In [6] Albert Visser shows that ILP completely axiomatizes all schemata about provability and relative interpretability that are provable in finitely axiomatized theories. In this paper we introduce a system called ILP that completely axiomatizes the arithmetically valid principles of provability in and interpretability over such theories. To prove the arithmetical completeness of ILP we use a suitable kind of tail models; as a byproduct we obtain a somewhat modified proof of Visser's completeness result.

In [6] Albert Visser shows that ILP completely axiomatizes all schemata about provability and relative interpretability that are provable in finitely axiomatized theories. In this paper we introduce a system called $\text{ILP}^{\omega}$ that completely axiomatizes the arithmetically valid principles of provability in and interpretability over such theories. To prove the arithmetical completeness of $\text{ILP}^{\omega}$ we use a suitable kind of tail models; as a byproduct we obtain a somewhat modified proof of Visser's completeness result.

In this paper we study essential hereditary undecidability. Theories with this property are a convenient tool to prove undecidability of other theories. The paper develops the basic facts concerning essentially hereditary undecidability and provides salient examples, like a construction of essentially hereditarily undecidable theories due to Hanf and an example of a rather natural essentially hereditarily undecidable theory strictly below. We discuss the (non-)interaction of essential hereditary undecidability with recursive boolean isomorphism. We develop a reduction relation essential tolerance, or, in (...) the converse direction, lax interpretability that interacts in a good way with essential hereditary undecidability. We introduce the class of $$\Sigma ^0_1$$ Σ 1 0 -friendly theories and show that $$\Sigma ^0_1$$ Σ 1 0 -friendliness is sufficient but not necessary for essential hereditary undecidability. Finally, we adapt an argument due to Pakhomov, Murwanashyaka and Visser to show that there is no interpretability minimal essentially hereditarily undecidable theory. (shrink)

This article discusses the role of moment-to-moment affect dynamics in mental disorder and aims to integrate recent literature on this topic in the context of complex dynamical system theory. First, we will review the relevance of temporal and contextual aspects of affect dynamics in relation to psychopathology. Related to this, we will discuss recent insights resulting from a network view on affect dynamics in psychopathology. Next, we explore how we can reconcile literature findings from a perspective of complex dynamical system (...) theory. Finally, future directions with regard to personalized assessment of risk and diagnostic use are discussed. (shrink)

Argument schemes are abstractions substantiating the inferential connection between premise(s) and conclusion in argumentative communication. Identifying such conventional patterns of reasoning is essential to the interpretation and evaluation of argumentation. Whether studying argumentation from a theory-driven or data-driven perspective, insight into the actual use of argumentation in communicative practice is essential. Large and reliably annotated corpora of argumentative discourse to quantitatively provide such insight are few and far between. This is all the more true for argument scheme corpora, which tend (...) to suffer from a combination of limited size, poor validation, and the use of ad hoc restricted typologies. In the current paper, we describe the annotation of schemes on the basis of two distinct classifications: Walton’s taxonomy of argument schemes, and Wagemans’ Periodic Table of Arguments. We describe the annotation procedure for each, and the quantitative characteristics of the resulting annotated text corpora. In doing so, we extend the annotation of the preexisting US2016 corpus of televised election debates, resulting in, to the best of our knowledge, the two largest consistently annotated corpora of schemes in argumentative dialogue publicly available. Based on evaluation in terms of inter-annotator agreement, we propose further improvements to the guidelines for annotating schemes: the argument scheme key, and the Argument Type Identification Procedure. (shrink)

An immunizing strategy is an argument brought forward in support of a belief system, though independent from that belief system, which makes it more or less invulnerable to rational argumentation and/or empirical evidence. By contrast, an epistemic defense mechanism is defined as a structural feature of a belief system which has the same effect of deflecting arguments and evidence. We discuss the remarkable recurrence of certain patterns of immunizing strategies and defense mechanisms in pseudoscience and other belief systems. Five different (...) types will be distinguished and analyzed, with examples drawn from widely different domains. The difference between immunizing strategies and defense mechanisms is analyzed, and their epistemological status is discussed. Our classification sheds new light on the various ways in which belief systems may achieve invulnerability against empirical evidence and rational criticism, and we propose our analysis as part of an explanation of these belief systems’ enduring appeal and tenacity. (shrink)

In this paper we study 1. the frame-theory of certain bimodal provability logics involving the reflection principle and we study2. certain specific bimodal logics with a provability predicate for a subtheory of Peano arithmetic axiomatized by a non-standardly finite number of axioms.

This article takes up a text that Rancière published shortly after The Ignorant School Master appeared in French, 'École, production, égalité'[School, Production, Equality] (1988), in which he sketched the school as being preeminently the place of equality. In this vein, and opposed to the story of the school as the place where inequality is reproduced and therefore in need of reform, the article wants to recount the story of the school as the invention of a site of equality and as (...) primordially a public space. Inspired by Rancière, we indicate first how the actual (international and national) policy story about the school and the organizational technologies that accompany it install and legitimate profound inequalities, which consequently can no longer be questioned (and become 'invisible'). Second, the article recasts and rethinks different manifestations of equality and of 'public-ness' in school education and, finally, indicates various ways in which these manifestations are neutralized or immunized in actual discourses and educational technologies. (shrink)

This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.

In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give a characterization of the relations on assignments that can be generated by composition from tests and random resettings in the case that we are working over an infinite domain. These relations are precisely the ones expressible in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the way (...) these extensions interact with our notion of context. (shrink)

Moving images of animals have been popular from the beginning of the medium of film and fascinate us from childhood, and they show the cultural image that exists in a (human) society of (other) animals. This essay outlines how Disney rose to prominence in the first half of the 20th century by strongly humanizing (or anthropomorphizing) animals in his animated films and not taking them very seriously as animals. In the second half of that century, the BBC had great success (...) with nature series in which, on the contrary, scientific distance and the differences between humans and animals (‘anthropo-denial’) were central, and animals were seen primarily as objects. In recent decades, new insights into biology on the one hand and technological innovations in the media on the other have led to more diverse and ambivalent animal images. These reflect a growing awareness of the similarities between humans and other animals, with films and TV series using new images and stories to enable viewers to empathize with non-human living beings. (shrink)

In this challenging essay, Maarten Doorman argues that in art, belief in progress is still relevant, if not essential. The radical freedoms of postmodernism, he claims, have had a crippling effect on art, leaving it in danger of becoming meaningless. Art can only acquire meaning through context the concept of progress, then, is ideal as the primary criterion for establishing that context. The history of art, in fact, can be seen as a process of constant accumulation, works of art (...) commenting on one another and enriching one another's meanings. It is these complex interrelationships and the progress they create in both art and its observers that Doorman, in a display of great philosophical erudition, defends. (shrink)

In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations (...) from relation algebra. In addition, the logic has devices for expressing whether in a given state a certain instruction can be carried out, and whether that state can be arrived at by carrying out a certain instruction. (shrink)

Two of the tales mentioned in the title are in many ways typical of the great collections of stories to which they belong. What makes them conspicuous is no doubt the intensity of the erotic desire presented as the ultimate law which justifies even the most outrageous actions. The cult of eroticism is combined there with a cult of youth, which means disaster for the protagonists, who try to combine eroticism with advanced age. And yet the stories in question have (...) roots in a very different tradition in which overt eroticism is punished and can only reassert itself in a chastened form, its transformation being due to sacrifices made by the lover to become reunited with the object of his love. A medieval example of the latter tradition is here the Middle English romance, Sir Orfeo. All of the three narratives are conspicuously connected by the motif of the enchanted tree. The Middle Ages are associated with a tendency to moralize ancient literature, the most obvious example of which is the French anonymous work Ovide moralisé, and its Latin version Ovidius Moralizatus by Pierre Bersuire. In the case of The Merchant’s Tale and The Tale of the Enchanted Pear-Tree, we seem to meet with the opposite process, that is with a medieval demoralization of an essentially didactic tradition. The present article deals with the problem of how this transformation could happen and the extent of the resulting un-morality. Some use has also been made of the possible biblical parallels with the tales in question. (shrink)

The aim of the article is to investigate some of the possible sources of inspiration for Orwell’s concept of the artificial language called Newspeak, which, in his novel Nineteen Eighty-Four, is shown as an effective tool of enslavement and thought control in the hands of a totalitarian state. The author discusses, in this context, the putative links between Newspeak and really existing artificial languages, first of all Esperanto, and also between Orwell’s notion of “doublethink”, which is an important feature of (...) the totalitarian mentality, and Czesław Miłosz’s notion of “ketman”, developed in his book The Captive Mind. But the main emphasis is on the connection between Orwell’s book and the slightly earlier novel by C.S. Lewis, That Hideous Strength. It is well known that Orwell knew Lewis’s book and expressed his mixed feelings about it. There are many specific, though far from obvious, similarities between the two books, but what seems to have been particularly inspiring for Orwell was Lewis’s vision of a thoroughly degenerate language that is used for political manipulation rather than for communication. (shrink)

The reason of faith -- Thought and language -- Truth -- The Monologion arguments for the existence of God -- The Proslogion argument for the existence of God -- The divine attributes -- Thinking and speaking about God -- Creation and the word -- The Trinity -- Modality -- Freedom -- Morality -- Incarnation and atonement -- Original sin, grace, and salvation.

In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the set of axioms varies. We extend the Feferman framework in one important point: we allow the interpretation of number theory to vary.

A central claim of Jones & Love's (J&L's) article is that Bayesian Fundamentalism is empirically unconstrained. Unless constraints are placed on prior beliefs, likelihood, and utility functions, all behaviour is consistent with Bayesian rationality. Although such claims are commonplace, their basis is rarely justified. We fill this gap by sketching a proof, and we discuss possible solutions that would make Bayesian approaches empirically interesting.

In this paper I give a characterization of the closed fragment of the provability logic of $I \triangle_0 + \mathrm{EXP}$ with a propositional constant for $\mathrm{EXP}$. In three appendices many details on arithmetization are provided.

We show that a consistent, finitely axiomatized, sequential theory cannot prove its own inconsistency on every definable cut. A corollary is that there are at least three degrees of global interpretability of theories equivalent modulo local interpretability to a consistent, finitely axiomatized, sequential theory U.

Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, their logic, arrow logic can be studied from two different perspectives, and by two (complementary) methodologies: (...) modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tags. They show what the prices of desirable properties, such as decidability, (finite) axiomatisability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The research program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. The content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalised research program. (shrink)

In this paper we study local induction w.r.t. Σ1‐formulas over the weak arithmetic. The local induction scheme, which was introduced in, says roughly this: for any virtual class that is progressive, i.e., is closed under zero and successor, and for any non‐empty virtual class that is definable by a Σ1‐formula without parameters, the intersection of and is non‐empty. In other words, we have, for all Σ1‐sentences S, that S implies, whenever is progressive. Since, in the weak context, we have (at (...) least) two definitions of Σ1, we obtain two minimal theories of local induction w.r.t. Σ1‐formulas, which we call Peano Corto and Peano Basso.In the paper we give careful definitions of Peano Corto and Peano Basso. We establish their naturalness both by giving a model theoretic characterization and by providing an equivalent formulation in terms of a sentential reflection scheme.The theories Peano Corto and Peano Basso occupy a salient place among the sequential theories on the boundary between weak and strong theories. They bring together a powerful collection of principles that is locally interpretable in. Moreover, they have an important role as examples of various phenomena in the metamathematics of arithmetical (and, more generally, sequential) theories. We illustrate this by studying their behavior w.r.t. interpretability, model interpretability and local interpretability. In many ways the theories are more like Peano arithmetic or Zermelo Fraenkel set theory, than like finitely axiomatized theories as Elementary Arithmetic, and. On the one hand, Peano Corto and Peano Basso are very weak: they are locally cut‐interpretable in. On the other hand, they behave as if they were strong: they are not contained in any consistent finitely axiomatized arithmetical theory, however strong. Moreover, they extend, the theory of parameter‐free Π1‐induction. (shrink)