We investigate the join semilattice of modal operators on a Boolean algebra B. Furthermore, we consider pairs ⟨f,g⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle f,g \rangle $$\end{document} of modal operators whose supremum is the unary discriminator on B, and study the associated bi-modal algebras.

This paper deals with axiomatization problems for varieties of residuated meet semilattice-ordered monoids. An internal characterization of the finitely subdirectly irreducible RSs is proved, and it is used to investigate the varieties of RSs within which the finitely based subvarieties are closed under finite joins. It is shown that a variety has this closure property if its finitely subdirectly irreducible members form an elementary class. A syntactic characterization of this hypothesis is proved, and examples are discussed.

Contact algebra is one of the main tools in region-based theory of space. In it is generalized by dropping the operation Boolean complement. Furthermore we can generalize contact algebra by dropping also the operation meet. Thus we obtain structures, called contact join-semilattices and structures, called distributive contact join-semilattices. We obtain a set-theoretical representation theorem for CJS and a relational representation theorem for DCJS. As corollaries we get also topological representation theorems. We prove that the universal theory (...) of CJS and of DCJS is the same and is decidable. (shrink)

In this paper we show that the one-generated free three dimensional polyadic and substitutional algebras Fr1PA3 and Fr1SCA3 are not atomic. What is more, their corresponding logics have the Gödel’s incompleteness property. This provides a partial solution to a longstanding open problem of Németi and Maddux going back to Alfred Tarski via the book [12].

In this paper I address two important objections to the theory called ‘ Composition as Identity’ : the ‘wall-bricks-and-atoms problem’, and the claim that CAI entails mereological nihilism. I aim to argue that the best version of CAI capable of addressing both problems is the theory I will call ‘Atomic Composition as Identity’ which consists in taking the plural quantifier to range only over proper pluralities of mereological atoms and every non-atomic entity to be identical to the plurality (...) of atoms it fuses. I will proceed in three main steps. First, I will defend Sider’s Composition as identity. Oxford University Press, Oxford, pp 211–221, 2014) idea of weakening the comprehension principle for pluralities and I will show that :219–235, 2016a) it can ward off both the WaBrA problem and the threat of mereological nihilism. Second, I will argue that CAI-theorists should uphold an ‘atomic comprehension principle’ which, jointly with CAI, entails that there are only proper pluralities of mereological atoms. Finally, I will present a novel reading of the ‘one of’ relation that not only avoids the problems presented by Yi Composition as identity. Oxford University Press, Oxford, pp 169–191, 2014) and Calosi :429–443, 2016b, Am Philos Q 55:281–292, 2018) but can also help ACAI-theorists to make sense of the idea that a composite entity is both one and many. (shrink)

Introduction -- Light and life -- Biology and atomic physics -- Natural philosophy and human cultures -- Discussion with Einstein on epistemological problems in atomic physics -- Unity of knowledge -- Atoms and human knowledge -- Physical science and the problem of life.

Ethical reflection on the practice of war stands in a long tradition in Western philosophy and theology, a tradition which begins with the writings of Plato and Augustine and encompasses accounts of justified warfare offered by writers from the Medieval period to the present. Ethical reflection on nuclear war is of necessity a more recent theme. The past few years have seen an enormous increase in popular as well as scholarly concern with nuclear issues, and philosophers have joined theologians in (...) exploring the moral issues surrounding the harnessing of atomic forces in the service of war. (shrink)

RésuméLe gros de la recherche orientaliste consacrée à la littérature théologique islamique a négligé les idées théologiques Ibāḍī à portée cosmologique, ce qui a conduit à une compréhension incomplète de la théologie islamique et à un manque considérable dans la recherche occidentale. L'omission de ce mouvement important de l'Islam est compréhensible étant donné que les textes Ibāḍī ne sont accessibles, publiés, diffusés et traduits que de façon très partielle. Cette étude vise donc à combler certaines de ces lacunes dans la (...) recherche sur la première théologie islamique. Les objectifs de cet article sont de: 1) caractériser la littérature Ibāḍī classique portant sur la théorie atomiste de la substance et de l'accident; 2) examiner les textes d'auteurs Ibāḍī duiiie/ixesiècle dialoguant et discutant avec d'autres écoles théologiques islamiques, à savoir les Muʿtazilites pré-Bahshamiyya (Abū Hāshim al-Jubbāʾī, d. 321/933) et les Ashʿarites (Abū al-Ḥasan al-Ashʿarī, d. 324/936), en lien avec la théorie atomiste de la substance et de l'accident; 3) passer en revue le grand nombre d'opinions soutenues parmi les premiers théologiens Ibāḍī, et examiner les sources et les thèmes spécifiques susceptibles d'avoir influencé cette école de pensée diversifiée. Cet article cherche aussi à identifier des traits communs dans l'approche Ibāḍī durant la période de formation de la théologie islamique, et à explorer les voies grâce auxquelles ces premiers théologiens ont pu avoir accès à des thèmes cosmologiques antérieurs à l'Islam. (shrink)

This is the first commentary on Lucretius' theory of atomic motion, one of the most difficult and technical parts of De rerum natura. The late Don Fowler sets new standards for Lucretian studies in his awesome command both of the ancient literary, philological, and philosophical background to this Latin Epicurean poem, and of the relevant modern scholarship.

According to a common belief concerning the Mach-Boltzmann debate on atoms, the new experiments performed in microphysics at the turn of the 19th and 20th centuries confirmed Boltzmann’s atomic hypothesis and disproved Mach’s anti-atomic view. This paper intends to show that this belief is partially unjustified. Mach’s view on atoms consists in fact of different kinds of arguments. While the new experiments in microphysics refute indeed his scientific arguments against the atomic hypothesis, his epistemological arguments are unaffected. (...) In this regard, Mach’s epistemological approach remains relevant for today’s discussion on the status of the notion of atom. (shrink)

Assume T is stable, small and Φ(x) is a formula of L(T). We study the impact on $T\lceil\Phi$ of naming finitely many elements of a model of T. We consider the cases of $T\lceil\Phi$ which is ω-stable or superstable of finite rank. In these cases we prove that if T has $ countable models and Q = Φ(M) is countable and atomic or saturated, then any good type in S(Q) is τ-stable. If $T\lceil\Phi$ is ω-stable and (bounded, 1-based or (...) of finite rank) with $I(T, \aleph_0) , then we prove that every good p ∈ S(Q) is τ-stable for any countable Q. The proofs of these results lead to several new properties of small stable theories, particularly of types of finite weight in such theories. (shrink)

We compare diverse degrees of compactness and finiteness in Boolean algebras with each other and investigate the influence of weak choice principles. Our arguments rely on a discussion of infinitary distributive laws and generalized prime elements in Boolean algebras. In ZF set theory without choice, a Boolean algebra is Dedekind finite if and only if it satisfies the ascending chain condition. The Denumerable Subset Axiom implies finiteness of Boolean algebras with compact top, whereas the converse fails in ZF. Moreover, we (...) derive from DS the atomicity of continuous Boolean algebras. Some of the results extend to more general structures like pseudocomplemented semilattices. (shrink)

continent. 1.4 (2011): 279—285. Concerning its Transitive Nature, the Conversion of Native Americans of Spanish Colonial California, Indoctrinated Catholicism, & the Creation There’s no direct archaeological evidence that Jesus ever existed. 1 I memorized the Act of Contrition. I don’t remember it now, except the beginning: Forgive me Father for I have sinned . . . This was in preparation for the Sacrament of Holy Reconciliation, where in a confessional I confessed my sins to Father Scott, who looked like Jesus, (...) at least in Western cultural representations of Jesus since the middle ages, and if Jesus put on a few pounds. Father Scott was long-haired, redheaded, bearded, chubby, and tall. When he left church with the procession of altar servers and Eucharistic ministers, yelling, “Sing a Good Song Unto the Lord,” he smiled, hands folded, and he gazed over his parishioners, and bounced along. For four months every year he lived among the Crow Nation in Montana, where towards the end of his tenure at Our Lady of Refuge, they adopted him as an honorary member of their tribe. * This is the prayer we chanted, holding hands, every night before dinner: Bless us oh Lord, for these our gifts, which we are about to receive, our bounty through Christ, our Lord, Amen. Then we all said, God bless the cook! When we were with my grandparents, Grandpa said, God bless Chicky, and Holly, and Harvey, and Boots—all the dead dogs. * My sister tells me that she sits next to a handsome man on a flight across the country. After chitchat, she withdraws her book. She’s reading Kevin Sampsell’s A Common Pornography . After a few moments, the handsome man also reads from his book—his leather-bound Bible. Sister thinks, Oh, Jesus—too bad. She falls asleep. Later, settled in Nashville, she opens her volume and out falls a Jesus-covered card that reads, You can still find God and Salvation! Because that handsome God-fearing young man saw that word— pornography . * I suppose Father Jim’s dark hair, beard, and glasses made me think doctoral-ly of him. He called while I was in the midst of a breakup, after I’d twice attempted suicide, and my mother was desperate for help. She somehow found and phoned him. And Jim, now years out of Our Lady of Refuge’s parish, twenty years since my baptism, years even since he’d left the priesthood and the Catholic faith, still made the effort to bring me back into the fold. He said, “Have you seen a priest?” I did not respond, as I was more shocked to hear his voice than anything, so I said, “How are you, Father Jim? Sorry, I guess I shouldn’t call you ‘Father.’” And I said, “Why did you leave the priesthood? Do you have a girlfriend?” He said that I should call him just “Jim.” He said, “Do you need someone to talk to?” I said, “Not really.” He said, “Call your mother; she’s worried about you.” That was the last time I talked to Father Jim. * Mother let me know just how disappointed Jesus was. I cried and cried, and said I was sorry. Into my hands she placed my missal, ordered forty Rosaries. She said next Saturday I would go to confession. I hated confession. Who wouldn’t? * I realize, of course, that this page is a kind of confessional. * The Kumeyaay, Ipai, Tipai, Chumash, Esselen, Rumsen—all Native Americans of Alta California—shared similarities in their religions. Southern Californian tribes made use of Datura, or jimpson weed, a hallucinogen, for religious rituals. In the creation, God made brother sky and sister earth. Brother and sister mated, and sister gave birth to all things on Earth, including people, but it was difficult to distinguish people from all other aspects of Earth because everything was alive: granite and obsidian, the Pacific and its waves, the San Diego and Los Angeles Rivers. Wiyot—a hero—was very powerful, born from lightning, the son of the Creator and a virgin. When Wiyot thought that human women’s legs were more beautiful than Frog’s, Frog became jealous and poisoned Wiyot. The dying Wiyot went to all the people’s villages, and he distributed his power among them. He said, “When I die, I should be cremated.” The people built the fire and funeral pyre. When the fire was ready, and the people about to place Wiyot’s body upon it, Coyote came and snatched away Wiyot’s heart. * My friend Nick told me once how he ate some jimpson weed and that he hallucinated for three days. His family took a road trip and, while driving over the Sierra Nevada mountains, he kept seeing dinosaurs roaming the open meadows and charging down snowy slopes. So it’s no wonder that Native Americans who ingested this plant would have developed religion. * Walking Castroville’s streets after school I got into fights but mostly watched other boys scrabbling on the asphalt. I went to Burger King for Whoppers. Me and my friends cussed. Antonio admonished me when I said, “damn,” while strutting a sidewalk alongside the church. He said, “Jaime”—pronounced Hi-May, which was what all the Mexicans called me—“you’re crazy, eh. Don’t cuss at the church.” He meant while at church, as in, within its vicinity. I said, “We’re not in church.” Once we’d crossed the street, Tony said, “Damn dude, you’re fuckin crazy!” * Blessed Father Fray Junípero Serra raised the Eucharistic goblet to his lips, and candlelight danced on the blood’s tiny waves. Incense clouded the church so completely that some of the Pame natives grew nauseous. So, too, felt Blessed Father Fray Junípero Serra later that night, as he bent over a ceramic bowl and vomited blood, not only the Lord’s, but his own, for poison had laced the sacred vessel into which he poured the sacrament. The physician tending to the sick prelate urged him to take the remedy he’d prepared. But Blessed Father Fray Junípero Serra refused, said that he would pray, for he had never taken any medicine in his life, and he never would. * The Chumash of El Valle de Los Osos called themselves the Stishni, separating themselves from Chumash of other regions, those varying tribes of the central California coast that spoke mutually unintelligible dialects of their Hokan language. This made learning their languages impossible for the Spanish friars, to say nothing of translating the Doctrina. Thus the priests baptized few natives, despite the help that the tribes offered the fledgling settlements in the form of meat and acorn meal, which the Spaniards found repugnant. Some from these cultures, feeling threatened by the newcomers, shot flaming arrows into the thatched roofs of the mission structures. And why wouldn’t they feel threatened when priests chastised them for performing, for example, their Coyote Dance, wherein a man donning a coyote-skin-and-skull costume dances while a singer sings his tale, which laments the human feces strewn imaginatively about the Earth? Coyote, meantime, tries to get an onlooker to lick his genitals, and finally engages in public sexual intercourse with a female tribe member or two, then ends the dance by defecating. Though the Franciscans called such forbidden acts devilry , the Chumash maintained their Datura cult religion, along with the enforced Christianity. For the Chumash, the Earth was made of two enormous snakes that caused earthquakes when they slithered past one another—a vast reptilian tectonics. In the 20th century, long after Blessed Father Fray Junípero Serra and his cohorts had died, when asked by an anthropologist about religious contradictions, conflating the Datura and Christian cults, a Chumash man replied, incredulous: “But these are two different religions.” * When Portolá ordered that if by March 19th, the feast day of St. Joseph, the San Antonio had not arrived in San Diego Bay to relieve them, the Sacred Expedition to Nueva California would be abandoned, Blessed Father Fray Junípero Serra prayed a novena for San José’s intercession. And lo, a lookout sighted the San Antonio ’s sails—what seemed to the priest a miracle—that very Saint’s feast day. Europeans would stay in California, and Blessed Father Fray Junípero Serra would continue to reap a great harvest of souls for the Lord. By the end of mission secularization in 1836—sixty-six years after the San Antonio rescued the Spaniards—Native American populations in California had declined by seventy-three percent. * When Peter the Aleut would not renounce his Eastern Orthodox faith the padre of San Francisco had a toe severed from each foot with each refusal, totaling ten. The native Ohlones employed in this gruesome task—their obsidian chiseled knives tearing through skin and grinding bone—continued as per their orders, and cut off also each of Peter’s fingers (equals a total of twenty refusals). They quartered the martyr, spilled his bowels, as if from bear attack, attack by a bear in the shape of a Catholic. * Blessed Father Fray Junípero Serra absolutely believed that the slow rate of conversion for the native people was due to the influence of the Devil, who had been outraged by the coming of the Catholics to California, this region that he had long held in his dominion. * In his reception speech for the Nobel Prize for Literature, John Steinbeck said, “Man himself has become our greatest hazard and our only hope. So that today, St. John the Apostle may well be paraphrased: In the end is the Word, and the Word is Man—and the Word is with Men.” * In 1602, when Sebastián Vizcaíno and his friars sang mass on Catalina Island, as many as a hundred Pimungans witnessed the rite, asking by signs what it was about. According to Vizcaíno’s records, the Californians marveled not a little at the idea of Heaven and at the image of Jesus crucified. * Vizcaíno was brought to a prairie on Santa Catalina Island where the Pimungans worshipped their sun god. Upon the prairie they had placed an icon, a headless figure with horns protruding from the body, a figure that Vizcaíno predictably described as a demon. The Pimungans urged Vizcaíno not to approach the image of their deity, but he ignored them. He placed his crucifix against the wooden figurine and prayed the Our Father. Vizcaíno told the natives that his prayer was from Heaven, and that their god was the Devil. Vizcaíno held out his crucifix, encouraging the Pimungans to touch it and receive Jesus. He pointed at the sky and indicated Heaven. The Pimungans worshipped a sun deity, so they were impressed with this white man and his description of his god, for their gods seemed to be one and the same. It’s no wonder then that Vizcaíno’s diary reports the natives being pleased with this exchange. “Surely,” the diary says, “they will be converted to our Holy Faith.” * The Miwok women wailed and scratched at their faces when their men consorted with Sir Francis Drake and the other Englishmen who had landed on California’s coast in the summer of 1579. “The blood streaming downe along their brests, besides despoiling the upper parts of their bodies of those single coverings . . .they would with furie cast themselves upon the ground . . . on hard stones, knobby hillocks, stocks of wood, and pricking bushes.” Drake and his men fell themselves to their knees in prayer, their eyes Heavenward, so that the natives might see they prayed to God and they too might worship God then their eyes that had been so blinded by the deceiver might be opened. * Father Fray Antonio de la Ascención—Carmelite friar in Vizcaíno’s party—writes that the Indians of California can “easily and with very little labor be taught our Holy Catholic faith, and that they would receive it well and lovingly.” He calls for two hundred older and honorable soldiers to ensure brotherhood during the conquest, so that peace and love—the best tools to pacify pagans—should reign. The religious, the friar says, should likewise be wise and loving to easily quell animosities between Spaniards and the heathen, and therefore avoid war. The Spaniards should bring with them trinkets—beads, mirrors, knives—to distribute amongst the gentiles, so that they might come to love the Christians, and see “that they are coming to their lands to give them that of which they bring, and not to take away the Indians’ possessions, and may understand that they are seeking the good of their souls.” No women are to accompany the conquest, says Father Fray Antonio, “to avoid offenses to God.” * In 1955 Wallace Stevens admitted himself to St. Francis Hospital in Hartford, Connecticut. There, it’s rumored he converted to Catholicism before dying of stomach cancer, exclaiming to his priest after the baptism, “Now I am in the fold.” Stevens’s late-career poems seem less cynical, more in awe of being and death (read “Metaphor as Degeneration” from The Auroras of Autumn ). He could have chosen from at least three secular hospitals in Hartford at the time. * I was reading Stevens’s Collected Poems when I joined eHarmony and listed that as my “currently reading” book among the “more than twelve” books a year that I would read. I fell in love with my wife when she said, “Are you sending your work out to literary journals?” Prior to this, the first girl I talked to on the phone, when I explained my doctoral exams, said, “So, you’re like, reading Stephen King and stuff?” When I said not exactly she responded defensively: “He must be doing something right, since he makes all that money.” * Mom walked me, my brother, and sister, through the Stations of the Cross. We did this on Ash Wednesdays, or whenever she thought we needed extra God after church. It might’ve happened before church, though that’s unlikely because we were always late. Anyway, it’s easiest to walk the Stations of the Cross when there’s no one else around. To walk the actual Stations means one goes to Jerusalem and walks the Via Dolorosa to the Church of the Holy Sepulchre. So the Stations elsewhere—usually paintings, or low-relief sculptures upon church walls—serve as a kind of virtual Dolorosa. Mom held our hands and started from the rear of Our Lady of Refuge: the First Station. Mom said we should say a prayer at each Station and to think of all the pain Jesus went through so that we could go to Heaven. It was hard to keep thinking about that one thing for so long. My mind went to that Saturday’s little league game, to the donut and chocolate milk (our after-church reward from Castroville Bakery), and as I grew older I thought about girls. When you’re thirteen you can’t not think about the girl’s butt in the pew in front of yours as she kneels and stands to pray throughout mass. * It grew increasingly juvenile to lie awake at night daring myself to utter a simple sentence. Even if I said I didn’t believe in God, wouldn’t He know the truth? He was omniscient, like a narrator. Even the idea of Him as a him ceased making sense. Not only did this come with a budding realization of my paternalistic culture, but due to the simple question of why? If God was everything, everywhere, all knowing, then why would he be a man? There’s that question: If God is a man then God must have a penis, and if so, what for? * The Catholic Church incorporates some modern scientific research into its dogma concerning the formation of the Universe, Solar System, and Earth, as well as evolution. According to Catholic doctrine, in approximately the fifth millennia BCE, humans began to worship the one true God. Those humans were Adam and Eve, though the Church says humans had been around for thousands of years prior to Adam and Eve. The Church claims to be infallible. Every time the Church changes its doctrine it remains infallible. * One Catholic writer, Tom Meagher, writes that “Modernism[—]the idea that we come to our beliefs individually through emotional or personal experiences[—]has crept into our Catholic schools.” * Catholics believe that evil spirits, given power through Original Sin, can imbue ordinary inanimate objects of everyday use. Thus, such objects should be blessed in order to induce in them the desire to serve the good. Such objects are not limited to, but include, “new ships and boats, railways and trains, bridges, fountains, wells, cornmills, limekilns, smelting furnaces, telegrams, steam engines, and machines for providing electricity.” * In The Sound of Music Julie Andrews and Christopher Plummer sing together: “Nothing comes from nothing, nothing ever could...” * To explain competing theories on the very early universe, and pre-verse would be another book. What was the inflaton? Did (mem)branes collide, initiating the Big Bang, as opposed to Lemaître’s primordial atom, a singularity? Without a unified theory there’s gravity hanging out there, fucking everything up. We cannot make sense of the mechanics of the Planck Epoch—0-10-34 seconds into the Universe’s creation—named for Max Planck, who stumbled into the discovery of quantum mechanics in the early twentieth century. * My students often ask if I believe in God, since I espouse evolution, the Big Bang, Science, reject a strictly biblical or creationist theory of the Universe. I tell them that yes, I believe in God, though not the God that they imagine one must believe in. * When questioned regarding the rumor that, before his death, founder of quantum mechanics Max Planck had converted to Catholicism, he replied that he did not believe “in a personal God, let alone a Christian God.” * Physicist and Catholic priest George Lemaître, who formulated the theory and wrote the 1946 book The Primeval Atom Hypothesis , was made a household name by then-detractor Fred Hoyle, who pejoratively referred to the idea as a “Big Bang.” * Suicide is a mortal sin. To end one’s own life one must have despair, which is to lose hope, which is to lose faith, and to disbelieve in God. * Archaeology has uncovered graffiti in all of California’s missions—Indian pictographs inscribed into the adobe, covered with layers of whitewash. Native deities and depictions of cultural practices show that tribespeople never fully gave up their native traditions even after baptism and coming to the missions. There was something inside Native Californians that would never die. (shrink)

and in Sect. 5 should be reformulated as follows.

. In this paper we propose a new definition of entailment and construct a system S of predicate calculus based on this entailment. It is also shown that all well-known set theories can be based on the system S.

The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cut-free labelled sequent calculus with plural succedents . We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents . Moreover, using this equivalence, we give a new Hilbert-style axiomatizations for ∪R and ∪T and prove equivalence between two semantics for (...) the contractionless logics ∪RW and ∪TW. (shrink)

Hilbert algebras provide the equivalent algebraic semantics in the sense of Blok and Pigozzi to the implication fragment of intuitionistic logic. They are closely related to implicative semilattices. Porta proved that every Hilbert algebra has a free implicative semilattice extension. In this paper we introduce the notion of an optimal deductive filter of a Hilbert algebra and use it to provide a different proof of the existence of the free implicative semilattice extension of a Hilbert algebra as well as (...) a simplified characterization of it. The optimal deductive filters turn out to be the traces in the Hilbert algebra of the prime filters of the distributive lattice free extension of the free implicative semilattice extension of the Hilbert algebra. To define the concept of optimal deductive filter we need to introduce the concept of a strong Frink ideal for Hilbert algebras which generalizes the concept of a Frink ideal for posets. (shrink)

Purpose This study aims to examine the long-term effects of an Israeli digital literacy government program for disadvantaged populations, as they are perceived by participants of the program one year after completing the course. Design/methodology/approach Participants in the program were interviewed about the effects of participating in the program, their experiences and satisfaction, in retrospect, a year after they completed the program. Findings The main reasons for joining the program included cognitive motivations, mainly interest to become familiar with internet applications, (...) followed by employment aspiration. Positive benefits from participation included accumulated knowledge, confidence in using technology, empowerment and enhanced sense of self-efficacy. Interviewees also reported that as they could not practice or communicate with instructors once they completed the program, a significant portion of the accumulated gains faded. Social implications Social and practical implications: Digital technologies constitute key infrastructure to facilitate public participation, as well as for gaining social, political and economic capital. Therefore, there is a significant social value in reducing digital inequality by increasing digital literacy of disadvantaged populations, i.e. citizens with low socioeconomic status and low digital literacy. This study sheds light on the benefits gained from such programs, as perceived by past participants. Originality/value While previous studies evaluating digital literacy programs focus on specific technical improvements and short-term gains, this study investigates the long-term effects and shortcomings of the program as perceived by participants. (shrink)

We propose a model of natural language inference which identifies valid inferences by their lexical and syntactic features, without full semantic interpretation. We extend past work in natural logic, which has focused on semantic containment and monotonicity, by incorporating both semantic exclusion and implicativity. Our model decomposes an inference problem into a sequence of atomic edits linking premise to hypothesis; predicts a lexical semantic relation for each edit; propagates these relations upward through a semantic composition tree according to properties (...) of intermediate nodes; and joins the resulting semantic relations across the edit sequence. A computational implementation of the model achieves 70% accuracy and 89% precision on the FraCaS test suite. Moreover, including this model as a component in an existing system yields significant performance gains on the Recognizing Textual Entailment challenge. (shrink)

An atom is confined to a box in its ground state. An attempt is made to observe it in the left half of the box by scattering photons out of a photon wave packet passing through this half of the box. If no photons are scattered, the atom is missing. It is located on the right side of the box and its wave function is changed. The expectation value of the combined atom and photon energy is increased. For the other (...) alternative, that the atom is found on the left side, the expectation value is decreased. By including both alternatives, it is shown that the mean energy is conserved. (shrink)

In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...) predicative fragment of System F, called atomic System F. In this paper we show that this approach finds a general explanation within our equational study of second-order natural deduction, and a clear semantic justification in terms of parametricity. (shrink)

The Ontological Square is a categorial scheme that combines two metaphysical distinctions: that between types (or universals ) and tokens (or particulars ) on the one hand, and that between characters (or features ) and their substrates (or bearers ) on the other hand. The resulting four-fold classification of things comprises particular substrates, called substances , universal substrates, called kinds , particular characters, called modes or moments , and universal characters, called attributes . Things are joined together in facts by (...) primitive ontological ties or nexus . This article describes a logic that is meant to capture the basic intuitions behind the Ontological Square. Given a minimal correspondence between atomic logical form and ontological structure, the commitment to nexus as a distinct ontological category entails a rehabilitation of copulae as ties of predication. Thus, the Logic of the Ontological Square is a copula calculus rather than a predicate calculus; its soundness and completeness can be established with respect to a model akin to a so-called first-order semantics for standard second-order logic. (shrink)

Nature did not equip any of its creatures with wheels, but that means of locomotion was discovered anyway; an even swifter vehicle for the mind has been found in the atom—that irreducible unit which by virtue of its ubiquity provides reason with immediate access to alien objects, naturalizes nature, and urges an essential likeness beneath appearances so diverse that only an improbable imagination would even have placed them in a single world. The goal of atomism is to find one entity, (...) a building block which then in multiples constitutes the structures of reality and appearance. All that is needed, given this once and future One, is a set of transformational rules—and everything comes to life that has been dreamed of in the topologies of geometry, physics, history, even of metaphysics: a full representation of the world as it has been, is, will be. The ideology of atomism includes the assumption that, for structures distinguishable into parts and wholes, the parts precede the whole, temporally and logically. For the atomist, all structures can be analyzed in this way; that, in fact, turns out to be his definition of structure. This premise is already evident in the building-block universe first depicted by Democritus and Leucippus; it is no less present in the heady days of twentieth-century physics . It is slightly more pliable in latter-day atomists like Claude Lévi-Strauss and Noam Chomsky and their descendent structuralists; but here, too, atomic units of linguistic or social discourse are claimed as blind first causes of the sighted and complex structures allegedly derived from them. And if the followers of even these contemporary advocates find themselves still waiting for the promises of atomism to be kept, the imaginative turns of those promises—the binary code, the rules of an innate grammar—keep old expectations alive. In contrast to this general ideological assertion, the search for artistic atoms by poetics and aesthetic theory has lagged noticeably. We can see this disparity in the characteristic resistance to fragmentation by works of art; for many writers, the will of artistic appearance to exhibit itself as a whole, to insist on an undivided surface rather than on the elements within or beneath it, is precisely what distinguishes the structures of art from others. Even where a craftsmanlike impulse breaks into the surface of artistic unity , the pieces are usually counted teleologically: they matter as contributions to an effect, retrospectively. The artist himself, it is implied, deployed them in the first place to anticipate the unified surface; we , in turn, then understand them only in terms of that whole, not—with the atomist—by conjuring a unity from the earlier accidental joining of what then become accidental parts. (shrink)

Boolean algebras are one of the main algebraic tools in the region-based theory of space. T. Ivanova provided strong motivations for the study of mere semilattices with a contact relation. Another significant motivation for considering an even weaker underlying structure comes from event structures with binary conflict in the theory of concurrent systems in computer science. All the above-hinted notions deal with a binary contact relation. Several authors suggested the more general study of n-ary ‘hypercontact’ relations. A similar evolution (...) occurred in the study of the just mentioned event structures in computer science. To unify the above lines of research, in this paper, we study joining semilattices with a hypercontact relation. We provide representation theorems into Boolean algebras. With a single exception, our proofs are choice-free. We also present several examples and problems; in particular, we briefly discuss some connections with event structures and hypergraphs. (shrink)

The paper has two parts preceded by quite comprehensive preliminaries.In the first part it is shown that a subvariety of the variety ${\cal T}$ of all tense algebras is discriminator if and only if it is semisimple. The variety ${\cal T}$ turns out to be the join of an increasing chain of varieties ${\cal D}_n$, which are discriminator varieties. The argument carries over to all finite type varieties of boolean algebras with operators satisfying some term conditions. In the case (...) of tense algebras, the varieties ${\cal D}_n$ can be further characterised by certain natural conditions on Kripke frames.In the second part it is shown that the lattice of subvarieties of ${\cal D}_0$ has two atoms, the lattice of subvarieties of ${\cal D}_1$ has countably many atoms, and for $n>1$, the lattice of subvarieties of ${\cal D}_n$ has continuum atoms. The proof of the second of the above statements involves a rather detailed description of zero-generated simple algebras in ${\cal D}_1$.Almost all the arguments are cast in algebraic form, but both parts begin with an outline describing their contents from the dual point of view of tense logics. (shrink)

A continuum is here a primitive notion intended to correspond precisely to a path-connected subset of the usual euclidean space. In contrast, however, to the traditional treatment, we treat here continua not as pointsets, but as irreducible entities equipped only with a partial ordering ≤ interpreted as parthood. Our aim is to examine what basic topological and geometric properties of continua can be expressed in the language of ≤, and what principles we need in order to prove elementary facts about (...) them. Surprisingly enough ≤ suffices to formulate the very heart of continuity (=jumpless and gapless transitions) in a general setting. Further, using a few principles about ≤ (together with the axioms of ZFC), we can define points, joins, meets and infinite closeness. Most important, we can develop a dimension theory based on notions like path, circle, line (=one-dimensional continuum), simple line and surface (=two-dimensional continuum), recovering thereby in a rigorous way Poincaré's well-known intuitive idea that dimension expresses the ways in which a continuum can be torn apart. We outline a classification of lines according to the number of circles and branching points they contain. The ordering (C,≤) is a topped and bottomed, atomic, almost dense and complete partial ordering, weaker than a lattice. Continuous transformations from C to C are also defined in a natural way and results about them are proved. (shrink)

This article is about a spiritual response to environmental crisis, an emerging field of ethics that joins ecology and environmentalism with the awareness of sacred within the creation2. It investigates into the Vedic texts for finding out the philosophical attitude about the earth and our spiritual obligations and responsibilities to the planet in resolving environmental issues. In the vedic-tradition3, it is the course of experiencing nature as spiritual presence and the awareness to it about our conduct as the moral and (...) rational being. It is a world view that values all that in totality is called “nature” that is, generally, taken as “other” in contrast to human, as existence or spirit. The ethics of respect to “others”, against the effects of imperialistic, ideological conflicts, religious terrorism, industrial, atomic and corporate pollutions, must be worked out as a remedy. The basic argument of spiritual ecology lies in the view that we can find no God more than the spirit abiding in all units of the globe. One must have the view of spirit as ubiquitous principle in treating with and enjoying our needs with the things that the nature permeates as gifts of his care to it. Thus, spiritual ecology of the Vedic tradition has a therapeutic importance; it helps in cultivating our conduct and overcoming the fear of a risk against living on the earth. I am of the view that the rationality of a man and that of a nation is to be determined in proportion to the cultivation and progress of attitude and treatment with “other” but not the vice versa. (shrink)

By way of an example, Lewis imagines your being invited to join Schrödinger’s cat in its box for an hour. This box will either fill up with deadly poison fumes or not, depending on whether or not some radioactive atom decays, the probability of decay within an hour being 50%. The invitation is accompanied with some further incentive to comply (Lewis sets it up so there is a significant chance of some pretty bad but not life-threatening punishment if you (...) don’t get in the box). Lewis argues that the many minds theory implies that you should get in the box with the cat, despite this making it 50% likely you will die. (shrink)

In the last decade, the notion of triad was reintroduced by Eric Scerri, who suggested it as a possible categorical criterion to represent chemical periodicity. In particular, he reformulated the notion of triad in terms of atomic number instead of atomic weights; in this way, the value of the intermediate term of the triad became the exact average of the values of the two extremes. Following the inspiration of Scerri’s work, the main purpose of this article is to (...) obtain a representation where all the relations among the chemical elements that form the groups of the periodic system can be reconstructed on the basis of triads, without using electronic configurations. (shrink)

Boolean algebras are one of the main algebraic tools in the region-based theory of space. T. Ivanova provided strong motivations for the study of mere semilattices with a contact relation. Another significant motivation for considering an even weaker underlying structure comes from event structures with binary conflict in the theory of concurrent systems in computer science. All the above-hinted notions deal with a binary contact relation. Several authors suggested the more general study of n-ary ‘hypercontact’ relations. A similar evolution (...) occurred in the study of the just mentioned event structures in computer science. To unify the above lines of research, in this paper, we study joining semilattices with a hypercontact relation. We provide representation theorems into Boolean algebras. With a single exception, our proofs are choice-free. We also present several examples and problems; in particular, we briefly discuss some connections with event structures and hypergraphs. (shrink)

We examine the compromises that are actually made in modern scientific discourse concerning atoms. We conclude that even the ideals of clarity and consistency can be legitimately compromised in order to obtain other advantages.

The article demonstrates that to describe the property of atomicity of transactions in database systems, we need a three-valued logic with propositional connective characterized in the same way as Blamey’s interjunction. However, the article explains that since Blamey’s partial logic with interjunction is a logic without tautologies, it does not satisfy some salient conditions of being a logic of atomic transactions. The article introduces a logic of the considered kind, and provides an example of the formal exposition of the (...) case of an atomic transaction. Finally, the article explains the philosophical significance of the introduced logic. (shrink)

ABSTRACT In this paper I present and evaluate Leibniz’s two main arguments against the existence of atoms. In this context atoms are extended particles that are absolutely hard, homogeneous, indivisible, and indestructible by natural means. As we shall see, Leibniz’s arguments are flawed in a very instructive way. The first argument is in tension with the claim that God created the best possible world. The second argument overgeneralizes in an undesirable way. However, as I shall discuss in the last section (...) of the paper, even if the arguments are somehow defective, at least the first one contributes valuable insights to contemporary metaphysics. (shrink)

We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.

continent. 2.1 (2012): 6–21. The French philosopher and novelist Tristan Garcia was born in Toulouse in 1981. This makes him rather young to have written such an imaginative work of systematic philosophy as Forme et objet , 1 the latest entry in the MétaphysiqueS series at Presses universitaires de France. But this reference to Garcia’s youthfulness is not a form of condescension: by publishing a complete system of philosophy in the grand style, he has already done what none of us (...) in the older generation of speculative realists has done so far. His book is sophisticated, erudite, rigorous, imaginatively rich, and abundant in worldly wisdom– despite the author’s conclusion that wisdom does not exist. The quality and scope of Forme et objet took few observers by surprise, since Garcia has been treated as an emerging philosopher to watch across half a decade of Parisian oral tradition. But Garcia was not just the subject of rumor, being already well known to the French public as a writer of fiction. His debut novel, La meilleure part des hommes , 2 was awarded the 2008 Prix de Flore 3 and has already appeared in English as Hate: A Romance . 4 His follow-up novel, Mémoires de la jungle , 5 made clever use of a chimpanzee narrator. Nor was Garcia only published as a novelist before last November: his philosophical study L’Image 6 had already appeared when the author was just twenty-six, a year before he was crowned by the muses at the historic Café de Flore. And then in 2011, just months before the appearance of Forme et objet , Garcia published a widely distributed work entitled Nous, animaux et humains , 7 with its focus on Jeremy Bentham’s ideas about animals. Given this prolific and versatile track record, an optimistic scenario might envisage the young Garcia as one of those combined literary/philosophical talents who appear intermittently in France across the centuries: Jean-Paul Sartre is merely the most famous recent case. While more time is needed to see how Garcia will channel his impressive mental energies, Forme et objet displays such breadth of insight that its author has a good chance to emerge as one of the leading philosophers of his generation. If we accept Aristotle’s dictum that the peak mental age is fifty-one, then to read Garcia’s massive book is to gain some idea of what European philosophy might look like in the futuristic-sounding 2030’s. The present article is confined to Forme et objet . At 486 pages, the work is obviously daunting in size. Indeed, it is even longer than it sounds, given that many of its early sections are printed in a smaller typeface to designate them as supplemental commentary to the main flow of the argument. But while the length of the book reportedly led to delays in French publication, and will probably slow the inevitable appearance of an English translation, the length of the book should not deter interested readers– much of it results from Garcia’s teacherly writing style. Whereas Quentin Meillassoux’s prose displays an arctic economy of means, Garcia’s style is reminiscent of the repeated lessons of oral classroom proceedings. Rarely is the reader given fewer than three or four chances to master an idea before the author moves on to the next. In practice, the style feels welcoming rather than long-winded. Otherwise, the structure of Forme et objet is surprisingly simple. There is a useful Introduction of less than twenty pages. Then comes Book I: Formally , running to approximately 135 pages. Here Garcia outlines the most basic features of a thing “no matter what it is,” or n’importe quoi , an everyday phrase that Garcia shapes into a technical term. This part of the book feels at times like a more amiable version of Hegel’s Science of Logic , a parallel emphasized further by the threefold articulation of its theme: 1. Thing; 2. Thing and World; 3. Being and Understanding. This is followed by the much longer Book II: Objectively , totaling more than 300 pages. It contains sixteen essay-like meditations on specific kinds of objects—including time, animals, humans, history, gender, and death. Here each chapter rolls smoothly into the next, making this second part of the book feel more like a different work of Hegel: The Phenomenology of Spirit . But these are merely analogies. Garcia is no Hegelian, even if the book contains a few dialectical flourishes that seem to reflect his early enthusiasm for the Frankfurt School. Forme et objet ends with a six-page Coda, followed by the usual page of acknowledgments. In what follows, I will briefly summarize each of these four parts of the book before ending with some more general remarks. Before doing so, it will be useful to situate Garcia biographically (as much as I am able) and philosophically. Though Toulouse is his native city, his formative years were spent largely in Algeria, where his family has deep roots. During our sole private conversation, Garcia mentioned that his parents are professors of literature. 8 As a student of philosopher Garcia flourished so early that many of his current ideas date to his teenaged years: “There are sentences in Forme et objet that I wrote when I was seventeen,” he said in response to a question on that cold night on the Canal St.-Martin. I recalled that remark when reading his brilliant account, late in the book, of the central role of adolescence in contemporary culture. While many prodigies blow through their formal academic training without serious obstruction, Garcia’s student memories are rich in tales of isolation and struggle, though equally rich in gratitude for a half-dozen or so exceptional teachers who provided the intellectual space he needed: Meillassoux and Alain Badiou are simply two of the most prominent figures on that list. Though there are many points of agreement between Garcia’s philosophical position and my own, he not only reached his position years before reading my work, 9 he arrived along a rather different path: not through phenomenology, but via the Frankfurt School, which may be one of the reasons for his profound fascination with aesthetics. Garcia’s cultural background is as broad as one could wish: he is no less informed about punk rock and European football leagues than about the spiritualist roots of Bergson’s philosophy. Curious about everything and contemptuous towards nothing, Garcia can be expected to write insightfully on dozens of topics in the years to come. Given that his philosophy is so personally tantalizing in its agreements and disagreements with my own, and given the great internal richness of Forme et objet itself, the present review is no better than a first effort at coming to terms with the challenges posed by this minstrel from the rising generation. This is especially intriguing for older Generation X’ers like me, since confrontation with the younger generation is one of the many themes treated insightfully in Garcia’s book. 1. Introduction Garcia begins in defense of a so-called “flat ontology,” in which all things are equally things. While Roy Bhaskar 10 used this term pejoratively to refer to anti-realist philosophies that flatten everything onto an epistemic plane of human access, Manuel DeLanda 11 (an admirer of Bhaskar) reversed it into the positive principle that all realities are equally realities. Similar notions can be found in the “absistence” of Alexius Meinong, 12 the “irreduction” of Bruno Latour, 13 and my own critique 14 of the undermining/overmining pair. Also noteworthy is Levi Bryant’s use of the term “flat ontology” throughout The Democracy of Objects 15 and his earlier essay “The Ontic Principle.” 16 But for Garcia, flatness is only one face of the cosmos, and one that he ultimately declares to be rather impoverished. Even so, he always remains an advocate of a flat ontology. Insofar as everything is equally something, no matter what it is ( n’importe qui ), everything is equally a thing, equally solitary in its relation with world. This is why his book abounds in those long lists of random, ontologically equivalent entities that Ian Bogost has playfully termed “Latour Litanies.” 17 The first litany in Garcia’s book runs as follows: “We live in this world of things, where a cutting of acacia, a gene, a computer-generated image, a transplantable hand, a musical sample, a trademarked name, or a sexual service are comparable things.” (7) Yet Garcia is frankly dualistic; his flat ontology only lasts until page 159 and the end of Book I (entitled “Formally”), which deals entirely with things that are equally things. Thereafter Garcia turns his attention from things to objects, which are not flat in the least, but engage in hierarchical relations with one another. In agreement with both DeLanda and the speculative realists, Garcia proclaims that his book “proposes to put to the test a thought about things rather than a thought about our thought about things .” (8) Just as ducklings are “imprinted” (9) after hatching and treat the first creature they see as their mother, philosophers are imprinted by the idea with which they begin. Hence, philosophies that begin with human access will never truly find their way back to things. This makes Garcia rather suspicious of twentieth century philosophy, since “the twentieth century—to which in some way this work proposes to bid adieu—has been a period of theorizing modes of access to things rather than things...” (9) Among other possible benefits of the philosophy of things that Garcia proposes, it is fully able to account for thought as a special variant of things, while the reverse is not possible.(10) In Book I of Forme et objet , Garcia’s “things” are so flat, so de-determined, that he is forced to renounce some of the most basic features ascribed to things by most realists. As he tells us in his foreboding third footnote: “We will maintain that the solitude [of things] is less than unity, less than identity, and that it does not imply acceptance (any more than refusal) of the principle of non-contradiction.” (11) In a contemporary world cluttered with too many things, Garcia’s flat and formal plane provides us with some breathing room: “The formal plan of thought enables or re-enables us to cut short all accumulation—whether of knowing, experience, or action—by a simplicity, an impoverished surface...” (13) As Garcia says elsewhere in responding to a Deleuzian critic of the book, his starting point in flat ontology is designed to obstruct the claims of both analytic philosophy and Hegelianism: “Hence, this work seeks to protect each thing—real, imaginary, inconsistent, contradictory—both against Ockham’s Razor and against the Aufhebung or dialectical process.” 18 Yet contrary to the equalizing spirit of many flat ontologies, “we will add to our formal ontology of the equal, an objective ontology of the unequal.” (13) But initially, Garcia joins all flat ontologists in holding that everything is irreducible: “this irreducibility, which we will term the ‘chance’ of each thing... also marks the refusal of a positive thought that reduces things exclusively to natural things, or social things, or historical things, etc.” (15) This irreducible “chance” of a thing emerges as an important technical term in the book, always paired with its inverted brother, the “price to pay” ( prix à payer ). On pages 17-19, we find the only diagrams in the book. What they illustrate is that Garcia wishes to avoid two equally dangerous extremes. The first is the philosophy of substance, featuring the thing-in-itself as a mighty river fed by attributes as if by subordinate tributary streams. This model can be found in many of the classic thinkers of West and East alike. In it, “there is obviously a hierarchization between that which is dragged towards something other than itself, and this other which serves it as an ontological support while supporting its proper being.” (16) For Garcia, the second extreme worth avoiding is the philosophy of events: “One thus conceives trajectories of being, identified as events, facts, powers, intensities, or intentionality. These vectors of being come first, bearing and supporting being, displacing it, but without ever finding a stopping point, a buffer, an objective consistency.” (17) The first model gives us a thing too wrapped up in itself, too compact . This word “compact” (the French and the English are the same) is another technical term for Garcia. But if the “compact” model of things leads us to something more than things, the philosophy of events gives us less than things, by dissolving them into a play of vectors. Garcia’s alternative lies midway between these two extremes: Being enters the thing, being comes out of it. And a thing is nothing other than the difference between the enters and the being that comes out. Thus, the circuit of being is never halted. In the thing, there is never the thing-in-itself. And the thing is never in-itself, but outside of itself. Nonetheless, being is not eventally “pollinated” by vectors: it possesses an objecting halting-point... (19) This single idea is the key to Garcia’s book: the thing is neither a self-contained durable lump nor some sort of evental flux. Instead, the thing is the difference between its various components and its relations with its environment. Or stated differently: “the price to pay for this disposition is a circulation of being that systematically distinguishes two senses of things: that which is in the thing , and that in which the thing is , or that which encompasses it and that which it encompasses,” (19) translating comprendre here as “encompass.” 19 In a beautiful description of a piece of black slate, Garcia sums up the various minerals, qualities, and shapes that compose [ comprend ] it, and calls them “that which is in the thing,” (20) noting that this tells us nothing about “that in which [the slate] is”—namely, all the various situations in which the black slate can be found. Instead, the slate is the difference between these two: the most characteristic principle of Garcia’s philosophy. 2. Formally Book One of Forme et objet , “Formally,” is concerned with the formal equality of all things in a flat world. “Two questions mark the boundaries of reflection: of what is everything composed [ composé ], and: what do all things compose?” (27) Looking downward, we wish to know what everything is made of; looking upward, we want to know the ultimate result of the combination of all things. Here we must turn our attention to the thing n’importe quoi— no matter what it is. (30) Anything with finite qualities is obviously too specific to be relevant to global ontological questions. To an equal degree, something possessing all qualities (think of Whitehead’s God) 20 would not be n’importe quoi either, since it would still be too definite, even if incredibly vast. The same holds for contradictions, since these all differ from each other. The square circle, the non-white black white, and the non-city city are all too distinct to count as the thing no matter what it is. The n’importe quoi must be devoid of all specific qualities, including contradictory ones. In one of the more intriguing points in his book, so reminiscent of Meinong, Garcia proclaims that “the ‘no matter what it is’ is neither a reality nor an abstract construction, nor both of these at once; the ‘no matter what it is’ is simply the plane of equality of that which is real, that which is possible, that which is inexistent, that which is past, that which is impossible, that which is true, that which is false, that which is bad.”(39-40) Since everything has two faces, it would be a grievous mistake to focus on just one of them at the expense of the other, as physicalism or materialism do when reducing the world to minuscule physical underpinnings. For scientistic materialism, “it is either atoms, particles, or fields of force... which are the things.” (47-48) Moreover, “these more-than-things are accompanied by less-than-things: for example, ideas or facts of consciousness are determined by the state of matter and are not autonomous things, but manifestations reduced to secondary effects of material processes...” (48) On this point, Garcia’s position is in complete accord with my own critique of undermining and overmining. 21 Where we disagree is that Garcia is more deeply suspicious of the notion of substance, which I view as salvageable with a few needed changes, while Garcia sees this operation as hopeless: “A substance, in the history of philosophy, is the more-than-thing par excellence.” (51) Another agreement between our positions is visible when Garcia claims (correctly, in my opinion) “that it is vain to distinguish between things which are material and those which are not.” (52) Yet we also find an even more important disagreement, since for Garcia withdrawal cannot be the quality of a thing. Instead, the absence of a thing is simultaneous with it, embodied in all that is not it– the absence of the sculpture of a woman is to be found in the mold that appears at the same time as it, and thus withdrawal must be viewed as an “event” rather than as something pertaining to an object. For Garcia, nothing withdraws beyond access. Since we must distinguish between “that which is something” and “that which something is,” and since the former is identified with “no matter what it is is” and the latter with “ not no matter what it is,” we can say that “everything is thus a milieu, a fragile link between ‘no matter what it is’ and ‘ not no matter what it is.’” (62) And here we find Garcia’s critique of the thing-in-itself: “A thing is never defined en bloc . We can affirm that a thing is this or that, but that does not suffice. It is still necessary to state precisely that which is this thing .” (62) Stated differently, “something is not in itself : for that which is in the thing is not the thing, and that in which the thing is is not the thing.” (62) And here Garcia and I, facing the same evidence, draw opposite conclusions. For me, the fact that nothing can be identified with either its components or its concrete location means that the thing must be something in-itself distinct from both of these. Yet for Garcia, to be in-itself would mean to be identified with just one of these two extreme terms, and hence the thing can only be the difference between them. Garcia is equally suspicious of the classical tendency to view “unity” as a property of the thing, since in his eyes unity is too relational a property to belong to things. (65) While specific things are situated determinately with respect to other things, we are still speaking here about the thing no matter what it is, and this can be viewed only in terms of solitude, which all things share: a human being, a hand, or a chair or all equally things insofar as they are on their own , not insofar as they are one . (64) A thing is alone, and relates only to the one thing that is not another thing: world. In a striking parallel to my own argument for a partial revival of occasionalism, Garcia tells us that “the things communicate only by their solitude: it is because everything is equally on its own in the world that things can be together, enmeshed in one another.” (67) Alone in their solitude, things all relate to world, which serves as a mediator allowing them to become mixed up in one another. As we have seen, one reason that nothing can be in itself is because everything is in something else. For Garcia, “to be in something and to be something are equivalent.” (69) Stated more broadly, “being is thus the difference between the two aspects of each thing: that which is it, and that which it is.” (70) And even more vividly: “a thing is almost like a sack: there is that which one puts in the sack and that which remains outside the sack.” (70) But not quite like a sack, “since a thing is not a thin skin or film. Instead, a thing is comparable to a sack that is immaterial and without thickness: it is nothing other than the difference between that which is this thing and that which thing is, between content and container.” (71) Nothing can be in-itself because everything is two selves at once. For example, we cannot say that our self is defined by our consciousness: “Everything has a self because nothing is in itself. The self is not the quality of that which is related to itself (which is conscious, for example) or which thinks itself related to itself. Nonetheless, for an entity called ‘conscious’ to be related to itself, it is necessary that this very relation should be another thing than the self to which it is related.” (71) Consciousness cannot be the self, precisely because it is other than that of which it is conscious. Nothing is able to grasp itself. The self is “the function by which being and composition [ compréhension ] are mutually excluded...” (72) The self is “the point of shadow of everything that projects some light...” (72) The in-itself faces two opposite dangers: “For something to be in-itself is to be a self. Something which is a self flies out through one of its two sides... Stated differently, being in-itself is simply the possibility of a double failure.” (73) The in-itself can be termed compact : “There remains to us a means of thinking that which does not fully enter into the world, though without exiting from it. This means is what we call the compact.” (76) In a sense, the compact is the opposite of the world. For in the case of the world, everything enters it and it enters nothing; as for the compact, it enters the world (since it is something, after all) while nothing enters it. (77) The compact marks the presence of the impossible in the world. (78) It is not impossible, but possible only on the condition that it fails. (78) The time has come to speak of where a thing is located. “The sole condition of a thing is that of being in another thing than itself, and thus in another thing than something.” (78) A condition is “that which determines something, that which forms something, that in which something is.” (78) As for humans, “the condition of someone is his situation; my social condition is that which socially determines me, my place and my function...” (79) More generally, “to be conditioned is to find oneself reduced to that in which one is.” (79) Everything is conditioned, but nothing is reducible to this condition. To determine the condition of something is to determine in what it is. A thing is located in that which contradicts it, just as a statue exists in its mold, which is precisely that which it is not. Since the thing is finite and definite, its condition or form must be infinite and indefinite. That in which all things are is the world, which Garcia also terms “the whole.” (81) “To try to be in-itself is to attempt to remain outside the world. And indeed, to try to be in-itself is only a path of entry into the world.” (83) For Garcia, “the world is not the pre-existent container of the things it contains, a priori , nor the construction by the mind of a fictional ensemble of all things, a posteriori .” (85) Instead, the world is simultaneous with all things; the two always go together. The world cannot be a determinate world, such as the physical universe or mathematical space, since these are already too specific and limited. “Every determinate world, which is in fact a universe , is a ‘big thing’ [ grosse chose ]: it is a set, however vast, of composite things which itself embodies a thing.” (85) Every determinate world is really just a “big thing.” Stated differently, “it is nothing other than a balanced milieu between the things that compose it and the thing that it composes.” (85) We generally picture the world as a physical univer. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 27.2 (2003) 304-317 [Access article in PDF] Sovereign Love and Atomism in Racine's Bérénice Ellen Mcclure ALTHOUGH CRITICS HAVE NOTED links between the new science of the seventeenth century and the works of La Fontaine and Molière, 1 a similar influence of Epicureanism or even Cartesianism upon French classical tragedy is harder to trace. No two areas of seventeenth-century cultural life would seem farther apart than (...) the emerging science, with its rejection of Aristotelian categories as inadequate to experienced reality, and classical French tragedy, with its antimaterialism and claims to universal truth often bolstered by references to none other than Aristotle himself. Yet René Pintard reminds us that the 1660s and 1670s—the period when many of the tragedies we regard as "classical" were written—saw a strong renewal of interest in the philosophies articulated in the first half of the century. 2 So widespread was this interest that Pierre Gassendi's friend and follower Bernier was able to publish an edition and translation of the philosopher's works in 1674-1675 which proved to be a resounding success. It is hard to believe that the much-discussed new science somehow missed writers of tragedies, especially given the extensive contacts between Molière, La Fontaine and Racine.In this article, I demonstrate this influence by positing that Racine's play Bérénice, ostensibly a reworking of a well-known love story that Corneille was also producing on the Paris stage at the same time, is in part a reflection on the pressing question of what holds the universe together. Through his exploration of the possibility of satisfactory love between two independent sovereigns, Racine explores issues that the revival of Epicureanism had brought into the philosophical foreground. This reading of the play brings into focus the incredibly [End Page 304] important, yet too-often neglected, 3 role of Antiochus, the character whom Racine invented for his version of the play. I will show that his tragic in-betweenness offers a necessary alternative to Titus' and Bérénice's valorization of self-contained sovereignty. I Before embarking on a close reading of the play itself, however, I would like to offer a brief survey of the debate to which I believe Racine refers. Both Michel Foucault and Timothy Reiss have identified the seventeenth century as a transitional period between the age of correspondences exemplified in Aristotelian philosophy and the age of representation and quantification that characterized eighteenth-century thought. 4 This transition, however, was far from smooth, as philosophers sought to articulate a universe whose separate and radically de-hierarchized elements remained somehow joined together.For most seventeenth-century philosophers, the sacrifice of Aristotelian categories and scholasticism in no way lessened the imperative for a sense of divine order and causation. Gassendi's often self-contradictory efforts to reconcile Epicurus and Christianity provide perhaps the most striking example of this transitional struggle. The atomism posited by Epicurus through Lucretius posed particular difficulties for a Christian worldview. A world governed by the chance interactions of atoms eliminates any sense that things happen for a purpose; God cannot be the benevolent author and overseer of the universe. Gassendi's equal respect for atomism and for Christianity should be read as evidence of the profound struggle between separateness and interconnection (or, as Gassendi would call it, harmony) taking place during this period. 5 For, as Bloch points out, although Gassendi partially reconciled the demands of the two systems by situating atoms in an uncreated, infinite, and contiguous space and time, he continued to hold to the profoundly troubling existence of the void in the universe. Once again, the chief objection to the void implicit in atomism was religious, since if God is everywhere, the void cannot exist, and likewise, God cannot create nothing. The revival of stoicism supplied instead a vision of the universe ultimately comprised and held together by an ethereal pneuma that some neo-Stoics did not hesitate to identify as a sort of divine presence. 6 Descartes himself made heroic attempts, in his Principes... (shrink)

A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more intuitive arithmetical structures to establish the variable sharing property for (...) the systems discussed. (shrink)