We investigate a subsystem of minimal logic related to D. Vakarelov’s logic \, using the framework of subminimal logics by A. Colacito, D. de Jongh and A. L. Vargas. In the course of it, the relationship between the two semantics in the respective frameworks is clarified. In addition, we introduce a sequent calculus for the investigated subsystem, and some proof-theoretic properties are established. Lastly, we formulate a new infinite class of subsystems of minimal logics.

Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely (...) N4, as well as its non-constructive extension C3. For these systems, various observations concerning provable contradictions are made, using mainly a proof-theoretic approach. The topics covered in this paper include: how new contradictions are found from parts of provable contradictions; how to characterise provable contradictions in C3 that are constructive; how contradictions can be seen from the relative viewpoint of strong implication; and as an appendix an attempt at generating provable contradictions in C3. (shrink)

Strong negation is a well-known alternative to the standard negation in intuitionistic logic. It is defined virtually by giving falsity conditions to each of the connectives. Among these, the falsity condition for implication appears to unnecessarily deviate from the standard negation. In this paper, we introduce a slight modification to strong negation, and observe its comparative advantages over the original notion. In addition, we consider the paraconsistent variants of our modification, and study their relationship with non-constructive principles and connexivity.

H. Omori and H. Wansing introduced in a recent paper possible alternatives for the negation of the logic of first-degree entailment. One of their observations with regard to these alternative negations is that some of them turn out to induce negation inconsistency, meaning that some contradictions become provable (under an arbitrary premise) when used in place of the original negation. Omori and Wansing also considered a non-deterministic generalisation of such operators, but it was left open whether the generalised negation similarly (...) induces negation inconsistency. In this paper, we provide an answer to this question in the positive, and moreover look into further generalisation and characterisation of non-deterministic operators which satisfy the formal criteria of negation inconsistency and its pair notion of negation incompleteness in the setting of Omori and Wansing. (shrink)

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.

N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency of the (...) system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing. (shrink)

Intuitionistic logic formalises the foundational ideas of L.E.J. Brouwer’s mathematical programme of intuitionism. It is one of the earliest non-classical logics, and the difference between classical and intuitionistic logic may be interpreted to lie in the law of the excluded middle, which asserts that either a proposition is true or its negation is true. This principle is deemed unacceptable from the constructive point of view, in whose understanding the law means that there is an effective procedure to determine the truth (...) of all propositions. This understanding of the distinction between the two logics supports the view that negation plays a vital role in the formulation of intuitionistic logic.Nonetheless, the formalisation of negation in intuitionistic logic has not been universally accepted, and many alternative accounts of negation have been proposed. Some seek to weaken or strengthen the negation, and others actively supporting negative inferences that are impossible with it.This thesis follows this tradition and investigates various aspects of negation in intuitionistic logic. Firstly, we look at a problem proposed by H. Ishihara, which asks how effectively one can conserve the deducibility of classical theorems into intuitionistic logic, by assuming atomic classes of non-constructive principles. The classes given in this section improve a previous class given by K. Ishii in two respects: (a) instead of a single class for the law of the excluded middle, two classes are given in terms of weaker principles, allowing a finer analysis and (b) the conservation now extends to a subsystem of intuitionistic logic called Glivenko’s logic. This section also discusses the extension of Ishihara’s problem to minimal logic.Secondly, we study the relationship between two frameworks for weak constructive negation, the approach of D. Vakarelov on one hand and the framework of subminimal negation by A. Colacito, D. de Jongh, and A. L. Vargas on the other hand. We capture a version of Vakarelov’s logic with the semantics of the latter framework, and clarify the relationship between the two semantics. This also provides proof-theoretic insights, which results in the formulation of a cut-free sequent calculus for the aforementioned system.Thirdly, we investigate the ways to unify the formalisations of some logics with contra-intuitionistic inferences. The enquiry concerns paraconsistent logics by R. Sylvan and A. B. Gordienko, as well as the logic of co-negation by G. Priest and of empirical negation by M. De and H. Omori. We take Sylvan’s system as basic, and formulate the frame conditions of the defining axioms of the other systems. The conditions are then used to obtain cut-free labelled sequent calculi for the systems.Finally, we consider L. Humberstone’s actuality operator for intuitionistic logic, which can be seen as the dualisation of a contra-intuitionistic negation. A compete axiomatisation of intuitionistic logic with actuality operator is given, and comparisons are made for some related operators.Abstract prepared by Satoru Niki.E-mail:Satoru.Niki@rub.de. (shrink)

Ishihara's problem of decidable variables asks which class of decidable propositional variables is sufficient to warrant classical theorems in intuitionistic logic. We present several refinements to the class proposed by Ishii for this problem, which also allows the class to cover Glivenko's logic. We also treat the extension of the problem to minimal logic, suggesting a couple of new classes.

We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.

Examining a variety of bio-objects in contexts beyond the laboratory, Bio-Objects: Life in the 21st Century explores new ways of thinking about how novel bio-objects enter contemporary life, analysing the manner in which the boundaries between human and animal, organic and non-organic, and being 'alive' and the suspension of living, are questioned, destabilised and in some cases re-established.

Speculative Realism (SR) has often been characterised as a heterogeneous group of thinkers, united almost exclusively in their commitment to the critique of what Quentin Meillassoux terms ‘correlationism’ or what Graham Harman calls the ‘philosophy of (human) access.’ The terms ‘correlationism’ and ‘philosophy of access’ are in turn often treated – at times even by Meillassoux and Harman themselves – as synonymous. In this paper, I seek to analyse these terms to evaluate their similarities, but also possible differences. I shall (...) argue that the difference between the two terms ought to be retained and emphasised, since it hints at important differences between the positions of Harman and Meillassoux. (shrink)

Object-Oriented Ontology (OOO) is a contemporary form of realism concerned with the investigation of “objects” broadly construed. It may be characterised in terms of a metaphysical pluralism to the extent that it recognises infinitely many different kinds of emergent entities, and this fact in turn leads to a number of questions concerning the nature of objects and emergence in OOO: what is the precise meaning of an emergent entity in OOO? How has emergence been denied throughout the history of Western (...) thought? Is there a specific object-oriented account of emergence? What is the causal mechanism which provides the conditions of possibility for the generation of emergent entities? In this article, I aim to answer all these questions by constructing the first extensive account of real emergence in the context of Object-Oriented Ontology, and I also seek to tie this analysis to the notion of “vicarious” or indirect causation. (shrink)

We show that length initial submodels of S12 can be extended to a model of weak second order arithmetic. As a corollary we show that the theory of length induction for polynomially bounded second order existential formulae cannot define the function division.

In Graham Harman’s Object-Oriented Ontology (OOO), an apparent tension arises between his pursuit of a self-proclaimed “new theory of everything,” or general ontology, and his assertion that any ontology must be able to account for distinctions among various regions of being. This paper delves into this tension between universality and specificity, particularly concerning the question of animal ontology, and examines the potential for constructing an object-oriented animal ontology. By juxtaposing Harman’s perspectives with those of Matthew Calarco and other scholars, I (...) aim to demonstrate the feasibility of developing an animal ontology using the framework of OOO. (shrink)

There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory provide (...) appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view. (shrink)

S-Modulin is a frog homolog of recoverin. The function and the underlying mechanism of the action of these proteins are now understood in general. However, there remain some unsolved issues including; two distinct effects of S-modulin; Ca2+-dependent binding of S-modulin to membranes and a possible target protein; S-modulin-like proteins in other neurons. These issues are considered in this commentary.

In dieser Abhandlung versuchen wir die Theorie des Erhabenen bei Kant als eine Logik der reflektierenden Urteilskraft darzustellen, die den Ubergang des Sinnlichen ins Ubersinnliche ermoglicht. Die Urteilskraft bezieht die Spannung der Einbildungskraft vor dem Nicht-Darstellbaren auf das Ubersinnliche, und in dieser Beziehung sieht Kant "eine a priori im Subjekte liegende Zweckmassigkeit". Durch die Vorstellung der gewaltigen Natur kann unsere innere Idee erweckt werden, wenn wir berucksichtigen, "dass auf jene moralischen Anlagen bei jeder schicklichen Veranlassung Rucksicht genommen werden sollte". Durch (...) das Urteil uber das Erhabene erhalten wir eine Veranlassung fur diejenige Reflexion, die innerhalb der Natur auch die ubersinnliche Idee (oder ein gottliches Wesen) denkt. (edited). (shrink)

We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.

From the 1981 “Sexuality and Solitude” to the 1982 “Le combat de la chasteté” to the 1984 History of Sexuality, Volume 2, Michel Foucault’s published works have long recognized the influence of the historian of late antiquity, Peter Brown. With the 2018 publication of Foucault’s draft of Les Aveux de la chair (Confessions of the Flesh) bearing no mention of Brown, the depth of this influence requires further elaboration. Despite Brown not appearing in the “Index of Modern Authors,” Confessions of (...) the Flesh reflects Foucault’s debt to Brown for his readings of Augustine of Hippo and his conceptualizations of sexuality and subjectivity. Analyzing archival evidence alongside biographical narratives helps us better understand Brown’s vital influence as Foucault was shifting his History of Sexuality project, his archival practices, and his genealogy of subjectivity. Appreciating the textual and conceptual engagement between Foucault and Brown thus illuminates not only Confessions of the Flesh as Volume 4 in the History of Sexuality series but also the conceptual and methodological developments of both scholars in their disciplinary intersections. (shrink)

Two experiments (N1 = 141, N2 = 40) investigate two versions of Aristotle’s Thesis for the first time. Aristotle’s Thesis is a negated conditional, which consists of one propositional variable with a negation either in the antecedent (version 1) or in the consequent (version 2). This task allows us to infer if people interpret indicative conditionals as material conditionals or as conditional events. In the first experiment I investigate between-participants the two versions of Aristotle’s Thesis crossed with abstract versus concrete (...) task material. The modal response for all four groups is consistent with the conditional event and inconsistentwith the material conditional interpretation. This observation is replicated in the second experiment. Moreover, the second experiment rules out scope ambiguities of the negation of conditionals. Both experiments provide new evidence against thematerial conditional interpretation of conditionals and support the conditional event interpretation. Finally, I discuss implications formodeling indicative conditionals and the relevance of this work for experimental philosophy. (shrink)

I present a conceptual framework for classifying generalist and particularist approaches to conspiracy theories (CTs). Specifically, I exploit a probabilistic version of the hexagon of opposition which allows for systematically visualising the logical relations among basic philosophical positions concerning CTs. The probabilistic interpretation can also account for positions, which make weaker claims about CTs: e.g. instead of claiming ‘every CT is suspicious’ some theorists might prefer to claim ‘most CTs are suspicious’ and then ask about logical consequences of such claims. (...) Finally, I illustrate the proposed conceptual framework by selected claims about CTs drawn from the CT research literature. (shrink)

ZusammenfassungIst Biologie das jüngste Mitglied in der Familie von Big Science? Die vermehrte Zusammenarbeit in der biologischen Forschung wurde in der Folge des Human Genome Project zwar zum Gegenstand hitziger Diskussionen, aber Debatten und Reflexionen blieben meist im Polemischen verhaftet und zeigten eine begrenzte Wertschätzung für die Vielfalt und Erklärungskraft des Konzepts von Big Science. Zur gleichen Zeit haben Wissenschafts- und Technikforscher/innen in ihren Beschreibungen des Wandels der Forschungslandschaft die Verwendung des Begriffs Big Science gemieden. Dieser interdisziplinäre Artikel kombiniert eine (...) begriffliche Analyse des Konzepts von Big Science mit unterschiedlichen Daten und Ideen aus einer Multimethodenuntersuchung mehrerer großer Forschungsprojekte in der Biologie. Ziel ist es, ein empirisch fundiertes, nuanciertes und analytisch nützliches Verständnis von Big Biology zu entwickeln und die normativen Debatten mit ihren einfachen Dichotomien und rhetorischen Positionen hinter sich zu lassen. Zwar kann das Konzept von Big Science als eine Mode in der Wissenschaftspolitik gesehen werden – inzwischen vielleicht sogar als ein altmodisches Konzept –, doch lautet meine innovative Argumentation, dass dessen analytische Verwendung unsere Aufmerksamkeit auf die Ausweitung der Zusammenarbeit in den Biowissenschaften lenkt. Die Analyse von Big Biology zeigt Unterschiede zu Big Physics und anderen Formen von Big Science, namentlich in den Mustern der Forschungsorganisation, der verwendeten Technologien und der gesellschaftlichen Zusammenhänge, in denen sie tätig ist. So können Reflexionen über Big Science, Big Biology und ihre Beziehungen zur Wissensproduktion die jüngsten Behauptungen über grundlegende Veränderungen in der Life Science-Forschung in einen historischen Kontext stellen. (shrink)

We prove in the framework of Bishop's constructive mathematics that the sequential completion equation image of the space [MATHEMATICAL SCRIPT CAPITAL D] is filter-complete. Then it follows as a corollary that the filter-completeness of [MATHEMATICAL SCRIPT CAPITAL D] is equivalent to the principle BD-ℕ, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that equation image is identical with the filter-completion which was (...) provided by Bishop. (shrink)

Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. We report four experiments which investigate three rules of SYSTEMP, namely the AND, the LEFT LOGICAL EQUIVALENCE, and the OR rule. The actual inferences of the subjects are compared with the coherent normative upper and lower probability bounds derived from a non-infinitesimal probability semantics of SYSTEM P. We found a relatively good agreement of human reasoning and principles of nonmonotonic (...) reasoning. Contrary to the results reported in the ‘heuristics and biases’ tradition, the subjects committed relatively few upper bound violations (conjunction fallacies). (shrink)

This position paper advocates combining formal epistemology and the new paradigm psychology of reasoning in the studies of conditionals and reasoning with uncertainty. The new paradigm psychology of reasoning is characterized by the use of probability theory as a rationality framework instead of classical logic, used by more traditional approaches to the psychology of reasoning. This paper presents a new interdisciplinary research program which involves both formal and experimental work. To illustrate the program, the paper discusses recent work on the (...) paradoxes of the material conditional, nonmonotonic reasoning, and Adams’ Thesis. It also identifies the issue of updating on conditionals as an area which seems to call for a combined formal and empirical approach. (shrink)

We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the form if not-A, thenA, should not hold, since the conditional’s antecedent not-A contradicts its consequent A. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event $${A| \overline{A}}$$ A | A ¯ is $${p(A| \overline{A})=0}$$ p ( A | A ¯ ) = 0. (...) In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles: Aristotle’s theses, Aristotle’s Second Thesis, Abelard’s First Principle, and Boethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (like non-symmetry). Both approaches satisfy minimal requirements for a connexive logic. Finally, we compare both approaches conceptually. (shrink)

Eukaryotic genome DNA is wrapped around core histones and forms a nucleosome structure. Together with associated proteins and RNAs, these nucleosomes are organized three‐dimensionally in the cell as chromatin. Emerging evidence demonstrates that chromatin consists of rather irregular and variable nucleosome arrangements without the regular fiber structure and that its dynamic behavior plays a critical role in regulating various genome functions. Single‐nucleosome imaging is a promising method to investigate chromatin behavior in living cells. It reveals local chromatin motion, which reflects (...) chromatin organization not observed in chemically fixed cells. The motion data is like a gold mine. Data analyses from many aspects bring us more and more information that contributes to better understanding of genome functions. In this review article, we describe imaging of single‐nucleosomes and their tracked behavior through oblique illumination microscopy. We also discuss applications of this technique, especially in elucidating nucleolar organization in living cells. (shrink)

In an archived draft at the Bibliothèque nationale de France, Foucault describes two questions haunting him since 1963: “Why are we obliged to tell the truth about ourselves? Which truth?” Foucault poses these two questions in 1980 in drafts for his lectures at the University of California, Berkeley, and I see in these two questions two argumentative threads that weave through Foucault's changing History of Sexuality series over his last decade. These two threads correspond to the dimorphism Foucault frames in (...) Part III of Confessions of the Flesh between confessing monks and married men, that correlates with the distinction between “veridiction” and “juridiction” as two forms relating subjectivity and sexuality. To help tease out these threads, I make two recommendations for how to read Confessions of the Flesh in this following review essay: (1) situate Confessions of the Flesh in relation to Foucault's History of Sexuality series which spans his last decade from 1974 to 1984 and (2) untangle two major threads of Confessions of the Flesh in Foucault's treatment of Cassian and Augustine, as progenitors of veridiction and juridiction respectively, which together produce the conditions for modern disciplinary subjects. (shrink)

We define a theory of two-sort bounded arithmetic whose provably total functions are exactly those in ${\mathcal{F}_{LOGCFL}}$ by way of a generalized quantifier that expresses computations of SAC 1 circuits. The proof depends on Kolokolova’s conditions for the connection between the provable capture in two-sort theories and descriptive complexity.

We define a fragment of Primitive Recursive Arithmetic by replacing the defining axioms for primitive recursive functions by those for functions in some specific complexity class. In this note we consider such theory for AC0. We present a model-theoretical property of this theory, by means of which we are able to characterize its provably total functions. Next we consider the problem of how strong the induction scheme can be in this theory.