We investigate a simple game paradigm for intuitionistic logic, inspired by Wajsberg’s implicit inhabitation algorithm and Beth tableaux. The principal idea is that one player, ∃ros, is trying to construct a proof in normal form while his opponent, ∀phrodite, attempts to build a counter-model. The determinacy of the game implies therefore both completeness and semantic cut-elimination.

We study the intersection type assignment system as defined by Barendregt, Coppo and Dezani. For the four essential variants of the system (with and without a universal type and with and without subtyping) we show that the emptiness (inhabitation) problem is recursively unsolvable. That is, there is no effective algorithm to decide if there is a closed term of a given type. It follows that provability in the logic of "strong conjunction" of Mints and Lopez-Escobar is also undecidable.

The author analyses conceptual metaphors characteristic of one of the literary theories, the theory of intertextuality, employing the methods of cognitive linguistics, i.e. the cognitive theory of metaphor. He claims that the tools of this conception enable one to describe the idea of paradigm-change; in this context author considers the role of metaphor in science. By interpreting synonyms as different realizations of various Idealized Cognitive Models, he shows that the change of metaphors employed in talking about ‘what happens between texts’ (...) leads to evolutionary change from ‘influentology’ to ‘intertextuality’, a transformation closely related to the change of the subject of history of literature. The change of metaphors transforms the focus of literary theory ; its focus moves from the author to the reader, and from the act of creation to the act of reception. Within this perspective writing is no longer a creatio ex nihilo but an innovative re-creation of ‘what has already been read’. This change enables one to capture some paradoxical inversions, like the one which demonstrates how a subsequent texts influence texts prior to them. (shrink)

There is a simple technique, due to Dragalin, for proving strong cut-elimination for intuitionistic sequent calculus, but the technique is constrained to certain choices of reduction rules, preventing equally natural alternatives. We consider such a natural, alternative set of reduction rules and show that the classical technique is inapplicable. Instead we develop another approach combining two of our favorite tools—Klop’s ι-translation and perpetual reductions. These tools are of independent interest and have proved useful in a variety of settings; it is (...) therefore natural to investigate, as we do here, what they have to offer the field of sequent calculus. (shrink)

We give a syntactic translation from first-order intuitionistic predicate logic into second-order intuitionistic propositional logic IPC2. The translation covers the full set of logical connectives ∧, ∨, →, ⊥, ∀, and ∃, extending our previous work, which studied the significantly simpler case of the universal-implicational fragment of predicate logic. As corollaries of our approach, we obtain simple proofs of nondefinability of ∃ from the propositional connectives and nondefinability of ∀ from ∃ in the second-order intuitionistic propositional logic. We also show (...) that the ∀-free fragment of IPC2 is undecidable. (shrink)

Our life in this broken world requires tools to own and express our grief in ways that are connected to our faith in God. We find that the biblical genre of lament is appropriate to the task. However, we do not come to lament without baggage, and we sometimes require additional help in the form of symbolic capital borrowed from stories and songs. In this case, The Chronicles of Narnia provide such capital. As we reflect on these stories, we can (...) see lament in a new way that helps us bring our pain to God. As we engage in the discipline of lament, we are spiritually formed into the image of Jesus. (shrink)

One of Darwin’s purposes in writing The Origin of Species was to rebut the doctrine of separate creations. Moreover, the argument he was chiefly concerned with—which was both his target and the model of his own argument—was the familiar argument from design.

. For a fixed q  ℕ and a given Σ1 definition φ, where d is a parameter, we construct a model M of 1 Δ0 + ¬ exp and a non standard d  M such that in M either φ has no witness smaller than d or phgr; is equivalent to a formula ϕ having no more than q alternations of blocks of quantifiers.

We study the cube of type assignment systems, as introduced in Giannini et al. 87–126), and confront it with Barendregt's typed gl-cube . The first is obtained from the latter through applying a natural type erasing function E to derivation rules, that erases type information from terms. In particular, we address the question whether a judgement, derivable in a type assignment system, is always an erasure of a derivable judgement in a corresponding typed system; we show that this property holds (...) only for systems without polymorphism. The type assignment systems we consider satisfy the properties ‘subject reduction’ and ‘strong normalization’. Moreover, we define a new type assignment cube that is isomorphic to the typed one. (shrink)

To be able to believe that a dog with a broken paw is not really in pain when it whimpers is a quite extraordinary achievement even for a philosopher. Yet according to the standard interpretaion, this is just what Descartes did believe. He held, we are informed, the ‘monstrous’ thesis that ‘animals are without feeling or awareness of any kind’. The Standard view has been reiterated in a recent collection on animal rights, which casts Descartes as the villain of the (...) piece for his alleged view that animals merely behave ‘ as if they feel pain when they are, say, kicked or stabbed’. The basis for this widely accepted interpretation is Descartes' famous doctrine of ‘animal machine’ ; a doctrine that one critic condemns as ‘a grim fortaste of a mechanically minded age’ which ‘brutally violates the old kindly fellowship of living things’. (shrink)

We seem to talk about repeatable artworks, like symphonies, films, and novels, all the time. We say things like, "The Moonlight Sonata has three movements" and "Duck Soup makes me laugh". How are these sentences to be understood? We argue against the simple subject/predicate view, on which the subjects of the sentences refer to individuals and the sentences are true iff the referents of the subjects have the properties picked out by the predicates. We then consider two alternative responses that (...) involve reading these sentences as generics, similar to "The polar bear has four paws". The first response takes these sentences to be about kinds, and the second takes the relevant noun-phrases to act as predicates. We reject these accounts, but offer a third alternative which is informed by both, and which enables us to deny the existence of repeatable artworks while endorsing the truth of sentences seemingly about them. (shrink)

Palaeontology developed as a field dependent upon comparison. Not only did reconstructing the fragmentary records of fossil organisms and placing them within taxonomic systems and evolutionary lineages require detailed anatomical comparisons with living and fossil animals, but the field also required thinking in terms of behavioural, biological and ecological analogies with modern organisms to understand how prehistoric animals lived and behaved. Yet palaeontological material often worked against making easy linkages, bringing a sense of mystery and doubt. This paper will look (...) at an animal whose study exemplified these problems: the Chalicothere. Increasingly recognized as a specific type from finds across North America and Eurasia from the early nineteenth century onwards, these prehistoric mammals showed short back legs terminating in pawed feet, long front limbs ending in sharp claws, a long flexible neck, and herbivorous grinding teeth. The Chalicothere became a significant organism within palaeontological studies, as the unexpected mix of characters made it a textbook example against the Cuvierian notion of “correlation of parts,” while explaining how the animal moved, fed and behaved became puzzling. However, rather than prevent comparisons, these actually led to comparative analogies becoming flexible and varied, with different forms of comparison being made with varying methods and degrees of confidence, and with the anatomy, movement and behaviour of giraffes, bears, horses, anteaters, primates and other organisms all serving at various points as potential models for different aspects of the animal. This paper will examine some of the attempts to reconstruct and define the Chalicotheres across a long timescale, using this to show how multiple comparisons and analogies could be deployed in a reconstructive and evolutionary science like palaeontology, and illustrate some of the limits and tensions in comparative methods, as they were used to reconstruct organisms which were thought to be incomparable to any modern animal. (shrink)

Beginning with Jacques Derrida’s Beast and the Sovereign, I identify two forms of curiosity: 1) scientific curiosity, which proceeds through objective dissection and 2) therapeutic curiosity, which proceeds through observational confinement. Through an analysis of Derrida’s treatment of both sorts of curiosity, I notice and develop a third, deconstructive form of curiosity. Through repeated turn to the work of Sarah Kofman, I characterize this third curiosity as, by turns, linguistic, animal, and critical. As linguistic, this curiosity is a penchant for (...) wordplay and a keenness for the unsteady reservoirs of signification, resisting any clean dissection of meaning or the confinement of terms. As animal, it tracks a scent, regularly suspending its paw, as if to emphasize the meandering and precarious quality of knowledge. And as critical, it combats the illusions of pure revelation and instead draws attention to the conjuring trick, the systematic substitution of signs, undergirding it. Finally, I consider in what way Derrida’s resistance to philosophy may be read on the grounds not of a singular wonder but of multiple curiosities. (shrink)

“Not with that!” I shout. The hammer lies cradled in the Colonel’s folded arms. “You would not use a hammer on a beast, not on a beast!” In a terrible surge of rage I turn on the sergeant and hurl him from me. Godlike strength is mine. In a minute it will pass: let me use it while it lasts! “Look!” I shout. I point to the four prisoners who lie docilely on the earth, their lips to the pole, their (...) hands clasped to their faces like monkey’s paws, oblivious of the hammer, ignorant of what is going on behind them, relieved that the offending mark has been beaten from their backs, hoping that the punishment is at an end. I raise my broken hand to the sky. “Look!” I shout. “We are the great miracle of creation! But from.. (shrink)

The first system of intersection types, Coppo and Dezani [3], extended simple types to include intersections and added intersection introduction and elimination rules (( $\wedge$ I) and ( $\wedge$ E)) to the type assignment system. The major advantage of these new types was that they were invariant under β-equality, later work by Barendregt, Coppo and Dezani [1], extended this to include an (η) rule which gave types invariant under βη-reduction. Urzyczyn proved in [6] that for both these systems it (...) is undecidable whether a given intersection type is empty. Kurata and Takahashi however have shown in [5] that this emptiness problem is decidable for the sytem including (η), but without ( $\wedge$ I). The aim of this paper is to classify intersection type systems lacking some of ( $\wedge$ I), ( $\wedge$ E) and (η), into equivalence classes according to their strength in typing λ-terms and also according to their strength in possessing inhabitants. This classification is used in a later paper to extend the above (un)decidability results to two of the five inhabitation-equivalence classes. This later paper also shows that the systems in two more of these classes have decidable inhabitation problems and develops algorithms to find such inhabitants. (shrink)

The claim of consistent hemispheric specialisations across classes of chordates is undermined by the absence of population-based directional asymmetry of paw/hand use in rodents and primates. No homologue of the cerebral torque from right frontal to left occipital has been established in a nonhuman species. The null hypothesis that the torque is the sapiens-specific neural basis of language has not been disproved.

This piece, included in the drift special issue of continent. , was created as one step in a thread of inquiry. While each of the contributions to drift stand on their own, the project was an attempt to follow a line of theoretical inquiry as it passed through time and the postal service(s) from October 2012 until May 2013. This issue hosts two threads: between space & place and between intention & attention . The editors recommend that to experience the (...) drifiting thought that attention be paid to the contributions as they entered into conversation one after another. This particular piece is from the BETWEEN SPACE & PLACE thread: April Vannini, Those Between the Common * Laura Dean & Jesse McClelland, Ballard: A Portrait of Placemaking * Amara Hark Weber, Crossroad * Isaac Linder & Berit Soli-Holt, The Call of the Wild: Terro(i)r Modulations * Ashley D. Hairston, Momma taught us to keep a clean house * Sean Smith, The Garage (Take One) * * * * Momma taught us to keep a clean house. Dust the wood furniture every two weeks. Clean the bathrooms once a week. Wipe down the baseboards once a season (Those damn baseboards. I still got bruises on my knees from scrubbing those things). Sweep away the cobwebs—and pray that those spiders are either dead or delirious (Livin in the country don’t mean you like bugs, especially the ones with too many legs ). Didn’t matter that the house was full of stuff: Great-Grandma’s heirloom dresser, that weird Mammy salt shaker and matching Uncle Tom pepper grinder (Where the hell did Momma get those P.O.S.’s?), the outdated drapes from Belks, Dad’s favorite wooden TV tray, and that uuuuugly love seat that some crazy uncle thought was a glorious find from the Salvation Army (Momma tried to make it pretty with some pillows, but no amount of love could help that seat). Spring Cleaning meant pullin all that furniture away from the walls and holdin your breath to see what time collected in the crevices. Then you gotta be careful not to breathe out too heavy cause the dust would go flying fore you got a chance to catch it. If you didn’t, you’d quickly find out if you’re allergic to dust. Quarter cup of lemon Lysol in a bucket of steaming water and an old wash rag. Maybe two. A dust towel and citrus-scent Pledge. Me and my brothers would fight over who cleaned what. Somehow the twins always got the easy stuff: vacuuming or moving dirt around with the feather-duster. Finishing in enough time to fly down the street on their bikes with the neighborhood kids. Older sister never got off that easy. Each of my stubby fingers morphed into plump, lemon-fresh golden raisins by the time that whole damn house was done. I would finish just in time to sit with Nadine on the porch, counting the seconds til the sun turned off and the fireflies fluttered on. The craziest thing: despite all that cleaning, the house still smelled like Momma’s cookin. That Old House. Might have been some of Grandma’s and Great-Grandma’s cookin mixed in there too. Pork chops. Ham hock soaked in collards. Pinto beans and mustard greens. Corn bread and my Auntie’s famous macaroni and cheese. Didn’t matter if the oven was cold and the valve of the gas stove had been shut for days. A stranger woulda thought someone’d been slavin away in that kitchen for a week straight. No Sweet Citrus & Zest Fabreze back then. Lysol would mask the odors for a little while. Not long enough to overpower the 50 years of goodness marinated in buttermilk, kneaded with lard, and fried in Crisco that’d been embedded in the wallpaper and window treatments. All that grime—dead skin, hair follicles, Carolina clay, carpet lint, yippee-little-dog fur—was evidence of life. We were a socially-awkward newly-minted teenager, two rowdy twin boys, a multi-tasking mother, and a road-warrior father. Eventually a strangely-feline Yorkie was added to the mix. And don’t forget about the stray distant relative stopping by unannounced. No corner of that damn house was unmarked. Hand-sewn pillows in the living room that we were forbidden to breathe on somehow had tiny burnt orange paw prints on them (sneaky little dog). It drove Momma crazy. And tore up my fingernails. They still won’t grow back right. Wipe all that shit off just for it to build up again. But that house was inherited and fully paid for. No reason to move. I did move. I was ready to move on. Move up. Move out. Over that small town. Into the big city. Here the streets take on the smells of Momma’s house. Plus piss, shit, and unbathed skin. A hot day means everything cooks and stews in its own juices, making the stench 10x more intense. The apartment is another story. 11 floors up. Big, east-facing windows. Great view of the skyline dotted with some green foliage. And the great lake. Immaculate. Odorless. Not even a trace of tobacco from the previous tenant’s bad habits. No lingering scent of lemon Lysol. No street stench seeping through the window panes. No stray cat hairs. Or dog fur. Not a speck of dust. Futon. Throw pillows. Photos. Knickknacks. Bowls of fresh citrus. Cursedly-assembled desk set from IKEA. Yet the void is too big to fill. Too clean. (shrink)

The bear, says Hierocles, is aware that its head is easily injured, and instinctively uses its paws as a protection. The three following lines in the papyrus are badly damaged– καν εί π.ε … δεηθεί Του | βαλανεíον κρημν | πáλιν ύ;β εθεíησιν ε | αυΤήν. This is followed by a description of what the bear does when it is pursued and comes to a precipice. It inflates itself and trusts to the inflation to break its fall. It is hardly (...) possible to restore the damaged lines. Von Arnim thinks that the sense required is: ‘wenn die Bärin, vom Jäger verfolgt, eines Bades bedarf oder auf ihrer Flucht an einen Abgrund kommt,πáλιν ύπ èψίησιν εαψτήν’ But a sensible bear would hardly think of taking a bath when pursued by the hunter. It might take to the water; but the Greek for this would be somewhat different. As I read the passage, there is no reference to the bear as pursued by the hunter till line 34, where I would read πоιεî δè τò τοιóνδε , since the phrase εί δ υν διοκμéνμ in line 38 is resumptive, and implies that the pursuit must have been alluded to before. But before line 35 H. is only describing what the bear does to protect its head in the ordinary routine of its life when it is not harassed by the hunter. It wants a bath, and finds that it cannot reach the water without clambering down an overhanging bank It will not climb down head foremost, but guards its head by sliding backwards down the bank. As the bear would want its bath because it was hot, it is perhaps not too hazardous to conjecture that some phrase such as xs03F0xs2135ν ει π ε<ζομéν πνíγηι δεμθεíν του β. should find its place in line 31. (shrink)

This paper offers a close reading of PAW Media animation My Name is Danny. Drawing across a growing body of recent Central and Western Desert experimental cinema, this paper asks what is at stake in the turn to animation. Rather than escapism or otherworldly fabrications which have little to do with lived experience of the “real,” animation in this context has potent everyday exigencies and politics. The capacity for bringing to life literally – animate – is here linked to the (...) primacy of a sentient landscape; an object world already alive and enlivened with motion, movement, sensation. The question for contemporary filmmaking is how to engage country and its viscera today. How to keep country/ancestor/story alive literally through sentient forms of affective exchange; a project which animation, as this paper will explore, uniquely provides. Drawing on the phenomenology of Merleau-Ponty and Deleuze, as well as the animation theory of Cholodenko, Lemarre and others, this paper argues for a radical reconsideration of animation not as incompatible with tradition but in fact as facilitating traditional ontologies of affect and sensation in a national context of remote Aboriginal Australia “under occupation.”. (shrink)

Leo Strauss’ controversial theory of esoteric philosophy, as presented in Persecution and the Art of Writing, sparked a fierce debate. Opponents and proponents of the theory utilised a wide range of perspectives to support their arguments. By investigating esoteric philosophy from a sociolinguistic perspective, this paper introduces a novel perspective to the Strauss dispute. In PAW Strauss is mistaken regarding esotericism and its role in philosophy. On one hand it is reasonable to endorse Strauss’ persuasive account on the origins of (...) esoteric writing. The Straussian account provides a plausible sociological background as to why philosophy, per se became an esoteric fliedH. On the other hand it seems as Strauss ascribed undue significance to possible clandestine massages that may be found within works of philosophy because philosophy is mostly already done in an esoteric linguistic space. (shrink)

About a month ago, I went to a university to give a lecture. During the questions-and-answers and discussion, a young fellow standing in the last row drew a good deal of attention: "Some people today show concern for spiritual values but are very helpless where material life is concerned." However, he said, "more people are pursuing only material benefits and have absolutely no spiritual requirements." You may perhaps doubt that people today truly, as he indicated, regard the spiritual and the (...) material as "fish-and-bear's-paws"—if you want the one, you have to give up the other. (shrink)

The clearest instances of Time experience in music can be observed when the melodic and harmonic structure of a work announces the approach to a climax, for example, the finale. A goal is established in the awareness of the listener and acts as an independent system toward which music is striving. Most other examples that come to mind are extra-musical, that is, they refer to music in relation to something outside of it. A listener who instead of moving with the (...) flow of the musical happening remains outside of it and watches the arriving and passing of phrase after phrase as though he were watching a parade from a viewing stand places himself in a separate temporal system whose relation to that of the music itself is governed by Time. Compare also the radio performance scheduled to finish on the hour or the state of mind of a concertgoer anxious to make the 11:20 suburban train home. A literary narrative, like music, tends to be perceived as an ongoing flow. No reference to time is relevant for a description of the sequential action. The work sprouts and grows. But whenever the continuity is broken , the appearances may form separate systems. The only medium that can bridge the gap may be Time, in which both are embedded. This is generally considered a compositional flaw. A skillful narrator avoids such a break by providing a filament that connects past and present appearances "amodally," as psychologists call it, that is, the way a train's progress is seen as remaining uninterrupted even when it is hidden for a moment by a tunnel. But when Time is embodied as an authentic literary character, such as the "devouring Time" of Shakespeare's nineteenth sonnet, which blunts the lion's paws and plucks the tiger's teeth, it becomes an active system of its own and thus deserves the capitalization. Rudolf Arnheim is the author of Art and Visual Perception: A Psychology of the Creative Eye, Toward a Psychology of Art, and The Dynamics of Architectural Form. His contributions to Critical Inquiry are "On the Nature of Photography" and "A Plea for Visual Thinking". (shrink)

Pooh rubbed his nose with his paw, and said that the Heffalump might be walking along, humming a little song, and looking up at the sky, wondering if it would rain, and so he wouldn't see the Very Deep Pit until he was half-way down, when it would be too late. Jerry Fodor is loath to have content be constituted, even in part, by inferential relations. This loathing, I will argue, gets him into trouble. In his latest book, Concepts, Fodor (...) contrasts informational atomism, his view of concepts and their content, with inferential role theory. The latter, he argues, is almost certainly false. This strikes cognitive science at its core, he adds, since the major theories of concepts currently in vogue in cognitive science are all variants on inferential role theory. (shrink)

Contents: Preface. SCIENTIFIC WORKS OF MARIA STEFFEN-BATÓG AND TADEUSZ BATÓG. List of Publications of Maria Steffen-Batóg. List of Publications of Tadeusz Batóg. Jerzy POGONOWSKI: On the Scientific Works of Maria Steffen-Batóg. Jerzy POGONOWSKI: On the Scientific Works of Tadeusz Batóg. W??l??odzimierz LAPIS: How Should Sounds Be Phonemicized? Pawe??l?? NOWAKOWSKI: On Applications of Algorithms for Phonetic Transcription in Linguistic Research. Jerzy POGONOWSKI: Tadeusz Batóg's Phonological Systems. MATHEMATICAL LOGIC. Wojciech BUSZKOWSKI: Incomplete Information Systems and Kleene 3-valued Logic. Maciej KANDULSKI: Categorial Grammars with (...) Structural Rules. Miros??l??awa KO??L??OWSKA-GAWIEJNOWICZ: Labelled Deductive Systems for the Lambek Calculus. Roman MURAWSKI: Satisfaction Classes - a Survey. Kazimierz _WIRYDOWICZ: A New Approach to Dyadic Deontic Logic and the Normative Consequence Relation. Wojciech ZIELONKA: More about the Axiomatics of the Lambek Calculus. THEORETICAL LINGUISTICS. Jacek Juliusz JADACKI: Troubles with Categorial Interpretation of Natural Language. Maciej KARPI??N??SKI: Conversational Devices in Human-Computer Communication Using WIMP UI. Witold MACIEJEWSKI: Qualitative Orientation and Grammatical Categories. Zygmunt VETULANI: A System of Computer Understanding of Texts. Andrzej WÓJCIK: The Formal Development of van Sandt's Presupposition Theory. W??l??adys??l??aw ZABROCKI: Psychologism in Noam Chomsky's Theory . Ryszard ZUBER: Defining Presupposition without Negation. PHILOSOPHY OF LANGUAGE AND METHODOLOGY OF SCIENCES. Jerzy KMITA: Philosophical Antifundamentalism. Anna LUCHOWSKA: Peirce and Quine: Two Views on Meaning. Stefan WIERTLEWSKI: Method According to Feyerabend. Jan WOLE??N??SKI: Wittgenstein and Ordinary Language. Krystyna ZAMIARA: Context of Discovery - Context of Justification and the Problem of Psychologism. (shrink)

Pooh rubbed his nose with his paw, and said that the Heffalump might be walking along, humming a little song, and looking up at the sky, wondering if it would rain, and so he wouldn't see the Very Deep Pit until he was half-way down, when it would be too late. Jerry Fodor is loath to have content be constituted, even in part, by inferential relations. This loathing, I will argue, gets him into trouble. In his latest book, Concepts, Fodor (...) contrasts informational atomism, his view of concepts and their content, with inferential role theory. The latter, he argues, is almost certainly false. This strikes cognitive science at its core, he adds, since the major theories of concepts currently in vogue in cognitive science are all variants on inferential role theory. (shrink)