We set $\mathscr{D} = \langle\mathscr{D}, \leq_L, \tt\#\rangle$ , where D is the set of degrees of nonconstructibility for countable sets of countable ordinals. We show how to define inductively over this structure the degrees of such sets of ordinals in K, the core model, and the next few core models thereafter, i.e. without reference to mice, premice or measurable cardinals.

A short core model induction proof of $\mathsf {AD}^{L(\mathbb {R})}$ from $\mathsf {TD} + \mathsf {DC}_{\mathbb {R}}$.

We extend the core model induction technique to a choiceless context, and we exploit it to show that each one of the following two hypotheses individually implies that , the Axiom of Determinacy, holds in the of a generic extension of : every uncountable cardinal is singular, and every infinite successor cardinal is weakly compact and every uncountable limit cardinal is singular.

The value-free ideal for science holds that values should not influence the core features of scientific reasoning. We defend the difference-to-inference model of value-permeation, which holds that value-permeation in science is problematic when values make a difference to the inferences made about a hypothesis. This view of value-permeation is superior to existing views, and it suggests a corresponding maxim—namely, that scientists should strive to eliminate differences to inference. This maxim is the basis of a novel value-free ideal for (...) science. -/- . (shrink)

A new approach to Hume's problem of induction that justifies the optimality of induction at the level of meta-induction. Hume's problem of justifying induction has been among epistemology's greatest challenges for centuries. In this book, Gerhard Schurz proposes a new approach to Hume's problem. Acknowledging the force of Hume's arguments against the possibility of a noncircular justification of the reliability of induction, Schurz demonstrates instead the possibility of a noncircular justification of the optimality of (...) class='Hi'>induction, or, more precisely, of meta-induction (the application of induction to competing prediction models). Drawing on discoveries in computational learning theory, Schurz demonstrates that a regret-based learning strategy, attractivity-weighted meta-induction, is predictively optimal in all possible worlds among all prediction methods accessible to the epistemic agent. Moreover, the a priori justification of meta-induction generates a noncircular a posteriori justification of object induction. Taken together, these two results provide a noncircular solution to Hume's problem. Schurz discusses the philosophical debate on the problem of induction, addressing all major attempts at a solution to Hume's problem and describing their shortcomings; presents a series of theorems, accompanied by a description of computer simulations illustrating the content of these theorems (with proofs presented in a mathematical appendix); and defends, refines, and applies core insights regarding the optimality of meta-induction, explaining applications in neighboring disciplines including forecasting sciences, cognitive science, social epistemology, and generalized evolution theory. Finally, Schurz generalizes the method of optimality-based justification to a new strategy of justification in epistemology, arguing that optimality justifications can avoid the problems of justificatory circularity and regress. (shrink)

Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216 89–117] and Steel [PFA implies AD L, J. Symbolic Logic70 1255–1296], we show that the failure of square principle at a singular strong limit cardinal implies that there is a nontame mouse. The proof presented is the first inductive step beyond L of the core model induction that is aimed at getting a model of ADℝ + "Θ is regular" from the failure of square (...) at a singular strong limit cardinal or PFA. (shrink)

Leadership ostracism denotes a severe work stressor, potentially entailing more serious negative effects than other types of workplace ostracism. However, scholars have paid relatively little attention to ostracism carried out by leaders, leaving the phenomenon insufficiently accounted for in the literature. Hence, the present study aims to explore the content and typology of leadership ostracism behavior by in-depth interviews and inductive analyses based on grounded theory, in order to give a thorough presentation and description of the leadership ostracism concept as (...) perceived and construed by Chinese subordinates. Respondents were invited using a snowball sampling technique, and the final sample consisted of twenty-six individuals employed in different Chinese firms. Based on the reported experience of the interviewees, eleven concrete leadership ostracism behaviors emerged from the data. Further analyses revealed a leadership ostracism behavioral typology model reflecting five core categories, i.e. general ignoring, neglect, exclusion, differential treatment and undermining. These findings appear to partly replicate and partly expand on previous conceptualizations of workplace ostracism, indicating that leadership ostracism is a distinct variant of the phenomenon, eligible to be studied in its own right. The present study also discusses certain culture-specific aspects of leadership ostracism that can be taken into consideration in future studies. (shrink)

In Beauty and Revolution in Science, James McAllister advances a rationalistic picture of science in which scientific progress is explained in terms of aesthetic evaluations of scientific theories. Here I present a new model of aesthetic evaluations by revising McAllister’s core idea of the aesthetic induction. I point out that the aesthetic induction suffers from anomalies and theoretical inconsistencies and propose a model free from such problems. The new model is based, on the one (...) hand, on McAllister’s original model and on further developments by Theo Kuipers in his “Beauty, a Road to the Truth?”. On the other hand, it is based on empirical findings about affection and emotion, and a naturalistic aesthetic theory. The new model is thus a naturalistic model with a wider explanatory range and much more internal consistency that McAllister’s. (shrink)

We introduce 0• as a sharp for an inner model with a proper class of strong cardinals. We prove the existence of the core model K in the theory “ does not exist”. Combined with work of Woodin, Steel, and earlier work of the author, this provides the last step for determining the exact consistency strength of the assumption in the statement of the 12th Delfino problem pp. 221–224)).

Let 0 < n < ω. If there are n Woodin cardinals and a measurable cardinal above, but $M_{n+1}^{\#}$ doesn't exist, then the core model K exists in a sense made precise. An Iterability Inheritance Hypothesis is isolated which is shown to imply an optimal correctness result for K.

We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, (...) λ □κ, κ□κ*. We prove that if holds in V. As an application, we show that ZFC + PFA Con. We also obtain one Woodin cardinal as a lower bound on the consistency strength of stationary reflection at κ+ for a singular, countably closed limit cardinal κ such that # exists; likewise for the failure of □κ* at such a κ. (shrink)

We prove that in all Mitchell-Steel core models, □ κ holds for all κ. (See Theorem 2.). From this we obtain new consistency strength lower bounds for the failure of □ κ if κ is either singular and countably closed, weakly compact, or measurable. (Corallaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ (...) κ holds iff κ is not subcompact. (See Theorem 15; the only if direction is essentially due to Jensen.). (shrink)

We prove covering theorems for K, where K is the core model below the sharp for a strong cardinal, and give an application to stationary set reflection.

This paper introduces the real core model K() and determines the extent of scales in this inner model. K() is an analog of Dodd-Jensen's core model K and contains L(), the smallest inner model of ZF containing the reals R. We define iterable real premice and show that Σ1∩() has the scale property when vR AD. We then prove the following Main Theorem: ZF + AD + V = K() DC. Thus, we obtain the (...) Corollary: If ZF + AD +()L() is consistent, then ZF + AD + DC + α < ω2 -AD is also consistent. (shrink)

Let N be a transitive model of ZFC such that ωN ⊂ N and P(R) ⊂ N. Assume that both V and N satisfy "the core model K exists." Then KN is an iterate of K. i.e., there exists an iteration tree J on K such that J has successor length and $\mathit{M}_{\infty}^{\mathit{J}}=K^{N}$. Moreover, if there exists an elementary embedding π: V → N then the iteration map associated to the main branch of J equals π ↾ (...) K. (This answers a question of W. H. Woodin, M. Gitik, and others.) The hypothesis that P(R) ⊂ N is not needed if there does not exist a transitive model of ZFC with infinitely many Woodin cardinals. (shrink)

We survey the definition and fundamental properties of the family of short core models, which extend the core model K of Dodd and Jensen to include α-sequences of measurable cardinals . The theory is applied to various combinatorial principles to get lower bounds for their consistency strengths in terms of the existence of sequences of measurable cardinals. We consider instances of Chang's conjecture, ‘accessible’ Jónsson cardinals, the free subset property for small cardinals, a canonization property of ω (...) ω , and a non-closure property of elementary embeddings of the universe. In some cases, equiconsistencies are obtained. (shrink)

In this paper we shall answer some questions in the set theory of L, the universe of all sets constructible from the reals. In order to do so, we shall assume ADL, the hypothesis that all 2-person games of perfect information on ω whose payoff set is in L are determined. This is by now standard practice. ZFC itself decides few questions in the set theory of L, and for reasons we cannot discuss here, ZFC + ADL yields the most (...) interesting “completion” of the ZFC-theory of L.ADL implies that L satisfies “every wellordered set of reals is countable”, so that the axiom of choice fails in L. Nevertheless, there is a natural inner model of L, namely HODL, which satisfies ZFC.. The superscript “L” indicates, here and below, that the notion in question is to be interpreted in L.) HODL is reasonably close to the full L, in ways we shall make precise in § 1. The most important of the questions we shall answer concern HODL: what is its first order theory, and in particular, does it satisfy GCH?These questions first drew attention in the 70's and early 80's. (shrink)

If there is no inner model with a cardinal κ such that o(κ) = κ ++ then the set K ∩ H ω 1 is definable over H ω 1 by a Δ 4 formula, and the set $\{J_\alpha[\mathscr{U}]: \alpha of countable initial segments of the core model K = L[U] is definable over H ω 1 by a Π 3 formula. We show that if there is an inner model with infinitely many measurable cardinals then (...) there is a model in which $\{J_\alpha [\mathscr{U}]: \alpha is not definable by any Σ 3 formula, and K ∩ H ω 1 is not definable by any boolean combination of Σ 3 formulas. (shrink)

We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.

If there is no inner model with a cardinal $\kappa$ such that $o = \kappa^{++}$ then the set $K \cap H_{\omega_1}$ is definable over H$_{\omega_1}$ by a $\Delta_4$ formula, and the set $\{J_\alpha[\mathscr{U}] : \alpha < \omega_1\}$ of countable initial segments of the core model $K = L[\mathscr{U}]$ is definable over $H_{\omega_1}$ by a $\Pi_3$ formula. We show that if there is an inner model with infinitely many measurable cardinals then there is a model in (...) which $\{J_\alpha [\mathscr{U}] : \alpha < \omega_1\}$ is not definable by any $\Sigma_3$ formula, and $K \cap H_{\omega_1}$ is not definable by any boolean combination of $\Sigma_3$ formulas. (shrink)

Agent-based models derive the behavior of artificial socio-economic entities computationally from the actions of a large number of agents. One objection is that highly idealized ABMs fail to represent the real world in any reasonable sense. Another objection is that they at best show how observed patterns may have come about, because simulations are easy to produce and there is no evidence that this is really what happens. Moreover, different models may well yield the same result. I will rebut these (...) objections by focusing on an often neglected, but crucial function of ABMs. Building on Gelfert’s account of the exploratory uses of scientific models I show that, in the absence of an accepted underlying theory, successful ABMs lend inductive support to assumptions concerning certain structural feutures of the behavioral rules employed. One core step towards this goal is what I call multiple-model robustness analysis. (shrink)

In this paper we shall answer some questions in the set theory of L, the universe of all sets constructible from the reals. In order to do so, we shall assume ADL, the hypothesis that all 2-person games of perfect information on ω whose payoff set is in L are determined. This is by now standard practice. ZFC itself decides few questions in the set theory of L, and for reasons we cannot discuss here, ZFC + ADL yields the most (...) interesting “completion” of the ZFC-theory of L.ADL implies that L satisfies “every wellordered set of reals is countable”, so that the axiom of choice fails in L. Nevertheless, there is a natural inner model of L, namely HODL, which satisfies ZFC.. The superscript “L” indicates, here and below, that the notion in question is to be interpreted in L.) HODL is reasonably close to the full L, in ways we shall make precise in § 1. The most important of the questions we shall answer concern HODL: what is its first order theory, and in particular, does it satisfy GCH?These questions first drew attention in the 70's and early 80's. (shrink)

Science should tell us what the world is like. However, realist interpretations of physics face many problems, chief among them the pessimistic meta induction. This book seeks to develop a realist position based on process ontology that avoids the traditional problems of realism. Primarily, the core claim is that in order for a scientific model to be minimally empirically adequate, that model must describe real experimental processes and dynamics. Any additional inferences from processes to things, substances (...) or objects are not warranted, and so these inferences are shown to represent the locus of the problems of realism. The book then examines the history of physics to show that the progress of physical research is one of successive eliminations of thing interpretations of models in favor of more explanatory and experimentally verified process interpretations. This culminates in collections of models that cannot coherently allow for thing interpretations, but still successfully describe processes. (shrink)

We study the Magidor iteration of Prikry forcings, and the resulting normal measures on κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa}$$\end{document}, the first measurable cardinal in a generic extension. We show that when applying the iteration to a core model below 0¶\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${0^{\P}}$$\end{document}, then there exists a natural correspondence between the normal measures on κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa}$$\end{document} in the ground (...) class='Hi'>model, and those of the generic extension. (shrink)

We follow [8] in asking when a set of ordinals $X \subseteq \alpha$ is a countable union of sets in K, the core model. We show that, analogously to L, and X closed under the canonical Σ 1 Skolem function for K α can be so decomposed provided K is such that no ω-closed filters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erdős-type property.

We show that if there is no inner model with a Woodin cardinal and the Steel core model K exists, then every Jónsson cardinal is Ramsey in K, and every δ-Jónsson cardinal is δ-Erdös in K. In the absence of the Steel core model K we prove the same conclusion for any model L[E] such that either V = L[E] is the minimal model for a Woodin cardinal, or there is no inner (...) class='Hi'>model with a Woodin cardinal and V is a generic extension of L[E]. The proof includes one lemma of independent interest: If V = L[A], where A $\subset$ κ and κ is regular, then L κ [A] is a Jónsson algebra. The proof of this result, Lemma 2.5, is very short and entirely elementary. (shrink)

Straightening the current ‘value-laden turn’ (VLT) in the philosophical literature on values in science, and reviving the legacy of the value-free ideal of science (VFI), this paper argues that the influence of extra-scientific values should be minimised—not excluded—in the core phase of scientific inquiry where claims are accepted or rejected. Noting that the original arguments for the VFI (ensuring the truth of scientific knowledge, respecting the autonomy of science results users, preserving public trust in science) have not been satisfactorily (...) addressed by proponents of the VLT, it proposes four prerequisites which any model for values in the acceptance/rejection phase of scientific inquiry should respect, coming from the fundamental requirement to distinguish between facts and values: (1) the truth of scientific knowledge must be ensured; (2) the uncertainties associated with scientific claims must be stated clearly; (3) claims accepted into the scientific corpus must be distinguished from claims taken as a basis for action. An additional prerequisite of (4) simplicity and systematicity is desirable, if the model is to be applicable. Methodological documents from international institutions and regulation agencies are used to illustrate the prerequisites. A model combining Betz’s conception (stating uncertainties associated with scientific claims) and Hansson’s corpus model (ensuring the truth of the scientific corpus and distinguishing it from other claims taken as a basis for action) is proposed. Additional prerequisites are finally suggested for future research, stemming from the requirement for philosophy of science to self-reflect on its own values: (5) any model for values in science must be descriptively and normatively relevant; and (6) its consequences must be thoroughly assessed. (shrink)

We show that if there is no inner model with a Woodin cardinal and the Steel core model K exists, then every Jonsson cardinal is Ramsey in K, and every $\delta$-Jonsson cardinal is $\delta$-Erdos in K. In the absence of the Steel core model K we prove the same conclusion for any model L$[\mathscr{E}]$ such that either V = L$[\mathscr{E}]$ is the minimal model for a Woodin cardinal, or there is no inner (...) class='Hi'>model with a Woodin cardinal and V is a generic extension of L$[\mathscr{E}]$. The proof includes one lemma of independent interest: If V = L$[\mathscr{A}]$, where A $\subset$ $\kappa$ and $\kappa$ is regular, then L$_\kappa$[A] is a Jonsson algebra. The proof of this result, Lemma 2.5, is very short and entirely elementary. (shrink)

In this paper, I review two related lines of computational research: discovery of scientific knowledge and causal models of scientific phenomena. I also report research on quantitative process models that falls at the intersection of these two themes. This framework represents models as a set of interacting processes, each with associated differential equations that express influences among variables. Simulating such a quantitative process model produces trajectories for variables over time that one can compare to observations. Background knowledge about candidate (...) processes enables search through the space of model structures and associated parameters to find explanations of time-series data. I discuss the representation of such process models, their use for prediction and explanation, and their discovery through heuristic search, along with their interpretation as causal accounts of dynamic behavior. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

This paper argues that the linguistic approach to analyzing induction, according to which induction is a type of inference or argument composed of statements or propositions, is unsuitable to account for scientific reasoning. Consequently, a novel approach to induction in model-based science is suggested. First, in order to show their adherence to the linguistic treatment of induction, two strategies are reviewed: (i) Carnap and Reichenbach’s attempts to justify induction and (ii) Norton’s recent material theory (...) of induction. Second, three reasons are provided to support the claim that the linguistic treatment of induction is insufficient in accounting for model-based reasoning in science. Finally, a framework focused on models—rather than statements or propositions—is suggested to address induction in science. William Whewell’s theory of induction is briefly outlined as an example of a non-propositional treatment of induction that is consistent with model-based scientific practice. (shrink)

Under what conditions does machine learning (ML) model opacity inhibit the possibility of explaining and understanding phenomena? In this article, I argue that nonepistemic values give shape to the ML opacity problem even if we keep researcher interests fixed. Treating ML models as an instance of doing model-based science to explain and understand phenomena reveals that there is (i) an external opacity problem, where the presence of inductive risk imposes higher standards on externally validating models, and (ii) an (...) internal opacity problem, where greater inductive risk demands a higher level of transparency regarding the inferences the model makes. (shrink)

This article attempts to examine Nihonjinron, the popular essentialist genre in Japan, which purports to analyse Japan's quintessence and cultural core by using three concepts - nationality, ethnicity and culture - synonymously. The focus of the paper will be placed on: (1) the widespread political bases of Nihonjinron and its internal divisions; (2) its changing features in the face of globalization; (3) the possible productive uses of Nihonjinron at both conceptual and theoretical levels; and (4) the dilemma of inter-societal (...) and intra-societal cultural relativism, which the Nihonjinron debate has highlighted. The paper presents an outline of an inductive, pluralistic, multicultural model of analysis as a possible alternative. (shrink)

The multitude of training models and curricula for the specialty of clinical neuropsychology around the world has led to organized activities to develop a framework of core competencies to ensure sufficient expertise among entry-level professionals in the field. The Standing Committee on Clinical Neuropsychology of the European Federation of Psychologists’ Associations is currently working toward developing a specialty certification in clinical neuropsychology to establish a cross-national standard against which to measure levels of equivalency and uniformity in competence and service (...) provision among professionals in the field. Through structured interviews with experts from 28 European countries, we explored potential areas of core competency. Specifically, questions pertained to the perceived importance of a series of foundational, functional, and other competencies, as well as current training standards and practices, and optimal standards. Our findings revealed considerable agreement on academic and clinical training, despite varied actual training requirements currently, with fewer respondents relegating importance to training in teaching, supervision, and research, and even fewer to skills related to management, administration, and advocacy. European expert clinical neuropsychologists were in agreement with previous studies regarding the importance of sound theoretical and clinical training but management, administrative, and advocacy skills were not central to their perspective of a competent specialist in clinical neuropsychology. Establishing a specialty certificate in clinical neuropsychology based on core competencies may enable mobility of clinical neuropsychologists across Europe, and, perhaps, provide an impetus for countries with limited criteria to reconsider their training requirements and harmonize their standards with others. (shrink)

Robustness analysis (RA) is the prescription to consider a diverse range of evidence and only regard a hypothesis as well-supported if all the evidence agrees on it. In contexts like climate science, the evidence in support of a hypothesis often comes in the form of model results. This leads to model-based RA (MBRA), whose core notion is that a hypothesis ought to be regarded as well-supported on grounds that a sufficiently diverse set of models agrees on the (...) hypothesis. This chapter, which is the first part of a two-part review of MBRA, begins by providing a detailed statement of the general structure of MBRA. This statement will make visible the various parts of MBRA and will structure the discussion in the remainder of the chapter. The chapter explicates the core concepts of independence and agreement, and it discusses what they mean in the context of climate modeling. The statement shows that MBRA is based on three premises, which concern robust properties, common structures, and so-called robust theorems. The chapter analyzes what these involve and what problems they raise in the context of climate science. In the next chapter, which is the second part of the review, an analysis of how the conclusions of MBRA can be justified is provided. (shrink)