Lloyd Humberstone’s recently published Philosophical Applications of Modal Logic presents a number of new ideas in modal logic as well explication and critique of recent work of many others. We extend some of these ideas and answer some questions that are left open in the book.

In this paper, I will interpret a short passage from Hegel’s Doctrine of Essence on the relation between causality and life. In this passage, Hegel rejects using causal language to analyze phenomena of the living. This rejection is puzzling though, if one takes Hegel’s account of causality into account. By discussing the passage, I hope to shed some light on Hegel’s understanding of life and its relation to causality. After presenting my reading of the causality chapter (2.), the passage itself (...) will be interpreted (3.). Afterwards, I pose some interpretative problems concerning the passage and discuss it critically (4.). Finally, I will use passages from the Encyclopedia and the Logic of the Concept to further clarify Hegel’s main claim in the passage by contrasting it to his concept of life (5.). I close with a summary of the results and some open questions. (shrink)

This note shows that the permutation instructions presented by Zardini (2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the noncontractive theory of truth IKTωare inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTωending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counterexample is of the kind that leaves open the question whether cut can be shown to be eliminable (...) in the sequent calculus for IKTωwith an alternative strategy. (shrink)

"These notes are about the process of design: the process of inventing things which display new physical order, organization, form, in response to function." This book, opening with these words, presents an entirely new theory of the process of design. In the first part of the book, Christopher Alexander discusses the process by which a form is adapted to the context of human needs and demands that has called it into being. He shows that such an adaptive process will (...) be successful only if it proceeds piecemeal instead of all at once. It is for this reason that forms from traditional un-self-conscious cultures, molded not by designers but by the slow pattern of changes within tradition, are so beautifully organized and adapted. When the designer, in our own self-conscious culture, is called on to create a form that is adapted to its context he is unsuccessful, because the preconceived categories out of which he builds his picture of the problem do not correspond to the inherent components of the problem, and therefore lead only to the arbitrariness, willfulness, and lack of understanding which plague the design of modern buildings and modern cities. In the second part, Mr. Alexander presents a method by which the designer may bring his full creative imagination into play, and yet avoid the traps of irrelevant preconception. He shows that, whenever a problem is stated, it is possible to ignore existing concepts and to create new concepts, out of the structure of the problem itself, which do correspond correctly to what he calls the subsystems of the adaptive process. By treating each of these subsystems as a separate subproblem, the designer can translate the new concepts into form. The form, because of the process, will be well-adapted to its context, non-arbitrary, and correct. The mathematics underlying this method, based mainly on set theory, is fully developed in a long appendix. Another appendix demonstrates the application of the method to the design of an Indian village. (shrink)

The Russian conquest of Central Asia marked the beginning of record-keeping for Qazaq arbitrators and customary law. It remains obscure how bīs complied with the colonial regulations obliging them to record their court proceedings. I approach this issue first by questioning the utility of extra-judicial sources crafted in Russian at the instigation of colonial bureaucrats; hence, I argue that the comparison alone of ’ādat-related judicial records written in Turki with šarī’a court certificates allows situating the legal terminology applied by Qazaq (...) arbitrators within the discursive tradition of Islamic law. By way of illustrating my approach, I offer a close reading of a report of a murder case adjudicated according to Qazaq customary law in the vicinity of Khiva in 1895. My commentary on the summary of the trial sheds light on the interplay of customary and Islamic law in the region. In addition, it challenges earlier interpretations of the use of the exculpatory oath among the Qazaqs. (shrink)

The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears (...) to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. A notion of inherited identity of derivations is introduced for derivations in a cut-free sequent system for Almukdad and Nelson’s constructive paraconsistent logic N4 with strong negation. The notion is obtained by identifying sequent rules the application of which has no effect on the identity of derivations. Then the notion of inherited identity is used to define a bilateralist notion of synonymy between formulas, which is a relation drawing more fine-grained distinctions between formulas than strong equivalence. (shrink)

This note gives a new proof of the 'operational extensionality' property of Abramsky's lazy lambda calculus-namely the coincidence of contextual equivalence with a co-inductively defined notion of 'applicative bisimilarity'. This purely syntactic results is here proved using a logical relation between the syntax and its denotational semantics. The proof exploits a mixed inductive/coinductive characterisation of the logical relation recently discovered by the author.

In lieu of an abstract, here is a brief excerpt of the content:92 A NOTE ON SMITH'S TERM "NATURALISM" The reader of contemporary Hume literature may feel exasperated when reading recent authors. A conspicuous example is A.J. Ayer (Hume, 1982; see index, Art, Natural beliefs), who declares they endorse Kemp Smith's view of Hume's "naturalism" without sufficiently clarifying what they — or Smith — might exactly mean by this term. Charles W. Hendel, in the 1963 edition of his 1924 Studies (...) in the Philosophy of David Hume, adds eight pages of a new preface and thirty-one pages of a review of Hume scholarship between 1925 and 1962, and he speaks at great length there of his life-long friendship and cooperation with Norman Kemp Smith and appreciation of his work. He says (p. xlviii), "There is a disposition today to assimilate Hume's thought to naturalism as understood in the contemporary sense." He does not say what this "contemporary sense" is, and the statement just quoted seems to have served as the seal of approval and the legitimation of this questionable practice. Hendel's new, 1963, material mentions Smith's discussion of Hume's "naturalism" — but refers only to Smith's early work, "The Naturalism of Hume," Mind, 14, 1905, 149-173 and 335-347, not to Smith's famous The Philosophy of David Hume of 1941, even though he deems that work "of great consequence for Hume scholarship" (p. xxxviii) and a "masterwork" (p. xxxix). The early work (1905) of Smith is already mentioned by Hendel in the body of the 1924 work (p. 361), although there, clearly, the word "naturalism," whatever its meaning is, and however contemporary then, is not necessarily the "contemporary sense" of 1962. The work which clearly (if implicitly) distinguishes between the traditional sense and Smith's 1905 sense of "naturalism" is John Laird's Hume's 93 Philosophy of Human Nature, 1932, 1967. We find there a discussion of Hume's naturalism (beginning of Chapter II), as well as of Hume's "Naturalism" (Chapter VI, fifth and fourth paragraphs from the end), with reference to Smith's 1905 work. Now, the traditional sense of "naturalism" is straightforward and seems to have been instituted by Pierre Bayle to designate the view of the world as devoid of all supernatural intervention, the view of the world as "disenchanted," to use the equivalent term accredited to Max Weber. Clearly, all Epicureans and neoEpicureans, Hume included, were naturalists in this sense. This is not the sense in which Smith uses it in his 1905 essay, "The Naturalism of Hume." The first part of this essay opposes T. H. Green's traditional reading of Hume as a philosopher who streamlined the ideas of Locke and Berkeley and proposes to replace it with the view of Hume's view as "naturalism." "Hume's... naturalistic view of reason," we are told (p. 158), "is a new theory of belief": Humean belief, on Smith's new reading, "is not caused by knowledge but precedes it, and as it is not caused by knowledge it is not destroyed by doubt" (p. 165). Smith declared his reading quite revolutionary, yet it may be endorsed without rejecting Green's reading. Smith does not even attempt to re-interpret in detail the passages which prima facie conform to Green's reading. The second part of his essay is the application of his revolutionary reading to psychology and to ethics. Smith devotes the preface of his The Philosophy of David Hume (1941) to a revision of his 1905 study. It seems he did not alter his attitude towards the first part but only to the second: he thought the starting point of Hume's study was his concern not for "naturalism" but for "moral philosophy, or the science of human nature" (opening words of Hume's Inquiry, cf. Hendel, op. cit., p. xlvi). This statement has to do 94 with emphasis, not with the meanings of terms or with ascriptions of views (and it is erroneous, or at least limited; but this is another matter). This is not to deny that Hume was a naturalist in Bayle's sense, as everyone today agrees. Most philosophers today share this naturalism with Hume. "His attitude and way of... (shrink)

Situation Theory and Its Applications, Vol. 1 . Robin Cooper, Kuniaki Mukai, and John Perry (Eds.). Lecture Notes No. 22. ...

There are broad and narrow senses of hermeneutic application as well as of hermeneutic praxis. The broad sense of hermeneutic application means using what one has already understood in some later situation. Hermeneutic praxis in the narrow sense refers to an interpreter using a hermeneutic theory to interpret written or spoken language. The narrow sense of hermeneutic application is discussed by Hans‐Georg Gadamer in Truth and Method as the central problem of philosophical hermeneutics. Friedrich Schleiermacher had noted (...) that the lax practice of hermeneutics, which had been previously the main form of hermeneutics, assumes that understanding usually succeeds and that interpretation is only called for in difficult cases where misinterpretation might occur. Usually, after one has understood, interpreted, and applied an order to the concrete situation, one would carry out that order as it was understood. This action that follows from understanding is hermeneutic praxis in the broad sense. (shrink)

The purpose of the study is to consider the theoretical aspects of innovative education, as well as to analyze the practical application of innovative technologies in foreign language classes for students of engineering specialties. The article notes that innovative educational technologies are based on three interrelated components: competence-based approach; modern teaching methods; modern learning infrastructure. Scientific novelty lies in an attempt to analyze the innovative practice of teachers and determine the main advantages of innovative technologies in teaching a (...) foreign language to students of technical universities. As a result, such advantages of these technologies were identified as the development of all types of speech activity of students, an individual approach to learning, an increase in motivation for learning a language, the ability to express oneself creatively, the formation of a personality capable of solving professionally oriented tasks. (shrink)

L’impérialisme économique, entendu comme une certaine relation entre disciplines scientifiques, est défendu par certains et rejeté par d’autres. Ces réactions sont toutefois rarement fondées sur des valeurs et des normes de recherche scientifique explicites. Or, lorsque l’on s’efforce de les rendre explicites, ces normes se révèlent plus complexes et plus floues qu’il n’y paraît. Certains considèrent qu’elles font partie intégrante de la définition du concept d’impérialisme économique ; d’autres, dont je fais partie, considèrent qu’elles sont extérieures à ce concept. Dans (...) les deux cas, l’application des normes est sélective et ambiguë. Elles peuvent être mobilisées, selon la sélection et l’interprétation à laquelle on procède, pour soutenir ou pour critiquer l’impérialisme économique. L’article recense différentes normes méthodologiques et sociales de recherche scientifique – par exemple le souhait d’une portée large, l’unification, l’originalité, l’exactitude empirique, l’universalisme, l’humilité épistémique, la réceptivité à la critique, la diversité, la justice épistémique, la disposition à jouer ( playfulness ) – et il montre comment elles peuvent être invoquées dans les controverses. Ces notes critiquent certaines analyses normatives de l’impérialisme économique. Elles résument et développent également ma propre analyse. Elles ne livrent toutefois pas de conclusion définitive. (shrink)

L’impérialisme économique, entendu comme une certaine relation entre disciplines scientifiques, est défendu par certains et rejeté par d’autres. Ces réactions sont toutefois rarement fondées sur des valeurs et des normes de recherche scientifique explicites. Or, lorsque l’on s’efforce de les rendre explicites, ces normes se révèlent plus complexes et plus floues qu’il n’y paraît. Certains considèrent qu’elles font partie intégrante de la définition du concept d’impérialisme économique ; d’autres, dont je fais partie, considèrent qu’elles sont extérieures à ce concept. Dans (...) les deux cas, l’application des normes est sélective et ambiguë. Elles peuvent être mobilisées, selon la sélection et l’interprétation à laquelle on procède, pour soutenir ou pour critiquer l’impérialisme économique. L’article recense différentes normes méthodologiques et sociales de recherche scientifique – par exemple le souhait d’une portée large, l’unification, l’originalité, l’exactitude empirique, l’universalisme, l’humilité épistémique, la réceptivité à la critique, la diversité, la justice épistémique, la disposition à jouer ( playfulness ) – et il montre comment elles peuvent être invoquées dans les controverses. Ces notes critiquent certaines analyses normatives de l’impérialisme économique. Elles résument et développent également ma propre analyse. Elles ne livrent toutefois pas de conclusion définitive. (shrink)

A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises (...) designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics. (shrink)

Fuzzy logics are systems of logic with infinitely many truth values. Such logics have been claimed to have an extremely wide range of applications in linguistics, computer technology, psychology, etc. In this note, we canvass the known results concerning infinitely many valued logics; make some suggestions for alterations of the known systems in order to accommodate what modern devotees of fuzzy logic claim to desire; and we prove some theorems to the effect that there can be no fuzzy logic which (...) will do what its advocates want. Finally, we suggest ways to accommodate these desires in finitely many valued logics. (shrink)

Jewish tradition has a long-standing commitment to justice, equity and compassion toward society's most vulnerable members, including its working-class. It has produced a substantial literature describing appropriate practice in business relations and the ethics of the marketplace. Less well-known, however, are its prescriptions for employee productivity and accountability. These elements are considered here within the context of contemporary organization, and with particular application to the school of quality management associated with W. Edwards Demings.This paper is an expanded version of (...) the Herbert H. Schiff Lecture in Management and Administration, delivered at Yeshiva University, July 8, 1992. It is dedicated to the memory of my beloved mother, Mrs. Chana Schnall. (shrink)

The entrepreneurial element is one of the aspects emphasized in the primary school mathematics education curriculum in Malaysia. However, previous studies have found that application of entrepreneurial elements in mathematics teaching is still lacking. This study was therefore conducted to identify the real challenges that mathematics teachers face in applying the entrepreneurial element in mathematics teaching. This study is qualitative case study which involved six primary school mathematics teachers. Semi-structured interviews, observation, document analysis and field notes were used (...) for the data collection process in this study. The data obtained was analyzed using the constant comparative analysis method to determine themes and sub-themes. The findings were that a teacher’s knowledge, teaching style, limited time of teaching, and attitudes, and in-service courses and training are among the identified challenges in applying entrepreneurial elements in mathematics teaching. This study expands knowledge and the literature on the challenges faced by school mathematics teachers in applying entrepreneurial elements in mathematics teaching. Various initiatives need to be taken to ensure that all the challenges can be overcome, and ultimately enable the entrepreneurial elements to be applied to students more widely. (shrink)

ABSTRACT In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's ?useful? four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.

ABSTRACT- In this paper my aim is to concentrate on the concepts like predicate, properties and classes; with an aim to understand the reason behind the re-applicability of general terms. It must also be noted that here general terms are supposed to be found in the predicate place of a proposition as properties and how they are ascribed to objects which may be mentioned in the subject place. This paper harps on the issue of; what acts as a deciding factor (...) behind such act of classification. A clear effort has been made as to the reason behind our grouping of objects and what we actually search for while choosing an object under a class. I have tried to make my point on the issue that at most we can call our act of classification as natural instead of calling a class as natural. For this I have particularly chosen an article of Anthony Quinton namely, ‘Properties and Classes’ (1958 vol-58, Issue 1, 1st June Proceedings of the Aristotelian Society). (shrink)

The notion of a bilattice was rst introduced by Ginsburg (see Gin]) as a general framework for a diversity of applications (such as truth maintenance systems, default inferences and others). The notion was further investigated and applied for various purposes by Fitting (see Fi1]- Fi6]). The main idea behind bilattices is to use structures in which there are two (partial) order relations, having di erent interpretations. The two relations should, of course, be connected somehow in order for the mathematical structure (...) to be useful. It is not clear, however, what this connection should be. Ginsberg, for example, has made the connection through an extra operation of negation. Fitting, on the other hand, has investigated connections in the form of conditions on the structure (such as being interlaced { see below). These conditions are independent of the existence, or even the possibility to de ne, operations like Ginsberg's negation.* Fitting de nes, accordingly, notions like \an interlaced bilattice", \a distributive bilattice", \a bilattice with negation" and others. He does not provide, however, any de nition of the notion of bilattice itself (without an extra modi er). I was unable to nd anywhere, in fact, a de nition which will cover all the structures which were called \bilattice" in the literature. (shrink)

The idea of a property's being supervenient on a class of properties is familiar from much philosophical literature. We give this idea a linguistic turn by converting it into the idea of a predicate symbol's being supervenient on a set of predicate symbols relative to a (first order) theory. What this means is that according to the theory, any individuals differing in respect to whether the given predicate applies to them also differ in respect to the application of at (...) least one of the predicates in the set. The latter relationship we show turns out to coincide with something antecedently familiar from work on definability: with what is called the piecewise (or modelwise) definability, in the theory in question, of the given predicate in terms of those in the set. (shrink)

Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or not. (...) It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and model-theoretic consequence. Every model-theoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely, the homophonic interpretation that does not substitute anything. Applications to free logic, and theories and languages other than set theory are sketched. (shrink)

The book has two di sti ncti ve features. One is that while philosophers’discussions of externalism tend to be very technical, Rowlands presents his own discussion in an accessible manner. The second, more distinctive than the first, is that Rowlands treats the concept of externalism as a topic in both analytic and continental traditions of philosophy. In Chapter 2 Rowlands introduces the Cartesian internalist conception of the mind, which appears inconsistent with externalism. Rowlands claims that Cartesianism consists of three types (...) of thesis: ontological, epistemological and axiological. Throughout the book he focuses on the ontological thesis, except for Chapter 8, where he discusses the epistemological thesis, and Chapter 11, where he discusses the axiological thesis. The rest of the book is roughly divided into two parts. In the first, Rowlands discusses the relationship between externalism and idealism, the latter of which is, according to him, a natural development of internalism. Rowlands advances his discussion by treating Edmund Husserl as an internalist and idealist, and Jean-Paul Sartre and Wittgenstein as externalists. In the second, he examines content externalism. He finds content externalism unsatisfactory and tries to establish a more robust form of externalism, which he calls ‘ vehicle externalism’ . He shows that vehicle externalism is applicable to conscious experience, which, on the face of it, has nothing to do with externalism. There are at least two possible impressions that readers might have about this book. The first is that the book is unfocused because it covers a number of distinct topics in two different traditions by relying on the widest construal of the term ‘ external i sm’ . A reader only interested in recent topics on content externalism in epistemology and the philosophy of mind—i.e. externalism and authoritative self-knowledge, externalism and scepticism, externalism and memory and so on—might have this impression.. (shrink)

Counterfactual definiteness is supposed to underlie the Bell theorem. An old controversy exists among those who reject the theorem implications by rejecting counterfactual definiteness and those who claim that, since it is a direct consequence of locality, it cannot be independently rejected. We propose a different approach for solving this contentious issue by realizing that counterfactual definiteness is an unnecessary and inconsistent assumption. Counterfactual definiteness is not equivalent to realism or determinism neither it follows from locality. It merely reduces to (...) an incongruent application of counterfactual reasoning. Being incompatible with falsifiability, it constitutes an unjustified assumption that goes against the scientific method rigor. Correct formulations of the Bell theorem’s bases show it is absent either as a fundamental hypothesis or as a consequence of something else. Most importantly, we present a coherent Bell inequality derivation carefully devised to show explicitly and convincingly the absence of incompatible experiments or counterfactual reasoning. Thus, even admitting that counterfactual definiteness could be a consistent assumption, the necessary conclusion is that it is irrelevant for the inequality formulation and can be safely ignored when discussing Bell’s inequality philosophical and physical implications. (shrink)

A common misconception among logicians is to think that intuitionism is necessarily tied-up with single conclusion calculi. Single conclusion calculi can be used to model intuitionism and they are convenient, but by no means are they necessary. This has been shown by such influential textbook authors as Kleene, Takeuti and Dummett, to cite only three. If single conclusions are not necessary, how do we guarantee that only intuitionistic derivations are allowed? Traditionally one insists on restrictions on particular rules: implication right, (...) negation right and universal quantification right are required to be single conclusion rules. In this note we show that instead of a cardinality restriction such as one-conclusion-only, we can use a notion of dependency between formulae to enforce the constructive character of derivations. The system we obtain, called FIL for full intuitionistic logic, satisfies basic properties such as soundness, completeness and cut elimination. We present two motivating applications of FIL and discuss some future work. (shrink)

The space CS(R) has a unique “Borel structure” in the following sense. Note that there is a natural mapping from R¥ onto CS(R}; namely, taking ranges. We can combine this with any Borel bijection from R onto R¥ in order to get a “preferred” surjection F:R ® CS(R).

In this contribution we shall characterize matrix consequence operation determined by a direct product and an ultraproduct of a family of logical matrices. As an application we shall describe finite consequence operations with the help of ultrapowers.

Parkinson’s Disease can be treated with the use of microelectrode recording and stimulation. This paper presents a data stream classifier that analyses raw data from micro-electrodes and decides whether the measurements were taken from the subthalamic nucleus (STN) or not. The novelty of the proposed approach is based on the fact that distances based on raw data are used. Two distances are investigated in this paper, i.e. Normalized Compression Distance (NCD) and Lempel-Ziv Jaccard Distance (LZJD). No new features needed to (...) be extracted due to the fact that in the case of high-dimensional data the process is extremely time-consuming. The k-nearest neighbour (k-NN) was chosen as the classifier due to its simplicity, which is essential in data stream classification. Results obtained from classifiers based on k-NN: k-NN, k-NN were compared with Probabilistic Approximate Window (k-NN with PAW); k-NN with Probabilistic Approximate Window and Adaptive Windowing (k-NN with PAW and ADWIN); and Self Adjusting Memory k-NN (SAM k-NN), which use the proposed distances, with the performance of the same classifiers but using standard Euclidean distance. Prequential accuracy was chosen as the performance measure. The results of the experiments performed with the described approach are in most cases better, i.e. the performance measures for kNN classifiers that use NCD and LZJD distances are better by up to 8.5 per cent and 14 per cent, respectively. Moreover, the proposed approach performs better when compared with other stream classification algorithms, i.e. Hoeffding Tree, Naive Bayes, and Leveraging Bagging. In the discussed case, an improvement of classification rate of up to 17.9 per cent when using Lempel-Ziv Jaccard Distance instead of the Euclidean was noted. (shrink)

Hans Hahn, mathematician, philosopher and co-founder of the Vienna Circle, attempted to reconcile the validity and applicability of both logic and mathematics with a strict empiricism. This article begins with a review of this attempt, focusing on his view of the relation of language to logic and his answer to the question of why we need logic. I then turn to some recent work by Stephen Yablo in an attempt to show that Yablo's fictionalism, and in particular his use of (...) metaphor, can shed light on Hahn's philosophy of logic. (shrink)

The paper studies two formal schemes related to -completeness.LetS be a suitable formal theory containing primitive recursive arithmetic and letT be a formal extension ofS. Denoted by (a), (b) and (c), respectively, are the following three propositions (where (x) is a formula with the only free variable x): (a) (for anyn) ( T (n)), (b) T x Pr T (–(x)–) and (c) T x(x) (the notational conventions are those of Smoryski [3]). The aim of this paper is to examine the (...) meaning of the schemes which result from the formalizations, over the base theoryS, of the implications (b) (c) and (a) (b), where ranges over all formulae. The analysis yields two results overS : 1. the schema corresponding to (b) (c) is equivalent to ¬Cons T and 2. the schema corresponding to (a) (b) is not consistent with 1-CON T. The former result follows from a simple adaptation of the -incompleteness proof; the second is new and is based on a particular application of the diagonalization lemma. (shrink)

This article argues that an engagement with the powerful critical insights of Žižek’s theory of ideology and practice of cultural critique is a necessary step for any art historical methodology which aims to fully account for a work of art’s function within the society of its creation and reception, and to explain how it came to play such a role. However, any attempt to situate cultural artefacts within historically contingent networks of social relations requires an account of historical change incompatible (...) with any formalist or transcendentalist methodology. Moreover, if it is to be of any use as an academic discourse, art history must be able to account for the specifities of ‘art’ as a distinct—but not autonomous—sphere of human activity. It is precisely these two issues that a wholesale importation of Žižek’s writing into the domain of art history encounters. A solution must be found whereby the critical lessons of Žižek are not ‘lost in translation’. In this vein, the present article begins by outlining Žižek’s conception of ideology and elucidating the problematic consequences of any straightforward application of its parameters as an art historical methodology. It then reads the interventions of Jacques Rancière and Judith Butler as providing the necessary theoretical tools by which one can construct the possibility of a powerful Žižekian art historical methodology. (shrink)