dispute -- 2nd qabas. On the three kinds of essential antecedence and constructing the demonstration by way of essential priority (taqaddum bi'l-dhat) -- 3rd qabas. The two kinds of separate posteriority and constituting the demonstration by way of eternal priority -- 4th qabas. Quotations from the book of (...) god and the traditions of his messenger, and from the traditions of the lofty and pure imams -- 5th qabas. Concerning the mode of existence of the unqualified natures and the path of the demonstration by the mode of the existence of the nature -- 6th qabas. On the continuity of time and motion; setting up the course of the demonstration with respect to the continuity of the magnitude of time according to the natural system in two ways; establishing the finitude of extended continuous quantity; and invalidating a numerical infinity -- With respect to successive temporal creatures -- 7th qabas. A series of abridged arguments, unsound dialectical arguments, and criticism of certain syllogisms and controversial sophistical doubts according to the two extremes of the two groups -- 8th qabas. Inquiry into the power of God and his will after completing what remains in the care of the intellect, through the use of decisive utterance, to solve some of the difficulties and dilemmas caused by doubt and the confusions arising from idle fancies -- 9th qabas. On establishing the intelligible substances and the stages of the system of existence in the two chains of beginning and return -- 10th qabas. The decisive doctrine on the secret of predetermination (qada') and fate (qadar), how evil is related to predetermination, the colocynth of truth on prayer and its granting, and the return of the command to god in the beginning and the end -- Glossary-- Bibliography. (shrink)

The paper deals with the non-usual interpretation of the main works of an-Niffary as an original and specific guide in the Sufi terminology. The specific character of the text obliges a reader to treat the text more attentively that to the ordinary texts created by the human being. The most famous Sufi treatises on Sufism and its terminology are Qushayri and Hudjwiri's works,which contain definitions of most important Sufi terms and notions. Niffary works are not so well-known, but they also (...) can be regarded in a sense as a specific guidebook on Sufi terminology. The paper deals with the peculiarities of understanding by those three mystics the Sufi term “ma'arifa”, which sometimes is mistranslated as gnosis. One of the basic distinction in such an understanding is that for Niffary there is no outward sign of successful attainment of mystical knowledge. Further both Qushayri and Hudjwiri point out that the Sufi practice can not contradict the Sunna. Meanwhile Niffary says that Sunna is significant only if there is ma'arifa, not vice versa. (shrink)

This is a book on madness wisdom in Arabic-Islamic civilization.

This is an elaboration and a critique of Ibn Arabi's cosmology written in his book "Shajarah Al-Kawn".