We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.

In this paper we present two families of probability logics (denoted _QLP_ and \(QLP^{ORT}\) ) suitable for reasoning about quantum observations. Assume that \(\alpha \) means “O = a”. The notion of measuring of an observable _O_ can be expressed using formulas of the form \(\square \lozenge \alpha \) which intuitively means “if we measure _O_ we obtain \(\alpha \) ”. In that way, instead of non-distributive structures (i.e., non-distributive lattices), it is possible to relay on classical logic extended with (...) the corresponding modal laws for the modal logic \({\textbf{B}}\). We consider probability formulas of the form \(CS_{z_{1},\rho _{1}; \ldots ; z_{m},\rho _{m}} \square \lozenge \alpha \) related to an observable _O_ and a possible world (vector) _w_: if _a_ is an eigenvalue of _O_, \(w_{1}\),..., \(w_{m}\) form a base of a closed subspace of the considered Hilbert space which corresponds to eigenvalue _a_, and if _w_ is a linear combination of the basis vectors such that \(w=c_{1}\cdot w_{1}+ \cdots + c_{m}\cdot w_{m}\) for some \(c_{i}\in {\mathbb {C}}\), then \(\Vert c_{1}-z_{1}\Vert \le \rho _{1}\),..., \(\Vert c_{m}-z_{m}\Vert \le \rho _{m}\), and the probability of obtaining _a_ while measuring _O_ in the state _w_ is equal to \(\Sigma _{i=1}^{m}\Vert c_{i}\Vert ^{2}\). Formulas are interpreted in reflexive and symmetric Kripke models equipped with probability distributions over families of subsets of possible worlds that are orthocomplemented lattices, while for \(QLP^{ORT}\) also satisfy ortomodularity. We give infinitary axiomatizations, prove the corresponding soundness and strong completeness theorems, and also decidability for _QLP_-logics. (shrink)

The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend |$\textbf {PTEL}$| to axiomatize the corresponding first-order logic.

We study a propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| with both future and past temporal operators, with non-rigid set of agents and the operators for agents’ knowledge and for common knowledge and with probabilities defined on the sets of runs and on the sets of possible worlds. A semantics is given by a class |${\scriptsize{\rm Mod}}$| of Kripke-like models with possible worlds. We prove decidability of |$\textbf {PTEL}$| by showing that checking satisfiability of a formula in |${\scriptsize{\rm Mod}}$| is (...) equivalent to checking its satisfiability in a finite set of finitely representable structures. The same procedure can be applied to the class of all synchronous |${\scriptsize{\rm Mod}}$|-models. We give an upper complexity bound for the satisfiability problem for |${\scriptsize{\rm Mod}}$|⁠. (shrink)

In this paper we present two types of logics and \ ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance between the probabilities of (...) α and β is less than or equal to ρ”, respectively. Logics of the later type formalize processes of thinking where information are coded by p-adic numbers. We use the same operators as above, but in this formalism K r,ρ α means “the p-adic code of the information α belongs to the p-adic ball with the center r and the radius ρ”, while D ρ α,β means “the p-adic distance between codes of α and β are less than or equal to ρ”. The corresponding strongly complete axiom systems are presented and decidability of the satisfiability problem for each logic is proved. (shrink)

In Less Than Nothing, the pinnacle publication of a distinguished career, Slavoj i ek argues that it is imperative that we not simply return to Hegel but that we repeat and exceed his triumphs, overcoming his limitations by being even more ...

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)

With a new introduction by the author In this deliciously polemical work, a giant of cultural theory immerses himself in the ideas of a giant of French thought.

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)

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)

The main goal of this work is to present the proof-theoretical and model-theoretical approaches to probabilistic logics which allow reasoning about independence and probabilistic support. We extend the existing formalisms [14] to obtain several variants of probabilistic logics by adding the operators for independence and confirmation to the syntax. We axiomatize these logics, provide corresponding semantics, prove that the axiomatizations are sound and strongly complete, and discuss decidability issues.

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)

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image. (shrink)

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image. (shrink)

A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P ≥s (with the intended meaning ‘‘the probability is at least s’’). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.

With his characteristic wit, Zizek addresses the burning question of how to reformulate a leftist project in an era of global capitalism and liberal-democratic ...

We study structures equipped with generic predicates and/or automorphisms, and show that in many cases we obtain simple theories. We also show that a bounded PAC field is simple. 1998 Published by Elsevier Science B.V. All rights reserved.

We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form $$\langle H, \mu \rangle $$ that needs not be a probability space. More precisely, though H needs not be a Boolean algebra, the corresponding monotone function (we call it measure) $$\mu : H \longrightarrow [0,1]_{\mathbb {Q}}$$ satisfies the following condition: if $$\alpha $$, $$\beta $$, $$\alpha \wedge \beta $$, (...) $$\alpha \vee \beta \in H$$, then $$\mu (\alpha \vee \beta ) = \mu (\alpha ) + \mu (\beta ) - \mu (\alpha \wedge \beta )$$. Since the range of $$\mu $$ is the set $$[0,1]_{\mathbb {Q}}$$ of rational numbers from the real unit interval, our logic is not compact. In order to obtain a strong complete axiomatization, we introduce an infinitary inference rule with a countable set of premises. The main technical results are the proofs of strong completeness and decidability. (shrink)

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 shows that a promising alternative view can be found in a surprising source: the writings of Søren Kierkegaard. I argue that in light of two of his central (...) epistemological commitments—belief-credence dualism and epistemic permissivism about outright belief—Kierkegaard holds that practical considerations can affect what we ought to believe without either encroaching on or (necessarily) conflicting with epistemic rationality. The central idea is that practical considerations can determine which among the epistemically permitted outright doxastic attitudes one should all-things-considered adopt. In addition to constituting a novel, systematic interpretation of Kierkegaard’s account of how practical considerations affect what we ought to believe, this suggests that Kierkegaard holds a distinctive and underexplored view that constitutes a serious philosophical rival to dominant contemporary views. (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)

We present a propositional and a first-order logic for reasoning about higher-order upper and lower probabilities. We provide sound and complete axiomatizations for the logics and we prove decidability in the propositional case. Furthermore, we show that the introduced logics generalize some existing probability logics.

We present a propositional and a first-order logic for reasoning about higher-order upper and lower probabilities. We provide sound and complete axiomatizations for the logics and we prove decidability in the propositional case. Furthermore, we show that the introduced logics generalize some existing probability logics.

On Islamic teachings, written by an army officer and educationist from Pakistan.

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)

Ghazzālī, 1058-1111; Kīmiyā-yi saʻādat -Criticism and interpretation ; Ghazzālī, Aḥmad ibn Muḥammad, -1126; Savāniḥ -Criticism and interpretation ; Ghazzālī, Aḥmad ibn Muḥammad, -1126; Baḥr al-muḥabbat fī asrār al-muvaddat fītafsīr Sūrah-i Yūsuf -Criticism.

Donald Davidson has made enormous contributions to the philosophy of action, epistemology, semantics and philosophy of mind and today is recognized as one of the most important analytical philosophers of the late twentieth century. _Donald Davidson: Truth, Meaning and Knowledge_ addresses * Davidson's writings on epistemology and theory of language with their implications of ontology and philosophy of mind * the central issue of whether truth is the ultimate goal of enquiry, challenged by contributions from Richard Rorty and Paul Horwich (...) * Davidson's approach to semantics and applied linguistics as addressed by Kirk Ludwig, Gabriel Segal, Peter Pagin, Stephen Neale, Herman Cappelen and Ernie Lepore and Reinaldo Elugardo * Davidson's advances in the philosophy of mind in relation to the views of Williard V. Quine, John McDowell and Peter F. Strawson, in essays by Roger Gibson and Anita Avramides. (shrink)

We suggest an approach to studying consciousness that focuses on its evolutionary origins. The proposed framework is inspired by the study of the transition from inanimate matter to life, which proved extremely useful for understanding what 'life' entails. We follow the theoretical and methodological scheme put forward by Tibor Ganti, who suggested a marker for the transition to life -- an evolved feature that is sufficient for ascribing dynamic persistence to a minimal living system and that can serve as a (...) point of departure for reconstructing it. We apply this approach to consciousness and suggest an overt behavioural trait -- unlimited associative learning -- as a candidate transition marker. We show that the enabling system of UAL instantiates the set of properties that are considered jointly sufficient for minimal consciousness, and discuss the experimental predictions and the implications of our approach for the taxonomic distribution of consciousness in the animal world. (shrink)