Advances in Natural Deduction A Celebration of Dag Prawitz's Work /
Author(s)Pereira, Luiz Carlos.
Haeusler, Edward Hermann.
de Paiva, Valeria.
SpringerLink (Online service)
Mathematical Logic and Formal Languages.
Mathematical Logic and Foundations.
Logic, Symbolic and mathematical.
Logique symbolique et mathématique
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Abstractedited by Luiz Carlos Pereira, Edward Hermann Haeusler, Valeria de Paiva.
Chapter 1. Generalizaed elimination inferences; Schroeder-Heister, Peter -- Chapter 2. Revisiting Zucker's work on the Correspondence between Cut-Elimination and Normalisation; Urban, Christian -- Chapter 3. Proofs, Reasoning and the Metamorphosis of Logic; Joinet, Jean-Baptiste -- Chapter 4. Natural Deduction for Equality: The Missing Entity; de Quieroz, Ruy J.G.B. and de Oliveira, Anjolina G -- Chapter 5. Proof-theoretical Conception of Logic; Legris, Javier -- Chapter 6. On the Structure of Natural deduction Derivations for "Generally"; Vana, Leonardo B., Veloso, Paulo A.S. , and Veloso, Sheila R.M -- Chapter 7. Type Theories from Barendregt's Cube for Theorem Provers; Seldin, Jonathan P -- Chapter 8. What is propositional logic, a theory of, if anything?; Chateaubriand, Oswaldo -- Chapter 9. Categorical Semantics of Linear Logic for All; de Paiva, Valeria -- Chapter 10. Rough sets and proof-theory; Bellin, Gianluigi -- Chapter 11. Decomposition of Reduction; Zimmermann, Ernst -- Chapter 12. An approach to general proof theory and a conjecture of a kind of completeness of intuitionistic logic revisited; Prawitz, Dag.
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Sexuated Topology and the Suspension of Meaning: A Non-Hermeneutical Phenomenological Approach to Textual AnalysisBailey, Steven (2014-07-31)This study assumes the subject's pursuit of meaning is generally incapacitating and should be suspended. It aims to demonstrate how such a suspension is theoretically accomplished by utilizing Lacan's formulae of sexuation integrated with his work in discourse theory and topology. Part I places this study into context by examining scholarship from the established fields of hermeneutics, phenomenology, (post)structuralism, aesthetic theory and psychoanalysis in order to extract out their respective theory of meaning. These theories reveal that an historical struggle with meaning has been underway since the Reformation and reaches near crisis proportions in the 20th century. On the one hand this crisis is mollified by the rise of Heideggerian-Gadamerian hermeneutical phenomenology which questions traditional epistemological approaches to the text using a new ontological conceptualization of meaning and a conscious rejection of methodology. On the other hand this crisis is exacerbated when the ubiquitous nature of meaning is itself challenged by (post)structuralism's discovery of the signifier which inscribes a limit to meaning, and by the domains of sense and nonsense newly opened up by aesthetic theory. These historical developments culminate in the field of psychoanalysis which most consequentially delimits a cause of meaning said to be closely linked to the core of subjectivity. Part II extends these findings by rigorously constructing out of the Lacanian sexuated formulae a decidedly non-hermeneutical phenomenological approach useful in demonstrating the sexual nature of meaning. Explicated in their static state by way of an account of their original derivation from the Aristotelian logical square, it is argued that these four formulae are relevant to basic concerns of textual theory inclusive of the hermeneutical circle of meaning. These formulae are then set into motion by integrating them with Lacan's four discourses to demonstrate the breakdown of meaning. Finally, the cuts and sutures of two-dimensional space that is topology as set down in L'étourdit are performed to confirm how the very field of meaning is ultimately suspended from a nonsensical singular point known in Lacanian psychoanalysis as objet a. The contention is that by occupying this point the subject frees himself from the debilitating grip of meaning.
Scatterplot Matrices of the Geomorphic Structure of the Mariana Trench at Four Tectonic Plates (Pacific, Philippine, Mariana and Caroline): a Geostatistical Analysis by ROcean University of China; CSC Scholarship; Institute of Geology Russian Academy of Science (RAS); Lemenkova , Polina (HAL CCSD, 2019-01-29)International audience
Ibn Ḥazm on Heteronomous Imperatives and Modality. A Landmark in the History of the Logical Analysis of NormsSavoirs, Textes, Langage (STL) - UMR 8163 ( STL ) ; Université de Lille-Centre National de la Recherche Scientifique ( CNRS ); STL: UMR 8163; Rahman , Shahid; Zidani , Farid; Young , Walter , (HAL CCSD, 2018-06-05)The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for the studies of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken.As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner.A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be.This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II.A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III.Leibniz and Hypothetical Imperatives in Law.IV.Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”.