This research partially answers the question raised by Goncharov about the size of the class of positive elements of a Roger's semilattice. We introduce a notion of effective infinity of classes of computable enumerations. Then, using finite injury priority method, we prove five theorems which give sufficient conditions to be effectively infinite for classes of all enumerations without repetitions, positive undecidable enumerations, negative undecidable enumerations and all computable enumerations of a family of r.e. sets. These theorems permit to strengthen (...) the results of Pour-El, Pour-El and Howard, Ershov and Khutoretskii about existence of enumerations without repetitions and positive undecidable enumerations. (shrink)

The author of the article studies the creative legacy of Yuriy Mamleev, trying to establish the correlation between of his philosophical and fiction writings. The conventional editorial distinction between philosophical and literary texts as different and autonomous categories is rejected. Instead of the idea, that philosophical and fictional aspects of texts by Mamleev are inextricably linked, it is claimed that they should be considered together. In the author’s opinion, these texts present different perspectives and implementations of his oeuvre that contains (...) the rational dimension and on the other hand – irrational dimension of artistic images and obscure allusions. Mamleev’s writings considered by means of 5 crucial “metathemes”: Аbyss and the “Ultimate relationships” concerned with it, the Mystery which has two levels – one cognizable and the another – uncoognizable in principal, the “root of self-being” and metaphysic of “I”, death and immortality, Russia and the Russian soul which are existed between West and East with special historical and cosmological mission. It is concluded that these 5 metathemes pervade all Mamleev’s texts and comprise his spiritual search. The characters of Mamleev’s fiction are mostly people of post-Soviet world, who ask questions with no set answers to become acquainted with the secrets of being. At the same time they are concerned with their own existence, their self destiny. Their actions are extraordinary and illogical. Supposedly Mamleev’s artistic images not only correspond with his philosophical ideas, for instance – utrism or the “Ultimate relationships”, but also reveal them from unexpected perspective. The author determines that distinction between philosophy and literature of Mamleev is incorrect, as these areas are conflated. Any distinction of this kind will ruin the logic of Mamleev’s thinking and outlook. Thus, metaphysical realism can be viewed as the crossing, distinction blurring area, productive and creative transgression. Or as the situation when philosophy is more than it is itself. (shrink)

Let ???? be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of ???? in which the image of R (¬R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on ???? and R, a necessary and sufficient condition for the existence of a computable copy ℬ of ???? in which the image of R (¬R, resp.) (...) is simple (immune, resp.). (shrink)

We will study the question about decidability for Boolean algebras with first elementary characteristic one. The main problem is sufficient conditions for decidability of Boolean algebras with recursive representation for extended signature by definable predicates. We will use the base definitions on recursive and constructive models from [2, 4–6, 10, 11] but on Boolean algebras from [1, 8].

In the paper A. I. Malcev's problem on the characterization of axioms for classes with strong homomorphisms is being solved.

The Hanf number for a set S of sentences in \ is the least infinite cardinal \ such that for all \, if \ has models in all infinite cardinalities less than \, then it has models of all infinite cardinalities. Friedman asked what is the Hanf number for Scott sentences of computable structures. We show that the value is \. The same argument proves that \ is the Hanf number for Scott sentences of hyperarithmetical structures.

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

Computable structures of Scott rank ${\omega_1^{CK}}$ are an important boundary case for structural complexity. While every countable structure is determined, up to isomorphism, by a sentence of ${\mathcal{L}_{\omega_1 \omega}}$ , this sentence may not be computable. We give examples, in several familiar classes of structures, of computable structures with Scott rank ${\omega_1^{CK}}$ whose computable infinitary theories are each ${\aleph_0}$ -categorical. General conditions are given, covering many known methods for constructing computable structures with Scott rank ${\omega_1^{CK}}$ , which guarantee that the (...) resulting structure is a model of an ${\aleph_0}$ -categorical computable infinitary theory. (shrink)

The twentieth century is drawing to a close, and the twenty-first century is about to begin. Please tell us how you see the past, and look forward to the future.

We show that for every computable limit ordinal α, there is a computable structure A that is $\Delta _\alpha ^0 $ categorical, but not relatively $\Delta _\alpha ^0 $ categorical (equivalently. it does not have a formally $\Sigma _\alpha ^0 $ Scott family). We also show that for every computable limit ordinal a, there is a computable structure A with an additional relation R that is intrinsically $\Sigma _\alpha ^0 $ on A. but not relatively intrinsically $\Sigma _\alpha ^0 $ (...) on A (equivalently, it is not definable by a computable $\Sigma _\alpha $ formula with finitely many parameters). Earlier results in [7], [10], and [8] establish the same facts for computable successor ordinals α. (shrink)

Žižek as comedian: jokes in the service of philosophy.

In this provocative and original work, Slavoj Zizek takes a look at the question of human agency in a postmodern world. From the sinking of the Titanic to Hitchcock's Rear Window, from the operas of Wagner to science fiction, from Alien to the Jewish Joke, the author's acute analyses explore the ideological fantasies of wholeness and exclusion which make up human society. Linking key psychoanalytical and philosophical concepts to social phenomena such as totalitarianism and racism, the book explores the political (...) significance of these fantasies of control. In so doing, The Sublime Object of Ideology represents a powerful contribution to a psychoanalytical theory of ideology, as well as offering persuasive interpretations of a number of contemporary cultural formations. -- Back cover. (shrink)

As a slew of recent work in epistemology has brought out, there is a range of cases where there's a strong temptation to say that prudential and (especially) moral considerations affect what we ought to believe. There are two distinct models of how this can happen. On the first, “reasons pragmatist” model, the relevant prudential and moral considerations constitute distinctively practical reasons for (or against) belief. On the second, “pragmatic encroachment” model, the relevant prudential and moral considerations affect what one (...) is epistemically justified in believing. The pragmatic encroachment model appears to have several advantages over reasons pragmatism, and this has led many recent philosophers to endorse the former. However, in this paper we argue that a version of reasons pragmatism can be (at least largely) saved from these purported disadvantages once paired with an independently plausible permissivism about epistemically justified outright belief. This hybrid view—“permissivist pragmatism”—holds that when there is more than one epistemically permitted doxastic attitude, practical (including moral) considerations can determine which epistemically permitted doxastic attitude one all-things-considered ought to have. This view avoids both the problems faced by simple versions of reasons pragmatism, and those that distinctively attend pragmatic encroachment, while preserving the advantages of each view. (shrink)

Kierkegaard's pseudonym Johannes Climacus famously defines faith as a risky “venture” that requires “holding fast” to “objective uncertainty.” Yet puzzlingly, he emphasizes that faith requires resolute conviction and certainty. Moreover, Climacus claims that all beliefs about contingent propositions about the external world “exclude doubt” and “nullify uncertainty,” but also that uncertainty is “continually present” in these very same beliefs. This paper argues that these apparent contradictions can be resolved by interpreting Climacus as a belief‐credence dualist. That is, Climacus holds that (...) beliefs and credences (i.e., degrees of belief) are two irreducibly distinct types of mental states. Beliefs are resolutions that close inquiry, thereby excluding doubt and reflecting subjective certainty by disregarding the possibility of error. Credences, by contrast, reflect assessments of evidential probabilities, thereby encoding a recognition of “objective uncertainty” by acknowledging the possibility of error. In addition to solving a vexing interpretive puzzle and showing how Kierkegaard anticipates contemporary views about the nature of belief and credence, this paper demonstrates that Kierkegaard developed a sophisticated account of the nature of belief, doubt, and certainty that merits serious philosophical consideration. (shrink)

[Ḥeleḳ rishon] Or Torah, ʻavodat ha-tefilah, darkhe ha-Ḥasidut, ḥinukh ha-banim, maśa u-matan be-emunah, midot ṭovot -- Ḥeleḳ sheni. Miḳṿeh meṭaher, ʻavodat ha-tefilah, hanhagat ha-shulḥan, or Torah.

On the dominant contemporary accounts of how practical considerations affect what we ought to believe, practical considerations either encroach on epistemic rationality by affecting whether a belief is epistemically justified, or constitute distinctively practical reasons for belief which can only affect what we ought to believe by conflicting with epistemic rationality. This paper argues that Søren Kierkegaard offers a promising alternative view on which practical considerations can affect what we ought to believe without either encroaching on or (necessarily) conflicting with (...) epistemic rationality by determining which among the epistemically permitted outright doxastic attitudes one should all‐things‐considered adopt. (shrink)

The latest book by the Slovenian critic Slavoj Zizek takes the work of French philosopher Gilles Deleuze as the beginning of a dazzling inquiry into the realms of radical politics, philosophy, film (Hitchcock, Fight Club ), and psychoanalysis. Of Organs without Bodies Joan Copjec ( Imagine There's No Woman ) has written: "With all his ususal humor and invention, Zizek -- the acknowledged master of the 180 degree turn -- here takes a trip into "enemy" territory to deliver Deleuze of (...) a marvelously rebellious child, one that seriously challenges Deleuze's other progeny with a surprising but convincing bid for succession. Those who thought Deleuze's forward march into the future would follow a straight path are forced to rethink their stance. From now on all readings of Deleuze will have to take a detour through this important -- even necessary -- book." Eric Santner ( On the Psychopathology of Everyday Life ) describes Organs without Bodies as offering "an entirely new degree of conceptual clarity and political urgency. Through his deep engagement with the logic of Deleuze's project, Zizek opens up new possibilities of thought beyond the terms of the current political debates on globalization, democratization, war on terror. Once again, Zizek has produced an utterly timely and radically untimely meditation." Recently profiled in The New Yorker , and hailed by the Village Voice as "the giant of Ljubljana," Zizek is one of the most provocative and entertaining thinkers at work today. (shrink)

Book synopsis: In this combative major new work, philosophical sharpshooter Slavoj Zizek looks for the kernel of truth in the totalitarian politics of the past. Examining Heidegger's seduction by fascism and Foucault's flirtation with the Iranian Revolution, he suggests that these were the 'right steps in the wrong direction.' On the revolutionary terror of Robespierre, Mao and the bolsheviks, Zizek argues that while these struggles ended in historic failure and horror, there was a valuable core of idealism lost beneath the (...) bloodshed. A redemptive vision has been obscured by the soft, decentralized politics of the liberal-democratic consensus. Faced with the coming ecological crisis, Zizekk argues the case for revolutionary terror and the dictatorship of the proletariat. A return to past ideals is needed despite the risks. In the words of Samuel Beckett: 'Try again. Fail again. Fail better.'. (shrink)

In celebration of the 250th anniversary of the birth of G.W.F. Hegel, Slavoj Žižek gives us a reading of a philosophical giant that changes our way of thinking about the post-human era we are entering. No ordinary study of Hegel, Hegel in a Wired Brain reveals our time as it appears through Hegel's eyes. Focusing in on the idea of the wired brain, this is a philosophical analysis of what happens when a direct link between our mental processes and a (...) digital machine emerges. Here Žižek explores the phenomenon of a wired brain affect, and the notion of singularity subsequently arising when we can share our thoughts and experiences with others. He hones in on the key question of how it affects our experience and status as free human individuals, dealing with what happens with the human spirit, our subjectivity and the very essence of being-human when a machine can read, action and disperse our thoughts. With characteristic verve and energy, Žižek connects Hegel to the world we live in and shows why he is much more fun than anyone gives him credit for, and why the 21st century might just be Hegelian. (shrink)

With the disintegration of state socialism, we are witnessing this eruption of enjoymnet in the re-emergence of aggressive nationalism and racism. With the lid of repression lifted, the desires that have emerged are from from democratic. To explain this apparent paradox, says Slavoj Zizek, socialist critical thought must turn to psychoanalysis. For They Know Not What They Do seeks to understand the status of enjoyment within ideological discourse, from Hegel through Lacan to these political and ideological deadlocks. The author's own (...) enjoyment of "popular culture" makes this an engaging and lucid exposition, in which Hegel joins hands with Rossellini, Marx with Hitchcock, Lacan with Frankenstein, high theory with Hollywood melodrama. (shrink)

Whenever the membranes of the egg in which the foetus emerges on its way to becoming a new-born are broken, imagine for a moment that something flies off, and that one can do it with an egg as easily as with a man, namely the hommelette, or the lamella. The lamella is something extra-flat, which moves like the amoeba. It is just a little more complicated. But it goes everywhere. And as it is something - I will tell you shortly (...) why - that is related to what the sexed being loses in sexuality, it is, like the amoeba in relation to sexed beings, immortal - because it survives any division, and scissiparous intervention. And it can turn around. Well! This is not very reassuring. But suppose it comes and envelopes your face while you are quietly asleep... I can't see how we would not join battle with a being capable of these properties. But it would not be a very convenient battle. This lamella, this organ, whose characteristic is not to exist, but which is nevertheless an organ - I can give you more details as to its zoological place - is the libido. It is the libido, qua pure life instinct, that is to say, immortal life, irrepressible life, life that has need of no organ, simplified, indestructible life. It is precisely what is subtracted from the living being by virtue of the fact that it is subject to the cycle of sexed reproduction. And it is of this that all the forms of the objet a that can be enumerated are the representatives, the equivalents. Every word has a weight here, in this deceivingly poetic description of the mythic creature called by Lacan "lamella". Lacan imagines lamella as a version of what Freud called "partial object": a weird organ which is magically autonomized, surviving without a body whose organ it should have been, like a hand that wonders around alone in early Surrealist films, or like the smile in Alice in Wonderland that persists alone, even when the Cheshire cat's body is no longer present: "'All right', said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone. 'Well! I've often seen a cat without a grin', thought Alice; 'but a grin without a cat! It's the most curious thing I ever saw in my life!'" The lamella is an entity of pure surface, without the density of a substance, an infinitely plastic object that can not only incessantly change its form, but can even transpose itself from one to another medium: imagine a "something" that is first heard as a shrilling sound, and then pops up as a monstrously distorted body. A lamella is indivisible, indestructible, and immortal - more precisely, undead in the sense this term has in horror fiction: not the sublime spiritual immortality, but the obscene immortality of the "living dead" which, after every annihilation, re-composes themselves and clumsily goes on. As Lacan puts it in his terms, lamella does not exist, it insists: it is unreal, an entity of pure semblance, a multiplicity of appearances which seem to envelop a central void - its status is purely fantasmatic. This blind indestructible insistence of the libido is what Freud called "death drive," and one should bear in mind that "death drive" is, paradoxically, the Freudian name for its very opposite, for the way immortality appears within psychoanalysis: for an uncanny excess of life, for an "undead" urge which persist beyond the cycle of life and death, of generation and corruption. This is why Freud equates death drive with the so-called "compulsion-to-repeat," an uncanny urge to repeat painful past experiences which seems to outgrow the natural limitations of the organism affected by it and to insist even beyond the organism's death - again, like the living dead in a horror film who just go on. This excess inscribes itself into the human body in the guise of a wound which makes the subject "undead," depriving him of the capacity to die : when this wound is healed, the hero can die in peace. (shrink)

According to the thesis of doxastic wronging, our beliefs can non-derivatively wrong others. A recent criticism of this view claims that proponents of the doxastic wronging thesis have no principled grounds for denying that credences can likewise non-derivatively wrong, so they must countenance pervasive conflicts between morality and epistemic rationality. This paper defends the thesis of doxastic wronging from this objection by arguing that belief bears distinctive relationships to inquiry and blame that can explain why beliefs, but not credences, can (...) non-derivatively wrong. First, forming a belief (but not updating one’s credence) closes inquiry, and suspending judgment (but not updating one’s credence) opens inquiry. Consequently, beliefs can distinctively wrong others by prematurely closing inquiry or inappropriately opening inquiry. Second, beliefs (but not credences) can constitute blame. Unfittingly blaming someone can wrong them, and hence beliefs which constitute unfitting blame can distinctively wrong. In addition to defending the claim that only beliefs can non-derivatively wrong, this paper gestures towards an ethics of belief which attends to the relationship between belief and attitudes such as inquiry, faith, trust, and blame. (shrink)

According to a traditional interpretation of Kierkegaard, he endorses a strong form of direct doxastic voluntarism on which we can, by brute force of will, make a “leap of faith” to believe propositions that we ourselves take to be improbable and absurd. Yet most leading Kierkegaard scholars now wholly reject this reading, instead interpreting Kierkegaard as holding that the will can affect what we believe only indirectly. This paper argues that Kierkegaard does in fact endorse a restricted, sophisticated, and plausible (...) version of direct doxastic voluntarism. On Kierkegaard’s view, when we take ourselves to be in an epistemically permissive situation, we have the ability to form outright beliefs (but not credences) at will in virtue of our ability to voluntarily 1) open or close inquiry and 2) determine our attitude towards epistemic risk. (shrink)

Although doubt (Tvivl) and despair (Fortvivlelse) are widely recognized as two central and closely associated concepts in Kierkegaard’s authorship, their precise relationship remains opaque in the extant interpretive literature. To shed light on their relationship, this paper develops a novel interpretation of Kierkegaard’s understanding of the connection between despair and our agency over our beliefs, and its significance for Kierkegaard’s ethics of belief. First, I show that an important yet largely overlooked form of Kierkegaardian despair involves either failing to take (...) ethico-religious responsibility for one’s practical agency over one’s beliefs, or misusing one’s practical agency over one’s beliefs by refusing to recognize or comply with externally given ethico-religious norms governing belief. Second, I argue that Kierkegaard takes properly exercising one’s agency over one’s beliefs to matter because beliefs are partly constitutive of the theological virtues (faith, hope, and love) that Kierkegaard regards as the cure for despair. (shrink)