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Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall \,\lambda (...) < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred–O–RFN{0=1}.Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, ${\rm{RCA}}_0^{\rm{*}}$ be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,$${\rm{ATR}}_0 \equiv {\rm{RCA}}_0^{\rm{*}} + {\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - RFN}}\,_{{\bf{\Pi }}_2^1 } \left.$$We may even replace ${\rm{RCA}}_0^{\rm{*}}$ by the weaker ECA0, the second-order analogue of Elementary Arithmetic.Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles. (shrink)

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical completeness theorem with respect to PA is obtained for LR.

The egg behaves as a prospective cell sustaining the developmental processes of the future embryo. In biosemiotic terms, this apparent teleonomic behaviour can be accounted for without referring to the exclusive causal role played by its genetic makeup. We envision two different processes that are uniquely found in the oocyte: (1) the first involves the mechanisms by which large amounts of mRNA accumulate in the ooplasm to establish the embryo axes prior to fertilization; (2) the second involves transfer of an (...) excess of maternally supplied ribosomes to the oocyte to provide the future embryo with newly synthesized proteins. In this paper, we argue that the information required to sustain embryonic development is not due to any physical properties of the zygotic DNA and the maternal mRNAs, but to their spatially and temporally ordered relationship in the zygote’s internal space. (shrink)

DNA replication is both highly conserved and controlled. Problematic DNA replication can lead to genomic instability and therefore carcinogenesis. Numerous mechanisms work together to achieve this tight control and increasing evidence suggests that post‐translational modifications (phosphorylation, ubiquitination, SUMOylation) of DNA replication proteins play a pivotal role in this process. Here we discuss such modifications in the light of a recent article that describes a novel role for the deubiquitinase (DUB) USP7/HAUSP in the control of DNA replication. USP7 achieves this function (...) by an unusual and novel mechanism, namely deubiquitination of SUMOylated proteins at the replication fork, making USP7 also a SUMO DUB (SDUB). This work extends previous observations of increased levels of SUMO and low levels of ubiquitin at the on‐going replication fork. Here, we discuss this novel study, its contribution to the DNA replication and genomic stability field and what questions arise from this work. (shrink)

Translator's summary The translated paper is an extract, published in 1945, of an unpublished thesis, of both historical and technical import, dealing with notions of definability and their relation to invariance under automorphisms. The author develops a metamathematical Galois theory, and discusses and anticipates some aspects of higher-order model theory in an informal but conceptually rich manner.

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is obtained for LR.

A well known theorem proved by J. Paris and H. Friedman states that BΣn +1 is a Πn +2-conservative extension of IΣn . In this paper, as a continuation of our previous work on collection schemes for Δn +1-formulas , we study a general version of this theorem and characterize theories T such that T + BΣn +1 is a Πn +2-conservative extension of T . We prove that this conservativeness property is equivalent to a model-theoretic property relating Πn-envelopes and (...) Πn-indicators for T . The analysis of Σn +1-collection we develop here is also applied to Σn +1-induction using Parsons' conservativeness theorem instead of Friedman-Paris' theorem.As a corollary, our work provides new model-theoretic proofs of two theorems of R. Kaye, J. Paris and C. Dimitracopoulos : BΣn +1 and IΣn +1 are Σn +3-conservative extensions of their parameter free versions, BΣ–n +1 and IΣ–n +1. (shrink)

By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only consistent Πn+1-theory which extends the scheme of induction for parameter free Πn+1-formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first-order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain (...) results on the quantifier complexity, finite axiomatizability and relative strength of schemes for Δn+1-formulas. (shrink)

For families all over the world, going through a pandemic has presented a number of challenges. In particular, social distancing measures involving the closure of schools and day care centers, as well as increasing work hours at home, made parents face very demanding situations. However, we know little about whether parents’ burnout levels are influenced by the age of their children. This study sought to determine whether levels of parental burnout are higher in families with at least one child under (...) the age of four than in families with older children. The second goal was to explore whether having children under 4 years of age moderates the relationship between parental cooperation and PB. A cross-sectional study was conducted with a sample of 651 participants since May 18th until August 27th, 2020. The main results showed that child age is a predictor of PB. Besides, having a child aged 0–4 years old moderates the relationship between parental cooperation and PB. Finally, it was found that in cases where there was at least one child under 4 years of age in the family, with one of the partners who worked remotely, the respondent’s PB rose by 7.9 points. The implications of these results with respect to the consideration of children’s ages in the different parental scenarios were discussed. (shrink)

Reseña critica de los trabajos presentados en el encuentro italo-germano sobre Vico celebrado en Merano, 8-9 de Mayo de 1995, con la participación de G. Cotroneo, D. Barbieri, J. Seifert, K. Flasch, H. Seidl y G. Patella.A critical review of the papers submined at the Italian-German Meeting on Vico held at Merano during May, 8th and 9th 1995. References are made to G. Cotroneo, D. Barbieri, J. Seifert, K. Flasch, H. Seidl and G. Patella.

This paper is devoted to the algebraization of theories in which, as in Peano arithmetic, there is a formula, Theor(x), numerating the set of theorems, and satisfying Hilbert-Bernays derivability conditions. In particular, we study the diagonalizable algebras, which are been introduced by R. Magari in [6], [7]. We prove that for every natural number n, the n-freely generated algebra $\germ{J}_{n}$ is not functionally free in the equational class of diagonalizable algebras; we also prove that the diagonalizable algebra of Peano arithmetic (...) is not an element of the equational class generated by $\{\germ{J}_{n}\}$. (shrink)

Guaspari (J Symb Logic 48:777–789, 1983) conjectured that a modal formula is it essentially Σ1 (i.e., it is Σ1 under any arithmetical interpretation), if and only if it is provably equivalent to a disjunction of formulas of the form ${\square{B}}$ . This conjecture was proved first by A. Visser. Then, in (de Jongh and Pianigiani, Logic at Work: In Memory of Helena Rasiowa, Springer-Physica Verlag, Heidelberg-New York, pp. 246–255, 1999), the authors characterized essentially Σ1 formulas of languages including witness comparisons (...) using the interpretability logic ILM. In this note we give a similar characterization for formulas with a binary operator interpreted as interpretability in a finitely axiomatizable extension of IΔ 0 + Supexp and we address a similar problem for IΔ 0 + Exp. (shrink)

In this paper, I look at Susan Stebbing’s articles and reviews that critically engage logical positivism. These appeared before the publication of A.J. Ayer’s Language, Truth and Logic and helped shape the early British reception of logical positivism. I highlight Stebbing’s adoption of G.E. Moore’s tripartite distinction between knowing a proposition, understanding it, and giving an analysis of it and, in light of this distinction, her focus on whether the principle of verifiability can ground a plausible account of communication. Stebbing (...) thinks not, and I reconstruct her reasons, as well as her own account of communication. In doing this, I relate her criticisms to her rejection of methodological solipsism and her dissatisfaction with the logical positivist treatment of statements about other minds and the past. I also argue that Stebbing’s work provides a bridge to later criticisms of logical positivism from ordinary language philosophers. Foregrounding Stebbing’s engagement with logical positivism, especially her focus on communication, paints a fuller picture of how the logical positivists came to be part of analytic philosophy despite having different concerns than many of the British philosophers engaging their work. (shrink)

Dans un travail anterieur j’ai essaye de montrer que Heidegger a finalement refuse de faire place, dans sa philosophie, a la notion platonicienne d’idee, bien qu’elle semblait, selon un certain point de vue, etre une figure capable de representer l’ouverture originelle de l’être qui était au coeur des recherches de Heidegger dans les annees qui entourent Etre et Temps. La raison de cela, a mon avis, est que l’approche aristotelicienne de la philosophie de Platon par Heidegger explicitement adoptee conduisait au (...) bout du compte a interpreter l’idee de Platon comme une substance. Mais qu’en est‑il de l’idee du bien, qui pour sa determination teleologique et pour sa collocation au‑dela de l’ousia d’un cote semblait repondre aux besoins propres a la pensee heideggerienne, et d’un autre cote etait plus refractaire a la substantialisation aristotelicienne? La these que je soutiens est que Heidegger, tout en ayant cultive pour longtemps le projet d’utiliser l’idee du bien comme un precedent important de son ontologie, a finalement decide que ce projet n’etait pas possible, parce que la connotation ethique de cette idee etait largement dominante sur l’aspect ontologique. (shrink)

In this paper, I fill out the received view of logical positivism within professional philosophy against which Thomas Kuhn’s Structure appeared. To do this, I look at the methodological dimensions of ordinary language criticisms of logical positivist analysis from P.F. Strawson and J.L. Austin. While no one would confuse Strawson and Austin for philosophers of science, I look to their criticisms given the general porousness of sub-disciplinary boundaries in mid-20th century philosophy, the prominence of ordinary language philosophy in the 1950s, (...) and also because Kuhn was likely aware of their criticisms via Stanley Cavell. Their main charge is that the positivists base their ideal language analysis on an impoverished, yet overreaching account of meaning because they ignore ordinary linguistic practices. I then show how these methodological criticisms run parallel to points Kuhn makes against logical positivist approaches to the study of scientific knowledge. The parallels I draw emphasize methodological, rather than doctrinal dissatisfaction in mid-20th century philosophy with logical positivism’s perceived neglect of linguistic and scientific practices. An insight shared by these parallel criticisms is that logical positivists cannot declare linguistic and scientific practices irrelevant to their philosophical aims without an antecedent investigation of the practices under question. (shrink)

In Hájek et al. (J Symb Logic 65(2):669–682, 2000) the authors introduce the concept of supersound logic, proving that first-order Gödel logic enjoys this property, whilst first-order Łukasiewicz and product logics do not; in Hájek and Shepherdson (Ann Pure Appl Logic 109(1–2):65–69, 2001) this result is improved showing that, among the logics given by continuous t-norms, Gödel logic is the only one that is supersound. In this paper we will generalize the previous results. Two conditions will be presented: the first (...) one implies the supersoundness and the second one non-supersoundness. To develop these results we will use, between the other machineries, the techniques of completions of MTL-chains developed in Labuschagne and van Alten (Proceedings of the ninth international conference on intelligent technologies, 2008) and van Alten (2009). We list some of the main results. The first-order versions of MTL, SMTL, IMTL, WNM, NM, RDP are supersound; the first-order version of an axiomatic extension of BL is supersound if and only it is n-potent (i.e. it proves the formula ${\varphi^{n}\,\to\,\varphi^{n\,{+}\,1}}$ for some ${n\,\in\,\mathbb{N}^+}$ ). Concerning the negative results, we have that the first-order versions of ΠMTL, WCMTL and of each non-n-potent axiomatic extension of BL are not supersound. (shrink)

L’articolo affronta il problema delle implicazioni politiche dei tumulti causati dalle ondate di cattivi raccolti e scarsità di cereali in Gran Bretagna nel XVIII secolo. Il dibattito e i documenti dell’epoca non sembrano convalidare le ipotesi critiche connesse con l’idea foucaultiana di governamentalità o con la difesa smithiana di libero commercio dei grani. Più feconde appaiono le tesi di E.P. Thompson e J. Bohstedt, entrambe legate al rapporto tra sussistenze, deferenza e stabilità sociale. Sono anche prese in considerazione le misure (...) relative ai distillati e le reazioni popolari alle stesse. (shrink)

The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375–381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727–732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, (...) produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this problem. (shrink)

Le philosophe américain Charles S. Peirce ne trouva, malgré ses efforts, guère d’interlocuteurs en France. On le considéra comme un mathématicien et logicien, un physicien et un psychologue fiable, mais son œuvre philosophique fut systématiquement distordue au gré des controverses franco-françaises. Nous mettons l’accent sur les lectures d’André Lalande et de Louis Couturat qui contribuèrent néanmoins à faire reconnaître en France l’originalité du père du pragmaticisme.Despite his efforts, the American philosopher Charles S. Peirce found hardly any interlocutors in France. (...) He was considered mostly as a mathematician and logician, a physicist and a reliable psychologist, but his philosophical work was systematically distorted in consequence of “Franco-French” disputes. We emphasize here the readings of André Lalande and Louis Couturat who made significant contributions towards the recognition in France of the originality of the founding father of Pragmaticism. (shrink)