By a result of L.D. Beklemishev, the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over any $$\Pi _2$$ -axiomatizable base theory extending Elementary Arithmetic collapses to its first level. We prove that this result cannot in general be extended to base theories of arbitrary quantifier complexity. In fact, given any recursively enumerable set of true $$\Pi _2$$ -sentences, S, we construct a sound $$(\Sigma _2 \! \vee \! \Pi _2)$$ -axiomatized theory T extending S such that the (...) hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over T is proper. Our construction uses some results on subrecursive degree theory obtained by L. Kristiansen. (shrink)

For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained restricting the schemes of induction, minimization and (a version of) collection to Δ n+1 (T) formulas. We obtain conditions on T (T is an extension of B * Δ n+1 (T) or Δ n+1 (T) is closed (in T) under bounded quantification) under which IΔ n+1 (T) and LΔ n+1 (T) are equivalent. These conditions depend (...) on Th Πn +2 (T), the Π n+2 –consequences of T. The first condition is connected with descriptions of Th Πn +2 (T) as IΣ n plus a class of nondecreasing total Π n –functions, and the second one is related with the equivalence between Δ n+1 (T)–formulas and bounded formulas (of a language extending the language of Arithmetic). This last property is closely tied to a general version of a well known theorem of R. Parikh. Using what we call Π n –envelopes we give uniform descriptions of the previous classes of nondecreasing total Π n –functions. Π n –envelopes are a generalization of envelopes (see [10]) and are closely related to indicators (see [12]). Finally, we study the hierarchy of theories IΔ n+1 (IΣ m ), m≥n, and prove a hierarchy theorem. (shrink)

We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.

We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.

We characterize the sets of all Π2 and all equation image theorems of IΠ−1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ−n + 1 is conservative over IΣ−n with respect to equation image sentences cannot be extended to Πn + 2 sentences. © 2011 WILEY-VCH Verlag (...) GmbH & Co. KGaA, Weinheim. (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)

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)

This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are Δ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta_1}$$\end{document} provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether IΔ0+¬exp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I\Delta_0 + \neg \mathit{exp}}$$\end{document} implies BΣ1\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B\Sigma_1}$$\end{document} to a purely recursion-theoretic question. (shrink)

In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that IΔ n+1 (T) is Π n+2 –axiomatizable. In particular, IΔ n+1 (IΔ n+1 ) gives an axiomatization of Th Π n+2 (IΔ n+1 ) and is not finitely axiomatizable. This fact relates the fragment IΔ n+1 (IΔ n+1 ) to induction (...) rule for Δ n+1 –formulas. Our arguments, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons’ conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for Π n+2 and Δ n+1 formulas (see [2]). (shrink)

The state of computing science and, particularly, software engineering and knowledge engineering is generally considered immature. The best starting point for achieving a mature engineering discipline is a solid scientific theory, and the primary reason behind the immaturity in these fields is precisely that computing science still has no such agreed upon underlying theory. As theories in other fields of science do, this paper formally establishes the fundamental elements and postulates making up a first attempt at a theory in this (...) field, considering the features and peculiarities of computing science. The fundamental elements of this approach are informons and holons, and it is a general and comprehensive theory of software engineering and knowledge engineering that related disciplines (e.g., information systems) can particularise and/or extend to take benefit from it (Lakatos’ concepts of core theory and protective belt theories). (shrink)

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)

This article uses a well-defined setting to suggest an optimistic view about the distributional effects of immigration. Section 2 provides a general picture of the native-immigrant differences in labour force participation, unemployment, and occupational and educational attainment, taking skill levels and years since immigration into account. Section 3 investigates the inequality impact of immigration by summarizing the potential labour market impacts and the wage and employment consequences. Section 4 deals with the potentially slow integration of immigrants into the labour market (...) of the host country, as well as with the role that self-selection and selection through politically set admission rules can play for the performance in the labour market. It also considers cultural or ethnic identity as an independent factor potentially affecting economic success and discusses the consequences for inequality. Section 5 concludes. (shrink)

Known as the Darwin of the twenty-first century, the German biologist Ernst Walter Mayr (1904-2005) studied a great variety of subjects such as Ornithology, Genetics, Evolution, Classification, History, and Philosophy of Biology. This scientist was a giant of the previous century and an icon of Evolutionary Biology. He became famous for his Biological Species Concept and his conclusion that allopatry is the main cause for the origin of species. He provided a decisive contribution to the New Systematics and was the (...) pioneer of the punctuated equilibrium idea. Mayr was one of the main architects of the evolutionary synthesis as also of the Neo-Darwinian wave. Evaluated together, all of his works reveal several elements of his ambition – to organize a philosophical conception inherent for Biology. An assiduous defender of autonomous Biology, Mayr asserted that four sets of factors in Biology differ from those in the Exact Sciences: (I) refutation of essentialism, mechanism, vitalism, and teleology; (II) some physical principles cannot be applied to Biology; (III) absence of general laws in Biology; and (IV) basic principles of biology and their specific character cannot be applied to the inanimate world. The present study took as an axis a minor or even invisible theme from the Ernst Mayr literature and aims to analyze critically the theoretical and epistemological basis that subsidizes – or not– the affirmation that Biology is an autonomous Science. - O biólogo alemão Ernst Walter Mayr (1904-2005), conhecido como o Darwin do século XXI, trabalhou com uma grande variedade de temas: Ornitologia, Genética, Evolução, Classificação, História e Filosofia da Biologia. Esse cientista foi um dos gigantes do século XX e um ícone para a Biologia Evolutiva. Ficou famoso com o seu Conceito Biológico de Espécie e sua conclusão de que a alopatria era a principal causa da origem das espécies. Forneceu uma contribuição decisiva à Nova Sistemática, foi precursor da ideia de equilíbrio pontuado e um dos principais arquitetos da síntese evolutiva, bem como do movimento Neodarwinista. Quando avaliados em conjunto, seus trabalhos revelam os diversos elementos de sua ambição – organizar um corpo de concepções filosóficas próprias da Biologia. Defensor assíduo de uma Biologia autônoma, Mayr afirmou que há quatro conjuntos de fatores que diferenciam a Biologia do conjunto das Ciências Exatas: (I) refutação do essencialismo, do mecanicismo, do vitalismo e da teleologia; (II) convicção de que certos princípios da Física não podem ser aplicados à Biologia; (III) ausência de leis naturais universais em Biologia; e (IV) percepção do caráter único de certos princípios básicos da Biologia não aplicáveis ao mundo inanimado. O presente artigo tomou por eixo um tema aparentemente menor ou mesmo invisível na obra de Ernst Mayr e pretende realizar uma análise crítica acerca de suas bases teóricas e epistemológicas que subsidiaram – ou não – a afirmação da Biologia como uma Ciência autônoma. (shrink)

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease, primarily leading to the degeneration of motor neurons. The traditional focus on motor neuron‐centric mechanisms has recently shifted towards understanding the contribution of non‐neuronal cells, such as microglia, in ALS pathophysiology. Advances in induced pluripotent stem cell (iPSC) technology have enabled the generation of iPSC‐derived microglia monocultures and co‐cultures to investigate their role in ALS pathogenesis. Here, we briefly review the insights gained from these studies into the role of microglia in ALS. (...) While iPSC‐derived microglia monocultures have revealed intrinsic cellular dysfunction due to ALS‐associated mutations, microglia‐motor neuron co‐culture studies have demonstrated neurotoxic effects of mutant microglia on motor neurons. Based on these findings, we briefly discuss currently unresolved questions and how they could be addressed in future studies. iPSC models hold promise for uncovering disease‐relevant pathways in ALS and identifying potential therapeutic targets. (shrink)

Disjunctivism about perceptual appearances, as I conceive of it, is a theory which seeks to preserve a naïve realist conception of veridical perception in the light of the challenge from the argument from hallucination. The naïve realist claims that some sensory experiences are relations to mind-independent objects. That is to say, taking experiences to be episodes or events, the naïve realist supposes that some such episodes have as constituents mind-independent objects. In turn, the disjunctivist claims that in a case of (...) veridical perception like this very kind of experience that you now have, the experiential episode you enjoy is of a kind which could not be occurring were you having an hallucination. The common strategy of arguments from hallucination set out to show that certain things are true of hallucinations, and hence must be true of perceptions. For example, it is argued that hallucinations must have non-physical objects of awareness, or that such states are not relations to anything at all, but are at best seeming relations to objects. In insisting that veridical perceptual experience is of a distinct kind from hallucination, the disjunctivist denies that any of these conceptions of hallucination challenges our conception of veridical perceptions as relations to mind-independent objects. More specifically, I assume that the disjunctivist advocates naïve realism because they think that this position best articulates how sensory experience seems to us to be just through reflection. If the disjunctivist is correct in this contention, then anyone who accepts the conclusion of the argument from hallucination must also accept that the nature of sensory experience is other than it seems to us to be. In turn, one may complain that any such error theory is liable to lead to sceptical consequences. A Humean scepticism about the senses launches a challenge about our knowledge of the world through questioning the conception we have of what sense experience is, and how it can provide knowledge of the world. (shrink)

Disjunctivism about perceptual appearances, as I conceive of it, is a theory which seeks to preserve a na.

A common finding is that information order influences belief revision (e.g., Hogarth & Einhorn, 1992). We tested personal experience as a possible mitigator. In three experiments participants experienced the probabilistic relationship between pieces of information and object category through a series of trials where they assigned objects (planes) into one of two possible categories (hostile or commercial), given two sequentially presented pieces of probabilistic information (route and ID), and then they had to indicate their belief about the object category before (...) feedback. The results generally confirm the predictions from the Hogarth and Einhorn model. Participants showed a recency effect in their belief revision. Extending previous model evaluations the results indicate that the model predictions also hold for classification decisions, and for pieces of information that vary in their diagnostic values. Personal experience does not appear to prevent order effects in classification decisions based on sequentially presented pieces of information and in belief revision. (shrink)