Contextualism and the Skeptic: Comments on Engel

Mylan Engels paper (2004) is divided into two parts: a negative part, criticizing the costs of contextualism and a constructive part proposing a noncontextualist resolution of the skeptical problem. I will only address the constructive part here. The constructive part is composed of three elements: (i) a reconstruction or reformulation of the original skeptical argument, which draws on the notion of epistemic possibility (e-possibility), (ii) a distinction between two senses of knowledge (and two corresponding kinds of e-possibility): fallibilistic and infallibilistic, and (iii) an argument which tries to hoist the skeptic by their own petard, namely the closure principle (CP). As I will argue, there are two ways to understand Engels anti-skeptical argument. Only in one interpretation does the argument depend on the proposed reconstruction of the skeptical argument in terms of e-possibility. But this version of the argument is unsound. More importantly, the skeptic has a strong prima facie objection at her disposal, which applies to both interpretations of the argument. If this objection is valid, Engels argument does not hold. But once it is invalidated, his argument is superfluous.     

Syntactical results on the arithmetical completeness of modal logic

In this paper the PA-completeness of modal logic is studied by syntactical and constructive methods. The main results are theorems on the structure of the PA-proofs of suitable arithmetical interpretationsS of a modal sequentS, which allow the transformation of PA-proofs ofS into proof-trees similar to modal proof-trees. As an application of such theorems, a proof of Solovay's theorem on arithmetical completeness of the modal system G is presented for the class of modal sequents of Boolean combinations of formulas of the form p _i,m _i=0, 1, 2, ... The paper is the preliminary step for a forthcoming global syntactical resolution of the PA-completeness problem for modal logic.     

On the consistency of a three-valued logical calculus

[This résumé was published in English in Matematicheskii Sbornik along with the article.]The present paper contains an investigation of a three-valued logical calculus (the system) previously described by the author [Recueil Mathématique 4 (46), 2 (1938)].A constructive consistence proof is given for a part of this calculus rendering the results previously published concerning the Russell paradox. A method for a non-constructive completeness proof for the complete calculus is briefly indicated.     

Jewish values and sociopsychological perspectives on aging

The Jewish approach to aging and the aged is constructive. If one no longer works, guilt is inappropriate. Old age may be a sabbath of human life. In our culture, older people are led to low self-esteem less by their age than by occupational and economic status. Hence fundamental social change is needed if there is to be dignity and quality in life for older people. Old age can become, as it should, the high point of the human career.He is a rabbi in the Central Conference of American Rabbis. Among his books isEmpathy.     

Nietzsche's agon with ressentiment: towards a therapeutic reading of critical transvaluation

This paper examines the therapeutic implications of Nietzsche's critique of ressentiment and revenge as our signature malady. §I examines the obstacles to a therapeutic reading of Nietzsche's thought, including his anti-teleological tendencies and the value he places on sickness. Then there is the energetic problem of finding resources to tackle ressentiment, given the volitional exhaustion of modern nihilism. Finally, the self-referential implications of Nietzsche's critique of slave values threaten to trap his thought in a futile ressentiment against ressentiment. If the impulse to cure or redeem us from revenge through critical destruction repeats the logic of revenge, then the challenge for a therapeutic reading is to think through the transformation of revenge on the basis of repetition.An agonal reading of Nietzsche's philosophical practice is proposed to tackle these problems in §II.In Homer's Contest (1872), Nietzsche describes the transference (Übertragung) of Hesiod's evil Eris – goddess of war and destruction – into the good Eris of the contest or agon: destructive impulses are affirmed as stimulants, but also transformed into culture-building forces through an agonal regime of limited aggression. By superimposing this regime, as a model for Nietzsche's textual confrontations, on their unconscious text of embodied ressentiment, a therapeutic perspective emerges, based on three principles: affirmation; mutual empowerment; and externalisation. The agon performs an affirmative transformation of revenge on the basis of a fertile repetition: destructive affects (as in ressentiment) are transferred into constructive deeds of mutual antagonism. Through Nietzsche's agonal discourse, a reactive regime of internalised aggression is externalised in active deeds of limited philosophical aggression – a therapeutic transformation of (self-)destructive into constructive, philosophical impulses.     

Mathematical Proof Theory in the Light of Ordinal Analysis

We give an overview of recent results in ordinal analysis. Therefore,we discuss the different frameworks used in mathematical proof-theory, namely subsystem of analysis including reversemathematics, Kripke–Platek set theory, explicitmathematics, theories of inductive definitions,constructive set theory, and Martin-Löfs typetheory.     

Deduction chains for common knowledge

Deduction chains represent a syntactic and in a certain sense constructive method for proving completeness of a formal system. Given a formula , the deduction chains of are built up by systematically decomposing into its subformulae. In the case where is a valid formula, the decomposition yields a (usually cut-free) proof of . If is not valid, the decomposition produces a countermodel for . In the current paper, we extend this technique to a semiformal system for the Logic of Common Knowledge. The presence of fixed point constructs in this logic leads to potentially infinite-length deduction chains of a non-valid formula, in which case fairness of decomposition requires special attention. An adequate order of decomposition also plays an important role in the reconstruction of the proof of a valid formula from the set of its deduction chains.     

Cut-free sequent and tableau systems for propositional Diodorean modal logics

We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logicsS4.3, S4.3.1 andS4.14. When the modality is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points.Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulaeX the superformulae involved are always bounded by a finite set of formulaeX* _L depending only onX and the logicL. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive.Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these latter systems. The techniques are due to Hintikka and Rautenberg.Presented byDov M. Gabbay     

The Definition of Moral Dilemmas: A Logical Confusion and a Clarification

This discussion note deals with Jurriaan de Haan's paper The Definition of Moral Dilemmas: A Logical Problem (Ethical Theory and Moral Practice 4(3), 2001, pp. 267–284). In the first, critical part I will point out a confusion in the logical analysis of the paper in question. In the second, constructive part I will indicate how the analysis of moral dilemmas should proceed within the framework of a possible world semantics.     

Four bootstrap confidence intervals for the binomial-error model

Confidence intervals for the mean function of the true proportion score ( _x ), where andx respectively denote the true proportion and observed test scores, can be approximated by the Efron, Bayesian, and parametric empirical Bayes (PEB) bootstrap procedures. The similarity of results yielded by all the bootstrap methods suggests the following: the unidentifiability problem of the prior distributiong() can be bypassed with respect to the construction of confidence intervals for the mean function, and a beta distribution forg() is a reasonable assumption for the test scores in compliance with a negative hypergeometric distribution. The PEB bootstrap, which reflects the construction of Morris intervals, is introduced for computing predictive confidence bands for x. It is noted that the effect of test reliability on the precision of interval estimates varies with the two types of confidence statements concerned.The Authors are indebted to the Editor and anonymous reviewers for constructive suggestions and comments. The authors wish to thank Min-Te Chao and Cheng-Der Fuh for some useful suggestions at earlier stages of writing this paper.     

An extension of the partial credit model with an application to the measurement of change

The partial credit model is considered under the assumption of a certain linear decomposition of the item × category parameters _ih into basic parameters _j. This model is referred to as the linear partial credit model. A conditional maximum likelihood algorithm for estimation of the j is presented, based on (a) recurrences for the combinatorial functions involved, and (b) using a quasi-Newton approach, the so-called Broyden-Fletcher-Goldfarb-Shanno (BFGS) method; (a) guarantees numerically stable results, (b) avoids the direct computation of the Hesse matrix, yet produces a sequence of certain positive definite matricesB _k ,k=1, 2, ..., converging to the asymptotic variance-covariance matrix of the . The practicality of these numerical methods is demonstrated both by means of simulations and of an empirical application to the measurement of treatment effects in patients with psychosomatic disorders.The authors thank one anonymous reviewer for his constructive comments. Moreover, they thankfully acknowledge financial support by the Österreichische Nationalbank (Austrian National Bank) under Grant No. 3720.     

Hybrids of the -translation for

In [W. Burr, Functional interpretation of Aczel's constructive set theory, Annals of Pure and Applied Logic 104 (2000) 31–73] Wolfgang Burr presents a functional interpretation of constructive set theory in all finite types, , in a theory of constructive set functionals. is a subtheory of , containing bounded quantifiers only. His interpretation theorem reduces the consistency problem of (and certain extensions thereof) to the consistency problem of .We want to study admissible rules in , i.e. rules under which is closed. To do so, we study a Troelstra-style q-hybrid of, in fact, a modification ^× of Burr's translation. We introduce this modification in order to close a minor gap in Burr's proof of the functional interpretation of the schema of (Strong Collection).First of all, but surely after a short introduction, we analyse the less complex translation of modified realisation ^mr and its hybrids ^mq and ^mrt.     

Ideal evidence, relevance and second-order probabilities

Conclusion The concepts of supportive evidence and of relevant evidence seem very closely related to each other. Supportive evidence is clearly always relevant as well. But must relevant evidence be defined as evidence which is either supportive or weakeking? In an explicit or implicit manner, this is indeed the position of many philosophers. The paradox of ideal evidence, however, shows us that this is to restrictive. Besides increasing or decreasing the probability attached to some hypothesis, evidence can alter or interact with the background assumptions underlying the hypothesis.In most circumstances, the (post hoc) relevance of evidence can indeed be judged by its effect on the confidence one attaches to hypotheses. Occasionally, as in the circumstances described by Example I, and more generally called the Paradox of Ideal Evidence, the relevance of evidence to an hypothesis can only be understood by appeal to a broader sense.In Memory of My Father. Yehoshua Bar-HillelThe author wishes to thank Haim Gaifman for a most thoughtful and constructive review of an earlier draft of this paper.     

On a complexity-based way of constructivizing the recursive functions

Let g _E(m, n)=o mean that n is the Gödel-number of the shortest derivation from E of an equation of the form (m)=k. Hao Wang suggests that the condition for general recursiveness mn(g _E(m, n)=o) can be proved constructively if one can find a speedfunction _{s s}, with _s(m) bounding the number of steps for getting a value of (m), such that mn _s(m) s.t. g _E(m, n)=o. This idea, he thinks, yields a constructivist notion of an effectively computable function, one that doesn't get us into a vicious circle since we intuitively know, to begin with, that certain proofs are constructive and certain functions effectively computable. This paper gives a broad possibility proof for the existence of such classes of effectively computable functions, with Wang's idea of effective computability generalized along a number of dimensions.We are grateful to an anonymous referee for Studia Logica for valuable advice leading to substantial improvements in the presentation of the main definitions and theorem.     

Diagrammatic Reasoning: Some Notes on Charles S. Peirce and Friedrich A. Lange

According to the received view, Charles S. Peirce's theory of diagrammatic reasoning is derived from Kant's philosophy of mathematics. For Kant, only mathematics is constructive/synthetic, logic being instead discursive/analytic, while for Peirce, the entire domain of necessary reasoning, comprising mathematics and deductive logic, is diagrammatic, i.e. constructive in the Kantian sense. This shift was stimulated, as Peirce himself acknowledged, by the doctrines contained in Friedrich Albert Lange's Logische Studien (1877 Lange, F.A. 1877. Logische Studien: Ein Beitrag zur Neubegründung der formalen Logik und der Erkenntnisstheorie, H. Cohen, ed., Iserlohn: Verlag von J. Baedeker (LS). [Google Scholar]). The present paper reconstructs Peirce's reading of Lange's book, and illustrates what, according to Peirce, was right and what was problematic in Lange's account of reasoning. It further seeks to explain how Peirce's theory of deductive reasoning was a combination of Kant's philosophy of mathematics and Lange's philosophy of logic.     

Gender, Race, and Class in Organizational Contexts

Creating settings that support diversity has been a long-standing concern of community psychology. In this paper, I propose two qualities as important aspects of organizational contexts that support the meaningful participation of diverse groups:(a) a culture of connection and (b) recognition of multiple realities. For each theme, I first examine countervailing values that can undermine meaningful participation of nondominant groups. I suggest that organizational values for independence and a press for sameness can contribute to settings where members of traditionally oppressed groups will be prevented from meaningful participation. I also suggest that fostering a culture of connectedness that actively legitimizes multiple realities is a constructive alternative. To illustrate these points, I share observations based on experiences in manufacturing, educational, and community-based settings. Then, I explore two dynamics that are important when confronting the countervailing values and building more inclusive contexts: (a) accountability for impact and (b) privilege dynamics. Last, I turn to some possibilities for change through a stance of connected disruption.     

A Proof-theoretical Analysis of Semiconstructive Intermediate Theories

In the 80's Pierangelo Miglioli, starting from motivations in the framework of Abstract Data Types and Program Synthesis, introduced semiconstructive theories, a family of large subsystems of classical theories that guarantee the computability of functions and predicates represented by suitable formulas. In general, the above computability results are guaranteed by algorithms based on a recursive enumeration of the theorems of the whole system. In this paper we present a family of semiconstructive systems, we call uniformly semiconstructive, that provide computational procedures only involving formulas with bounded complexity. We present several examples of uniformly semiconstructive systems containing Harrop theories, induction principles and some well-known predicate intermediate principles. Among these, we give an account of semiconstructive and uniformly semiconstructive systems which lie between Intuitionistic and Classical Arithmetic and we discuss their constructive incompatibility.     

Aggressive behavior in normal and deviant members of intact versus mother-only families

Single-parent families have been identified as using more coercion and aggression to elicit compliance than intact families. The present study compared 9 mother-only and 15 intact families from a referred clinical sample to 9 mother-only and 16 intact nonreferred normal families using a family behavioral observation code. Clinical families emitted higher rates of aggressive behavior than normals, and mother-only emitted higher rates than intact. However, mother-only normals had lower rates than intact clinical families. The intact versus mother-only factor appears to be less important in understanding aggression than do the specific interactional patterns of family members.Support for this research was provided in part by NIMH grant 1 RO3 MN31509 CD, through the Center for the Study of Crime and Delinquency, and by support from the Indiana State University Faculty Research Committee. This is part of a 10-year project conducted by the Oregon Social Learning Center examining aggressive child families, and primary data collection was performed through the Oregon Social Learning Center. Appreciation is expressed to Betty Brummet, Gayle Home, and Patricia Reinker for assistance in data collection, to Brian Bauske and Barry Van Dyck for assistance in computer analyses, and to the staff of the Oregon Social Learning Center for constructive assistance.