Modal Logic

The paper argues for the applicability of the notion of collective truth as opposed to distributive truth, that is, truth at times or possibilia taken in groups rather than individually. The underlying reasoning is that there are transtemporal and transworld relationships, e.g., those involving the relations of <being a descendant of> and <thinking about>. Relationships are (one type of) truth-makers. Hence, there are transtemporal and transworld truth-makers. Therefore, there is transtemporal and transworld truth, i.e., collective truth. A semantics is developed (formalized in the appendix) which embodies the notion of collective truth, and which thereby, it is argued, has various advantages over standard intensional semantics. For example, it avoids a commitment to certain impossible entities.

In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic $$\mathbf{G}$$ G . More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel frames $$\langle W, \pi \rangle $$ ⟨ W , π ⟩ , where W is a non-empty set of worlds and $$\pi : W \mathop {\rightarrow }[0,1]$$ π : W → [ 0 , 1 ] is a possibility distribution on W. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(G) with the axiom (D), provided that we restrict ourselves to normalised Gödel Kripke frames, i.e. frames $$\langle W, \pi \rangle $$ ⟨ W , π ⟩ where $$\pi $$ π satisfies the normalisation condition $$\sup _{w \in W} \pi (w) = 1$$ sup w ∈ W π ( w ) = 1 .

This tutorial is about design and proof of design of reliable systems from unreliable components. It teaches the concept and techniques of fault-tolerance, at the same time building a formal theory where this property can be specified and verified. The theory eventually supports a range of useful design techniques, especially for multiple faults. We extend CCS, its bisimulation equivalence and modal logic, under the driving principle that any claim about fault-tolerance should be invariant under the removal of faults from the assumptions (faults are unpredictable); this principle rejects the reduction of fault-tolerance to "correctness under all anticipated faults". The theory is applied to the range of examples and eventually extended to include considerations of fault-tolerance and timing, under scheduling on the limited resources. This document describes the motivation and the contents of the tutorial.

Logic of Proofs (LP) has been introduced in 2] as a collection of all valid formulas in the propositional language with labeled logical connectives t] ]() where t is a proof term with the intended reading of t] ]F as \t is a proof of F". LP is supplied with a natural axiom system, completeness and decidability theorems. LP may express some constructions of logic which have been formulated or/and interpreted in an informal metalanguage involving the notion of proof, e.g. the intuitionistic logic and its Brauwer-Heyting-Kolmogorov semantics, classical modal logic S 4, etc (cf. 2]). In the current paper we demonstrate how the intuitionistic propositional logic I nt can be directily realized into the Logic of Proofs. It is shown, that the proof realizability gives a fair semantics for I nt.

Chez Deleuze Albertine et la Chine sont promues au titre de mondes possibles. Une telle promotion ne trouve son statut conceptuel exact que dans la logique modale mathématisée comme celle de Prior munie des TWA de Geach, qui permet aussi de déceler chez Deleuze l'équivalent d'un modèle de Kripke.

This paper introduces and discusses three models of the linguistic representation of Future: a determinist model, a stochastic model and the model of True Prophetic knowledge. All three models coexist in natural languages and are represented both in their grammatical systems as well as in the text-building / discourse strategies speakers and authors apply to.

Kit Fine has proposed a new solution to what he calls 'a familiar puzzle' concerning modality and existence. The puzzle concerns the argument from the alleged truths 'It is necessary that Socrates is a man' and 'It is possible that Socrates does not exist' to the apparent falsehood 'It is possible that Socrates is a man and does not exist'. We discuss in detail Fine's setting up of the 'puzzle' and his rejection, with which we concur, of two mooted solutions to it. (One of these uses standard, Kripkean, notions, and the other rests on work done by Arthur Prior.) We set out, and reject, the philosophy of modality underlying Fine's new solution, and we defend an alternative response to the alleged puzzle. Our solution follows the work of David Wiggins in distinguishing between the sentential operator 'It is necessary that' and the predicate modifier 'necessarily'. We briefly provide this distinction with a possible-world semantics on which it is neither a necessary truth, in some sense, that Socrates exists nor true, in some sense, that Socrates necessarily exists.

Meta-programming languages provide infrastructure to generate and execute object programs at run-time. In a typed setting, they contain a modal type constructor which classifies object code. These code types generally come in two flavors: closed and open. Closed code expressions can be invoked at run-time, but the computations over them are more rigid, and typically produce less efficient residual object programs. Open code provides better inlining and partial evaluation of object programs, but once constructed, expressions of this type cannot in general be evaluated.Recent work in this area has focused on combining the two notions into a sound system. We present a novel way to achieve this. It is based on adding the notion of names from the work on Nominal Logic and FreshML to the λ -calculus of proof terms for the necessity fragment of modal logic S4. The resulting language provides a more fine-grained control over free variables of object programs when compared to the existing la...

Labeled transition systems are key structures for modeling computation. In this paper, we show how they lend themselves to ordinary logical analysis (without any special new formalisms), by introducing their standard first-order theory. This perspective enables us to raise several basic model-theoretic questions of definability, axiomatization and preservation for various notions of process equivalence found in the computational literature, and answer them using well-known logical techniques (including the Compactness theorem, Saturation and Ehrenfeucht games). Moreover, we consider what happens to this general theory when one restricts attention to special classes of transition systems (in particular, finite ones), as well as extended logical languages (in particular, infinitary firstorder logic). We hope that this puts standard logical formalisms on the map as a serious option for a theory of computational processes. As a side benefit, our approach increases comparability with several other existing formalisms over labeled transition systems (such as Process Algebra or Modal Logic). We provide some pointers to this effect, too.

The core of D. Lewis' many con tribution to philosophy, including his work in philosophical ontolo gy, intensional logic and semantics, probability and decision theory, and topics within philosophy of science as well as a distinguished philosophy of mind, dan ve understood as the development of a philosophical postion that is centered around his conception of Humean supervenience. If we accept the thesis that i t is physical science and not philosophical reasoning that will eventually arrive at the basic constituents of all matter pertaining in our world will supervene on the class of physical truht in the following sense: there are no truth in any compartment of our world that cannot be accounted for in terms of differences and similarities among those properties and external space-time relationsthat are fundamental to our world accordint to physical science.
Together the published essays challenge  aspects of Lewis' philosophy, posing new questions  and opening up new points of view in one of contemporary philosophy's most  ingenious and independent authors.

Rowman & Littlefield, Lanham, Maryland.

https://rowman.com/ISBN/9780742512009/Reality-and-Humean-Supervenience-Essays-on-the-Philosophy-of-David-Lewis

Memory logics are modal logics whose semantics is specified in terms of relational models enriched with additional data structure to represent memory. The logical language is then extended with a collection of operations to access and modify the data structure. In this paper we study their satisfiability and the model checking problems. We first give sound and complete tableaux calculi for the memory logic ML( k , r , e ) (the basic modal language extended with the operator r used to memorize a state, the operator e used to wipe out the memory, and the operator k used to check if the current point of evaluation is memorized) and some of its sublanguages. As the satisfiability problem of ML( k , r , e ) is undecidable, the tableau calculus we present is non terminating. Hence, we furthermore study a variation that ensures termination, at the expense of completeness, and we use model checking to ensure soundness. Secondly, we show that the model checking problem is PSpace-complete.

Resumo: O Autor examina as estruturas modais dos discursos sociais não-literários caracterizados pela
modalidade do saber (discursos noológicos) e dos discursos caracterizados pela modalidade do crer
(discursos doxológicos), procurando confrontá-las para verificar de que maneira suas diferenças
específicas implicam em diferentes visões de mundo, até mesmo antagônicas entre si.

Against the usual attribution of propositional logic to Chrysippus as its founder, it is our contention in this paper that a brief text in Analytics shows that Aristotle already knew the modus ponens, modus tollens and the affirmation of the consequent in a conditional statement. Although he does not name the corresponding rules, his terminology is similar to the one used by the Stoics. Our interpretation of the text fits in with today's propositional logic, without any need to introduce an additional rule with validity problems.

1972. Weak and Strong Completeness in Sentential Logic, Logique et Analyse 59/60, 429–34.  MR0337476 (49 #2245)

This is another study illustrating the fruitfulness of thinking of “logics” as three-part systems composed of a language, a semantics [or model theory] and a deductive system [or proof theory]. For simplicity we take a fixed language for sentential logic [or propositional logics] with a fixed standard two-valued semantics, but we “vary” deductive systems. In the 1960s when this paper was written, it was still widely assumed that a “logic” was “determined” by its theorems, by what it could “prove”. The vague assumption was that once the theorems were fixed, it was somehow automatic which conclusions were derivable from given premises.
The purpose of this paper is to give a method which weakens deriving power of a sentential logic while leaving proving power unchanged. In particular if the method is applied to a strongly complete logic the resultant will not have strong completeness but it will retain weak completeness. Moreover, because of the nature of the method two added facts obtain.
First, weak completeness of the resultant is always an obvious corollary to weak completeness of the operand, so that no new completeness proof need be constructed. Second, failure of strong completeness in the resultant is always obvious, so no multi-valued matrices need be constructed. The method applies to all sentential logics formulated using only axiom schemes and schematically statable rules. These results reaffirm, generalize, and simplify a result of Hiz [Journal of Symbolic Logic, 24 (1959), pp. 193-202].

Resumen El propósito de este artículo es mostrar el modo en que Borges, en su relato Tigres azules, desarrolla varias ideas interesantes en torno a la lógica, el lenguaje y las matemáticas. El punto de partida es el escepti-cismo borgeano sobre la capacidad de la lógica clásica para abordar el problema de la verdad y los mundos imposibles. Se defiende que ob-jetos inconsistentes e, incluso, autocontradictorios no necesariamente dan lugar a mundos física o lógicamente imposibles. Se sugiere que las paradojas que Borges construye en el cuento no son paradojas de autorreferencia, sino variantes de la paradoja de Moore y de las para-dojas de implicación material, por lo que para superarlas se requiere un enfoque no-clásico que neutralice ECQ, esto es, un sistema de lógica paraconsistente. Abstract Tigres azules of J. L. Borges. Logic, Truth and Impossible Worlds. The aim of this text is show how Borges, in his story Tigres azules, develops several interesting ideas about logic, language and mathematics. The starting point is Borgesian skepticism about the ability of classical logic to take the problem of truth and impossible worlds. It is defended that inconsistent and even self-contradictory objects do not necessarily give rise to physically or logically impossible worlds. It is suggested that the paradoxes that Borges constructs in the story

████████████████████████████████████████████████████████ 0.INTRODUCCIÓN 1.Una de las características más relevantes del método de pensar mediante mundos posibles es que permite plantear los problemas del mundo real de manera sistemática, escrupulosa y ordenada. Imaginar mundos posibles es proponer un recurso argumentativo, también es realizar un experimento en el pensamiento, en el que comparamos las cosas de nuestro cosmos con orbes ideales, por ejemplo, un planeta sin rozamiento en física o un mercado con información perfecta en economía. 1 2.¿Cómo imaginan los lógicos modales este multiuniverso de mundos posibles? Además de contar con una concepción de la realidad existente, de los mundos posibles y de las lógicas mismas; tanto los lógicos como los filósofos de la lógica utilizan metáforas y otros recursos gráficos para expresar sus concepciones modales. Si hacemos una brevísima crónica mencionando algunos hitos importantes de la historia de la lógica, encontraremos que muchas veces los filósofos modales explican sus concepciones sobre los mundos posibles mediante recursos gráficos. Carlos Areces (2011) considera que los lógicos piensan mediante gráficos. 2 Nuestra hipótesis es que analizar las metáforas, los diagramas y modelos desarrollados por estos autores puede iluminarnos sobre sus concepciones acerca de los mundos posibles.

La publication des Soixante-quinze feuillets de Marcel Proust conduit à relire "Contre Sainte-Beuve". Et la leçon des deux lectures est que, dans l'anamorphose demandée pour comprendre "A la Recherche du Temps perdu", l'édition augmentée de "Proust et les signes",  seule, donne le bon point de vue.

This paper presents a two-dimensional modal logic for reasoning about the changing patterns of knowledge and social relationships in networks organised on the basis of a symmetric &#x27;friendship&#x27;relation, providing a precise language for exploring &#x27;logic in the community&#x27;[11]. Agents are placed in the model, allowing us to express such indexical facts as &#x27;I am your friend&#x27;and &#x27;You, my friends, are in danger&#x27;.

La  semántica  de  mundos  posibles  (SMP)  se  articula  como  una  de  las teorías  lógicas  y  filosóficas  más  importantes  de  nuestro  tiempo.  Los  célebres  mundos posibles  forman  y  han  formado  parte  en  las  últimas  décadas  de  la  jerga  filosófica  de autores  de  la  llamada  corriente  analítica.  Se  ha  tratado,  además,  de  una  teoría  apta para  el  tratamiento  y  abordaje  de  múltiples  tópicos  y  problemas  que  han  aquejado  a los  filósofos  de  todos  los  tiempos.  Con  el  presente  artículo,  tendremos  como  foco  de atención  el  origen,  preparación  y  consolidación  de  SMP  y  sus  nociones  centrales  de la  mano  de  algunos  de  sus  principales  gestores.

Questa tesi intende presentare l’implicazione connessiva da due punti di vista: uno logico (parte I) e uno storico (parte II). Nell’introduzione si darà un rapido sguardo ai paradossi dell’implicazione materiale e si indicheranno alcuni tentativi di soluzione: in particolare, si presenteranno i vari approcci connessivi, con particolare attenzione per quello di Graham Priest. Nel capitolo 1 della parte I, si presenterà sintassi e semantica della logica connessiva PrC, così come è esposta in Priest [47], servendosi dei modelli kripkeani. Si mostreranno anche alcune proprietà peculiari della nozione di conseguenza logica connessiva: essa è transitiva e chiusa sotto modus ponens ma non è riflessiva, né monotona né chiusa sotto sostituzione uniforme. I principi connessivi sono validi in tale semantica, però delle tesi di Boezio sono valide solo le versioni deboli, ovvero quelle che hanno per connettivo principale un’implicazione materiale. Verrà poi definita una nuova semantica per PrC, equivalente alla precedente, ma la cui relazione di accessibilità è esplicitata ed è una relazione di equivalenza. Inoltre, si mostrerà come sia possibile, tramite una funzione di traduzione e la sua inversa, tradurre, salva veritate, formule di PrC in formule della logica modale S5 e viceversa. Nel capitolo 2, verrà rapidamente descritto un calcolo di sequenti etichettati per S5 e si accennerà alle proprietà del suddetto calcolo. In seguito, si definirà un calcolo etichettato per PrC (rispetto alla semantica con relazione di equivalenza), chiamato G3.PrC: se ne presenteranno le regole e si dimostreranno i due risultati fondamentali di validità e completezza per G3.PrC. Nella parte II, analizzeremo il passo degli Analitici Primi nel quale alcuni logici rintracciano alcune delle più famose formule connessive. Dopo un commento del passo e una rapida panoramica su alcune delle più autorevoli esegesi del brano, si esporrà una nuova interpretazione del testo, che si basa sui capitoli degli Analitici che fanno da contesto al passaggio in questione: lo Stagirita vorrebbe dimostrare che una conclusione vera non può seguire per necessità da premesse false. Si motiveranno, sulla base della filosofia aristotelica, le due tesi che fungono da base alla nuova interpretazione proposta: (i) le regole logiche cui Aristotele fa riferimento sono semantiche (in termini moderni: lo Stagirita starebbe parlando della nozione di conseguenza logica); (ii) con le due lettere A e B, Aristotele intende le due premesse di un sillogismo (A) e la conclusione (B) e non due enunciati qualsiasi (non sarebbero, dunque, variabili enunciative tout court). Infine, si analizzeranno le tre figure sillogistiche per saggiare la validità del ragionamento aristotelico nella nuova esegesi data, mostrando come, sebbene insorgano alcune difficoltà, sia possibile affermare che la nuova interpretazione valida l’argomento dello Stagirita.

Le genre littéraire « science-fiction » (ou « SF »), qui semble stimuler la pensée à divers titres, est pris entre une contrainte étrange (la thématisation presque folklorique de la « technoscience » future) et une variabilité infinie tout autour de cette contrainte. Nous nous proposons d’analyser les arcanes de ce genre à la lumière de la notion, empruntée à A. Badiou, de « procédure de vérité », qui est un puissant modèle pour ce type de tensions productives. Conformément à cette lecture, qui suggère que la SF cache, en un sens, un mystérieux « cœur » procédural, nous proposons de modéliser une partie de ce noyau fuyant par la notion, empruntée à B. Stiegler, de « désajustement », notion qui caractérise le rapport périodiquement et systématiquement problématique du technique et du social. Nous élaborons ensuite deux constats. Premièrement, la guerre froide théorique entre la « philosophie analytique » (méthodologiquement centrée sur la logique mathématique) et la « philosophie continentale » (tout le reste de la philosophie mondiale contemporaine !) fait toujours rage de nos jours : notamment du fait de l’alliance « politique » de la logique et de l’informatique. Deuxièmement, le rêve (propre aux analytiques) de l’« intelligence artificielle » a vécu et les omniprésentes retombées technologiques de l’informatique (dont l’internet), qui sont censées jouer comme puissant argument de marketing pro-analytique, ne sont en fait qu’un triste et trompeur lot de consolation, cachant une agonie théorique désespérée qui se transforme en rage pratique méthodique. Partant de ces deux constats et en nous appuyant sur l’analyse de l’articulation « fantasme/perversion » proposée par J. Lacan et précisée par S. Žižek (comme symétrisation « a<>$ » du mathème « $<>a »), nous proposons de voir dans le genre SF, lu comme « désajustement onirisé », un prisme possible et puissant, révélateur d’une bataille théorique capitale de cette guerre froide philosophique. Dans cette bataille, peu visible sinon, qui tourne autour du statut théorique et politique du « rêve », il y va de l’autorité, du fantasme et de la perversion d’un « complexe logico-informatique » (tristement comparable au « complexe militaro-industriel »), ainsi que de son projet, tout aussi dangereux qu’insistant, d’effacer tout à fait du champ du pensable et de l’agir la notion mathématique et philosophique de « structure ».

Davidson offers a coherentist account of knowledge (though not, despite his title, a coherence theory truth). But his defense of coherentism fails; indeed, his famous Omniscient Interpreter argument turns out to be a simply modal fallacy!

Adapted from the latter part of chapter 3 of EVIDENCE AND INQUIRY, this paper was published in Spanish in 1999.

The well-known necessary-consequence/necessary-consequent ambiguity—a species of segmentation, scope, and structural ambiguities—is found in conditional sentences such as:

(A) If zero is oblong, then necessarily some square is oblong.

A can read as expressing a proposition to the effect that “some square is oblong” is a necessary consequence of “zero is oblong”. This necessary-consequence segmentation parses A with the adverb as part of the discontinuous modal connective ‘if … then necessarily’. The consequent ‘some square is oblong’ is non-modal. Alternatively, the adverb can be taken instead as part of the consequent yielding the necessary-consequent segmentation: A can read as expressing roughly that the modal proposition “necessarily some square is oblong” is a material consequence of “zero is oblong”. Brackets indicate segmentation:

Necessary-consequence segmentation
[If] zero is oblong, [then necessarily] some square is oblong.

Necessary-consequent segmentation
If zero is oblong, then [necessarily some square is oblong].

Similar confusing ambiguities arise in logic texts where ‘valid’, ‘logical’, ‘necessary’, ‘sound’, ‘derivable’, and the like occur before ‘conclusion’, ‘inference’, ‘deduction’ and the like.

This paper, supplementing [1], compares corresponding segmentations of various conditional sentences. E.g., taking both “necessities” as logical, the following have different truth-values—first true, second false. The second implies the first.

[If] Twain is Clemens, [then necessarily] Clemens is Twain.
If Twain is Clemens, then [necessarily Clemens is Twain].

The first says that “Clemens is Twain” follows logically from “Twain is Clemens”; the second that “Clemens is Twain” is logically necessary if Twain is Clemens.

A modal logic with non-traditional predication theory is laid out that allows one to talk in a meaningful way about nonexistent objects and partially specified fictional objects. Description theory with an existence predicate is used for giving examples.

The logic uses an extension and an anti-extension for predicates; it remains bivalent and is not paraconsistent. It less expressive than, similar, and closely related to Priest's account and other uses of partial logics in the tradition of Belnap.

The author analyses the validity of a certain variation of Anselm's "ontological argument", namely the modal-logical version from Charles Hartshorne (1897-2000). He firstly studies the origin of Hartshome's arguments, whose
starting point is an interpretation of Anselm; secondly, the modal-logical argument from Hartshorne will be presented together with its presuppositions and implications. Finally, the author proposes an evaluation of Hartshorne's approach.

One of the most pressing objections against Divine simplicity is that it entails what is commonly termed a ‘modal collapse’, whereby all contingency is eliminated and every true proposition rendered necessarily true. In this paper, I show that a common form of this argument is in fact famously invalid and examine two ways in which the opponent of Divine simplicity might try to repair the argument. I conclude that there is no clear way of repairing the argument that does not beg the question against the doctrine of Divine simplicity.

This work (hereafter OCP) is comparable in many ways to the Cambridge Dictionary of Philosophy (CDP). Both are modeled on the dictionary format; both are multi-authored; both are very popular; both are in second edition. For many purposes, OCP and CDP are interchangeable. However, Cambridge charges about half of the price Oxford wants. I have spent many happy hours with both. I own both editions of each. Each has its excellent and useful entries, and each has its mediocre or useless entries. In OCP, ignoratio elenchi exemplifies the former; axiom the latter.
The axiom entry is one of the shortest in the book, 70 words; the entry Montague, Richard is twice as long. Some of the entries are more than ten times as long. The axiom entry gives a dogmatic version of the evasive conventionalist view with no mention of epistemic issues such as certainty or self-evidence, nothing on various axiom/postulate distinctions, and nothing on the views of Aristotle, Frege, or Hilbert. Its sole reference is the 1974 edition of Quine’s Methods of Logic, hardly a locus classicus on the topic.
After comparing many of the logic entries, I would conclude that those in the CDP are usually better. The two entries on Church's thesis are written by equally qualified experts. Both imply correctly that Church's thesis is not a proposition admitting of mathematical proof or disproof in the usual sense: it is a proposal to "identify" the pre-theoretic intuitive concept of "effectively calculable function" with the mathematically precise number-theoretic property "recursiveness". The CDP entry is several times as long as the OCP and it is much more informative concerning the historical and philosophical importance of Church's thesis. A somewhat different comparison applies to the entries titled Church, Alonzo. Again, the CDP entry is much longer and much more informative than the OCP. Both entries are flawed.

FROM THE BACK COVER: What is the essential nature of meaning? . . . . . This book answers by examining interpretive theories from the past and present. It finds that an historical struggle with meaning has been underway since the Reformation, a struggle that reaches crisis proportions in the 20th century. On the one hand, this crisis is mollified by Heidegger's hermeneutical phenomenology, which argues that we are always already in a meaningful relationship to the objects of the world. On the other hand, this crisis is exacerbated when phenomenology, structuralism, and aesthetic theory directly make meaning into an object of study. . . . . . . . . These historical developments culminate with the psychoanalyst Jacques Lacan, whose non-hermeneutical phenomenology delimits a cause of meaning said to be closely linked to the core of subjectivity. Intriguingly, Lacan's work reveals meaning to be sexual in nature. By integrating his notion of sexual difference with his work in discourse theory and topology, this book demonstrates how the subject's struggle with meaning can be suspended.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GENERAL DESCRIPTION: Broadly speaking, the majority of books on Jacques Lacan focus on the earlier periods of his career. They also tend to target the psychoanalytic clinical community, or else discuss his work in various political, social, and cultural contexts. But in almost all cases these books refrain from a detailed exegesis of his actual texts. They instead prefer to comment on his theoretical apparatus as a whole before turning to its practical implications. . . . . . This book positions itself against this grain. Firstly, it closely analyzes some half-dozen key Lacanian texts. This analysis is organized under a single thematic – the question of meaning – in order to advance the reader's understanding of the trajectory of Lacan's thought across his entire career, as well as to promote the book's thesis that the field of meaning can be suspended. Accordingly, an initial chapter takes up the hermeneutical tradition from Flacius onward. This is then supplemented by a chapter which surveys phenomenological, structuralist and aesthetic theories of meaning and their differing methods of textual analysis. Together these two chapters provide a unique context for the sustained analysis of Lacan's texts which begins in the third chapter, an analysis that forms the bulk of the book's content. This contextualization potentially widens the book's appeal to any scholar wishing to explore his relationship to those textual objects he interacts with on a daily basis. And because this book assumes the reader has little to no familiarity with Lacan, the reader will find patient explanations of the basics of his theories before slowly being led up to the more difficult theories of his late years. Again the argument is that Lacan has something to offer all scholars. His work is not just reserved for psychoanalysts. . . . . . It is with his late theories that the serious student of Lacan will find the book's most original contribution. For in the fourth chapter a detailed account is provided of how Lacan derived his infamous formulae of sexuation from Aristotelian logic. These formulae are then extensively discussed against the backdrop of interpretive theory and textual analysis, showing how these formulae capture much more than just the difference between the sexes. Strikingly, this difference is also found to run through meaning itself, something the final chapter aims to demonstrate. It does this by amalgamating three key components of late-Lacan: sexuation, discourse theory and his use of topological spaces. This amalgamation is a first in the literature. But this amalgamation is not just useful in demonstrating the book's thesis. It further suggests how seemingly divergent aspects of late-Lacanian theory can be made to work together.

The use of ‘‘levels of abstraction’’ in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section ‘‘Some Definitions and Preliminary Examples’’ the nature and applicability of the epistemological method of levels of abstraction is clarified. In section ‘‘A Classic Application of the Method of Abstraction’’, the philosophical fruitfulness of the new method is shown by using Kant’s classic discussion of the ‘‘antinomies of pure reason’’ as an example. In section ‘‘The Philosophy of the Method of Abstraction’’, the method is further specified and supported by distinguishing it from three other forms of ‘‘levelism’’: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems.

[If you refer to the paper, please send me a message.] The textbook-like history of analytic philosophy is a history of myths, re-ceived views and dogmas. Though mainly the last few years have witnessed a huge amount of historical work that aimed to reconsider our narratives of the history of ana-lytic philosophy there is still a lot to do. The present study is meant to present such a micro story which is still quite untouched by historians. According to the received view Kripke has defeated all the arguments of Quine against quantified modal logic and thus it became a respectful tool for philosophers. If we accept the historical interpreta-tion of the network between Quine, Kripke and modal logic, which is to be presented here, we have to conclude that Quine’s real philosophical animadversions against the modalities are still on the table: though Kripke has provided some important (formal-logical) answers, Quine’s animadversions are still viable and worthy of further considera-tion.