In its first meaning, a logic is a collection of closely related artificial languages. There are certain languages called first‐order languages, and together they form first‐order logic. In the same spirit, there are several closely related languages called modal languages, and together they form modal logic. Likewise second‐order logic, deontic logic and so forth.

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest (...) in exploring the foundations of multialgebras applied to the study of logic systems. -/- It is well known from universal algebra that, for every signature Sigma, there exist algebras over Sigma which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of Sigma-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms (or propositional formulas, in the context of logic). Equivalently, the forgetful functor, from the category of Sigma-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor U, from the category of Sigma-multialgebras to Set, does not have a left adjoint. -/- In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices (which selects how a homomorphism approaches indeterminacies), there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that U does not have a left adjoint. (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest (...) in exploring the foundations of multialgebras applied to the study of logic systems. It is well known from universal algebra that, for every signature \, there exist algebras over \ which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of \-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms. Equivalently, the forgetful functor, from the category of \-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor \, from the category of \-multialgebras to Set, does not have a left adjoint. In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices, there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that \ does not have a left adjoint. (shrink)

Commentators agree that Derrida's criteria for an event were stringent: it had to be unique, unpredictable and unanticipatable; it must come as a surprise that defies all conceptualization, comprehension, appropriation. Can any historical occurrence pass such rigorous tests and be considered an event? The question now extends to whether Derrida's writings or life should constitute an event. This article traces Derrida's use of the word ‘event’ or ‘événement’ from ‘Signature Event Context’ and early readings of Nietzsche, Blanchot, and Benjamin (...) through his 2001 paper, ‘The Impossible Possibility of Saying the Event’. Analysis shows that where Derrida appears to concede the independent existence of past events this illusion is created linguistically by supplements, the future anterior tense, and speech acts. His unsuccessful attempt to exemplify ‘events’ that were distinguishable from merely ‘what happens’ assimilates them into the latter category, which he likened to ‘rain’, a banal, minimal catachresis of nothing. The implication is that what we call history resembles a Beckett-like condition of apparent insight that reverts, on reflection, to emptiness. (shrink)

A Dedekind algebra is an order pair (B, h) where B is a non-empty set and h is a similarity transformation on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are 0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type which occur in (...) the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. It is shown that configuration signatures can be used to characterize the homogeneous, universal and homogeneous-universal Dedekind algebras. This characterization is used to prove various results about these subclasses of Dedekind algebras. (shrink)

It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (\(\textit{CABA}\)s) taking a set to its power-set and, conversely, a complete, atomic Boolean algebra to its set of atomic elements. Of course, such a correspondence induces an equivalence between the opposite category of \(\textbf{Set}\) and the category of \(\textit{CABA}\)s. We modify this result by taking multialgebras over a signature \(\Sigma\), specifically those whose non-deterministic operations cannot return the empty-set, to \(\textit{CABA}\)s with their (...) zero element removed (which we call a \(\textit{bottomless Boolean algebra}\)) equipped with a structure of \(\Sigma\)-algebra compatible with its order (that we call \(\textit{ord-algebras}\)). Conversely, an ord-algebra over \(\Sigma\) is taken to its set of atomic elements equipped with a structure of multialgebra over \(\Sigma\). This leads to an equivalence between the category of \(\Sigma\)-multialgebras and the category of ord-algebras over \(\Sigma\). The intuition, here, is that if one wishes to do so, non-determinism may be replaced by a sufficiently rich ordering of the underlying structures. (shrink)

A Dedekind Algebra is an ordered pair (B,h) where B is a non-empty set and h is an injective unary function on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called configurations of the Dedekind algebra. There are N0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on omega called its configuration signature. The configuration signature of a Dedekind algebra counts the number of configurations in the (...) decomposition of the algebra in each isomorphism type.The configuration signature of a Dedekind algebra encodes the structure of that algebra in the sense that two Dedekind algebras are isomorphic iff their configuration signatures are identical. Configuration signatures are used to establish various results in the first-order model theory of Dedekind algebras. These include categoricity results for the first-order theories of Dedekind algebras and existence and uniqueness results for homogeneous, universal and saturated Dedekind algebras. Fundamental to these results is a condition on configuration signatures that is necessary and sufficient for elementary equivalence. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Secrecy and Autonomy in Lewis CarrollSusan ShererVictorian novels quiver with morbid secrets and threatening discoveries. Unseen rooms, concealed doors, hidden boxes, masked faces, buried letters, all appear (and disappear) with striking regularity in the fiction of Victorian England. So many of these secret spaces contain children, and especially little girls, little girls in hidden spaces. The young Jane Eyre sits behind a curtain in the hidden window seat, escaping (...) the vindictive wrath of John Reed. Repulsed by her angry brother, Maggie Tulliver flees to the house attic, fantasizing that her family will fear that she has died. Little Dorrit withdraws from the common space of the Marshalsea into her private room above the prison, and Little Nell hides behind trees and walls, silently observing clandestine meetings. Finally the seven-year-old Alice falls down a rabbit-hole into a Wonderland, the dreamspace of her own psyche.Of these images, none can be more embedded in our cultural imagination than the child Alice dropping into the subterranean well of Wonderland. Indeed, of the many celebrated scenes in the Alice narratives, the most memorable, most potent, most quoted is Alice’s initial descent to the bottom of the rabbit-hole. The lastingness of this scene seems even greater when we realize that, although neither Carroll in Alice’s Adventures Underground nor Tenniel in the first edition of Wonderland illustrated the moment with a picture, it still became (along with the Mad Hatter’s tea party) one of the signature images of the Alice stories. Why, we must ask, did the Victorians retain, with a powerful tenacity, this vision of a little girl moving through a tight space toward the hidden world of Wonderland?The answer to this question is not—at least not wholly—that the scene simply represents a child’s metaphorical progress through the [End Page 1] birth canal 1 and that this, in turn, symbolizes some kind of rite of passage, a movement towards some deeper knowledge. For then how do we explain Alice’s conspicuous lack of internal development in both stories? Indeed, for a narrative that thematizes motion, Alice’s psychical growth remains disturbingly static. Throughout both narratives, Alice displays little emotional variation, for when she is not frustrated or anxious, she is, for the most part, vapid or expressionless. In fact, one is immediately struck by her coolness and indifference as she drops through the rabbit-hole. 2 Thus, because scene changes in Wonderland and Looking-Glass rarely betoken any emotional or intellectual modulations, Alice’s falling into Wonderland signals no internal transition.But the image does relocate her body and within this fictive world, location is everything. The scene gestures Alice’s departure, her separation, her movement towards an autonomy of which every child dreams when, in play, retreating to a hidden space. A child’s impulse to hide, to create a secret space, is one of the most compelling of all human wishes, the wish for autonomy and autarchy—“to be cut off from the word and yet owner of the world.” 3 Throughout Victorian literature, the fantasy of autonomy sets children dreaming of far-away worlds and hidden gardens. The young Cathy and Heathcliff flee to the isolated moors, filling the open, empty space with dreams of unrestricted freedom. Little Dorrit envisages the locked garden behind the Marshalsea as an alternative world to the foul prison atmosphere. And what are the Brontës’s Angria and Gondol but disconnected, self-governing realms imagined from the standpoint of childhood powerlessness? The image, then, of Alice’s fall begins to fulfill this powerful wish for autonomy, which culminates, finally, in Alice’s self-coronation at the end of Looking-Glass. Yet it is only within the child’s willing imagination that a secret space can encroach so closely upon autonomy, for as we shall see, secrecy and autonomy are irreconcilable not only in the demanding world of realism, but even in the more elastic world of Carrollian fantasy.IAlice’s descent into Wonderland and her entrance into the Looking-Glass kingdom would seem like ripe metaphors for Carroll to explore the thoughts and fantasies of Alice’s psyche. What could be more... (shrink)

A Dedekind algebra is an ordered pair (B, h), where B is a non-empty set and h is a similarity transformation on B. Among the Dedekind algebras is the sequence of the positive integers. From a contemporary perspective, Dedekind established that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. The purpose here is to show that this seemingly isolated result is a consequence of more general results in the model theory of second-order (...) languages. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ?0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on ? called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type that occurs in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. The second-order theory of any countably infinite Dedekind algebra is categorical, and there are countably infinite Dedekind algebras whose second-order theories are not finitely axiomatizable. It is shown that there is a condition on configuration signatures necessary and sufficient for the second-order theory of a Dedekind algebra to be finitely axiomatizable. It follows that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Five Poems AMIT MAJMUDAR Observing Orpheus I hear the meaning turn back in his throat like Eurydice on the way up from the darkness. Music’s meaning is its making. As for me, I am one more animal in his entourage, learning a new thirst, finding a new south. None of us knew we had this instinct in us. If deserts hide wildflowers until first rain, bright ears are blossoming (...) out of our skulls. He doesn’t have much longer. I know this myth. A God douses the fire with a beehive. The Maenads smear their faces with a warpaint made of stoneground fireflies and pine sap. Hands—hands like his, that drew music through lyre strings into our forest like pieces of bread through a prison fence— are reaching for his body now, his lyre. Their weapons are hands, nothing but hands. They are infinite. They are enough. arion 27.1 spring/summer 2019 Her Metamorphoses First a beetle, body armor forged of chitin, exoskeleton he’ll never bruise, Undiscovered, unapologetically hermetic on her own Galapagos. Next a fruit bat, echolocating tangerines like a blind woman singing up at stars. Then a patio lizard, sunning herself for as long as she needs, A better place for keeping warm than bed with him. Next a sleek water moccasin, quick to make out another woman’s heat signature on his neck, Even quicker to strike. A caterpillar to poke holes in his lying roses And from that destruction to fashion two beautiful wings for herself. A buzzard, to clean up the roadside pile he left of her. A woman in full with no more soft blind pupa stages of her life cycle left, No more forms to force herself to fit for the sake of his pleasure, No more shapeshifts, no more slimming stripes, no more abdominal crunches: Just this body, just this last name, just this apartment, just this bowl of midnight cereal. Just her. 106 five poems Sisyphus Shove hard, shove, shove hard, eyes bloodshot, knees bent Till your boulder goes weightless and races ahead in descent. Force its dark door open inch by grim inch, Shove hard, shove, shove hard, eyes bloodshot, knees bent, Heels dug deep in hell’s steep hillside, teeth clenched. What gravity strips from you, gravity grants you again. Shove hard, shove, shove hard, eyes bloodshot, knees bent Till your body goes weightless and races ahead in ascent. Amit Majmudar 107 A Trinket for Persephone A deathwatch beetle burrows in the pale hall of your marrow, your underground, your tube of bone on which you’re riding home alone. This blackwinged locket with your soul emerges rattling from a hole, a rattle in your emptied throat, the diva’s final, graceless notes, a clicking echoed in the rafters, this bugbear insect coming after to scuttle across the marshy chest, sinkhole navel, and pubic nest out to the yard, below the porch untrackable by any torch until this bug with you inside has burrowed to the other side. It drops into the underworld, as if from some cocoon unfurled, to scale a queenly wrist and rest your brooch of black upon her breast. 108 five poems Four Ways of Looking at Argus 1. His Vigil These hundred eyes, these hundred balloons Tied to the boy-small wrist of my mind Are down to ninety-nine. I lost one to a bee sting late last June— I never thought of them as fragile Until that pinprick broke my vigil. I’m slowing down. I didn’t blink in time. I have no inkling why I keep This vigil—surely not to watch, Panoptic from this mountaintop, A heifer drifting off to sleep? I’m here, I must be here, to see A signal fire from the east That warns of Olympus under siege And Ares gory from a rout, Athena’s owl’s eyes gouged out, The naiads naked in a pen, The whole world given up to men. The Gods will need a monster then. 2. After Martial Hermes was in a fix: He needed lullabies To shutter Argus’s one hundred eyes And get the tethered heifer—coal-eyed Io—free Of Hera’s... (shrink)

God has major reasons for intervening in human history by becoming incarnate himself—to identify with our suffering, to provide atonement for our sins, and to reveal truths. Given there is at least a significant probability that there is a God, there is at least a modest probability that he would become incarnate and live a life and provide teaching appropriate to one who sought thereby to realize these goals. Jesus lived and taught in the appropriate way. If it was God (...) incarnate who did so live and teach, he would need to show us that it was God who had done so, and so could be expected to put his signature on that life and teaching by a super-miracle, such as the Resurrection. So there is a modest prior probability in advance of considering the direct historical evidence of the Resurrection, to expect that it would happen to someone who lived and taught as Jesus did. Jesus is the only person in human history about whom there is significant evidence both that he led the appropriate kind of life, and that his life was culminated by a super-miracle. So we do not need too many witnesses to the empty tomb or too many witnesses who claimed to have talked to the risen Jesus, to make it probable that Jesus did indeed rise. We do have some such witness evidence, which it is very improbable would occur unless the Resurrection occurred. In consequence it is overall very probable that the Resurrection occurred. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Secrecy and Autonomy in Lewis CarrollSusan ShererVictorian novels quiver with morbid secrets and threatening discoveries. Unseen rooms, concealed doors, hidden boxes, masked faces, buried letters, all appear (and disappear) with striking regularity in the fiction of Victorian England. So many of these secret spaces contain children, and especially little girls, little girls in hidden spaces. The young Jane Eyre sits behind a curtain in the hidden window seat, escaping (...) the vindictive wrath of John Reed. Repulsed by her angry brother, Maggie Tulliver flees to the house attic, fantasizing that her family will fear that she has died. Little Dorrit withdraws from the common space of the Marshalsea into her private room above the prison, and Little Nell hides behind trees and walls, silently observing clandestine meetings. Finally the seven-year-old Alice falls down a rabbit-hole into a Wonderland, the dreamspace of her own psyche.Of these images, none can be more embedded in our cultural imagination than the child Alice dropping into the subterranean well of Wonderland. Indeed, of the many celebrated scenes in the Alice narratives, the most memorable, most potent, most quoted is Alice’s initial descent to the bottom of the rabbit-hole. The lastingness of this scene seems even greater when we realize that, although neither Carroll in Alice’s Adventures Underground nor Tenniel in the first edition of Wonderland illustrated the moment with a picture, it still became (along with the Mad Hatter’s tea party) one of the signature images of the Alice stories. Why, we must ask, did the Victorians retain, with a powerful tenacity, this vision of a little girl moving through a tight space toward the hidden world of Wonderland?The answer to this question is not—at least not wholly—that the scene simply represents a child’s metaphorical progress through the [End Page 1] birth canal 1 and that this, in turn, symbolizes some kind of rite of passage, a movement towards some deeper knowledge. For then how do we explain Alice’s conspicuous lack of internal development in both stories? Indeed, for a narrative that thematizes motion, Alice’s psychical growth remains disturbingly static. Throughout both narratives, Alice displays little emotional variation, for when she is not frustrated or anxious, she is, for the most part, vapid or expressionless. In fact, one is immediately struck by her coolness and indifference as she drops through the rabbit-hole. 2 Thus, because scene changes in Wonderland and Looking-Glass rarely betoken any emotional or intellectual modulations, Alice’s falling into Wonderland signals no internal transition.But the image does relocate her body and within this fictive world, location is everything. The scene gestures Alice’s departure, her separation, her movement towards an autonomy of which every child dreams when, in play, retreating to a hidden space. A child’s impulse to hide, to create a secret space, is one of the most compelling of all human wishes, the wish for autonomy and autarchy—“to be cut off from the word and yet owner of the world.” 3 Throughout Victorian literature, the fantasy of autonomy sets children dreaming of far-away worlds and hidden gardens. The young Cathy and Heathcliff flee to the isolated moors, filling the open, empty space with dreams of unrestricted freedom. Little Dorrit envisages the locked garden behind the Marshalsea as an alternative world to the foul prison atmosphere. And what are the Brontës’s Angria and Gondol but disconnected, self-governing realms imagined from the standpoint of childhood powerlessness? The image, then, of Alice’s fall begins to fulfill this powerful wish for autonomy, which culminates, finally, in Alice’s self-coronation at the end of Looking-Glass. Yet it is only within the child’s willing imagination that a secret space can encroach so closely upon autonomy, for as we shall see, secrecy and autonomy are irreconcilable not only in the demanding world of realism, but even in the more elastic world of Carrollian fantasy.IAlice’s descent into Wonderland and her entrance into the Looking-Glass kingdom would seem like ripe metaphors for Carroll to explore the thoughts and fantasies of Alice’s psyche. What could be more... (shrink)

Demonic composition, demonic refinement and demonic union are alternatives to the usual ‘angelic’ composition, angelic refinement (inclusion) and angelic (usual) union defined on binary relations. We first motivate both the angelic and the demonic via an analysis of the behaviour of non-deterministic programs, with the angelic associated with partial correctness and demonic with total correctness, both cases emerging from a richer algebraic model of non-deterministic programs incorporating both aspects. Zareckiĭ has shown that the isomorphism class of algebras of binary relations (...) under angelic composition and inclusion is finitely axiomatized as the class of ordered semigroups. The proof can be used to establish that the same axiomatization applies to binary relations under demonic composition and refinement, and a further modification of the proof can be used to incorporate a zero element representing the empty relation in the angelic case and the full relation in the demonic case. For the signature of angelic composition and union, it is known that no finite axiomatization exists, and we show the analogous result for demonic composition and demonic union by showing that the same axiomatization holds for both. We show that the isomorphism class of algebras of binary relations with the ‘mixed’ signature of demonic composition and angelic inclusion has no finite axiomatization. As a contrast, we show that the isomorphism class of partial algebras of binary relations with the partial operation of constellation product and inclusion (also a ‘mixed’ signature) is finitely axiomatizable. (shrink)

What is a paradigm? -- Theory of signatures -- Philosophical archeology.

Every person has his/her own unique signature that is used mainly for the purposes of personal identification and verification of important documents or legal transactions. There are two kinds of signature verification: static and dynamic. Static(off-line) verification is the process of verifying an electronic or document signature after it has been made, while dynamic(on-line) verification takes place as a person creates his/her signature on a digital tablet or a similar device. Offline signature verification is not (...) efficient and slow for a large number of documents. To overcome the drawbacks of offline signature verification, we have seen a growth in online biometric personal verification such as fingerprints, eye scan etc. In this paper we created CNN model using python for offline signature and after training and validating, the accuracy of testing was 99.70%. (shrink)

This paper presents a theory of empty names that is consistent with direct-reference theory and Millianism.

Emptiness means that all entities are empty of, or lack, inherent existence - entities have a merely conceptual, constructed existence. Though Nagarjuna advocates the Middle Way, his philosophy of emptiness nevertheless entails nihilism, and his critiques of the Nyaya theory of knowledge are shown to be unconvincing.

Astrobiologists are aware that extraterrestrial life might differ from known life, and considerable thought has been given to possible signatures associated with weird forms of life on other planets. So far, however, very little attention has been paid to the possibility that our own planet might also host communities of weird life. If life arises readily in Earth-like conditions, as many astrobiologists contend, then it may well have formed many times on Earth itself, which raises the question whether one or (...) more shadow biospheres have existed in the past or still exist today. In this paper, we discuss possible signatures of weird life and outline some simple strategies for seeking evidence of a shadow biosphere. Key Words: Weird life—Multiple origins of life—Biogenesis—Biomarkers—Extremophiles—Alternative biochemistry. Astrobiology 9, 241–249. (shrink)

John Stuart Mill (1843) thought that proper names denote individuals and do not connote attributes. Contemporary Millians agree, in spirit. We hold that the semantic content of a proper name is simply its referent. We also think that the semantic content of a declarative sentence is a Russellian structured proposition whose constituents are the semantic contents of the sentence’s constituents. This proposition is what the sentence semantically expresses. Therefore, we think that sentences containing proper names semantically express singular propositions, which (...) are propositions having individuals as constituents. For instance, the sentence ‘George W. Bush is human’ semantically expresses a proposition that has Bush himself as a constituent. Call this theory Millianism. Many philosophers initially find Millianism quite appealing, but find it much less so after considering its many apparent problems. Among these problems are those raised by non-referring names, which are sometimes (tendentiously) called empty names. Plausible examples of empty names include certain names from fiction, such as ‘Sherlock Holmes’, which I shall call fictional names, and certain names from myth and false scientific theory, such as ‘Pegasus’ and ‘Vulcan’, which I shall call mythical names. I have defended Millianism from objections concerning empty names in previous work (Braun 1993). In this paper, I shall re-present those objections, along with some new ones. I shall then describe my previous Millian theory of empty names, and my previous replies to the objections, and consider whether the theory or replies need revision. I shall next consider whether fictional and mythical names are really empty. I shall argue that at least some utterances of mythical names are. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Jacques Derrida INTERPRETING SIGNATURES (NIETZSCHE/HEIDEGGER): TWO QUESTIONS T1HE first question concerns die name Nietzsche, die second has to do with the concept of totality. Let us begin widi chapters 2 and 3 of Heidegger's Nietzsche — dealing with "The Eternal Recurrence of the Same" and "The Will to Power as Knowledge," respectively. We will be turning especially to the subsection on chaos ["The Concept of Chaos," I, pp. 562-70] (...) and to "The Alleged Biologism of Nietzsche" ["Nietzsches angeblicher Biologismus"]. In view ofme fact mat the same interpretation is regularly at work throughout, the risks involved in choosing diis strategy are, I hope, quite limited. In each instance, a single system of reading is powerfully concentrated and gadiered together. It is directed at gadiering togedier the unity and the uniqueness of Nietzsche's diinking, which, as a fulfilled unity, is itself in a fair way to being the culmination of occidental metaphysics. Nietzsche would be precisely at the crest, or ridge, atop the peak of diis fulfillment. And thus he would be looking at both sides, down both slopes. What about diis unity — diis doubled unity? What is its connection to the name — or rather, the signature — of Nietzsche? Does Heidegger take any account of this question — which others might call biographical, autobiographical, or autographical — of the singularity of a signature ostensibly the proper name of Nietzsche? To put the matter anodier way, if one can glimpse behind Heidegger's reading of Nietzsche the foundations of a general reading of Western metaphysics, men die question Translated by Diane Michelfelder and Richard E. Palmer. 246 Jacques Derrida247 arises: To what extent does this interpretation of metaphysics in its totality and as a whole contain an interpretive decision about die unity or singularity of thinking? And to what extent does this interpretive decision also presuppose a decision about die "biographical," about the proper name, the autobiographical, and about signature — about the politics of signature? ' Heidegger's position on this subject I will indicate first ofall widi a summarizing and simplifying statement, which one could, I hope, demonstrate is not wrong: there is a unity in Nietzschean thought even if it is not that of a system in the classical sense. This unity is also its uniqueness, its singularity. A thesis explicidy advanced by Heidegger is that every great thinker has only one thought. This uniqueness was neither constituted nor threatened, neither gadiered together nor brought about, through a name or proper name — nor by the life of Nietzsche, either normal or insane. This unique unity is something it draws from the unity of Western metaphysics which is gathered together mere at its crest, which one could also compare to the simple unity of a line created by a fold. The result of all this is that biography, autobiography, the scene or the powers of the proper name, of proper names, signatures, and so on, are again accorded minority status, are again given the inessential place diey have always occupied in the history ofmetaphysics. This points to the necessity and place of a questioning which I can only sketch here. Such would be a simplified version of the question. Now let us read Heidegger a little more closely and seek to confirm the strongest coherence of his interpretation or, beyond its coherence, his deepest thought. As a provisional concession to die classical norms of reading, let us take this book at its beginning, or even before its beginning at the beginning ofthe preface. Naturally, diis preface was, like so many odiers, written later. As we know, the book goes back to a series of lectures given between 1936 and 1940, and to some treatises written between 1940 and 1946. One should take most careful note of these dates if one is to bring this interpretation, as a whole and in detail, into connection with the historicopolitical and institutional field of its presentation. The preface, however, dates from 1961. The intention of the two pages in mis case, as almost always, is to justify the publication of this collection by reference to the essential unity ofits totality: "This publication, rethought (nachgedacht) as a whole (als Ganzes) should provide a glimpse ofthe path ofthought... (shrink)

This paper focuses on empty mind, transitional space and the dissolving of the self object function.

Signature-based model-independent searches for new physics form an explorative component of High Energy Physics experiments that aims at avoiding biases toward beyond-the-standard-model theo...

This paper considers the problem of assigning meanings to empty natural kind terms. It does so in the context of the Twin-Earth externalist-internalist debate about whether the meanings of natural kind terms are individuated by the external physical environment of the speakers using these terms. The paper clarifies and outlines the different ways in which meanings could be assigned to empty natural kind terms. And it argues that externalists do not have the semantic resources to assign them meanings. (...) The paper ends on a sceptical note concerning the fruitfulness of using the Twin-Earth setting in debates about the semantics of empty natural kind terms. (shrink)

Do trees of life have roots? What do these roots look like? In this contribution, I argue that research on the origins of life might offer glimpses on the topology of these very roots. More specifically, I argue (1) that the roots of the tree of life go well below the level of the commonly mentioned ‘ancestral organisms’ down into the level of much simpler, minimally living entities that might be referred to as ‘protoliving systems’, and (2) that further below, (...) a system of roots gradually dissolves into non-living matter along several functional dimensions. In between non-living and living matter, one finds physico-chemical systems that I propose to characterize by a ‘lifeness signature’. In turn, this ‘lifeness signature’ might also account for a diverse range of biochemical entities that are found to be ‘less-than-living’ yet ‘more-than-non-living’. (shrink)

Abstract: In this paper I offer an account of a particular variety of perception of absence, namely, visual perception of empty space. In so doing, I aim to make explicit the role that seeing empty space has, implicitly, in Mike Martin's account of the visual field. I suggest we should make sense of the claim that vision has a field—in Martin's sense—in terms of our being aware of its limitations or boundaries. I argue that the limits of the (...) visual field are our own sensory limitations, and that we are aware of them as such. Seeing empty space, I argue, involves a structural feature of experience that constitutes our awareness of our visual sensory limitations, and thus, in virtue of which vision has a field. (shrink)

What is the adequate terminology to talk about animal behaviour? Is terminology referring to mental or emotional states anthropomorphic and should therefore be prohibited or is it a necessary means to provide for an adequate description and should be encouraged? This question was vehemently discussed in the founding phase of Ethology as a scientific discipline and still is. This multi-layered problem can be grasped by using the concept of methodological signatures, developed by Köchy et al.. It is designed to analyse (...) and systematically compare animal research approaches by examining their common parameters. By examining the works of Konrad Lorenz and Nikolaas Tinbergen, this paper offers new insights both on a methodological and theoretical level. Methodologically, the application of the concept of methodological signatures is illustrated; theoretically, the principles of Classic Ethology are analysed. My aim is to illustrate how the problem of scientific access to animal subjectivity was addressed in the history of Ethology by analysing statements about animal sentience. For this purpose, I will first outline the general discussion about animal subjectivity and the tension between anthropomorphism and empirical adequacy. I introduce my own theoretical and methodological framework before presenting an analysis of Lorenz’ and Tinbergen’s methodological signatures. Thereby, I show how the question of terminology is deeply embedded in a network of epistemological, methodological and ontological concepts and establish key characteristics in regard to ethological approaches to animal subjectivity. Finally, I shed light on the possibility of using this typology to examine current frameworks of animal welfare research. (shrink)

What are the meanings of empty names such as ‘Vulcan,’ ‘Pegasus,’ and ‘Santa Claus’ in such sentences as ‘Vulcan is the tenth planet,’ ‘Pegasus flies,’ and especially ‘Santa Claus does not exist’?Our view, developed in Adams et al., consists of a direct-reference account of the meaning of empty names in combination with a pragmatic-implicature account of why we have certain intuitions that seem to conflict with a direct-reference account.

Legitimacy is a concept that has been largely forgotten by the deconstructive discourse on law and politics. This article seeks, on the one hand, to reassess the role of legitimacy in deconstruction and, on the other hand, to bring deconstructive thinking to bear on the concept of legitimacy. By re-reading Derrida’s “Declarations of Independence” through the lenses of his later texts on sovereignty and (counter)signature, it is argued that, rather than being deconstructible, legitimacy is deconstructing any self-founding of law (...) and power. As such, legitimacy functions not as an evaluative concept of law and order but as a constantly insisting demand that facilitates the principles of responsibility and responsiveness. (shrink)

Recent evidence that young children seem to both understand false belief in one sense, but not in another, has led to two-systems theorizing about mindreading. By analyzing the most detailed two-systems approach in studying social cognition—the theory of mindreading defended by Ian Apperly and Stephen Butterfill—I argue that that even when dutifully constructed, two-systems approaches in social cognition struggle to adequately define the mindreading systems in terms of signature processing limits, an issue that becomes most apparent when investigating mindreading (...) in infancy. I end the article by developing several challenges that face any two-systems account of mindreading. (shrink)

If possible worlds are conjunctions of states of affairs, as in David Armstrong’s combinatorial theory, then is the empty world to be thought of as the null conjunction of states of affairs? The proposal seems plausible, and has received support from David Efird, Tom Stoneham, and Armstrong himself. However, in this paper, it is argued that the proposal faces a trilemma: either it leads to the absurd conclusion that the actual world is empty; or it reduces to a (...) familiar representation of the empty world in which the concept of a null conjunction plays no role; or it needs to make room for the null individual of certain non-classical mereologies. (shrink)

In several areas of Mathematical Logic and Computer Science one would ideally like to use the set F orm(L) of all formulas of some first-order language L for some goal, but this cannot be done safely. In such a case it is necessary to select a subset of F orm(L) that can safely be used. Three main examples of this phenomenon are: • The main principle of naive set theory is the comprehension schema: ∃Z(∀x.x ∈ Z ⇔ A).

Mark Siderits’s contributions to the study of Indian philosophy have long included rational reconstruction of arguments and positions typical of the Madhyamaka school of Buddhist thought. A widely-known expression of this tradition’s core contention – “the ultimate truth is that there is no ultimate truth” – is widely attributed to Siderits, and my own studies of Madhyamaka have from the outset been influenced by his philosophically sophisticated work. Nonetheless, I have always resisted Siderits’s predilection for characterizing Madhyamaka as exemplifying anti-realism, (...) as well as the notion that this tradition’s concerns are best characterized as semantic. On my reading, the insight aptly expressed by Siderits’s signature formulation is better characterized as transcendental – as identifying, that is, something presupposed by the very fact that pursuit of the Buddhist path is in the first place intelligible. Siderits, then, would dispel his formulation’s air of paradox by taking it to mean, “it is ultimately true that no statement corresponds to the ultimate nature of reality.” I have taken the same statement as aptly expressing the contention, rather, that “it is ultimately true” – that is, practically incontrovertible once it has been clarified, by Madhyamaka critique, what it would mean for anything to be ‘ultimately real’ – “that there are no ultimately real existents.” While these make sense as philosophically distinct emphases, it is reasonable to wonder whether there is any practically significant difference between these ideas. By way of honoring Mark Siderits’s influence on my own understanding, this essay explores the extent and significance of our divergent emphases. (shrink)

Can there be improvised recipes? This paper argues that improvised recipes are possible. I call them instantaneous-recipes. They emerge at the same instant where a dish is also prepared. The improvisational freedom of instantaneous-recipes is displayed in the spontaneity of using what is available in terms of ingredients, tools, utensils, and techniques. Similar to what graffiti writers do while tagging – that is, leaving their signatures on – a wall or the side of a train car, in creating their (...) class='Hi'>signature dishes, improvisers of the kitchen are forced to adapt on the spot to changing contextual conditions just like a missing or newly available ingredient, a technical failure, or a mistake. Analogously to tags, improvised recipes are formally imperfect: they do not comply with established ones and are often rough, unpolished, broken, and disordered. But their imperfections are not aesthetic flaws, but merits. Imperfectionism in cooking, as I call the view rejecting the idea that only perfect instantiations of pre-existing recipes afford positive aesthetic experiences, is linked with three values: aesthetic, humanistic, and sustainable. By bringing imperfect features within the domain of gastronomic appreciation, instantaneous-recipes broaden the range of our aesthetic palette, while also reminding us of our finitude as humans. By encouraging creative uses of available ingredients and leftovers, improvisation in the kitchen also embodies a more sustainable approach to food waste. (shrink)

Emptiness is a strange phenomenon that haunts us in many ways. Most of us have felt empty at one time or another, though we don’t often talk about it. We have a sense that something is missing in life. This absence extends beyond human experience to the physical world. As contemporary science has revealed to us on both a macroscopic and subatomic level, curiously, the vast majority of the universe is composed mostly of nothing but empty space. Emptiness (...) is “abundant” and beckons for our attention. Drawing on the Judeo-Christian wisdom of the Bible, in conversation with Eastern and Celtic thought, David Arthur Auten offers us an eye-opening and profoundly practical examination of the much neglected gift of absence. Nothing, ironically, turns out to be endlessly fascinating and significant. (shrink)

The problem of empty terms is one of the focal issues in analytic philosophy. Russell’s theory of descriptions, a proposal attempting to solve this problem, attracted much attention and is considered a hallmark of the analytic tradition. Scholars of Indian and Buddhist philosophy, e.g., McDermott, Matilal, Shaw and Perszyk, have studied discussions of empty terms in Indian and Buddhist philosophy. But most of these studies rely heavily on the Nyāya or Navya-Nyāya sources, in which Buddhists are portrayed as (...) opponents to be defeated, and thus do not truly reflect Buddhist views on this issue. The present paper will explore how Dignāga, the founder of Buddhist logic, deals with the issue of empty subject terms. His approach is subtle and complicated. On the one hand, he proposes a method of paraphrase that resembles Russell’s theory of descriptions. On the other, by relying on his philosophy of language—the apoha theory, he tends to fall into a panfictionalism. Through the efforts of his follower Dharmakīrti, the latter approach would become more acceptable among Indian and Tibetan Buddhists. Dignāga’s Chinese commentators, who were free from the influence of Dharmakīrti, dealt with the empty term issue in three ways: (1) by adhering to Dignāga’s method of paraphrase; (2) by allowing exceptions for non-implicative negation; and (3) by indicating the propositional attitude of a given proposition. Among these, the third proved most popular. (shrink)

A pivotal focus of exegesis of Nāgārjuna's Mūlamadhyamakakārïkā (MMK) for the past half century has been the attempt to decipher the text's philosophy of language, and determine how this best aids us in characterizing Madhyamaka thought as a whole. In this vein, MMK 24:18 has been judged of particular weight insofar as it purportedly insists that the concepts pratītyasamutpāda (conditioned co-arising) and śūnyatā (emptiness), both indispensable to Buddhist praxis, are themselves only "nominal" or "conventional," that is, they are merely labels (...) that do not referentially signify anything that can be taken to be an ontologically ultimate reality. In various guises, as a result of this explication, Nāgārjuna's thought has been seen to embrace an overarching linguistic nominalism or conventionalism in which words, whether they are used for the purposes of theory or practice, though they serve as commonly accepted currency in the transactions of worldly business (vyavahāra), are in the end only ideas (prajñapti) or metaphysical fabrications (prapanca). This interpretation is largely due to tenaciously inaccurate translations and expositions of MMK 24:18 and their dependence on Candrakīrti's peculiar analysis of this verse in his Prasannapadā. This essay will attempt to correct both the diction of the major translations of MMK 24:18 and the fictions of nominalism and conventionalism that the consequent interpretations of this stanza have perpetuated. The argument that will be developed in the course of this essay is that Candrakīrti's reading of this verse proffers a strong form of linguistic nominalism that Nāgārjuna himself does not embrace. It will be shown, based on everything else found in the MMK, that Nāgārjuna, rather than advocating the mere nominal or conventional status of terms such as pratītyasamutpāda and sunyata, demands they be accepted as both pedagogically useful and even referentially accurate descriptions of the world as it is. (shrink)

In my dissertation (UCLA 2002), I argue that, by appropriating Fregean resources, Millians can solve the problems that empty names pose. As a result, the debate between Millians and Fregeans should be understood, not as a debate about whether there are senses, but rather as a debate about where there are senses.

I dub a certain central tradition in philosophy of language (and mind) the de re tradition. Compelling thought experiments show that in certain common cases the truth conditions for thoughts and public-language expressions categorically turn on external objects referred to, rather than on linguistic meanings and/or belief assumptions. However, de re phenomena in language and thought occur even when the objects in question don't exist. Call these empty de re phenomena. Empty de re thought with respect to numeration (...) is explored in this paper, and such thought with respect to hallucinations is touched on. (shrink)

What are the meanings of empty names such as ‘Vulcan,’ ‘Pegasus,’ and ‘Santa Claus’ in such sentences as ‘Vulcan is the tenth planet,’ ‘Pegasus flies,’ and especially ‘Santa Claus does not exist’?Our view, developed in Adams et al., consists of a direct-reference account of the meaning of empty names in combination with a pragmatic-implicature account of why we have certain intuitions that seem to conflict with a direct-reference account.

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding (...) the possible observation—as well as conceptual overthrow—of this geometric ether. (shrink)

Aristotle draws what are, by our lights, two unusual relationships between predication and existence. First, true universal affirmations carry existential import. If ‘All humans are mortal’ is true, for example, then at least one human exists. And secondly, although affirmations with empty terms in subject position are all false, empty negations are all true: if ‘Socrates’ lacks a referent, then both ‘Socrates is well’ and ‘Socrates is ill’ are false but both ‘Socrates is not well’ and ‘Socrates is (...) not ill’ are true. In this paper, I conjecture that for Aristotle predications have mereological truth conditions: for example, ‘Socrates is pale’ is true just in case Socrates is a part of the mereological sum of pale things. The existential import of universal affirmations and the semantic profile of empty negations follow from this mereological semantics. (shrink)

This paper excavates the practice-oriented background and therapeutic significance of emptiness in the Madhyamaka philosophy attributed to Nāgārjuna and Sengzhao. Buddhist emptiness unravels experiential and linguistic reification through meditation and argumentation. The historical contexts and uses of the word indicate that it is primarily a practical diagnostic and therapeutic concept. Emptiness does not lead to further views or truths but, akin to yet distinct from Ajñāna and Pyrrhonian skepticism, the suspension of assertion. This sense of emptiness as a practice can (...) be traced in the intercultural transmission of Madhyamaka from Nāgārjuna, its paradigmatic philosopher, to Sengzhao 僧肇, its first pivotal indigenous Chinese representative. (shrink)

Philosophers and theorists have long been puzzled by humans' ability to talk about things that do not exist, or to talk about things that they think exist but, in fact, do not. _Empty Names, Fiction, and the Puzzles of Non-Existence_ is a collection of 13 new works concerning the semantic and metaphysical issues arising from empty names, non-existence, and the nature of fiction. The contributors include some of the most important researchers working in these fields. Some of the papers (...) develop and defend new positions on these matters, while others offer important new perspectives and criticisms of the existing approaches. The volume contains a comprehensive introductory essay by the editors, which provides a survey of the philosophical issues concerning empty names, the various responses to these issues, and the literature on the subject to date. (shrink)

Mental files, in Recanati's framework, function as 'singular terms in the language of thought' ; they serve to think about objects in the world (and to store information about them). But they have a derived, metarepresentational function : they serve to represent how other subjects think about objects in the world. To account for the metarepresentational use of files, Recanati introduces the notion of an 'indexed file', i.e. a vicarious file that stands, in the subject's mind, for another subject's file (...) about an object. Using that notion, he argues, one can provide an analysis of attitude ascriptions and the conniving use of empty singular terms. (shrink)