Generalizations of partial meet contraction are introduced that start out from the observation that only some of the logically closed subsets of the original belief set are at all viable as contraction outcomes. Belief contraction should proceed by selection among these viable options. Several contraction operators that are based on such selection mechanisms are introduced and then axiomatically characterized. These constructions are more general than the belief base approach. It is shown that partial meet contraction (...) is exactly characterized by adding to one of these constructions the condition that all logically closed subsets of the belief set can be obtained as the outcome of a single (multiple) contraction. Examples are provided showing the counter-intuitive consequences of that condition, thus confirming the credibility of the proposed generalization of the AGM framework. (shrink)

We can often specify how we would contract by a certain sentence by saying that this contraction would coincide with some other contraction that we know how to perform. We can for instance clarify that our contraction by p&q would coincide with our contraction by p, or by q, or by {p, q}. In a framework where the set of potential outcomes is known, some contractions are “self-evident” in the sense that there is only one serious (...) candidate that can be the outcome of such a contraction. Contraction by a specific contractee (sentence or set of sentences to be contracted) is bootstrapped if it is specified by saying that it coincides with some such self-evident contraction. For a wide range of (multiple) contraction operators, contractions by any contractee can be bootstrapped. This means that the selection mechanism (selection function, incision function, etc.) can be replaced by a function called a bootstrapping selector that assigns to each contractee some “self-evident” contractee that yields the same outcome. With bootstrapping we can eliminate traditional extralogical components in contraction (e.g., selection functions) and replace them by bootstrapping selectors that reflect more closely the ways in which we actually reason and argue about belief contraction. (shrink)

Introduction -- "Every Legitimate Government is Republican": Rousseau's Debt to and Departure from Montesquieu on Republicanism -- What if There is no Legislator? Rousseau's History of the Government of Geneva -- Rousseau's Republican Citizenship: The Moral Psychology of The Social Contract -- Rousseau's negative liberty: Themes of domination and skepticism in The Social Contract -- Rousseau's Ancient Ends of Legislation: Liberty, Equality (& Fraternity) -- Property and Possession in Rousseau's Social Contract -- Political Equality Among Unequals -- On the Primacy (...) of Peoplehood: Nations and Nationalism in Rousseau's Social Contract -- Rousseau on Voting and Electoral Laws -- Rousseau and the puzzle of the Roman Republic -- Rousseau's Case against Democracy -- Rousseau's Dilemma or "Of Civil Religion" -- Entreating the Political: Politics and Theology in Rousseau's Social Contract -- Civil Religion and Political Unity: Social Contract 4.8. (shrink)

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.

This essay demonstrates proof-theoretically the consistency of a type-free theoryC with an unrestricted principle of comprehension and based on a predicate logic in which contraction (A (A B)) (A B), although it cannot holds in general, is provable for a wide range ofA's.C is presented as an axiomatic theoryCH (with a natural-deduction equivalentCS) as a finitary system, without formulas of infinite length. ThenCH is proved simply consistent by passing to a Gentzen-style natural-deduction systemCG that allows countably infinite conjunctions and (...) in which all theorems ofCH are provable.CG is seen to be a consistent by a normalization argument. It also shown that in a senseC is highly non-extensional. (shrink)

This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both (...) in general and under various natural constraints. (shrink)

In the most common approaches to belief dynamics, states of belief are represented by sets that are closed under logical consequence. In an alternative approach, they are represented by non-closed belief bases. This representation has attractive properties not shared by closed representations. Most importantly, it can account for repeated belief changes that have not yet been satisfactorily accounted for in the closed approach.

A logic is said to be contraction free if the rule from A→(A→B) to A→B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be robustly (...) class='Hi'>contraction free if there is no such operator expressible in its language. We show that a large class of finitely valued logics are each not robustly contraction free, and demonstrate that some other contraction free logics fail to be robustly contraction free. Finally, the sublogics of Łω (with the standard connectives) are shown to be robustly contraction free. (shrink)

The outcome set of a belief change operator is the set of outcomes that can be obtained with it. Axiomatic characterizations are reported for the outcome sets of the standard AGM contraction operators and eight types of base-generated contraction. These results throw new light on the properties of some of these operators.

As a fundamental feature of our existence, melancholy is an inescapable characteristic of our ontological constitution. However, there is a distance between the clinical condition of melancholia and the human feeling, the capacity to feel sorrow and nostalgia. In this sense, melancholy and melancholia are similar but different. During the XIX century just few among philosophers have tried to described melancholy in terms of disorder, using philosophical tools rather than clinical definitions, drifting the accent from melancholy to melancholia. Hegel has (...) been one of them, one that has seen inside the depth of human being in order to understand and describe what is the “the nocturnal point of the contraction”: melancholia, in terms of clinical condition. The philosophical exploration of madness and its parameters is essentially an ontological project: this is how Hegel addresses “the Concept of derangement in general” and melancholia in particular, anticipating most of Freud’s consideration on this topic. (shrink)

There is an apparent contradiction within Levinas’s work: on the one hand, Levinas upholds an account of existence that seemingly requires a creation narrative, while maintaining, on the other hand, that an account of the ethical import of that existence needs no recourse to the divine. This seeming contradiction results from a fundamental misunderstanding concerning Levinas’s account of creation and its logical consequences concerning the divine. This paper aims to clarify this misunderstanding by exploring the similarities between and influence of (...) F. W. J. Schelling’s work on Levinas’s thereby providing a more complete picture of both author’s respective accounts of genesis and the existence of God. (shrink)

In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet (...) class='Hi'>contraction over that theory. The purpose of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open. (shrink)

Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, G¨ardenfors and Makinson (AGM) [1] describes postulates which a rational belief revision and contraction operations should satisfy. The AGM postulates have been (...) perceived as characterising idealised rational reasoners, and the corresponding belief change operations are considered unsuitable for implementable agents due to their high computational cost [3]. The main result of this paper is showing that an efficient (linear time) belief contraction operation nevertheless satisfies all but one of the AGM postulates for contraction. This contraction operation is defined for a realistic rule-based agent which can be seen as a reasoner in a very weak logic; although the agent’s beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of contraction for our agent. (shrink)

The Fitzgerald-Lorentz contraction hypothesis, proposed as an explanation of the Michelson-Morley result, fails to account for the Kennedy-Thorndike result. Hence, Grünbaum argues, the hypothesis has been falsified. However, the contraction hypothesis as formulated by Lorentz is false for the very fundamental reason that it entails a contradiction, namely, the consequence that light waves must have a variable velocity along what by definition is taken to be a rest length. Furthermore, the attempt to resolve this contradiction by coupling the (...) Fitzgerald-Lorentz contraction with the hypothesis that clock rates are a function of velocity, is open to a sound, methodological objection. The Michelson-Morley result is fully satisfied, provided only that the lengths of the interferometer arms, in the longitudinal and transverse positions, are thought to be related to one another in a certain ratio, and this ratio may be interpreted as a contraction in both arms. Since this twofold contraction hypothesis suffices to explain both the Michelson-Morley and the Kennedy-Thorndike results, and since it entails no contradiction, there is no need to correct both the length of rods and the rate of clocks. Therefore, the combined clock-rod hypothesis, and with it the Fitzgerald-Lorentz contraction hypothesis, must be rejected. (shrink)

Background: The proprioceptive neuromuscular facilitation reciprocal contraction pattern has the potential to increase the maximum rate of torque development. However, it is a more complex resistive exercise task and may interfere with improvements in the maximum rate of torque development due to motor skill learning, as observed for unidirectional contractions. The purpose of this study was to examine the cost-benefit of using the PNF exercise technique to increase the maximum rate of torque development.Methods: Twenty-six participants completed isometric maximal extension-to-flexion (...) or flexion-only contractions at the wrist. Ten of the assigned contractions were performed on each of three sessions separated by 48-h for skill acquisition. Retention was assessed with 5 contractions performed 2-weeks after acquisition. Torque and surface electromyographic activity were analyzed for evidence of facilitated contractions between groups, as well as alterations in muscle coordination assessed across test sessions. The criterion measures were: mean maximal isometric wrist flexion toque; the maximal rate of torque development ; root-mean-square error variability of the rate of torque versus torque phase-plane; the rate of wrist flexion muscle activation ; a coactivation ratio for wrist flexor and extensor sEMG activity; and wrist flexor electromechanical delay.Results: There were no significant differences between groups with respect to maximal wrist flexion torque, dτ/dtmax or RMSE variability of torque trajectories. Both groups exhibited a progressive increase in maximal strength and in dτ/dtmax from the start of acquisition to retention. RMSE was lowest after a 2-week rest interval. There were no significant differences between groups in the rate of muscle activation or the coactivation ratio. There was a reduction in coactivation that was retained after a 2-week rest interval. Alternatively, EMD was significantly greater in the experimental group across all sessions. However, both groups had a similar pattern of improvement to the third consecutive day of testing, but returned close to baseline value after the 2-week rest interval.Discussion: The wrist extension-to-flexion contraction pattern did not result in a greater maximal rate of torque development than simple contractions of the wrist flexors. There was no difference between groups with respect to motor skill learning. The main adaptation in neuromotor control was a decrease in coactivation, not the maximal rate of muscle activation. (shrink)

This paper offers a particular intuitionistic negation completion of Urquhart's system C resulting in a super-intuitionistic contractionless propositional logic equivalent to Dummett's LC without contraction.

Summary A recurrent theme in the philosophical literature on the special theory of relativity is the question as to the reality of the Lorentz contraction. It is often suggested that there is a difference between the Lorentz-FitzGerald contraction in the pre-relativistic ether theory and the Lorentz contraction from special relativity in the sense that the former is a real contraction of matter conditioned by dynamical laws, whereas the latter should be compared with the apparent changes in (...) the size of objects when the perspective of the observer changes. It is here shown, however, that the same laws of nature which are operative in the Lorentz-FitzGerald contraction also condition the relativistic Lorentz contraction. The relevant distinction therefore is not between the reality of the two contractions. What is at issue is the difference in explanatory structure of the pre-relativistic theory on the one hand and the special theory of relativity on the other. In the course of the argument the question of the conventionality of simultaneity is also discussed. (shrink)

In this paper, a semantics for predicate logics without the contraction rule will be investigated and the completeness theorem will be proved. Moreover, it will be found out that our semantics has a close connection with Beth-type semantics.

The aim of this paper is to show that the implicational fragment BKof the intuitionistic propositional calculus (IPC) without the rules of exchange and contraction has the finite model property with respect to the quasivariety of left residuation algebras (its equivalent algebraic semantics). It follows that the variety generated by all left residuation algebras is generated by the finite left residuation algebras. We also establish that BKhas the finite model property with respect to a class of structures that constitute (...) a Kripke-style relational semantics for it. The results settle a question of Ono and Komori [OK85]. (shrink)

This article presents Catherine Malabou and Alain Badiou as theorists of contraction and its related operations of self-reflexivity and infinite iteration. Trading on these commonalities, the article hopes to draw out Malabou’s and Badiou’s respective formalist commitments. On Badiou’s side, it sharpens the question of what is at stake in something as regulated as a “procedure”; on Malabou’s, it recognizes formal stakes to plasticity that often go unrecognized because of her penchant for biology. The article then concludes with a (...) broad comparison of these two thinkers in terms of their accounts of potential and imagines the critiques each might leverage against the other. Where Malabou might well regard Badiou to be too tightly constraining the shape of the future, Badiou is likely to find in Malabou one more instance of a naïve democratic materialism. (shrink)

Evidence is reviewed here that inositol (1, 4, 5) trisphosphate (Ins P3) is a key signal in translating the electrophysiological event in muscle stimulation into the molecular‐mechanical events of contraction. Not least, these findings raise questions about the suitability of the term ‘second messenger’.

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour (...) of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. (shrink)

Mordechai Rotenberg, who is well known for his work on the pessimistic impact of Protestant ethics on the Western social sciences, presents here a systematic study derived from, and based on, Judeo-Hasidic ethics. Proceeding from the cabalistic-Hasidic concept of contraction (tzimtsum), according to which God's voluntary withdrawal into Himself to evacuate space for the world serves as a model for human behavior, Professor Rotenberg shows that it is not personal-social construction, but self- and social contraction, that explains how (...) the "is" and the "ought" of society are developed and maintained. (shrink)

We develop a vector space semantics for verb phrase ellipsis with anaphora using type-driven compositional distributional semantics based on the Lambek calculus with limited contraction of Jäger. Distributional semantics has a lot to say about the statistical collocation based meanings of content words, but provides little guidance on how to treat function words. Formal semantics on the other hand, has powerful mechanisms for dealing with relative pronouns, coordinators, and the like. Type-driven compositional distributional semantics brings these two models together. (...) We review previous compositional distributional models of relative pronouns, coordination and a restricted account of ellipsis in the DisCoCat framework of Coecke et al. :1079–1100, 2013). We show how DisCoCat cannot deal with general forms of ellipsis, which rely on copying of information, and develop a novel way of connecting typelogical grammar to distributional semantics by assigning vector interpretable lambda terms to derivations of LCC in the style of Muskens and Sadrzadeh Logical aspects of computational linguistics, Springer, Berlin, 2016). What follows is an account of ellipsis in which word meanings can be copied: the meaning of a sentence is now a program with non-linear access to individual word embeddings. We present the theoretical setting, work out examples, and demonstrate our results with a state of the art distributional model on an extended verb disambiguation dataset. (shrink)

ABSTRACT We consider evolution of knowledge bases caused by a sequence of basic steps of acquisition of a new information, either consistent or inconsistent with the original system. To make this process comply with the Principe of Minimal Change, a special evidence metric is introduced for measuring distance between states of knowledge. Then a novel semantics of knowledge bases is developed suggested by the heuristics of weighted maximally consistent subsets. The latter is efficiently applied to the processes of consistent and (...) inconsistent acquisition of knowledge, belief revision and contraction. (shrink)

The way we represent and perceive time has crucial implications for studying temporality in conscious experience. Contrasting positions posit that temporal information is separately abstracted out like any other perceptual property through specialized mechanisms or that time is represented through the temporality of experiences themselves. To add to this debate, we investigate alterations in felt time in conditions where only conscious visual experience is altered through perceptual switches while a bistable figure remains physically unchanged. We predicted that if perceived time (...) is a function of temporally evolving conscious content, then a break in it (here via a perceptual switch) would also lead to a break in felt time. In three experiments, we showed participants a Necker cube that was manipulated to induce a perceptual switch (experiments 1(a) and 1(b)) or left to switch on its own (experiment 2). We asked participants to report both perceptual switches and felt durations (experiments 1(a) and 2) or only estimate time (experiment 1(b)). Over these three experiments, we find evidence of contraction of felt time in trials with a perceptual switch, consistent with the idea that perceived time is a function of temporally evolving conscious experience. Additionally, we present a phenomenological demonstration to support our empirical data. Overall, the study provides evidence for temporal mirroring and isomorphism in visual experience, arguing for a link between the timing of experience and time perception. (shrink)

We show that the elimination rule for the multiplicative (or intensional) conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL m (the multiplicative fragment of Linear Logic) and RMI m (the system obtained from LL m by adding the contraction axiom and its converse, the mingle axiom.) An exception is R m (the intensional fragment of the relevance logic R, which is LL m together with the contraction axiom). Let SLL m and SR m (...) be, respectively, the systems which are obtained from LL m and R m by adding this rule as a new rule of inference. The set of theorems of SR m is a proper extension of that of R m , but a proper subset of the set of theorems of RMI m . Hence it still has the variable-sharing property. SR m has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLL m relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLL m corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element (in the first case we get the system BCK m , in the second - the system SR m ). Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts. (shrink)

We show that the elimination rule for the multiplicative conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL$_m$ and RMI$_m$ An exception is R$_m$. Let SLL$_m$ and SR$_m$ be, respectively, the systems which are obtained from LL$_m$ and R$_m$ by adding this rule as a new rule of inference. The set of theorems of SR$_m$ is a proper extension of that of R$_m$, but a proper subset of the set of theorems of RMI$_m$. Hence it still (...) has the variable-sharing property. SR$_m$ has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLL$_m$ relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLL$_m$ corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element. Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts. (shrink)

In [1], we established Gentzenizations for a good range of relevant logics with distribution, but, in the process, we added inversion rules, which involved extra structural connectives, and also added the sentential constantt. Instead of eliminating them, we used conservative extension results to relate them back to the original logics. In [4], we eliminated the inversion rules andtand established a much simpler Gentzenization for the weak sentential relevant logicDW, and also for its quantificational extensionDWQ, but a restriction to normal formulae (...) (defined below) was required to enable these results to be proved. This method was quite general and hope was expressed about extending it to other relevant logics.In this paper, we develop an innovative method, which makes essential use of this restriction to normality, to establish two simple Gentzenizations for the normal formulae of the slightly weaker logic B, and then extend the method to other sentential contraction-less logics. To obtain the first of these Gentzenizations, for the logicsBandDW, we remove the two branching rules (F&) and (T∨), together with the structural connective ‘,’, to simplify the elimination of the inversion rules andt. We then eliminate the rules (T&) and (F∨), thus reducing the Gentzen system to one containing only ˜ and → and their four associated rules, and reduce the remaining types of structures to four simple finite types. Subsequently, we re-introduce (T&) and (F∨), and also (F&) and (T∨), to obtain the second Gentzenization, which contains ‘,’ but no structural rules. (shrink)

In [1], we established Gentzenizations for a good range of relevant logics with distribution, but, in the process, we added inversion rules, which involved extra structural connectives, and also added the sentential constantt. Instead of eliminating them, we used conservative extension results to relate them back to the original logics. In [4], we eliminated the inversion rules andtand established a much simpler Gentzenization for the weak sentential relevant logicDW, and also for its quantificational extensionDWQ, but a restriction to normal formulae (...) (defined below) was required to enable these results to be proved. This method was quite general and hope was expressed about extending it to other relevant logics.In this paper, we develop an innovative method, which makes essential use of this restriction to normality, to establish two simple Gentzenizations for the normal formulae of the slightly weaker logic B, and then extend the method to other sentential contraction-less logics. To obtain the first of these Gentzenizations, for the logicsBandDW, we remove the two branching rules (F&) and (T∨), together with the structural connective ‘,’, to simplify the elimination of the inversion rules andt. We then eliminate the rules (T&) and (F∨), thus reducing the Gentzen system to one containing only ˜ and → and their four associated rules, and reduce the remaining types of structures to four simple finite types. Subsequently, we re-introduce (T&) and (F∨), and also (F&) and (T∨), to obtain the second Gentzenization, which contains ‘,’ but no structural rules. (shrink)

Many women are initially unable to contract the pelvic floor muscles (PFMs) properly, activating other muscle groups before, or instead of, PFM. Numerous authors have proved that biofeedback can be an ideal tool supporting learning of the PFM contraction. However, there is currently a lack of scientific data on how many biofeedback sessions are necessary in this educational process. In this study we aimed at assessing the effects of one-time electromyography (EMG) biofeedback session on the order in which PFM (...) are activated (so called firing order) during conscious contractions in relation to selected synergistic muscles in pregnant, continent women. A randomized controlled trial was conducted in 90 healthy nulliparous women with uncomplicated pregnancies and without diagnosed urinary incontinence. We divided the participants into a biofeedback group (50) and a control group (40). They were, respectively: 30 ± 4 and 30 ± 4 years old, at their 23 ± 5 or 25 ± 7 week of gestation and presented 23 ± 5 or 24 ± 5 kg/m2 BMI value (M + SD). Surface EMG with vaginal probes has been used to assess the PFM firing order in selected tasks: in five 3-s maximal contractions (quick flicks), five 10-s contractions, and in a 60-s contraction (static hold). We used the 1–5 scale, where “1” meant the best score, awarded when PFM was activated first in order. The most important finding of our study is that a single EMG biofeedback substantially improved the PFM contractions in pregnant women. First, when applying one-time biofeedback session, more women maintained correct technique or improved it in the second assessment, compared to the control group (73 vs. 65%). Secondly, using the quantitative and qualitative analysis with the Chi-square McNamara B/C test, in the biofeedback group we observed a statistically significant improvement of PFM firing order in four tasks: in the first quick flicks (p = 0.016), third quick flicks (p = 0.027), fifth quick flicks (p = 0.008), and in the first 10-s contractions (p = 0.046). In the control group we observed better outcome only in one motor task: in the fourth 10-s contraction (p = 0.009). Given the positive effects of a single session of EMG biofeedback on the firing order in the PFM contractions, it should be recommended for pregnant women without urinary incontinence to teach them how to perform PFM exercises correctly. (shrink)

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

Nicolas de Cues effectue au XVe siècle un geste métaphysique qui nous paraît décisif pour la métaphysique classique et particulièrement pour la philosophie de Leibniz : il élabore une métaphysique de la singularité créée à partir de l’affirmation de l’infinité du Principe. La puissance de l’infinité divine renforce la valeur de chaque créature singulière grâce à un dispositif d’expression de l’infini dans le fini. Cependant ce processus de singularisation universel ne va pas sans soulever des difficultés. Comment la singularité de (...) la créature peut-elle s’ouvrir à l’infini ? Comment les créatures singulières peuvent-elles former un monde commun et se rapporter à leur Principe sans abandonner leur puissance de distinction ? Nous exposerons trois temps de ce processus de singularisation : la déduction, par une métaphysique expressive de l’infini, de la singularité conçue comme contraction de l’Unité divine ; l’intégration cosmologique des êtres singuliers ainsi déduits ; enfin la destinée spirituelle de l’intériorisation mentale de l’ensemble du processus. (shrink)

본 논문은 형이상학의 구축이라는 관점에서 들뢰즈와 화이트헤드의 관계를 다룬다. 이들 두 철학자들 사이의 관계는 역사적이고 사실적인 관점에서 볼 때 들뢰즈가 『차이와 반복』이래로 화이트헤드를 참조하고 있으며 특히 『주름』에서 화이트헤드가 매우 중요한 위치를 차지하고 있다는 사실에서 확인된다. 무엇보다 두 형이상학자들 사이의 관계를 해명하는 것은 들뢰즈의 존재론 체계가 완성된 『차이와 반복』과 원숙한 시기의 화이트헤드의 형이상학적 체계가 잘 나타나 있는『과정과 실재』의 비교작업이 될 것이다. 이러한 비교연구를 위하여 우리는 특히 사건의 철학과 관련하여 들뢰즈의 화이트헤드 독해가 갖는 적합성과 한계를 살펴본 후, 화이트헤드의 파악 개념과 들뢰즈의 수동적 (...) 종합개념(첫 번째 수동적 종합: 응시, 수축, 만족)사이의 유사점과 차이점을 고찰하고 평가할 것이다. 만일 이 두 철학자들의 형이상학(존재론)에 어떤 심층의 연대가 존재한다고 한다면, 그들 모두 칸트의 초월론적 관념론을 넘어서고자 하는 그들의 방식에 있어서 공통적으로 지니는 유사한 철학적 지향점이 있다는 점일 것이며, 이는 경험론과 분리되지 않는 형이상학을 창조함으로써 수행된다고 할 수 있다. 그것들은 각각 초월론적 경험론과 사변적 경험론이다. (shrink)

In Ilić and Boričić, the right-handed cut-free sequent calculus $GRW$ for the contraction-less relevant logic $RW$ is defined. In this paper, we show that the enlargement of the system $GRW$ with the structural rule of intensional contraction presents the sequent system for the principal relevant logic $R$ but the rule of cut cannot be eliminated in $GRW+$.