Les anthropologues qui étudient les effets de la « modernité » en Mélanésie ont donné un souffle nouveau à la question de la personne relationnelle. On observe l’apparition de personnes plus individualisées, plus autonomes dans le contexte de la conversion au christianisme, de la consommation de biens et du travail salarié. Comportements sexuels et sensibilités des jeunes se transforment à la faveur de leur expérience d’idées nouvelles sur les rapports amoureux et de formes inédites d’érotisme, bien que toujours soumis à (...) de fortes contraintes structurelles. Savoir comment les autres expérimentent le monde est une vaste question examinée à partir de deux sources : les récits des jeunes sur eux-mêmes, et des histoires d’esprits, qui gagnent en autonomie mais conservent leur appartenance à des communautés façonnées par les réseaux de parenté et d’échange.Anthropologists concerned with the effects of « modernity » in Melanesia have injected new life into the topic of relational personhood. More individualized, self-owning persons are said to be emerging in the context of conversion to Christianity, commodity consumption, and wage labor. The sexual behaviors and sensibilities of young people change as they experiment with new ideas about romance and forms of sexual pleasure, albeit under considerable structural constraints. The broader problem of knowing how others experience the world is evaluated by examining two sources : the self-reports of young people, and stories about spirit beings, who become more self-owning but also retain membership in communities fashioned by the webs of kinship and exchange. (shrink)

Intra-hemispheric interference has been often observed when body parts with neighboring representations within the same hemisphere are stimulated. However, patterns of interference in early and late somatosensory processing stages due to the stimulation of different body parts have not been explored. Here, we explore functional similarities and differences between attention modulation of the somatosensory N140 and P300 elicited at the fingers vs. cheeks. In an active oddball paradigm, 22 participants received vibrotactile intensity deviant stimulation either ipsilateral or contralateral at the (...) fingers or cheeks. The ipsilateral deviant always covered a larger area of skin than the contralateral deviant. Overall, both N140 and P300 amplitudes were higher following stimulation at the cheek and N140 topographies differed between fingers and cheek stimulation. For the N140, results showed higher deviant ERP amplitudes following contralateral than ipsilateral stimulation, regardless of the stimulated body part. N140 peak latency differed between stimulated body parts with shorter latencies for the stimulation at the fingers. Regarding P300 amplitudes, contralateral deviant stimulation at the fingers replicated the N140 pattern, showing higher responses and shorter latencies than ipsilateral stimulation at the fingers. For the stimulation at the cheeks, ipsilateral deviants elicited higher P300 amplitudes and longer latencies than contralateral ones. These findings indicate that at the fingers ipsilateral deviant stimulation leads to intra-hemispheric interference, with significantly smaller ERP amplitudes than in contralateral stimulation, both at early and late processing stages. By contrast, at the cheeks, intra-hemispheric interference is selective for early processing stages. Therefore, the mechanisms of intra-hemispheric processing differ from inter-hemispheric ones and the pattern of intra-hemispheric interference in early and late processing stages is body-part specific. (shrink)

Notes on the life of Adolf Lindenbaum, a complete bibliography of his published works, and selected references to his unpublished results.

Adolf Lindenbaum Adolf Lindenbaum was a Polish mathematician and logician who worked in topology, set theory, metalogic, general metamathematics and the foundations of mathematics. He represented an attitude typical of the Polish Mathematical School, consisting of using all admissible methods, independently of whether they were finitary. For example, the axiom of choice was freely applied, … Continue reading Lindenbaum, Adolf →.

We consider formal theories synonymous with various free categories . Their Lindenbaum algebras may be described as the lattices of subobjects of a terminator. These theories have intuitionistic logic. We show that the Lindenbaum algebras of second order and higher order arithmetic , and set theory are not isomorphic to the Lindenbaum algebras of first order theories such as arithmetic . We also show that there are only five kernels of representations of the free Heyting algebra on (...) one generator in these Lindenbaum algebras. (shrink)

In this paper, we study some classes of logical structures from the universal logic standpoint, viz., those of the Tarski- and the Lindenbaum-types. The characterization theorems for the Tarski- and two of the four different Lindenbaum-type logical structures have been proved as well. The separations between the five classes of logical structures, viz., the four Lindenbaum-types and the Tarski-type have been established via examples. Finally, we study the logical structures that are of both Tarski- and a (...) class='Hi'>Lindenbaum-type, show their separations, and end with characterization, adequacy, minimality, and representation theorems for one of the Tarski–Lindenbaum-type logical structures. (shrink)

In this paper, we investigate the Lindenbaum algebra ℒ of the theory T fin = Th of the class M fin of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its Gödel numeration γ is a [Formula: see text]-numeration. Moreover, the quotient algebra /ℱ, γ/ℱ) modulo the Fréchet ideal ℱ is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These (...) conditions characterize uniquely the algebra ℒ; moreover, these conditions characterize up to recursive isomorphism the numerated Boolean quotient algebra /ℱ, γ/ℱ). These results extend the work of Trakhtenbrot [17] and Vaught [18] on the first order theory of the class of all finite models of a finite rich signature. (shrink)

This paper revisits the life of Adolf Lindenbaum in light of new research findings, then looks at two areas among many—metric spaces, and decompositions of point sets—where his work has been underappreciated.

Janina Hosiasson-Lindenbaum is a known figure in philosophy of probability of the 1930s. A previously unpublished manuscript fills in the blanks in the full picture of her work on inductive reasoning by analogy, until now only accessible through a single publication. In this paper, I present Hosiasson’s work on analogical reasoning, bringing together her early publications that were never translated from Polish, and the recently discovered unpublished work. I then show how her late work relates to Rudolf Carnap’s approach (...) to “analogy by similarity” developed in the 1960s. Hosiasson turns out to be a predecessor of the line of research that models analogical influence as inductive relevance. A translation of Hosiasson’s manuscript concludes the paper. (shrink)

We discuss the problem raised by Miller to re-prove the well-known equivalences of some Lindenbaum theorems for deductive systems without an application of the Axiom of Choice. We present five special constructions of deductive systems, each of them providing some partial solutions to the mathematical problem. We conclude with a short discussion of the underlying philosophical problem of deciding, whether a given proof satisfies our demand that the Axiom of Choice is not applied.

We prove that the first order theory of the fixed point algebra corresponding to an r.e. consistent theory containing arithmetic is hereditarily undecidable.

We prove, by using the concept of schematic interpretation, that the natural embedding from the category ISL, of intuitionistic sentential pretheories and i-congruence classes of morphisms, to the category CSL, of classical sentential pretheories and c-congruence classes of morphisms, has a left adjoint, which is related to the double negation interpretation of Gödel-Gentzen, and a right adjoint, which is related to the Law of Excluded Middle. Moreover, we prove that from the left to the right adjoint there is a pointwise (...) epimorphic natural transformation and that since the two endofunctors at CSL, obtained by adequately composing the aforementioned functors, are naturally isomorphic to the identity functor for CSL, the string of adjunctions constitutes an adjoint cylinder. On the other hand, we show that the operators of Lindenbaum-Tarski of formation of algebras from pretheories can be extended to equivalences of categories from the category CSL, respectively, ISL, to the category Bool, of Boolean algebras, respectively, Heyt, of Heyting algebras. Finally, we prove that the functor of regularization from Heyt to Bool has, in addition to its well-known right adjoint (that is, the canonical embedding of Bool into Heyt) a left adjoint, that from the left to the right adjoint there is a pointwise epimorphic natural transformation, and, finally, that such a string of adjunctions constitutes an adjoint cylinder. (shrink)

We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra.

In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of inference, familiar from Gentzen, in which one may consider multiple conclusions rather than single formulas. Scott used this idea to good effect in a number of projects including the axiomatization of many-valued logics (of various kinds) and a reconsideration of the motivation of C.I. Lewis. Since he left the subject it has been vigorously prosecuted (...) by a number of authors under the heading of abstract entailment relations where it has found an important role in both algebra and theoretical computer science. In this essay we go back to the beginnings, as presented by Scott, in order to make some comments about Scott’s cut rule, and show how much of Scott’s main result may be applied to the case of single-conclusion logic. (shrink)

. Dzik [2] gives a direct proof of the axiom of choice from the generalized Lindenbaum extension theorem LET. The converse is part of every decent logical education. Inspection of Dzik’s proof shows that its premise let attributes a very special version of the Lindenbaum extension property to a very special class of deductive systems, here called Dzik systems. The problem therefore arises of giving a direct proof, not using the axiom of choice, of the conditional . A (...) partial solution is provided. (shrink)

In this paper we prove that the preordering $\lesssim $ of provable implication over any recursively enumerable theory $T$ containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function $F$ for $\lesssim $. A recursive function $F$ is a density function if it computes, for $A$ and $B$ with $A\lnsim B$, an element $C$ such that $A\lnsim C\lnsim B$. The function is extensional if it preserves $T$-provable equivalence. Secondly, we prove a (...) general result that implies that, for extensions of elementary arithmetic, the ordering $\lesssim $ restricted to $\Sigma_{n}$-sentences is uniformly dense. In the last section we provide historical notes and background material. (shrink)

This paper will take into account the Lindenbaum property in Orthomodular Quantum Logic (OQL) and Partial Classical Logic (PCL). The Lindenbaum property has an interest both from a logical and a physical point of view since it has to do with the problem of the completeness of quantum theory and with the possibility of extending any semantically non-contradictory set of formulas to a semantically non-contradictory complete set of formulas. The main purpose of this paper is to show that (...) both OQL and PCL cannot satisfy the Lindenbaum property. (shrink)

In the paper we give a sucient condition of the Interpolation Property in propositional calculi; then we establish the power of the class of the systems with Craig's property. Next we show that there does not exist a minimal R0-system with Craig-Godel-Lindenbaum's property. Finally, we generalize Sobocinski-Tarskis theorem concerning Sobocinski-Tarski's property.

The present paper is a continuation of [6] and [7]. Thus the content of this paper is the following. At first we establish properties of systems S 2 n and S 2∗ n , where systems S 2 n and S 2∗ n are extensions of Rasiowa-S lupecki’s systems Sn and S ∗ n . Then we shall show that for every cardinal number m there exist a system ST 4 m of propositional calculus and a system SP 4 m (...) of predicate calculus such that the system ST 4 m has exactly m Lindenbaum’s oversystems and the system SP 4 m has exactly m Lindenbaum’s oversystems, where 1 ≤ m ≤ 2 ℵ0. (shrink)

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