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 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)

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.

There is a growing interest in how people conceptualise the legal domain for the purpose of legal knowledge systems. In this paper we discuss four such conceptualisations (referred to as ontologies): McCarty's language for legal discourse, Stamper's norma formalism, Valente's functional ontology of law, and the ontology of Van Kralingen and Visser. We present criteria for a comparison of the ontologies and discuss the strengths and weaknesses of the ontologies in relation to these criteria. Moreover, we critically review the (...) criteria. (shrink)

In his _Between Logic and the World_, in the course of presenting his theory of generics, Nickel (Between logic and the world, Oxford University Press, 2016) argues for a theory of characteristicness, or “genericity”, which states that a property is characteristic for a kind if and only if its presence among the members of that kind is explicable by some explanatory domain that recognizes the existence of that kind in the course of engaging the explanatory strategies made available by that (...) explanatory domain. I argue that this notion of genericity is too narrow, excluding properties characteristic for kinds that go unrecognized in such explanatory domains. In particular, Nickel’s theory excludes some characteristic properties of anthropic kinds, such as lilies and cedars, members of which have properties that may be similarly exploited in various human practices despite having divergent geneses. I argue for a generalization of Nickel’s view of genericity where explicability of presence is only one sort of genericity, with others, such as practicability, being possible too. (shrink)

This paper is concerned with the logical structure of arithmetical theories. We survey results concerning logics and admissible rules of constructive arithmetical theories. We prove a new theorem: the admissible propositional rules of Heyting Arithmetic are the same as the admissible propositional rules of Intuitionistic Propositional Logic. We provide some further insights concerning predicate logical admissible rules for arithmetical theories.

In his paper "Undecidability without arithmetization," Andrzej Grzegorczyk introduces a theory of concatenation $\mathsf{TC}$. We show that pairing is not definable in $\mathsf{TC}$. We determine a reasonable extension of $\mathsf{TC}$ that is sequential, that is, has a good sequence coding.

There is a “Pragmatist turn” visible in the field of organization science today, resulting from a renewed interest in the work of Pragmatist philosophers like Dewey, Mead, Peirce, James and others, and in its implications for the study of organizations. Following Wicks and Freeman, in the past decade Pragmatism has also entered the field of business ethics, which, however, has not been uniformly applauded in that field. Some scholars fear that Pragmatism may enhance already existing positivist and managerialist tendencies in (...) current business ethics, while others see more emancipatory potential in Pragmatism, arguing that it complements and supports stakeholder theory. In this paper, a comparison of the philosophical underpinnings of Pragmatist and Critical conceptions of business ethics is offered, concentrating on the Pragmatism of John Dewey and the Critical theory of the Frankfurt School, in particular of Axel Honneth. It is argued that these two developed along two converging lines. Along the first line, Dewey was far more skeptical and critical of capitalism than is often thought. Along the second line, the reactions to Pragmatism of Frankfurt School Critical theorists developed over time from generally hostile, to partially inclusive, to more fully integrative. At the crossroads of these converging lines a Pragmatist Critical perspective is developed and exemplified, and its implications for business ethics are outlined. (shrink)

We argue that thinking of the man-machine comparison in terms of a contest involves, in a reasonable scenario, a criterion of success that is neutral. This is because we want to avoid a petitio principii. We submit, however, that, by looking at things this way, one makes the most essential human things invisible. Thus, in a sense, the contest approach is self-defeating.

This paper contains a careful derivation of principles of Interpretability Logic valid in extensions of I0+1.

In this paper we show how to interpret Robinson’s arithmetic Q and the theory R of Tarski, Mostowski, and Robinson as theories of cardinals in very weak theories of relations over a domain.

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.

This article critically evaluates the possible impact of the Charter on the relationship between the Court of Justice of the European Union and national constitutional courts. While it is premature to provide a definitive assessment of the kind of collaboration that these courts will develop, it is crucial to identify a number of features of the new landscape that will influence the direction in which the relationship between the CJEU and constitutional courts will evolve. This article discusses several reasons that (...) may result in better or a higher number of judicial interactions, as well as factors that may create tension or cause problems in the relationship between the CJEU and national constitutional courts. As such, it offers a framework that may help us to understand future post-Charter judgments by these courts setting out how they conceive their engagement with their counterpart on fundamental rights issues. (shrink)

In this note we derive Robinson???s Arithmetic from Hume???s Principle in the context of very weak theories of classes and relations.

In this paper we formulate a version of Second Incompleteness Theorem. The idea is that a sequential sentence has ‘consistency power’ over a theory if it enables us to construct a bounded interpretation of that theory. An interpretation of V in U is bounded if, for some n , all translations of V -sentences are U -provably equivalent to sentences of complexity less than n . We call a sequential sentence with consistency power over T a pro-consistency statement for T (...) . We study pro-consistency statements. We provide an example of a pro-consistency statement for a sequential sentence A that is weaker than an ordinary consistency statement for A . We show that, if A is $${{\sf S}^{1}_{2}}$$ , this sentence has some further appealing properties, specifically that it is an Orey sentence for EA . The basic ideas of the paper essentially involve sequential theories. We have a brief look at the wider environment of the results, to wit the case of theories with pairing. (shrink)

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.

In this paper we study the idea of theories with containers, like sets, pairs, sequences. We provide a modest framework to study such theories. We prove two concrete results. First, we show that first-order theories of finite signature that have functional non-surjective ordered pairing are definitionally equivalent to extensions in the same language of the basic theory of non-surjective ordered pairing. Second, we show that a first-order theory of finite signature is sequential (is a theory of sequences) iff it is (...) definitionally equivalent to an extension in the same language of a system of weak set theory called WS. (shrink)

This article critically analyzes the assumption that land is becoming increasingly scarce and that, therefore, farmland values are bound to rise across the globe. It investigates the process of land value creation, as well as its flipside: value erosion and stagnation, looking at the various mechanisms involved in each. As such, it is a study of how the financialization of agriculture affects the process of land commoditization. I show that, for farmland to be turned into an asset, a whole range (...) of conditions have to be fulfilled, presenting a typology of asset making in the context of farmland. Asset making, like commoditization, is a process of assemblage, and it is less straightforward and less stable than generally assumed. Further, I argue that ‘asset making’ is not a one-way process. The article is based on an analysis of global data on land values and the case of farmland investment in post-Soviet farmland. (shrink)

This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...) Here NNIL is the class of propositional formulas with no nestings of implications to the left . The identical embedding of IPC -derivability into a consequence relation has in many cases a left adjoint. The main tool of the present paper will be an algorithm to compute this left adjoint in the case of NNIL -preservativity. In the last section, we employ the methods developed in the paper to give a characterization the closed fragment of the provability logic of HA. (shrink)

A prevailing focus of global value chain (GVC) analysis has been on the dominance of highly consolidated Northern retailers over suppliers in the global South. The rise of regional and domestic value chains (RVCs/DVCs) within the Global South which intersect with GVCs, has been found to involve private governance by Southern lead firms. However, we have limited insight into the implications of this changing value chain context for the role of public governance, or different groups of workers. South African fruit (...) provides a rich example of rapid shifts in RVCs/DVCs governed by different private and public actors. The following two questions are addressed: How is the public–private governance of labour standards evolving in the context of RVCs and DVCs that intersect with GVCs? What are the implications for workers operating across different value chains? Conceptually, the paper draws on GVC analysis of governance and power, to examine the governance of labour standards across intersecting value chains. Our analysis highlights the intentional and unintentional mechanisms through which power and standard-setting are diffused away from Northern lead firms to a wider array of public and private actors operating across RVCs/DVCs. While existing analysis of governance and power focuses on singular GVCs, our study highlights diffusion of power across intersecting value chains, with significant and uneven implications for the public–private governance of labour standards. Our findings carry significant ethical implications for the governance of labour standards, as end-markets continue to shift South. (shrink)

The central result of this paper is the small‐is‐very‐small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a definable property has a small witness, i.e., a witness in a sufficiently small definable cut, then it shows that the property has a very small witness: i.e., a witness below a given standard number. Which cuts are sufficiently small will depend on the complexity of the formula defining the property. We draw various consequences from (...) the central result. E.g., roughly speaking, (i) every restricted, recursively enumerable sequential theory has a finitely axiomatized extension that is conservative with respect to formulas of complexity ; (ii) every sequential model has, for any n, an extension that is elementary for formulas of complexity, in which the intersection of all definable cuts is the natural numbers; (iii) we have reflection for ‐sentences with sufficiently small witness in any consistent restricted theory U; (iv) suppose U is recursively enumerable and sequential. Suppose further that every recursively enumerable and sequential V that locally inteprets U, globally interprets U. Then, U is mutually globally interpretable with a finitely axiomatized sequential theory. The paper contains some careful groundwork developing partial satisfaction predicates in sequential theories for the complexity measure depth of quantifier alternations. (shrink)

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)

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.

A Kripke model ? is a submodel of another Kripke model ℳ if ? is obtained by restricting the set of nodes of ℳ. In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas. This result is an analogue of the Łoś-Tarski theorem for the Classical Predicate Calculus.In Appendix A we prove that for theories with decidable identity we can take (...) as the embeddings between domains in Kripke models of the theory, the identical embeddings. This is a well known fact, but we know of no correct proof in the literature. In Appendix B we answer, negatively, a question posed by Sam Buss: whether there is a classical theory T, such that ℋT is HA. Here ℋT is the theory of all Kripke models ℳ such that the structures assigned to the nodes of ℳ all satisfy T in the sense of classical model theory. (shrink)

In this paper we study the interpretations of a weak arithmetic, like Buss’s theory $\mathsf{S}^{1}_{2}$, in a given theory $U$. We call these interpretations the arithmetics of $U$. We develop the basics of the structure of the arithmetics of $U$. We study the provability logic of $U$ from the standpoint of the framework of the arithmetics of $U$. Finally, we provide a deeper study of the arithmetics of a finitely axiomatized sequential theory.

In this paper a dialogue game for critical discussion is developed. The dialogue game is a formalisation of the ideal discussion model that is central to the pragma-dialectical theory of argumentation. The formalisation is intended as a preparatory step to facilitate the development of computational tools to support the pragma-dialectical study of argumentation. An important dimension of the pragma-dialectical discussion model is the role played by speech acts. The central issue addressed in this paper is how the speech act perspective (...) can be accommodated in the formalisation as a dialogue game. The starting point is an existing ‘basic’ dialogue game for critical discussion, in which speech acts are not addressed. The speech act perspective is introduced into the dialogue game by changing the rules that govern the moves that can be made and the commitments that these result in, while the rules for the beginning, for the end, and for the structure of the dialogue game remain unchanged. The revision of the move rules is based on the distribution of speech acts in the pragma-dialectical discussion model. The revision of the commitment rules is based on the felicity conditions that are associated with those speech acts. (shrink)

In the past decade, the concept of recognition appears to have acquired an important theoretical position in the work and organization literature. While in principle recognition denotes a positive and social form of freedom, in current-day organizations recognition may be often negative or instrumental. In order to capture this ambivalence in organizational recognitive conditions, the recent work of the American philosopher Judith Butler appears particularly applicable. The purpose of this paper is to explore theoretically to what extent her views on (...) recognition shed new light on the variety of recognition patterns in current-day organizations. Towards that purpose, this paper first turns to the ‘master-slave’ episode in the work of Hegel and its influential interpretation by Kojève, which are at the heart of Butler’s reading and conception of recognition. As a second step, the ambivalent conception of recognition in the work of Butler is discussed and critically assessed, while in the final section this conception is extended to work and organizations. (shrink)