Irrationality and egoism in Hegel’s account of right

ABSTRACT

Many interpreters argue that irrational acts of exchange can count as rational and civic-minded for Hegel – even though, admittedly, the persons who are exchanging their property are usually unaware of this fact. While I do not want to deny that property exchange can count as rational in terms of ‘mutual recognition’ as interpreters claim, this proposition raises an important question: What about the irrationality and arbitrariness that individuals as property owners and persons consciously enjoy? Are they mere vestiges of nature in Hegel’s system, or do they constitute a simple yet valid form of freedom that is not only a part of Hegel’s rational system of right, but its necessary starting point? I will argue the latter: The arbitrary, purely egoist self-definition of property owners is the simplest possible type of freedom for Hegel, which he dissects in order to show how the very arbitrary self-definition implicitly relies on an identity between persons, and hence foreshadows the more social forms of freedom Hegel will discuss later in his book. I make this argument by highlighting Hegel’s references to his discussion of atoms and freedom in his Logic of Being.     

Modal Logics of Succession for 2-Dimensional Integral Spacetime

We consider the problem of axiomatizing various natural successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the standard modal language (i.e. the language containing and ) is not finitely axiomatizable.     

“Four-Valued” Semantics for the Relevant Logic R

This paper sets out two semantics for the relevant logic R based on Dunn's four-valued semantics for first-degree entailments. Unlike Routley's semantics for weak relevant logics, they do not use two ternary accessibility relations. Unlike Restall's semantics, they capture all of R. But there is a catch. Both of the present semantics are neighbourhood semantics, that is, they include sets of propositions in the specification of their frames.     

CE is Not a Conservative Extension of E

The logic CE (for Classical E) results from adding Boolean negation to Anderson and Belnap"s logic E. This paper shows that CE is not a conservative extension of E.     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

Decidability of Quantified Propositional Intuitionistic Logic and S4 on Trees of Height and Arity ≤ω

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers p, p, where the propositional variables range over upward-closed subsets of the set of worlds in a Kripke structure. If the permitted accessibility relations are arbitrary partial orders, the resulting logic is known to be recursively isomorphic to full second-order logic (Kremer, 1997). It is shown that if the Kripke structures are restricted to trees of at height and width at most , the resulting logics are decidable. This provides a partial answer to a question by Kremer. The result also transfers to modal S4 and some Gödel–Dummett logics with quantifiers over propositions.     

A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.     

Predicate Logics on Display

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.     

A Note on the Interpolation Property in Tense Logic

It is proved that all bimodal tense logics which contain the logic of the weak orderings and have unbounded depth do not have the interpolation property.     

Extended Quantum Logic

The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.     

Constructing Finite Least Kripke Models for Positive Logic Programs in Serial Regular Grammar Logics

A serial context-free grammar logic is a normal multimodal logicL characterized by the seriality axioms and a set of inclusionaxioms of the form _ts1..._sk. Such an inclusion axiom correspondsto the grammar rule t s₁... s_k. Thus the inclusion axioms ofL capture a context-free grammar . If for every modal index t, the set of words derivable fromt using is a regular language, then L is a serial regular grammar logic. In this paper, we present an algorithm that, given a positivemultimodal logic program P and a set of finite automata specifyinga serial regular grammar logic L, constructs a finite leastL-model of P. (A model M is less than or equal to model M' iffor every positive formula , if M then M' .) A least L-modelM of P has the property that for every positive formula , P iff M . The algorithm runs in exponential time and returnsa model with size 2^O(n³). We give examples of P and L, for bothof the case when L is fixed or P is fixed, such that every finiteleast L-model of P must have size 2⁽ⁿ⁾. We also prove that ifG is a context-free grammar and L is the serial grammar logiccorresponding to G then there exists a finite least L-modelof _s p iff the set of words derivable from s using G is a regularlanguage.     

Cut-free tableau calculi for some propositional normal modal logics

We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G ⁰(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G ⁰are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the so-called analytical cut-rule.In addition we show that G ⁰is not compact (and therefore not canonical), and we proof with the tableau-method that G ⁰is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G ⁰is decidable and also characterised by the class of all frames for G ⁰.Research supported by Fonds zur Förderung der wissenschaftlichen Forschung, project number P8495-PHY.Presented by W. Rautenberg     

Semisimple Varieties of Modal Algebras

In this paper we show that a variety of modal algebras of finite type is semisimple iff it is discriminator iff it is both weakly transitive and cyclic. This fact has been claimed already in [4] (based on joint work by the two authors) but the proof was fatally flawed. Dedicated to the memory of Willem Johannes Blok     

Game Logic - An Overview

Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.     

Simulation and Transfer Results in Modal Logic – A Survey

This papers gives a survey of recent results about simulations of one class of modal logics by another class and of the transfer of properties of modal logics under extensions of the underlying modal language. We discuss: the transfer from normal polymodal logics to their fusions, the transfer from normal modal logics to their extensions by adding the universal modality, and the transfer from normal monomodal logics to minimal tense extensions. Likewise, we discuss simulations of normal polymodal logics by normal monomodal logics, of nominals and the difference operator by normal operators, of monotonic monomodal logics by normal bimodal logics, of polyadic normal modal logics by polymodal normal modal logics, and of intuitionistic modal logics by normal bimodal logics.