I describe an octagon of opposition and equivalence developed by fourteenth-century logicians, in particular by Jean Buridan in his Summulae de dialectica. This «square» of opposition displays complex logical relations, one of which is not found in the traditional square of opposition. The octagon allows expression of three kinds of sentences: quantified modal sentences, oblique sentences, and sentences with quantified predicates. The octagon shows that medieval logicians were working with a logic of relations, an identity logic, and (...) a modal logic not unlike the logic of our own day. (shrink)

In this paper the medieval octagons of opposition and equivalence are described and analized. One of them, the octagon for quantified predicates, is the simplest one and offers the pattern for the other two, the octagon for predicate with modal qualification and the octagon for quantified genitive and nominative sentences. Thus, the first is the princeps analogum for the other two, whose structure is more complex. Then we describe an internal square inside the octagon, the square (...) of the so-called disparatae sentences, which obey no law from the traditional Aristotelian square. (shrink)

The aim of this paper is to make sense of the Keynes–Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show how this structure is to be handled by means of a semantics of partition, thus computing logical relations between matching formulas with a semantic method that combines model theory and Boolean algebra.

In this paper we will argue that the ontology implicit in John Buridan’s modal octagon commits him to a form of contingentism. In particular, we will argue that Buridan is committed to denying the validity of the Barcan and converse Barcan formulae.

En el presente artículo describo un octágono de oposición y equivalencia desarrollado por lógicos del siglo XIV, especialmente por Jean Buridan en su Summulae de dialectica. Dicho �cuadro� de oposición ofrece relaciones lógicas muy complejas, alguna de las cuales no está presente en el cuadrado tradicional de oposición. El octágono nos servirá para expresar tres tipos de oraciones: oraciones modales cuantificadas, oraciones oblicuas y oraciones con cuantificación explícita del predicado. El octágono muestra que la lógica medieval del siglo XIV ofrece (...) ya una lógica de relaciones, una lógica de la identidad y una lógica modal comparable a la lógica de nuestros días. (shrink)

One of the manuscripts of Buridan’s Summulae contains three figures, each in the form of an octagon. At each node of each octagon there are nine propositions. Buridan uses the figures to illustrate his doctrine of the syllogism, revising Aristotle's theory of the modal syllogism and adding theories of syllogisms with propositions containing oblique terms (such as ‘man’s donkey’) and with ‘propositions of non-normal construction’ (where the predicate precedes the copula). O-propositions of non-normal construction (i.e., ‘Some S (some) (...) P is not’) allow Buridan to extend and systematize the theory of the assertoric (i.e., non-modal) syllogism. Buridan points to a revealing analogy between the three octagons. To understand their importance we need to rehearse the medieval theories of signification, supposition, truth and consequence. (shrink)

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...) the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. (shrink)

The traditional Square of Opposition consists of four sentence types. Two are universal and two particular; two are affirmative and two negative. Examples, where ‘S’ and ‘P’ designate the subject and the predicate, are: ‘every S is P’, ‘no S is P’, ‘some S is P’ and ‘some S is not P’. Taking the usual sentences of the square of opposition, quantifying over their predicates exhibits non-standard sentence forms. These sentences may be combined into non-standard Squares of Opposition , and (...) they reveal a new relationship not found in the usual Square. Medieval logicians termed ‘disparatae’ pairs of sentences like ‘every S is some P’ and ‘some S is every P’, which are neither subaltern nor contrary, neither contradictory nor subcontrary. Walter Redmond has designed a special language L to express the logical form of these sentences in a precise way. I will use this language to show how Squares of Opposition, standard and non-standard, form a complex network of relations which bring to .. (shrink)

Around the turn of the 20th century, Keynes and Johnson extended the well-known square of opposition to an octagon of opposition, in order to account for subject negation (e.g., statements like ‘all non-S are P’). The main goal of this paper is to study the logical properties of the Keynes-Johnson (KJ) octagons of opposition. In particular, we will discuss three concrete examples of KJ octagons: the original one for subject-negation, a contemporary one from knowledge representation, and a third one (...) (hitherto not yet studied) from deontic logic. We show that these three KJ octagons are all Aristotelian isomorphic, but not all Boolean isomorphic to each other (the first two are representable by bitstrings of length 7, whereas the third one is representable by bitstrings of length 6). These results nicely fit within our ongoing research efforts toward setting up a systematic classification of squares, octagons, and other diagrams of opposition. Finally, obtaining a better theoretical understanding of the KJ octagons allows us to answer some open questions that have arisen in recent applications of these diagrams. (shrink)

The Philosophy of Mixed Martial Arts: Squaring the Octagon, edited by Jason Holt and Mark Ramsay, is part of the Ethics and Sport Routledge book series. It is a general academic text that encompass...

This is the first book to pay MMA the serious philosophical attention it deserves. The book explores topics such as whether MMA qualifies as a martial art, the differences between MMA and the traditional martial arts, the aesthetic dimensions of MMA, the limits of consent and choice in MMA and whether MMA can promote moral virtues.

So called “shapes of opposition”—like the classical square of opposition and its extensions—can be seen as graphical representations of the ways in which types of statements constrain each other in their possible truth values. As such, they can be used as a novel way of analysing the subject matter of disputes. While there have been great refinements and extensions of this logico-topological tool in the last years, the broad range of shapes of opposition are not widely known outside of a (...) circle of specialists. This ignorance may lead to the presumption that the classical square of opposition fits all disputes. A broader view, which takes expanded shapes of opposition into account, may come to a more nuanced appraisal of possible disputes. Once we take other shapes of opposition into account, some alleged disputes may turn out to be Scheindisputes. In order to do the wide range of linguistic expressions justice and to differentiate Scheindisputes from real ones, a broader view is advised. To illustrate this point, I discuss the notion of “introspective disputes”. These are commonly reconstructed as obeying the square, but are more aptly reconstructed with a more complex octagon. If we reconstruct these disputes based on Buridan’s octagon, it becomes obvious that “introspective disputes” are likely Scheindisputes. (shrink)

. This papers examines formal properties of logical squares and their generalizations in the form of hexagons and octagons. Then, several applications of these constructions in philosophical analysis are elaborated. They concern contingency (accidentality), possibility, permission, axiological concepts (bonum and malum), the generalized Hume thesis (deontic and epistemic modalities), determinism, truth and consistency (in various senses. It is shown that relations between notions used in various branches of philosophy fall into the same formal scheme.

I present two logical systems to show the “analogy of proportionality„ common to several interpretations: modality (necessity and possibility), quantification, truth-functional relations, moral attitudes (deontic logic), states of knowledge (epistemic logic), and states of belief (doxastic logic). To display the two underlying analogical relations, I call upon the originally Scholastic convention, recently put to use again, of using squares, hexagons, and octagons “of opposition„. A combined epistemic–deontic logic happens to be found in the traditional “probabilist„ theory of the “good conscience„, (...) and I shall then briefly explain how this is so. (shrink)

In this paper, with reference to relationships of the traditional square of opposition, we establish all the relations of the square of opposition between complex sentences built from the 16 binary and four unary propositional connectives of the classical propositional calculus. We illustrate them by means of many squares of opposition and, corresponding to them—octagons, hexagons or other geometrical objects.

The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed.GraphicThe photo shows a prototype sculpture for the cube.

In order to elucidate his logical analysis of modal quantified propositions (e.g. ‘all men are necessarily mortal’), the 14th century philosopher John Buridan constructed a modal octagon of oppositions. In the present paper we study this modal octagon from the perspective of contemporary logical geometry. We argue that the modal octagon contains precisely six squares of opposition as subdiagrams, and classify these squares based on their logical properties. On a more abstract level, we show that Buridan’s modal (...) octagon precisely captures the interaction between two classical squares of opposition, viz. one for the quantifiers and one for the modalities. Finally, we argue that several aspects of our contemporary formal analyses were already hinted at by Buridan himself. (shrink)

In this AV column we will have a look at the DUMAND project, a new $10 million detector funded by the US Department of Energy for the detection of ultra-high energy neutrinos. DUMAND stands for Deep Underwater Muon And Neutrino Detector. It is now under construction in Hawaii and will come into operation in 1993-94. It is to be placed almost 3 miles deep on a level stretch of Pacific Ocean bottom about 18 miles west of Keahole Point on the (...) Island of Hawaii. Floats anchored to the ocean bottom about 40 meters apart and arranged in an octagon around a central junction point will support nine long vertical strings of sensitive light detectors. DUMAND will be connected to its land-based laboratory by bundles of fiber optics cables. AT&T will lay the cables to shore, and the US Navy's manned deep submersible DSV Sea Cliff will be used to connect, service, and repair the parts of the detector. (shrink)

Although nothing from the Byzantine church of St. Spyridon is preserved in situ today, the primary sources and surviving photographs of the structure indicate that it was built in the simple domed octagon design. In this article, some new architectural fragments which possibly belonged to the church are presented and evaluated, and new interpretations of the earlier restitution hypotheses are suggested. The presence of a domed octagon in Selymbria provides indirect evidence for the existence of the plan scheme (...) in Constantinople in the Middle Byzantine period and implies a reciprocal relationship between regional and Constantinopolitan architectural styles. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:April 3, 2010 (11:17 am) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE2902\russell 29,2 050 red.wpd 188 Reviews 1 A.yW. Brown, The Metaphysical Society (New York: Octagon, 1973), pp. 180–1. THE ETHICS OF BELIEF Sylvia Nickerson History & Philosophy of Science & Technology / U. of Toronto Toronto, on, Canada m5s 1k1 [email protected] Timothy J. Madigan. W.yK. CliVord and “The Ethics of Beliefz”. Newcastle, uk: CambridgeScholars Publishing, 2009. Pp. [x], 202. (...) isbn 1-84718-503-7. £29.99; us$44.99 (hb). The mathematician William Kingdon CliTord (1845–1879) is generally remembered as a potentially great man whose life was cut short before his genius was fully realized. During his lifetime CliTord was well known in London as a public intellectual and noted authority on science. He was also an iconoclast, a leader in the application of Darwinian principles to areas beyond biology, and a proponent of non-Euclidean geometry. Unlike other agnostics, CliTord did not mourn the loss of his religious belief, nor did he worry that a secularized society would bring about general social decay. While other scientiWc naturalists worried that a collapse of religion would destroy morality and lead to social disintegration, CliTord willingly ceded the universal truths religion oTered, embracing the uncertainty that scientiWc knowledge actually entailed. He even dared to call himself an atheist. However, CliTord’s death at age 34 curtailed the trace of his thought. What remains is consigned to his scant private notebooks and collected works. Perhaps it was the brevity of his life that has led to his neglect within the history of science; no comprehensive appraisal of his mathematical work has been written. CliTord’sbest-knownnon-mathematical statementisthat“itiswrongalways, everywhere, and for anyone, to believe anything upon insuUcient evidence.” This was the statement he defended in his lecture “The Ethics of Beliefz”, which he delivered to London’s Metaphysical Society in 1876. The Metaphysical Society, founded in 1869 to promote discussion between religious believers and scientiWc rationalists, ceased operation in 1880 after members could not Wnd enough common ground to begin debate. The rationalist position CliTord argues in “The Ethics of Beliefz” stands on the far side of the spectrum within this discourse. CliTord’s immoderate stance, along with his use of biblical rhetoric to argue a secularist position, was calculated to provoke conservative intellectuals and institutions.1 When his essay appeared in the January 1877 issue April 3, 2010 (11:17 am) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE2902\russell 29,2 050 red.wpd Reviews 189 of Contemporary Review, it proved antagonistic enough that it led in part to the dismissal of James Knowles as editor. Timothy Madigan’s book W.yK. CliVord and “The Ethics of Beliefz”z provides an introduction to and analysis of CliTord’s ethical philosophy. His goal is to outline the historical context from which CliTord’s most famous essay arose, and to analyze the merits and demerits of its argument through the viewpoints of critics and freethinkers from the nineteenth century to the present. Madigan gives a brief history of the Victorian crisis of faith, CliTord’s mathematical work, and the biographical details of his life. He presents the argument CliTord makes within “The Ethics of Beliefz”, and outlines the critical response from his contemporaries, including founding members of the Metaphysical Society William George Ward and Richard H. Hutton, poet Matthew Arnold, physiologist George John Romanes, and American psychologist and philosopher William James. Madigan also discusses the positions argued by other rationalists in the 1870s,1880sandlater(Leslie Stephen, Karl Pearson, FriedrichNietzsche, Charles Peirce and Bertrand Russell) and by modern philosophers who have contributed to the rationalist/religionist debate (C.yS. Lewis, J.yL. Mackie, Michael Martin, Peter van Inwagen, Susan Haack, Anthony Quinton, and Lorraine Code). In Chapter 6 Madigan presents his own defence of CliTord’s ethics of belief. While early sections of the book provide a helpful summary of previously published work, I found Madigan’s discussion of CliTord’s writings on psychology and theory of mind particularly valuable (pp. 58–65). Madigan notes positively that CliTord’s contribution helped steer the early development... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 67.4 (2006) 675-696 MuseSearchJournalsThis JournalContents[Access article in PDF]History of Religion Becomes Ethnology: Some Evidence from Peiresc's AfricaPeter N. Miller Bard Graduate CenterAbstractThe relationship between history of religion and ethnology on the one hand, and antiquarianism and them both, on the other, lie at the core of this essay. These lines of inquiry come together in the work of Nicolas Fabri de Peiresc (1580-1637), (...) the intellectually adventurous Provençal late humanist. Peiresc's correspondence with a renegade in Tunis, an adventurer in Ethiopia, and a missionary once based in Guinea provided him with remarkably direct information about the customs and practices—the moeurs—of contemporary sub-Saharan Africans. The content of these letters has not found its place in histories of anthropology or histories of antiquarianism.I.Bound up amidst Peiresc's copies of his letters to the Paduan antiquary Lorenzo Pignoria from the winter of 1615–16 is a text of four sides entitled, in large letters, "Delli Popoli della China" and continuing, in smaller ones, "written by P. Ioannes Pietro Maffei History of the Indies, Fr. Antonio di Saint Roman, in the History of the East Indies, Fr. Juan Gonzalez de Mendoza Augustino, in the books on China, and others." 1 The reading notes [End Page 675] that follow are interesting for one reason: though labelled "Delli Popoli della China" they are almost entirely about religion in China. At this stage of Peiresc's thinking at least, history of religion seems interchangeable with ethnography.In his letter to Pignoria of 4 January 1616, Peiresc acknowledges having time to page through ("di transcorrere un poco") Maffei, Gonzales, and Saint Roman where he found some information about figures they had discussed, and also about artificial grottoes used for domestic refrigeration, "which I did not note when I read it the first time." He asked if Pignoria wouldn't mind inquiring as to whether there was a more precise impression of a particular Chinese plaque or medallion—Pignoria had sent him one but Peiresc pronounced it "not as exact as I would like." 2Peiresc begins with the gods that were worshipped (these included deceased parents and friends, as well as the occasional living person) and auguries. This then leads to mention of the clothing and hair styles of those priests making offerings to the gods. Some of this information was derived from that octagonal medallion. Peiresc also noted down the presence of a vase, as if for libation, and other instruments for offerings.These authors, he continued, observed that the Chinese revered the God of Heaven above all the others. Peiresc recorded that Gonzalez mentioned that he was indicated by use of the first letter of the alphabet, that this character looked a bit like "AF," that it was called "Guant," that he was honored with a solemn festival every near year, at the new moon in March, with vocal and instrumental music during which his priests applied themselves for an entire day to a board groaning with meat, poultry, fish, and fruits (no wonder the earlier reference to the gluttony of the priests). For the greater veneration of the King he was called the "Son of Heaven."Mention of the King led to discussion of the monthly festivals in the provinces when priests bore a portrait of the King, on gold, through the streets with great reverence. But then, citing from Maffei, Peiresc proceeded to jot down observations made about Chinese seaside towns and the domestic interior. This, in turn, led to some observations about dining—and, therefore, feasting—practices.Finally, Peiresc returned to the aforementioned medallion, whose details now seemed to him to represent just such an honorific feast. But he was especially interested in the practice of indicating the name of God with a single Chinese character, or cipher. This reminded him, he wrote, that the [End Page 676] Basilidian gnostics, as recorded in Epiphanius, represented the god of heaven with the seven Greek vowels AEHIOUY. He... (shrink)

Values of some arbitrary parameters appearing in a geometrical model for elementary particles developed by MacGregor are compared with quantities associated with classical properties of blocks of charges±e interacting via Coulomb forces and hard-sphere repulsion only. If it is assumed that masses and radii of individual charged particles are related bymc 2=(2/3)(e 2/r) and thatmc 2=6.87 MeV, then the self-energiesM andM ± of 24-particle neutral blocks and 25-particle charged blocks composed of layers of three octagons and of a square sandwiched (...) by two distorted octagons satisfyM=70.1 MeV,M ±=74.2 MeV. The binding energyB nn of pairs of neutral blocks is given byB nn=4.9 MeV, and the maximum radius of the neutral block is 0.60 F. These four calculated parameter values lie within an average of 1% of the corresponding quantities for nonspinning quarks determined empirically by MacGregor. (shrink)

ABSTRACT The amount of biomedical research being conducted around the world has greatly expanded over the past 15 years, with particularly large growth occurring in low- and middle-income countries (LMICs). This increased focus on understanding and responding to disease burdens around the world has brought forth a desire to help LMIC institutions enhance their own capacity to conduct scientifically and ethically sound research. In support of these goals the Johns Hopkins-Fogarty African Bioethics Training Program (FABTP) has, for the past six (...) years, partnered with three research institutions in Africa (University of Botswana, Makerere University in Uganda, and the University of Zambia) to support research ethics capacity. Each partnership began with a baseline evaluation of institutional research ethics environments in order to properly tailor capacity strengthening activities and help direct limited institutional resources. Through the course of these partnerships we have learned several lessons regarding the evaluation process and the framework used to complete the assessments (the Octagon Model). We believe that these lessons are generalizable and will be useful for groups conducting such assessments in the future. (shrink)

continent. 2.2 (2012): 76–81 Comments on Eugene Thacker’s “Cosmic Pessimism” Nicola Masciandaro Anything you look forward to will destroy you, as it already has. —Vernon Howard In pessimism, the first axiom is a long, low, funereal sigh. The cosmicity of the sigh resides in its profound negative singularity. Moving via endless auto-releasement, it achieves the remote. “ Oltre la spera che piú larga gira / passa ’l sospiro ch’esce del mio core ” [Beyond the sphere that circles widest / penetrates (...) the sigh that issues from my heart]. 1 The axiomatic sigh of the pessimist is in a way the pure word of philosophy, a thought that thinks without you, speaks where you are not. The live pneumatic form of the soul’s eventual exit from the dead body’s mouth, the sigh restores consciousness to the funeral of being, to the passing away that is existence. Pessimism speaks in piercing aphorisms because first it sighs. “Beyond the sphere passeth the arrow of our sigh. Hafiz! Silence.” 2 … pessimism is guilty of that most inexcusable of Occidental crimes—the crime of not pretending it’s for real. To the pessimist, the ‘real’ world—the world on whose behalf we are expected to wake up in the morning—is a ceaseless index of its own unreality. The pessimist’s day is not an illumined space for the advancement of experience and action, but a permanently and inescapably reflective zone, the vast interior of a mirror where each thing is only insofar as it is, at best, a false image of itself. Within this speculative situation, inside the doubleness of the mirror, pessimism splits into two paths, false and true, one that tries to fix pessimism (establish a relation with the mirror) and decides in favor of the apparent real, and another that totally falls for pessimism (enters the mirror) and communes with the greater reality of the unreal. These two paths are distinguished by their relation to pessimism’s guilt vis-à-vis the world’s reality-project. The first form, that which remains pessimism for the world and puts on a smiling face, stays guilty to itself (i.e. unconscious) and thus turns hypocritical, becoming at once the pessimism of the commoner who really just wants things to be better for himself and the pessimism of the elite who wants to critically refashion reality in his own image. The general form of this worldly, hypocritical pessimism is the impulse to ‘make the world a better place’, which is the global mask under which the world is diurnally made worse. The second form, that which follows pessimism away from the world and ceases to put on a smiling face, refuses guiltiness as itself theessential Occidental mode of pretense and turns honest, becoming at once the intelligent pessimism required of all ordinary action and the radical pessimism necessary for self-knowledge: seeing that no one is capable of doing good. The general form of this universal, honest pessimism is the impulse not to worry, to give up and embrace dereliction, which is the only real way the world is actually improved. Where worldly pessimism is the engine productive of interminably warring secular and sacred religions (good-projects), universal pessimism strives hopelessly for the paradise of a supremely instantiated pessimus: things are getting so bad that there is no longer any time for them to get worse; things are so constantly-instantly worst that this is BEST. Cosmic pessimism is the mode of universal pessimism which can yet discourse with the world, which has not chosen silence and can spread the inconceivably BAD NEWS in an orderly form ( kosmos ) that the world can understand (if it wanted to). … the result of a confusion between the world and a statement about the world. That is what the world is (the result of a confusion between the world and a statement about the world). … a generalized misanthropy without the anthropos. Pessimism crystallizes around this futility—it is its amor fati , rendered as musical form. Pessimism’s love of fate is a blind love, a love of the blindness of being human in a cosmos conceived around the human’s eclipse, a heavy levitation in the contradictory space between the inescapability of its having been and the impossibility of its will-be. Pessimism’s song of futility is a sensible way of loving fate, with a minimum of eros, by means of a kind of matrimonial love of the fatal. As music, pessimism stays open to the irreparable and the inexorable without the binding of affirmation, in the apparent absence of the radical, infinitely surplus will that absolute amor fati seems to require. Crying, laughing, sleeping—what other responses are adequate to a life that is so indifferent? “Unless a man aspires to the impossible, the possible that he achieves will scarcely be worth the trouble of his achieving it. We should aspire to the impossible, to absolute and infinite perfection [….] The apocatastasis is more than a mystical dream: it is a norm of action, it is a beacon for high deeds [….] For true charity is a species of invasion [….] It is not charity to rock and lull our fellow men to sleep in the inertia and heaviness of matter, but rather to arouse them to anguish and torment of spirit.” 3 … the impossibility of ever adequately accounting for one’s relationship to thought. “The paroxysm of interior experience leads you to regions where danger is absolute, because life which self-consciously actualizes its roots in experience can only negate itself [….] There are no arguments [….] On the heights of despair, the passion for the absurd is the only thing that can still throw a demonic light on chaos [….] I live because the mountains do not laugh and the worms do not sing .” 4 It took three attempts before she was fully decapitated, all the while she continued, perhaps miraculously, to sing. According to the earliest account of Cecilia’s martyrdom, the beheading turns out worse. After not severing her head in three strokes, “the cruel executioner left her half dead” (seminecem eam cruentus carnifex dereliquit). 5 Cecilia’s effortlessly powerful endurance of the three strokes—a fitting icon for pessimism as an art of dereliction—demonstrates the “passivity and absence of effort [….] in which divine transcendence is dissolved.” 6 There’s a ghost that grows inside of me, damaged in the making, and there’s a hunt sprung from necessity, elliptical and drowned. Where the moving quiet of our insomnia offers up each thought, there’s a luminous field of grey inertia, and obsidian dreams burnt all the way down. Like words from a pre-waking dream. There is no reason to think that they are not. NOTES 1. Dante Alighieri. Vita Nuova . ed. and trans. Dino S. Cervigni and Edward Vasta. Notre Dame: University of Notre Dame Press. 1995. 41:10. 2. Hafiz of Shiraz. The Divan . trans. H. Wilberforce Clarke. London: Octagon Press. 1974. 10.9. 3. Miguel de Unamuno. The Tragic Sense of Life in Men and Nations . trans. Anthony Kerrigan. Princeton: Princeton University Press. 1972. 305-6. 4. E.M. Cioran. On the Heights of Despair . trans. Ilinca Zarifopol-Johnston. Chicago: University of Chicago Press. 1992. 9-10. 5. Giacomo Laderchi. S. Caeciliae Virg[inis] et Mart[yris] Acta. . . Rome. 1723. 38. 6. Georges Bataille. On Nietzsche . trans. Bruce Boone. London: Continuum. 2004. 135. See Nicola Masciandaro. “ Half Dead: Parsing Cecilia .” A Commentary on Eugene Thacker’s "Cosmic Pessimism" Gary J. Shipley Pessimism is the refusal to seek distraction, the refusal to remodel failure into a platform for further (doomed) possibilities, the refusal of comfort, the acceptance of the sickness of healthy bodies, the cup of life overflowing with cold vomit. If, as Ligotti suggests when discussing Invasion of the Body Snatchers , 1 humans prefer the anxieties of their familiar human lives to the contentment of an alien one, then the pessimist, we could argue, represents some perverted combination of the two, preferring (presuming he has a choice) the defamiliarization of human life to the contentment of its unquestioned mundanity. The quasi-religious state of mind that Wittgenstein would mention on occasion, that of “feeling absolutely safe,” 2 is a state the pessimist could only imagine being approximated by death, or perhaps some annihilative opiate-induced stupor. This Wittgensteinian commingling of certainty and faith looks every bit the futile gesture, a mere rephrasing of collapse or partial collapse. The only certainty open to the pessimist is that of the toxic formula of life itself—a formula known and lacuna-free. Certainty, far from being the gateway to deliverance, becomes the definitive impediment; and the possibility of salvation, as long as it remains, becomes crucially reliant on postulations of ignorance, epistemic gaps, a perennial incompleteness: “the perfect safety of wooed death […] the warm bath of physical dissolution, the universal unknown engulfing the miniscule unknown.” 3 The height of Leibniz’s Panglossian insanity nurtured the idea that our knowing everything—via the universal calculus—could be accurately described a triumph, as opposed to a nightmare in which our every futility is laid bare. Stagnancy and boredom are perhaps two of the greatest ills of Western civilisation, and the most potent pessimism tells you that you’re stuck with both. The most we can hope for, by way of salvation, is to throw open our despair to the unknown. The fact that Schopenhauer’s pessimism stopped short of morality and allowed him to play the flute, as Nietzsche complained, highlights the predicament of a man who despite having adorned nothingness with a smiling face still found himself alive. The demand here is that it be felt: a cross-contamination of intellect and emotion. The safety net of numerous parentheses makes for a failed philosophy, rather than a philosophy of failure. Depressives make bad pessimists, because, unless they choose to die, living will always infect them with necessities of hope, forcing them to find something, anything (all the various “as ifs”) to make existence tolerable. For as Cioran observed, while “[d]epressions pay attention to life, they are the eyes of the devil, poisoned arrows which wound mortally any zest and love of life. Without them we know little, but with them, we cannot live.” 4 And even when cured of our depressions we’ll find ourselves consumed, eaten alive by the hyper-clinical (borderline autistic) mania that replaces them: a predicament captured all too clearly in the microscriptual fictions of Robert Walser, where spectral men and women stifle their depressive madness with protective comas of detail, their failed assimilations buried beneath thick crusts of remote data. Like Beckett’s Malone their stories may have ended, but cruelly their lives have not. Pessimism is an extraneous burden (a purposeless weight) that makes everything else harder to carry, while at the same time scooping it out and making it lighter. If pessimism had a sound it would be the harsh non-noise of tinnitus—the way that every person would hear themselves if they refused their distractions long enough to listen: a lungless scream from the extrasolar nothing of the self. The music of pessimism—if indeed we can imagine such a thing—is the reverberating echo of the world’s last sound, conjectured but never heard, audible only in its being listened for. The one consolation of this hollow paradox of audibility being, that “he will be least afraid of becoming nothing in death who has recognized that he is already nothing now.” 5 The pessimist suffers a derangement of the real, a labyrinthitis at the nucleus of his being: he’s the stumbling ghost relentlessly surprised that others can see him. If Cioran’s refusal is manifested in sleep (when even saying ‘no’ is too much of a commitment), then Pessoa’s resides in the dreams inside that sleep. Pessoa chooses to exploit the fact that he’s being “lived by some murmuring non-entity both shadowy and muddied” 6 by growing more voids to live him. His is a Gnostic breed of sleep, “sleeping as if the universe were a mistake,” 7 a sleep that dreams through Thacker’s cosmic pessimism (“a pessimism of the world-without-us.”, “the unhuman orientation of deep space and deep time” 8 ), through the critical error of there being anything at all when there could be nothing. The metaphysical pessimist is someone who, however well life treats them, still desires to wake from it, as from the poisonous air of a bad dream. Pessimism is a paradox of age, being simultaneously young and old; its youth residing in a refusal to accept the authority of existence (its rich history, its inherent beneficence), a refusal to “get over” the horror of what it sees with its perpetually fresh eyes, and its maturity in the unceremonious disposal of the philosophical playthings (those futile architectures) of adolescence. As Thacker remarks: “Pessimism abjures all pretenses towards system—towards the purity of analysis and the dignity of critique.” 9 A sentiment shared with Pessoa, who duly categorizes those that choose to enact this futile struggle: “The creators of metaphysical systems and of psychological explanations are still in the primary stage of suffering.” 10 If the pessimist has shared a womb with anyone, it’s with the mystic and not the philosopher. As Schopenhauer tells us: “The mystic is opposed to the philosopher by the fact that he begins from within, whereas the philosopher begins from without. […] But nothing of this is communicable except the assertions that we have to accept on his word; consequently he is unable to convince.” 11 The crucial difference between the mystic and the pessimist is not the latter’s impassivity and defeatism, but his unwillingness/inability to contain in any way the spread of his voracious analyticity, his denial of incompleteness, his exhaustive devotion to failure. The truth of our predicament, though heard, is destined to remain unprocessed. Like the revelations of B.S. Johnson’s Haakon (“We rot and there’s nothing that can stop it / Can’t you feel the shaking horror of that?” 12 ) the pessimist’s truths are somehow too obvious to listen to, as if something inside us were saying, “Of course, but haven’t we gotten over that?” Pessimism is simple and ugly, and has no desire to make itself more complex or more attractive. The true moral pessimist knows that the Utilitarian’s accounts will always be in the red. He can see that for all his computational containments, his only honest path is a negative one, and that such a path has but one logical destination: that of wholesale human oblivion. Thacker notes how at the core of pessimism lies the notion of “the worst,” through which death is demoted by the all-pervasive suffering of a life that easily eclipses its threat. And so with doom made preferable to gloom, death begins to glint with promise, “like beauty passing through a nightmare.” 13 But even among pessimists suicide is, for the most part, thought to be an error. Schopenhauer, for instance, regarded suicide a mistake grounded in some fundamentally naïve disappointment or other. Pessoa too thought suicide an onerous escape tactic: “To die is to become completely other. That’s why suicide is a cowardice: it’s to surrender ourselves completely to life.” 14 There is a call here to be accepting of and creative with the puppetry of your being, an insistence that it’s somehow a blunder to attempt to hide in death from the horrors you find inlife. 15 Tied up with this perseverance is the slippery notion of the good death, for maybe, as Blanchot warns, suicide is rarely something we can hope to get right, for the simple reason that “you cannot make of death an object of the will.” 16 “Even in cases where the entire corpus of an author is pessimistic, the project always seems incomplete,” 17 and this is not simply because the project itself belies something yet to be disclosed, but because the project itself is a thing waiting. It waits on a cure it knows will not come, but for which it cannot do anything (as long as it continues to do anything) but wait. NOTES 1. See Thomas Ligotti. The Conspiracy Against the Human Race . New York: Hippocampus Press. 2010. 91. 2. Ludwig Wittgenstein. “A Lecture on Ethics.” Philosophical Review . (74) 1. 1965. 8. 3. Vladimir Nabokov. Pale Fire . New York: Vintage. 1989. 221. 4. E. M. Cioran. The Book of Delusions . trans. Camelia Elias. Hyperion. 5.1. (2010): 75. 5. Arthur Schopenhauer. The World as Will and Representation. vol. 2 . trans. E .F J. Payne. New York: Dover. 1966. 609. 6. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 67. 7. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 35. 8. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 68. 9. Ibid. 73. 10. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 341. 11. Arthur Schopenhauer. The World as Will and Representation. vol. 2 . trans. E .F J. Payne. New York: Dover. 1966. 610-11. 12. B.S Johnson. “You’re Human Like the Rest of Them.” in Jonathan Coe. Like a Fiery Elephant: The Story of B.S. Johnson . London: Picador. 2004. 177. 13. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 415. 14. Ibid. 199. 15. “Suicide is, after all, the opposite of the poem.” Anne Sexton. No Evil Star: Selected Essays, Interviews and Prose . ed. Steven Gould Axelrod. Ann Arbor: University of Michigan Press. 1985. 92. 16. Maurice Blanchot. The Space of Literature . trans. Ann Smock. Lincoln: University of Nebraska Press. 1989. 105. 17. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 75. (shrink)

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of (...) opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts. (shrink)

This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

© Springer International Publishing AG, part of Springer Nature 2018. Nearly all squares of opposition found in the literature represent both the Aristotelian relations and the duality relations, and exhibit a very close correspondence between both types of logical relations. This paper investigates the interplay between Aristotelian and duality relations in diagrams beyond the square. In particular, we study a Buridan octagon, a Lenzen octagon, a Keynes-Johnson octagon and a Moretti octagon. Each of these octagons is (...) a natural extension of the square, both from an Aristotelian perspective and from a duality perspective. The results of our comparative analysis turn out to be highly nuanced. (shrink)

We run into instances of material constitution everywhere we turn. Material constitution is the relation that obtains between an octagonal piece of metal and a Stop sign, between strands of DNA molecules and genes, between pieces of paper and dollar bills, between stones and monuments, between lumps of clay and statues, between human persons and their bodies—the list is endless. Although there has been a great deal of controversy recently about the nature of material constitution, I want to enter the (...) fray by setting out and defending an explicit definition of what it is for an object x to constitute an object y at time t. (shrink)

Koran manuscripts that fit comfortably within the palm of one’s hand are known as early as the 10th century CE.For the sake of convenience, all dates will be given in the common era (CE) without further mention, and not in the Islamic or Hijra calendar. Their minute and sometimes barely legible script is clearly not intended for comfortable reading. Instead, recent scholarship suggests that the manuscripts were designed to be worn on the body like pendants or fastened to military flag (...) poles. This is corroborated by some preserved cases for these books which feature lugs to attach a cord or chain, but also their rare occurrence in contemporary textual sources. While pendant Korans in rectangular codex form exist, the majority were produced as codices in the shape of an octagonal prism, and others as scrolls that could be rolled up into a cylindrical form. Both resemble the shapes of similarly dated and pre-Islamic amulets or amulet cases. Building on recent scholarship, I will argue in this article that miniature or pendant Koran manuscripts were produced in similar forms and sizes because of comparable modes of usage, but not necessarily by a deliberate imitation of their amuletic ‘predecessors’. The manuscripts’ main functions did not require them to be read or even opened; some of their cases were in fact riveted shut. Accordingly, the haptic feedback they gave to their owners when they carried or touched them was not one of regular books but one of solid objects (like amulets) or even jewellery, which then reinforced this practice. (shrink)

The main conclusion of Nigel Hiscock's important but ill‐arranged book is that the ground plans of abbeys and cathedrals of the tenth and eleventh centuries incorporate Platonic wisdom—hence the “wise” in the title catchwords, which come from Paul's first letter to the Corinthians . There Paul likens himself to a sapiens architectus who lays the foundations on which others erect the building. In three of the four translations in The Complete Parallel Bible, however, Paul does not declare himself wise but, (...) rather, “skilled” or “trained.” The discrepancy makes an emblem for Hiscock's investigation: Did the architects deliberately express geometrical ratios significant in Platonic philosophy in their designs or did they proceed by applying their practical skill and training to the lie of the land and the resources available? A subsidiary question is also symbolized in Paul's verse: Was the designer a wise cleric who set the proportions and left the heavy work to someone else?Hiscock builds his answers in two ways. For one, he delivers a chrestomathy of Platonic snippets known in the tenth century and a few telling quotations from wise clerics—the latter concern the expression of significant numbers in the church fabric: a baptistery is octagonal because of an association between creation and the number eight, and a church with a half‐dozen altars is complete because of the perfection of the number six. But, Hiscock emphasizes, numerology does not account for floor plans, and to test the wisdom of the designers he scrutinizes plans of two dozen churches, especially those associated with monastic reformers. He expresses his results in color‐coded lines superposed on the plans, some one hundred of which comprise a valuable appendix.An example will indicate the interest of the findings and the riskiness of the business. The crossing of the transept at St. Michael's Abbey, Hildesheim, makes a square ABCD, proceeding clockwise from A in the northeast corner. AD and BC prolonged give the line of nave piers, AB and DC prolonged that of the arms of the transept. Lines drawn from B at angles of 54° and 60° with BC cut CD extended in E and F, respectively, locating the end piers in the side aisles. Now 60°, as the invariable angle of a three‐sided figure all of whose parts are equal, carries a cornucopia of Platonic and Christian symbolism. Also 54°, because derivable from a pentagon, has the pregnant significance of the figure five, which is the sum of the first male and first female numbers. Repetition of the transept square fixes the nave piers. Then lines between piers, pillars, and pilasters make the special angles with the north‐south and east‐west lines of the grid all over the plan.How much of this construction is mere coincidence? Requiring the intervals between piers in the same line to be equal, we have DE = FE = FD/2. And so it is: / = 0.51. Otherwise put, if angle FBC is 60° and E divides FD equally, angle EBC must be 54° without reference to a pentagon. Against such arguments, Hiscock observes that his analysis has uncovered previously unknown relations between churches confirmed by documents and that his technique, when applied to large nineteenth‐century buildings with repeated bays such as the Crystal Palace, picks out relatively few structurally significant elements.Hiscock is senior lecturer on the design, theory, and history of architecture at Oxford Brookes University and a master craftsman. His scrupulously prepared color‐coded drawings contain much of interest and pleasure for a geometer. Has he definitively answered the old vexed question whether the sapiens architectus intended to express ancient wisdom in his plans? If the architect thus proposed, did his builder faithfully dispose? Paul again may give guidance. “The Lord knows the thoughts of the wise, that they are futile”. (shrink)

Recent work by Keyser in applied epistemology of experiment has focused on the iterative ‘production’ of knowledge: knowledge stabilizes within a given physical context and it is iteratively tested within that context to meet standards of reliability. This implies that in a given physical context (e.g., laboratory), the inferences, methods/techniques, and physical products form coherence relations with one another. We apply this epistemological stabilization account to the martial arts in order to argue that the context of stabilization dictates the training (...) methods, techniques, and even the philosophical concepts of a given martial arts system. We describe key elements of stabilization pertaining to rules, training methodology, warrior philosophy, and spectator/media tropes. The account of stabilization requires a case study that shows how a dynamic system is stabilized. We describe the stabilization of modern mixed martial arts by tracking it on a time scale, but also in different contexts (e.g., Pancrase, Pride, UFC). (shrink)

What is 'rebirth' in Buddhism? The contribution of hypnotic regression.

Many traditional martial artists assert that MMA is not a martial art, denying that the ‘martial skill’ of MMA constitutes a ‘martial art’, and citing the sportive and entertainment aspects of MMA competitions as antithetical to the spirit of martial arts, lacking the integrity, discipline, and tradition found in martial arts. Today, these criticisms are even more relevant in light of the fact that the typical MMA fighter no longer practices a single discipline but is versed in a variety of (...) techniques and utilizes a variety of strength and conditioning modalities. In addition, with the development of social media and mainstream media’s acceptance of MMA as a legitimate sport, MMA is now more than ever about entertainment. We argue that MMA is a martial art, but it is not always practiced as one. By drawing upon Socrates’ distinction in Plato’s Gorgias between ‘knacks’ and ‘crafts’, we clarify the difference between ‘martial skills’ and ‘martial arts’. Using this distinction, we examine whether the sportive and entertainment aspects of MMA are, in fact, antithetical to the spirit of martial arts. We argue that the latter is, but the former is not. (shrink)