We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our results show that (...) lattice structure and classical operations uniquely determine quantum logic underlying Hilbert space. As a consequence of our result, recent proposals for a deduction theorem with quantum operations in an orthomodular lattice as well as a, substitution of quantum operations for the usual standard Hilbert space ones in quantum logic prove to be misleading. Quantum computer quantum logic is also discussed. (shrink)

In a text written during his stay in Paris, Leibniz, to deny ontological reality to relations, employs an argument well known to the medieval thinkers and which later would be revived by Francis H. Bradley. If one assumes that relations are real and that a relation links any property to a subject – so runs the argument – then one falls prey to an infinite regress. Leibniz seems to be well aware of the consequences that this argument has for his (...) own metaphysical views, where the relation of inherence plays such a central role. Thus, he attempts first to interpret the relation of inherence as something ‘metaphoric’, originating from our ‘spatial way’ of looking at the surrounding world; and then he tries to reduce it to the part-whole relation which clearly he considers weaker, from the ontological point of view, than that of ‘being in’. (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

Objective Apeiron was founded in 1966 and has developed into one of the oldest and most distinguished journals dedicated to the study of ancient philosophy, ancient science, and, in particular, of problems that concern both fields. Apeiron is committed to publishing high-quality research papers in these areas of ancient Greco-Roman intellectual history; it also welcomes submission of articles dealing with the reception of ancient philosophical and scientific ideas in the later western tradition. The journal appears quarterly. Articles are peer-reviewed on (...) a double-blind basis. Topics ancient philosophy ancient science reception of ancient philosophical and scientific ideas in the later western tradition Article formats Original Articles. (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen that he was able to prove the normalization theorem only for intuitionistic natural deduction, but not for classical. To cover the latter, he developed classical sequent calculus and proved a corresponding theorem, the famous cut elimination result. Its proof was organized so that a cut elimination result for an intuitionistic sequent calculus came out as a special case, namely the one in which the sequents (...) have at most one formula in the right, succedent part. Thus, there was no need for a direct proof of normalization for intuitionistic natural deduction. The only traces of such a proof in the published thesis are some convertibilities, such as when an implication introduction is followed by an implication elimination [1934–35, II.5.13]. It remained to Dag Prawitz in 1965 to work out a proof of normalization. Another, less known proof was given also in 1965 by Andres Raggio.We found in February 2005 an early handwritten version of Gentzen's thesis, with exactly the above title, but with rather different contents: Most remarkably, it contains a detailed proof of normalization for what became the standard system of natural deduction. The manuscript is located in the Paul Bernays collection at the ETH-Zurichwith the signum Hs. 974: 271. Bernays must have gotten it well before the time of his being expelled from Göttingen on the basis of the racial laws in April 1933. (shrink)

Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in order to reprove weak and strong normalization for the simply-typed λ-calculus and for an extension by sum types with permutative conversions. The analogous treatment of a new system with generalized applications inspired by generalized elimination rules in natural deduction, advocated by von Plato, shows the flexibility of the approach which does not use the strong computability/candidate style à la Tait and (...) Girard. It is also shown that the extension of the system with permutative conversions by η-rules is still strongly normalizing, and likewise for an extension of the system of generalized applications by a rule of ``immediate simplification''. By introducing an infinitely branching inductive rule the method even extends to Gödel's T. (shrink)

This article illustrates ways in which the concepts of the norm and normativity are implicated in relations of power. Specifically, I argue that these concepts have come to function in a normalizing manner. I outline Michel Foucault’s thinking on the norm and normalization and then provide an overview of Jürgen Habermas’s thinking on the norm and normativity in order to show that Habermas’s conceptualizations of the norm and normativity are not, as he posits, necessary foundations for ethics and politics, (...) but in fact simply one philosophical approach among many. Uncritically accepting a Habermasian framework therefore produces normalizing effects and inhibits alternative and potentially emancipatory thinking about ethics and politics. Having problematized the requirement of normative foundations as it is currently articulated, I conclude by examining the emancipatory potential of a particular aspect of Foucault’s work for the practice of philosophy. (shrink)

At one point Rawls thought that “a normalization of interests attributed to the parties” is “common to social contract doctrines.” Normalization has a great appeal: once we specify the normalized perspective, we can generate strong and definite principles of justice. Public reasoning is restricted to those who reason from the eligible, normalized, perspective; those who fall outside the “normal” are to be dismissed as unreasonable, unjust, or illiberal. As Rawls’s political liberalism project developed he increasingly relaxed his (...) class='Hi'>normalization assumptions, allowing room for not only different conceptions of the good, but of justice. This paper explores the post-Rawlsian movement in public reason to maximally relax, or even abandon, normalizing assumptions, drawing on a maximal diversity of normative perspectives in public justification. The public reason project is at a critical juncture. Are we to look back, defending Rawls’s substantive conclusions by devising new defenses of normalization, circling the wagons around the cherished two principles? Or are we to seek to fulfill the promise of public reason as providing a common public and moral world in the midst of diversity? (shrink)

Many philosophers have recently defended the Maximise Expected Choiceworthiness (MEC) approach to moral uncertainty. Perhaps the most important problem for MEC is the problem of intertheoretic choiceworthiness unit comparisons; and one extant response to this problem is a technique called ‘variance normalization.’ Although there has been some short, scattered commentary on variance normalization in the philosophical literature, nobody has yet offered a detailed critical discussion of this proposal. This paper fills that lacuna, arguing that there are serious problems (...) which would need to be addressed before variance normalization could be invoked to rescue MEC from scepticism about intertheoretic comparisons. (shrink)

Public discourse often portrays users of artificial intelligence (AI) companionship applications as lonely and stigmatized, casting them as fundamentally different from non-users. These debates are often molded by fears that such technologies may foster isolation or even replace human relationships. However, few studies have directly compared users and non-users of AI companions in the general population. This study addresses this gap through a survey of 342 U.S. adults, including both users and non-users of AI companionship apps, and situates the findings (...) within the broader history of information and communication technologies (ICTs) adoption. Results indicate that users and non-users are largely similar in self-esteem, introversion, sociability, and friendship networks, directly contradicting stereotypes of maladjusted or socially isolated users. The one robust distinction was loneliness, which remained significant even after controlling for demographics. Qualitative findings showed that while non-users expressed concern that AI companions could displace human relationships, users typically described them as supplemental rather than substitutive, often providing a safe, non-judgmental space for expression. Notably, older participants expressed more favorable attitudes and supported less restrictive regulation, suggesting particular relevance of AI companions for aging populations. These findings complicate the narrative that AI companionship is inherently harmful or transformative in negative ways. Instead, they suggest continuity with earlier ICTs, where initial stigma and moral panic gradually gave way to normalization as technologies became integrated into everyday life. (shrink)

Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a version of Parigot’s free deduction. The elimination rules are “general,” but can be systematically simplified. Cut-elimination and normalization hold. Restriction to a single formula in the succedent yields intuitionistic versions of these systems. The rules also yield generalized lambda calculi providing proof terms for (...) natural deduction proofs as in the Curry-Howard isomorphism. Addition of an indirect proof rule yields classical single-conclusion versions of these systems. Gentzen’s standard systems arise as special cases. (shrink)

ellucci, C., Existential instantiation and normalization in sequent natural deduction, Annals of Pure and Applied Logic 58 111–148. A sequent conclusion natural deduction system is introduced in which classical logic is treated per se, not as a special case of intuitionistic logic. The system includes an existential instantiation rule and involves restrictions on the discharge rules. Contrary to the standard formula conclusion natural deduction systems for classical logic, its normal derivations satisfy both the subformula property and the separation property (...) and allow to establish a version of the midsequent theorem and Herbrand's theorem. (shrink)

In [gallier], general results (due to Coppo, Dezani and Veneri) relating properties of pure lambda terms and their typability in some systems with conjunctive types are proved in a uniform way by using the reducibility method.This paper gives a very short proof of the same results (actually, one of them is a bit stronger) using purely arithmetical methods.

The notion of ‘philosophical culture’ can be defined as the totality of conditions of philosophical thought and theory. Among these conditions is an awareness of the historical background of the philosophical culture in question. This awareness, which plays an important cognitive and normative role, often takes the form of a relatively independent discipline: history of philosophy. Over the last decade, Russian historians of philosophy have been attempting to make the repressed past accessible to contemporary philosophy, often modifying their earlier, Soviet (...) work. This can be illustrated with a survey of late Soviet and post-Soviet literature on the Russian philosopher, Vladimir Solov’ëv. (shrink)

This paper describes formalizations of Tait's normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. From the formal proofs programs are machine-extracted that implement variants of the well-known normalization-by-evaluation algorithm. The case study is used to test and compare the program extraction machineries of the three proof assistants in a non-trivial setting.

Less salient, lower contrast disks appear to be more numerous than more salient, higher contrast disks when intermingled in equal numbers into the same display, but they are equal in perceived numerosity when segregated into different displays. Comparative judgements indicate that the apparent numerosity of the lower contrast disks is unaffected by being intermingled with high contrast disks, whereas the high contrast disks are reduced in numerosity by being intermingled with the low contrast ones. Here, we report that this illusion (...) also occurs for absolute judgements of the numerosities of displays of from 20 to 80 disks. A model based on luminance-difference contrast normalization explains the illusory loss of high-contrast items along with veridical perception of the low-contrast ones. The model correctly predicts that perceived numerosity is linearly related to the square-root of the number of disks, with the extent of the illusion depending on an attentionally-weighted function of contrast and assimilation. (shrink)

Dave Eggers's satirical novel _The Every_ (2021), a sequel to _The Circle_ (2013), expands on some of the earlier novel's main themes while also illustrating and denouncing how surveillance practices are increasingly met with little resistance on the part of the population. Drawing on recent research on surveillance, such as Shoshana Zuboff's theorization of "surveillance capitalism" and Evan Selinger and Judy Rhee's concept of "favorably disposed normalization," this article examines surveillance practices in the society depicted in _The Every_ and (...) sheds light on the mechanisms through which Eggers puts forward his message of warning. Some reviewers have criticized the writer's plot and character development skills, as well as his inability to offer any alternatives to this world of mass digital surveillance. Nevertheless, this article argues that Eggers's narrative choices ultimately leave readers with a sense of unease that may at best lead them to take action. (shrink)

The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to (...) extend Seldin's normalization strategy to Peirce's rule by showing that every derivation Π in the implicational fragment can be transformed into a derivation Π' such that no application of Peirce's rule in Π' occurs above applications of →-introduction and →-elimination. As a corollary of Seldin's normalization strategy we obtain a form of Glivenko's theorem for the classical {→}-fragment. (shrink)

Secrecy and “social cocooning” are critical mechanisms allowing the normalization of corruption within organizations. Less studied are processes of normalization that occur when corruption is an “open secret.” Drawing on an empirical study of Greek public-sector organizations, we suggest that a second-order normalization process ensues among non-corrupt onlookers both inside and beyond the organization. What is normalized at this level is not corruption, but its tolerance, which we disaggregate into agent-focused tolerance and structure-focused tolerance. Emphasizing the importance (...) of non-corrupt bystanders, we claim that second-order normalization helps corruption persist in situations where its presence is openly acknowledged. This adds an important new dimension to normalization theory and we unpack its implications for both future research and practice in this area. (shrink)

We develop a dimension theory for D-semianalytic sets over an arbitrary non-Archimedean complete field. Our main results are the equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in characteristic 0. We also prove a parameterized version of normalization for D-semianalytic sets.

We give an elementary proof of the strong normalization of the atomic polymorphic calculus Fat.

This paper points out an error of Parigot's proof of strong normalization of second order classical natural deduction by the CPS-translation, discusses erasing-continuation of the CPS-translation, and corrects that proof by using the notion of augmentations.

The paper is inspired by and explicitly presupposes the readers’ knowledge of the Kürbis normalization procedure for the Milne tree-like natural deduction system _C_ for classical propositional logic. The novelty of _C_ is that for each conventional connective, it has only _general_ introduction and elimination rules, whose paradigm is the rule of proof by cases. The present paper deals with the Milne–Kürbis troublemaker—adding universal quantifier—caused by extending the normalization procedure to \(\mathbf {C^{\exists }_{\forall }} \), the first-order variant (...) of _C_. For both quantifiers, \( \mathbf {C^{\exists }_{\forall }}\) has only general quantifier rules, whose paradigm is the indirect rule of existential elimination. We propose the classical first-order tree-like natural deduction system \( \mathbf {NC^{\exists }_{\forall }}\) such that it contains all the propositional and half the quantifier rules of \(\mathbf {C^{\exists }_{\forall }}\) and differs from it with respect to the other half of the quantifier rules and the notion of a deduction. We show that in the case of \(\mathbf {NC^{\exists }_{\forall }} \), whose specifics is based on the Quine treatment of _flagged_ variables in the linear-style natural deduction system as well as on the Aguilera-Baaz treatment of _characteristic_ and _side_ variables for sequent-style calculi, the troublemaker doesn’t occur. In order to handle another specifics of \(\mathbf {NC^{\exists }_{\forall }}\) —an auxiliary notion of a _finished_ deduction that makes deductions _nonhereditary_—we show soundness and completeness of \( \mathbf {NC^{\exists }_{\forall }} \). While emphasizing the former with the help of the Smirnov technique, we additionally indicate a fixable gap in the Quine soundness argument. At last, the philosophical significance of the main result of this paper is developed in more detail. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Evaluation, Standards, Normalization: Historico-philosophical Formations and the Conditions of Possibility for Checklist Thought Bernadette Baker University of Wisconsin-Madison In education today a new vocabulary has emerged that is far more than just words. In the context of educational policy the setting of goals or objectives is now being subsumed under terms such as statewidestandards, child development is now being adjectivized by descriptors such as learning disability or emotionally (...) disturbed, and the evaluation ofclassroom-based performance is now being collated in aportfolio. These are more than just buzz words-at one level they are new ways of governing children and teachers, of organizing action, and of perceiving the world. What, for instance, does it tell us about ourselves when first-grade students Mikey, Enrique, Waldo, orDonal are introduced to visitors to the school by labels such as LD, ED, ADD, ADHD, and so forth, rather thanby their name? What does it tell us about ourselves when we say a curriculum or program of study is in line with the standards established somewhere else? And what story do we think is being narratedin the documentation of a child's performance in portfolio form across a semester or year? In consideringwhyterms suchasstandards, child development, or even evaluation have such contemporary currency I am necessarily drawn into a study of the timespaces in which they did not have such currency at all. This paper maps four moves into a moment that I think of as a rather long present-day-a present that is not simply this morning, yesterday, or the daybefore, but one that links the subjectivities ofthose now living in educational workto those made available about one hundred years ago. The four moves that I analyze here can be thought of as conditions of possibility for the operation of contemporary educational mies of reasoning, especially those that have formed around the resurgent popularity of"checklist thought" in reform efforts. The four moves collectively historicize how notions of standards, child development, and evaluation can pop up as commonsensical tropes through which to gather and degather action in the educational field. The first ofthese moves is that which flows from the operation ofan ideal to the operation of a norm. The second move is that which flows between the advent of statistics and the advent of eugenics. The third move is that which flows between the appearance ofnovels and fiction and the novel ficticityoffacts. And the fourth move is that which flows from the fictions of child development narratives to the stories that standards tell us. Collectively, these historico-philosophical moves will enable reconsideration of what we think evaluation, standards, and norms for child development actually narrate, lending food for thought to the specificityoftheir uptake in music education. From Ideal to Norm One way inwhichto examinethe shift from a seventeenth-century concept of the ideal to the nineteenth-century concept of the norm is by telling a story that was told in the early twentieth century. At this time when the educational field was formalizing, there was great care taken to record discussions held at conferences. When conferenceproceedings werepublished, theywere usually structured so that the presenter's paper©Philosophy ofMusic Education ReviewlO, no. 1 (Fall, 2002): 92-101. Bernadette Baker 93 was followed by a transcript of the conversation held after it. Like today, in the discussion time, audience members asked questions or made comments. Unlike today, the names of such participating audience members were typed into the proceedings and their specific questions or comments were written up as part ofreporting on the paper presented. In a discussion held at a conference in 1 905 on the topic of methods for training children labeledas feebleminded, apresenterhadspokenof the positive uses of a vegetable garden in the disciplining of feebleminded girls. The audience members relayed their own versions of experimenting with gardening and gathering, some complaining oftoo little space and others indicating the effects of having too many fields from which to gather. Dr. Dunlap was one such participant, indicatingimplicitlytheeffectsofhavingtoo many choices. In the spirit ofthe hunter/gatherer dichotomy, thegirlslabeledas feeblemindedatthe institutionwhereDr. Dunlap worked weresentout to pick com. The following story emerged. Dr. Dunlap: Our girls go out under an attendant and gather vegetables... (shrink)

The author suggests to look at media research from a historical perspective and compare the projects of the “golden period”, that is, the 1990s – early 2000s, with the works of recent years. After preliminary contextual explanations, choosing for a more detailed presentation projects of S. Zielinski and J. Parikka, the author shows how the tasks of media studies and their methodology change during the transition from large-scale panoramas claiming to build a new history from the perspectives of media to (...) often fragmented and situational analyses of components of chosen media (for example, the translation of color dispersion into the chemical language of a photograph of a distant star). This was the way by which archaeology, attentive to geological time, turned into archival work being done for “commercial use or machine learning”. This is how the radical approaches to media research characteristic of the first media theorists are leveled, because scientists publishing their works since the second half of the 2010s contribute to the normalization of media theory by bringing it to the long-discussed topics of other disciplines, such as cognitive functions or theories of signs. At the same time, media theory of recent years is being largely politicized, adopting governmental instructions and reducing the “variantology” and multiplicity of media that were developed earlier. (shrink)

In this paper we give a strong normalization proof for a set of reduction rules for classical logic. These reductions, more general than the ones usually considered in literature, are inspired to the reductions of Felleisen's lambda calculus with continuations.