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.

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 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.

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)

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)

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.

. 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.

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)

The objects called cubes of opposition have been presented in the literature in discordant ways. The aim of the paper is to offer a survey of such various kinds of cubes and evaluate their relation with an object, here called “Aristotelian cube”, which consists of two Aristotelian squares and four squares which are semiaristotelian, i.e. are such that their vertices are linked by some so-called Aristotelian relation. Two paradigm cases of Aristotelian squares are provided by propositions written in the language (...) of the logic of consequential implication, whose distinctive feature is the validity of two formulas, A $$\rightarrow $$ → B $$\supset \lnot $$ ⊃ ¬ (A $$\rightarrow $$ → $$\lnot $$ ¬ B) and A $$\rightarrow $$ → B $$\supset \lnot $$ ⊃ ¬ ($$\lnot $$ ¬ A $$\rightarrow $$ → B), expressing two different forms of contrariety. Part of section 1 is devoted to define the notions of rotation and of r-Aristotelian square, i.e. a square resulting from some rotation of an Aristotelian square. In section 2 this notion is extended to the one of a r-Aristotelian cube, i.e. of a cube resulting from some rotation of some square of an Aristotelian cube. This notion is used in the sequel to analyze various cubes of oppositions which can be found in the literature: (1) the one used by W. Lenzen to reconstruct Caramuel’s Octagon; (2) the one used by D. Luzeaux to represent the implicative relation among S5-modalities; (3) the one introduced by D. Dubois to represent the relations between quantified propositions containing positive predicates and their negations; (4) the one called Moretti cube. None of such cubes is strictly speaking Aristotelian but each of them may be proved to be r-Aristotelian. Section 5 discusses the assertion that Dubois cube was anticipated in a paper published by Reichenbach in 1952. Actually Dubois’ construction was anticipated by the so-called Johnson–Keynes cube, while the Reichenbach cube, unlike Dubois cube, is an instance of an Aristotelian cube in the sense defined in this paper. The dominance of such notion is confirmed by J.F. Nilsson’s cube, representing relations between propositions with nested quantifiers, and also by a cube introduced by S. Read to treat quantifiers with existential import. A cube similar to Read’s cube, introduced by Chatti and Schang, is shown to be r-Aristotelian. In section 6 the author remarks that the logic of the formulas occurring in the cubes of Chatti–Schang and Read have the drawback of not satsfying the law of Identity. He then proposes a definition of non-standard quantifiers which satisfies Identity, are independent of existential assumptions and such that their interrelations are represented by an Aristotelian cube. (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)

© 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)

The aim of this paper is to analyse categorical propositions and their oppositional relations in Avicenna’s frame. For Avicenna’s expression and conception of categorical propositions is different from those of the authors who preceded him, due to the various conditions he adds to these categorical propositions. These additions make the oppositional relations richer and give rise to many more figures than a simple square. Our analysis exhibits some of these figures by relating all kinds of quantified propositions in various ways. (...) We thus find many squares of oppositions, several octagons, two hexagons and many complex figures which are different from each other and have specific and original structures, due to the propositions they contain. The hexagons are of Blanché’s kind, but one of them is asymmetric. Some octagons are of Buridan’s kind, but one of them is very unusual and seems to be a reversal of Buridan’s octagon. These octagons can also be replaced by cubes, which are three dimensional figures having the same number of vertices. (shrink)

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)

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)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

The Editors express their gratitude and appreciation to the indi-viduals listed below who served as referees for Informal Logic for Volumes 31 (2011) and 32 (2012).

A common response to those who question the Law of Non-Contradiction is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to underlie them is the thought that there is a minimal set of logical resources without which rational debate is impossible. This chapter argues that this response is misguided. First, it defends non-apriorism in logic: the view that logic is in the same epistemic boat as other (...) scientific theories. It then offers an account of logical theory change in terms of this epistemology. The LNC is discussed in terms of this account of logical theory change, and it is shown that rational debate over this law can, and does, proceed. Finally, arguments for and against the LNC are discussed, and how and where non-a priori considerations arise in these arguments are illustrated. (shrink)

This paper articulates and defends a conception of logical form as semantic form revealed by a compositional meaning theory. On this conception, the logical form of a sentence is determined by the semantic types of its primitive terms and their mode of combination as it relates to determining under what conditions it is true. We develop this idea in the framework of truth-theoretic semantics. We argue that the semantic form of a declarative sentence in a language L is (...) revealed by a (canonical) proof of its T- sentence in an interpretive truth theory for L. We give a precise characterization of sameness of logical form between any two declarative sentences in any two languages in terms of the notion of corresponding proofs in interpretive truth theories for the languages. We illustrate the utility of this approach with a number of examples. We then extend the characterization to non-declaratives in a generalization of truth-theoretic semantics that appeals to fulfillment conditions, of which truth conditions are one variety. On this approach, logical forms are not reified, and the notion of sameness of logical form is treated as conceptually basic. We discuss the relation of this conception of logical form to the project of identifying logical constants, reviewing two approaches, one of which takes topic neutrality as central, the other recursion. We argue that the project of identifying logical constants for the purposes of classifying together valid arguments is largely independent of that identifying logical form of sentences, and urge an ecumenical approach to extending talk of logical constants beyond where it is currently well-grounded. (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense reasoning, expert systems implementation, (...) deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found in human reasoning. (...) Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

Tarski and Mautner proposed to characterize the "logical" operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively "logical", this lends support to the Tarski-Mautner proposal.

Logical positivism is often characterized as a set of naive doctrines on meaning, method, and metaphysics. In recent decades, however, historians have dismissed this view as a gross misinterpretation. This new scholarship raises a number of questions. When did the standard reading emerge? Why did it become so popular? And how could commentators have been so wrong? This essay reconstructs the history of a “caricature” and rejects the hypothesis that it was developed by ill-informed Anglophone scholars who failed to (...) appreciate the subtleties of European scientific philosophy. It argues that the received view has a more complicated history and was frequently promoted by the European positivists themselves. The essay shows that the view has roots in both American and European scientific philosophy and emerged as a result of the complex interplay between the two communities in the years before the intellectual migration. (shrink)

In this paper, we investigate the social herding phenomenon known as informational cascades, in which sequential inter-agent communication might lead to epistemic failures at group level, despite availability of information that should be sufficient to track the truth. We model an example of a cascade, and check the correctness of the individual reasoning of each agent involved, using two alternative logical settings: an existing probabilistic dynamic epistemic logic, and our own novel logic for counting evidence. Based on this analysis, (...) we conclude that cascades are not only likely to occur but are sometimes unavoidable by "rational" means: in some situations, the group’s inability to track the truth is the direct consequence of each agent’s rational attempt at individual truth-tracking. Moreover, our analysis shows that this is even so when rationality includes unbounded higher-order reasoning powers, as well as when it includes simpler, non-Bayesian forms of heuristic reasoning. (shrink)

This work is reprinted in John Dewey, The Middle Works, 1899-1924, Vol. 3.

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents the state (...) of the art in the area. (shrink)

Logical pluralism is the theory that there is more than one right logic. Logical instrumentalism is the view that a logic is a correct logic if it can be used to fruitfully pursue some deductive inquiry. Logical instrumentalism is a version of logical pluralism, since more than one logic can be used fruitfully. In this paper, I will show that a logical instrumentalist must accept linear logic as a correct logic, since linear logic is useful (...) for studying natural language syntax. I further show that this means that the logical instrumentalist must accept a wide range of connectives, in particular concatenation. I end by explaining why this is a feature rather than a bug. (shrink)

In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens and Universal Instantiation. I show (...) this through a detailed analysis of the ‘adoption problem’, which manifests something special about MP and UI. It appears that MP and UI underwrite the very nature of a logical rule of inference, due to all rules of inference being conditional and universal in their structure. As such, all logical rules presuppose MP and UI, making MP and UI self-governing, basic, unadoptable, and required in the meta-logic for the adequacy of any logical system. (shrink)